CINXE.COM

<!DOCTYPE html> <html lang="en" xmlns:fb="http://www.facebook.com/2008/fbml" class="wf-loading"> <head prefix="og: https://ogp.me/ns# fb: https://ogp.me/ns/fb# academia: https://ogp.me/ns/fb/academia#"> <meta charset="utf-8"> <meta name=viewport content="width=device-width, initial-scale=1"> <meta rel="search" type="application/opensearchdescription+xml" href="/open_search.xml" title="Academia.edu"> <title>Mathematical Biology Research Papers - Academia.edu</title>  <link href="//a.academia-assets.com/images/favicons/favicon-production.ico" rel="shortcut icon" type="image/vnd.microsoft.icon"> <link rel="apple-touch-icon" sizes="57x57" href="//a.academia-assets.com/images/favicons/apple-touch-icon-57x57.png"> <link rel="apple-touch-icon" sizes="60x60" href="//a.academia-assets.com/images/favicons/apple-touch-icon-60x60.png"> <link rel="apple-touch-icon" sizes="72x72" href="//a.academia-assets.com/images/favicons/apple-touch-icon-72x72.png"> <link rel="apple-touch-icon" sizes="76x76" href="//a.academia-assets.com/images/favicons/apple-touch-icon-76x76.png"> <link rel="apple-touch-icon" sizes="114x114" href="//a.academia-assets.com/images/favicons/apple-touch-icon-114x114.png"> <link rel="apple-touch-icon" sizes="120x120" href="//a.academia-assets.com/images/favicons/apple-touch-icon-120x120.png"> <link rel="apple-touch-icon" sizes="144x144" href="//a.academia-assets.com/images/favicons/apple-touch-icon-144x144.png"> <link rel="apple-touch-icon" sizes="152x152" href="//a.academia-assets.com/images/favicons/apple-touch-icon-152x152.png"> <link rel="apple-touch-icon" sizes="180x180" href="//a.academia-assets.com/images/favicons/apple-touch-icon-180x180.png"> <link rel="icon" type="image/png" href="//a.academia-assets.com/images/favicons/favicon-32x32.png" sizes="32x32"> <link rel="icon" type="image/png" href="//a.academia-assets.com/images/favicons/favicon-194x194.png" sizes="194x194"> <link rel="icon" type="image/png" href="//a.academia-assets.com/images/favicons/favicon-96x96.png" sizes="96x96"> <link rel="icon" type="image/png" href="//a.academia-assets.com/images/favicons/android-chrome-192x192.png" sizes="192x192"> <link rel="icon" type="image/png" href="//a.academia-assets.com/images/favicons/favicon-16x16.png" sizes="16x16"> <link rel="manifest" href="//a.academia-assets.com/images/favicons/manifest.json"> <meta name="msapplication-TileColor" content="#2b5797"> <meta name="msapplication-TileImage" content="//a.academia-assets.com/images/favicons/mstile-144x144.png"> <meta name="theme-color" content="#ffffff"> <script> window.performance && window.performance.measure && window.performance.measure("Time To First Byte", "requestStart", "responseStart"); </script> <script> (function() { if (!window.URLSearchParams || !window.history || !window.history.replaceState) { return; } var searchParams = new URLSearchParams(window.location.search); var paramsToDelete = [ 'fs', 'sm', 'swp', 'iid', 'nbs', 'rcc', // related content category 'rcpos', // related content carousel position 'rcpg', // related carousel page 'rchid', // related content hit id 'f_ri', // research interest id, for SEO tracking 'f_fri', // featured research interest, for SEO tracking (param key without value) 'f_rid', // from research interest directory for SEO tracking 'f_loswp', // from research interest pills on LOSWP sidebar for SEO tracking 'rhid', // referrring hit id ]; if (paramsToDelete.every((key) => searchParams.get(key) === null)) { return; } paramsToDelete.forEach((key) => { searchParams.delete(key); }); var cleanUrl = new URL(window.location.href); cleanUrl.search = searchParams.toString(); history.replaceState({}, document.title, cleanUrl); })(); </script> <script async src="https://www.googletagmanager.com/gtag/js?id=G-5VKX33P2DS"></script> <script> window.dataLayer = window.dataLayer || []; function gtag(){dataLayer.push(arguments);} gtag('js', new Date()); gtag('config', 'G-5VKX33P2DS', { cookie_domain: 'academia.edu', send_page_view: false, }); gtag('event', 'page_view', { 'controller': "by_tag", 'action': "show_one", 'controller_action': 'by_tag#show_one', 'logged_in': 'false', 'edge': 'unknown', // Send nil if there is no A/B test bucket, in case some records get logged // with missing data - that way we can distinguish between the two cases. // ab_test_bucket should be of the form <ab_test_name>:<bucket> 'ab_test_bucket': null, }) </script> <script type="text/javascript"> window.sendUserTiming = function(timingName) { if (!(window.performance && window.performance.measure)) return; var entries = window.performance.getEntriesByName(timingName, "measure"); if (entries.length !== 1) return; var timingValue = Math.round(entries[0].duration); gtag('event', 'timing_complete', { name: timingName, value: timingValue, event_category: 'User-centric', }); }; window.sendUserTiming("Time To First Byte"); </script> <meta name="csrf-param" content="authenticity_token" /> <meta name="csrf-token" content="Hj9mIZGlAS8ZmvkFHKyG36/B+Ola0EMdBHs0jTjlELZkXUpgBiy4+aBKCN+ohHtrtmzFfqtAxo85i4TNrErSxA==" /> <link href="/Documents/in/Mathematical_Biology?after=50%2C37424427" rel="next" /><link crossorigin="" href="https://fonts.gstatic.com/" rel="preconnect" /><link href="https://fonts.googleapis.com/css2?family=DM+Sans:ital,opsz,wght@0,9..40,100..1000;1,9..40,100..1000&family=Gupter:wght@400;500;700&family=IBM+Plex+Mono:wght@300;400&family=Material+Symbols+Outlined:opsz,wght,FILL,GRAD@20,400,0,0&display=swap" rel="stylesheet" /><link rel="stylesheet" media="all" href="//a.academia-assets.com/assets/design_system/common-10fa40af19d25203774df2d4a03b9b5771b45109c2304968038e88a81d1215c5.css" /> <meta name="description" content="View Mathematical Biology Research Papers on Academia.edu for free." /> <meta name="google-site-verification" content="bKJMBZA7E43xhDOopFZkssMMkBRjvYERV-NaN4R6mrs" /> <script> var $controller_name = 'by_tag'; var $action_name = "show_one"; var $rails_env = 'production'; var $app_rev = '9387f500ddcbb8d05c67bef28a2fe0334f1aafb8'; var $domain = 'academia.edu'; var $app_host = "academia.edu"; var $asset_host = "academia-assets.com"; var $start_time = new Date().getTime(); var $recaptcha_key = "6LdxlRMTAAAAADnu_zyLhLg0YF9uACwz78shpjJB"; var $recaptcha_invisible_key = "6Lf3KHUUAAAAACggoMpmGJdQDtiyrjVlvGJ6BbAj"; var $disableClientRecordHit = false; </script> <script> window.Aedu = { hit_data: null }; window.Aedu.SiteStats = {"premium_universities_count":15268,"monthly_visitors":"113 million","monthly_visitor_count":113692424,"monthly_visitor_count_in_millions":113,"user_count":277694179,"paper_count":55203019,"paper_count_in_millions":55,"page_count":432000000,"page_count_in_millions":432,"pdf_count":16500000,"pdf_count_in_millions":16}; window.Aedu.serverRenderTime = new Date(1732983552000); window.Aedu.timeDifference = new Date().getTime() - 1732983552000; window.Aedu.isUsingCssV1 = false; window.Aedu.enableLocalization = true; window.Aedu.activateFullstory = false; window.Aedu.serviceAvailability = { status: {"attention_db":"on","bibliography_db":"on","contacts_db":"on","email_db":"on","indexability_db":"on","mentions_db":"on","news_db":"on","notifications_db":"on","offsite_mentions_db":"on","redshift":"on","redshift_exports_db":"on","related_works_db":"on","ring_db":"on","user_tests_db":"on"}, serviceEnabled: function(service) { return this.status[service] === "on"; }, readEnabled: function(service) { return this.serviceEnabled(service) || this.status[service] === "read_only"; }, }; window.Aedu.viewApmTrace = function() { // Check if x-apm-trace-id meta tag is set, and open the trace in APM // in a new window if it is. var apmTraceId = document.head.querySelector('meta[name="x-apm-trace-id"]'); if (apmTraceId) { var traceId = apmTraceId.content; // Use trace ID to construct URL, an example URL looks like: // https://app.datadoghq.com/apm/traces?query=trace_id%31298410148923562634 var apmUrl = 'https://app.datadoghq.com/apm/traces?query=trace_id%3A' + traceId; window.open(apmUrl, '_blank'); } }; </script>  <link href="https://fonts.googleapis.com/css?family=Roboto:100,100i,300,300i,400,400i,500,500i,700,700i,900,900i" rel="stylesheet"> <link href="//maxcdn.bootstrapcdn.com/font-awesome/4.3.0/css/font-awesome.min.css" rel="stylesheet"> <link rel="stylesheet" media="all" href="//a.academia-assets.com/assets/libraries-a9675dcb01ec4ef6aa807ba772c7a5a00c1820d3ff661c1038a20f80d06bb4e4.css" /> <link rel="stylesheet" media="all" href="//a.academia-assets.com/assets/academia-bdb9e8c097f01e611f2fc5e2f1a9dc599beede975e2ae5629983543a1726e947.css" /> <link rel="stylesheet" media="all" href="//a.academia-assets.com/assets/design_system_legacy-056a9113b9a0f5343d013b29ee1929d5a18be35fdcdceb616600b4db8bd20054.css" /> <script src="//a.academia-assets.com/assets/webpack_bundles/runtime-bundle-005434038af4252ca37c527588411a3d6a0eabb5f727fac83f8bbe7fd88d93bb.js"></script> <script src="//a.academia-assets.com/assets/webpack_bundles/webpack_libraries_and_infrequently_changed.wjs-bundle-3e572e3b706c3ed2ec5b2c1cb44a411fadc81f62a97963cb7bd9c327a0a9d5f2.js"></script> <script src="//a.academia-assets.com/assets/webpack_bundles/core_webpack.wjs-bundle-2e8d3f30eaaddd1debd6ce4630b3453b23a23c91ac7c823ddf8822879835b029.js"></script> <script src="//a.academia-assets.com/assets/webpack_bundles/sentry.wjs-bundle-5fe03fddca915c8ba0f7edbe64c194308e8ce5abaed7bffe1255ff37549c4808.js"></script> <script> jade = window.jade || {}; jade.helpers = window.$h; jade._ = window._; </script>  <script id="tag-manager-head-root">(function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start': new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0], j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src= 'https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f); })(window,document,'script','dataLayer_old','GTM-5G9JF7Z');</script>  <script> window.gptadslots = []; window.googletag = window.googletag || {}; window.googletag.cmd = window.googletag.cmd || []; </script> <script type="text/javascript"> // TODO(jacob): This should be defined, may be rare load order problem. // Checking if null is just a quick fix, will default to en if unset. // Better fix is to run this immedietely after I18n is set. if (window.I18n != null) { I18n.defaultLocale = "en"; I18n.locale = "en"; I18n.fallbacks = true; } </script> <link rel="canonical" href="https://www.academia.edu/Documents/in/Mathematical_Biology" /> </head>   <body class='c-by_tag a-show_one logged_out u-bgColorWhite'>  <div id="fb-root"></div><script>window.fbAsyncInit = function() { FB.init({ appId: "2369844204", version: "v8.0", status: true, cookie: true, xfbml: true }); // Additional initialization code. if (window.InitFacebook) { // facebook.ts already loaded, set it up. window.InitFacebook(); } else { // Set a flag for facebook.ts to find when it loads. window.academiaAuthReadyFacebook = true; } };</script><script>window.fbAsyncLoad = function() { // Protection against double calling of this function if (window.FB) { return; } (function(d, s, id){ var js, fjs = d.getElementsByTagName(s)[0]; if (d.getElementById(id)) {return;} js = d.createElement(s); js.id = id; js.src = "//connect.facebook.net/en_US/sdk.js"; fjs.parentNode.insertBefore(js, fjs); }(document, 'script', 'facebook-jssdk')); } if (!window.defer_facebook) { // Autoload if not deferred window.fbAsyncLoad(); } else { // Defer loading by 5 seconds setTimeout(function() { window.fbAsyncLoad(); }, 5000); }</script> <div id="google-root"></div><script>window.loadGoogle = function() { if (window.InitGoogle) { // google.ts already loaded, set it up. window.InitGoogle("331998490334-rsn3chp12mbkiqhl6e7lu2q0mlbu0f1b"); } else { // Set a flag for google.ts to use when it loads. window.GoogleClientID = "331998490334-rsn3chp12mbkiqhl6e7lu2q0mlbu0f1b"; } };</script><script>window.googleAsyncLoad = function() { // Protection against double calling of this function (function(d) { var js; var id = 'google-jssdk'; var ref = d.getElementsByTagName('script')[0]; if (d.getElementById(id)) { return; } js = d.createElement('script'); js.id = id; js.async = true; js.onload = loadGoogle; js.src = "https://accounts.google.com/gsi/client" ref.parentNode.insertBefore(js, ref); }(document)); } if (!window.defer_google) { // Autoload if not deferred window.googleAsyncLoad(); } else { // Defer loading by 5 seconds setTimeout(function() { window.googleAsyncLoad(); }, 5000); }</script> <div id="tag-manager-body-root">  <noscript><iframe src="https://www.googletagmanager.com/ns.html?id=GTM-5G9JF7Z" height="0" width="0" style="display:none;visibility:hidden"></iframe></noscript>   <script> window.addEventListener('load', function() { if (document.querySelector('input[name="commit"]')) { document.querySelector('input[name="commit"]').addEventListener('click', function() { gtag('event', 'click', { event_category: 'button', event_label: 'Log In' }) }) } }); </script> </div> <script>var _comscore = _comscore || []; _comscore.push({ c1: "2", c2: "26766707" }); (function() { var s = document.createElement("script"), el = document.getElementsByTagName("script")[0]; s.async = true; s.src = (document.location.protocol == "https:" ? "https://sb" : "http://b") + ".scorecardresearch.com/beacon.js"; el.parentNode.insertBefore(s, el); })();</script><img src="https://sb.scorecardresearch.com/p?c1=2&c2=26766707&cv=2.0&cj=1" style="position: absolute; visibility: hidden" /> <div id='react-modal'></div> <div class='DesignSystem'> <a class='u-showOnFocus' href='#site'> Skip to main content </a> </div> <div id="upgrade_ie_banner" style="display: none;"><p>Academia.edu no longer supports Internet Explorer.</p><p>To browse Academia.edu and the wider internet faster and more securely, please take a few seconds to <a href="https://www.academia.edu/upgrade-browser">upgrade your browser</a>.</p></div><script>// Show this banner for all versions of IE if (!!window.MSInputMethodContext || /(MSIE)/.test(navigator.userAgent)) { document.getElementById('upgrade_ie_banner').style.display = 'block'; }</script> <div class="DesignSystem bootstrap ShrinkableNav no-sm no-md"><div class="navbar navbar-default main-header"><div class="container-wrapper" id="main-header-container"><div class="container"><div class="navbar-header"><div class="nav-left-wrapper u-mt0x"><div class="nav-logo"><a data-main-header-link-target="logo_home" href="https://www.academia.edu/"><img class="visible-xs-inline-block" style="height: 24px;" alt="Academia.edu" src="//a.academia-assets.com/images/academia-logo-redesign-2015-A.svg" width="24" height="24" /><img width="145.2" height="18" class="hidden-xs" style="height: 24px;" alt="Academia.edu" src="//a.academia-assets.com/images/academia-logo-redesign-2015.svg" /></a></div><div class="nav-search"><div class="SiteSearch-wrapper select2-no-default-pills"><form class="js-SiteSearch-form DesignSystem" action="https://www.academia.edu/search" accept-charset="UTF-8" method="get"><input name="utf8" type="hidden" value="✓" autocomplete="off" /><i class="SiteSearch-icon fa fa-search u-fw700 u-positionAbsolute u-tcGrayDark"></i><input class="js-SiteSearch-form-input SiteSearch-form-input form-control" data-main-header-click-target="search_input" name="q" placeholder="Search" type="text" value="" /></form></div></div></div><div class="nav-right-wrapper pull-right"><ul class="NavLinks js-main-nav list-unstyled"><li class="NavLinks-link"><a class="js-header-login-url Button Button--inverseGray Button--sm u-mb4x" id="nav_log_in" rel="nofollow" href="https://www.academia.edu/login">Log In</a></li><li class="NavLinks-link u-p0x"><a class="Button Button--inverseGray Button--sm u-mb4x" rel="nofollow" href="https://www.academia.edu/signup">Sign Up</a></li></ul><button class="hidden-lg hidden-md hidden-sm u-ml4x navbar-toggle collapsed" data-target=".js-mobile-header-links" data-toggle="collapse" type="button"><span class="icon-bar"></span><span class="icon-bar"></span><span class="icon-bar"></span></button></div></div><div class="collapse navbar-collapse js-mobile-header-links"><ul class="nav navbar-nav"><li class="u-borderColorGrayLight u-borderBottom1"><a rel="nofollow" href="https://www.academia.edu/login">Log In</a></li><li class="u-borderColorGrayLight u-borderBottom1"><a rel="nofollow" href="https://www.academia.edu/signup">Sign Up</a></li><li class="u-borderColorGrayLight u-borderBottom1 js-mobile-nav-expand-trigger"><a href="#">more&nbsp<span class="caret"></span></a></li><li><ul class="js-mobile-nav-expand-section nav navbar-nav u-m0x collapse"><li class="u-borderColorGrayLight u-borderBottom1"><a rel="false" href="https://www.academia.edu/about">About</a></li><li class="u-borderColorGrayLight u-borderBottom1"><a rel="nofollow" href="https://www.academia.edu/press">Press</a></li><li class="u-borderColorGrayLight u-borderBottom1"><a rel="nofollow" href="https://medium.com/@academia">Blog</a></li><li class="u-borderColorGrayLight u-borderBottom1"><a rel="false" href="https://www.academia.edu/documents">Papers</a></li><li class="u-borderColorGrayLight u-borderBottom1"><a rel="nofollow" href="https://www.academia.edu/terms">Terms</a></li><li class="u-borderColorGrayLight u-borderBottom1"><a rel="nofollow" href="https://www.academia.edu/privacy">Privacy</a></li><li class="u-borderColorGrayLight u-borderBottom1"><a rel="nofollow" href="https://www.academia.edu/copyright">Copyright</a></li><li class="u-borderColorGrayLight u-borderBottom1"><a rel="nofollow" href="https://www.academia.edu/hiring"><i class="fa fa-briefcase"></i> We're Hiring!</a></li><li class="u-borderColorGrayLight u-borderBottom1"><a rel="nofollow" href="https://support.academia.edu/"><i class="fa fa-question-circle"></i> Help Center</a></li><li class="js-mobile-nav-collapse-trigger u-borderColorGrayLight u-borderBottom1 dropup" style="display:none"><a href="#">less&nbsp<span class="caret"></span></a></li></ul></li></ul></div></div></div><script>(function(){ var $moreLink = $(".js-mobile-nav-expand-trigger"); var $lessLink = $(".js-mobile-nav-collapse-trigger"); var $section = $('.js-mobile-nav-expand-section'); $moreLink.click(function(ev){ ev.preventDefault(); $moreLink.hide(); $lessLink.show(); $section.collapse('show'); }); $lessLink.click(function(ev){ ev.preventDefault(); $moreLink.show(); $lessLink.hide(); $section.collapse('hide'); }); })() if ($a.is_logged_in() || false) { new Aedu.NavigationController({ el: '.js-main-nav', showHighlightedNotification: false }); } else { $(".js-header-login-url").attr("href", $a.loginUrlWithRedirect()); } Aedu.autocompleteSearch = new AutocompleteSearch({el: '.js-SiteSearch-form'});</script></div></div> <div id='site' class='fixed'> <div id="content" class="clearfix"> <script>document.addEventListener('DOMContentLoaded', function(){ var $dismissible = $(".dismissible_banner"); $dismissible.click(function(ev) { $dismissible.hide(); }); });</script> <div class="DesignSystem" style="margin-top:-40px"><div class="PageHeader"><div class="container"><div class="row"><style type="text/css">.sor-abstract { display: -webkit-box; overflow: hidden; text-overflow: ellipsis; -webkit-line-clamp: 3; -webkit-box-orient: vertical; }</style><div class="col-xs-12 clearfix"><div class="u-floatLeft"><h1 class="PageHeader-title u-m0x u-fs30">Mathematical Biology</h1><div class="u-tcGrayDark">14,690 Followers</div><div class="u-tcGrayDark u-mt2x">Recent papers in <b>Mathematical Biology</b></div></div></div></div></div></div><div class="TabbedNavigation"><div class="container"><div class="row"><div class="col-xs-12 clearfix"><ul class="nav u-m0x u-p0x list-inline u-displayFlex"><li class="active"><a href="https://www.academia.edu/Documents/in/Mathematical_Biology">Top Papers</a></li><li><a href="https://www.academia.edu/Documents/in/Mathematical_Biology/MostCited">Most Cited Papers</a></li><li><a href="https://www.academia.edu/Documents/in/Mathematical_Biology/MostDownloaded">Most Downloaded Papers</a></li><li><a href="https://www.academia.edu/Documents/in/Mathematical_Biology/MostRecent">Newest Papers</a></li><li><a class="" href="https://www.academia.edu/People/Mathematical_Biology">People</a></li></ul></div><style type="text/css">ul.nav{flex-direction:row}@media(max-width: 567px){ul.nav{flex-direction:column}.TabbedNavigation li{max-width:100%}.TabbedNavigation li.active{background-color:var(--background-grey, #dddde2)}.TabbedNavigation li.active:before,.TabbedNavigation li.active:after{display:none}}</style></div></div></div><div class="container"><div class="row"><div class="col-xs-12"><div class="u-displayFlex"><div class="u-flexGrow1"><div class="works"><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_12565062" data-work_id="12565062" itemscope="itemscope" itemtype="https://schema.org/ScholarlyArticle"><div class="header"><div class="title u-fontSerif u-fs22 u-lineHeight1_3"><a class="u-tcGrayDarkest js-work-link" href="https://www.academia.edu/12565062/Combinatorial_vector_fields_and_the_valley_structure_of_fitness_landscapes">Combinatorial vector fields and the valley structure of fitness landscapes</a></div></div><div class="u-pb4x u-mt3x"></div><ul class="InlineList u-ph0x u-fs13"><li class="InlineList-item logged_in_only"><div class="share_on_academia_work_button"><a class="academia_share Button Button--inverseBlue Button--sm js-bookmark-button" data-academia-share="Work/12565062" data-share-source="work_strip" data-spinner="small_white_hide_contents"><i class="fa fa-plus"></i><span class="work-strip-link-text u-ml1x" data-content="button_text">Bookmark</span></a></div></li><li class="InlineList-item"><div class="download"><a id="13ac7f2919630d403d2a4f441b5f7f6e" rel="nofollow" data-download="{"attachment_id":46084782,"asset_id":12565062,"asset_type":"Work","always_allow_download":false,"track":null,"button_location":"work_strip","source":null,"hide_modal":null}" class="Button Button--sm Button--inverseGreen js-download-button prompt_button doc_download" href="https://www.academia.edu/attachments/46084782/download_file?st=MTczMjk4MzU1Miw4LjIyMi4yMDguMTQ2&s=work_strip"><i class="fa fa-arrow-circle-o-down fa-lg"></i><span class="u-textUppercase u-ml1x" data-content="button_text">Download</span></a></div></li><li class="InlineList-item"><ul class="InlineList InlineList--bordered u-ph0x"><li class="InlineList-item InlineList-item--bordered"><span class="InlineList-item-text">by <span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a class="u-tcGrayDark u-fw700" data-has-card-for-user="31482800" href="https://independent.academia.edu/PeterStadler">Peter F . Stadler</a><script data-card-contents-for-user="31482800" type="text/json">{"id":31482800,"first_name":"Peter","last_name":"Stadler","domain_name":"independent","page_name":"PeterStadler","display_name":"Peter F . Stadler","profile_url":"https://independent.academia.edu/PeterStadler?f_ri=2963","photo":"/images/s65_no_pic.png"}</script></span></span></li><li class="js-paper-rank-work_12565062 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="12565062"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 12565062, container: ".js-paper-rank-work_12565062", }); });</script></li><li class="js-percentile-work_12565062 InlineList-item InlineList-item--bordered hidden u-tcGrayDark"><span class="percentile-widget hidden"><span class="u-mr2x percentile-widget" style="display: none">•</span><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 12565062; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-percentile-work_12565062"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></li><li class="js-view-count-work_12565062 InlineList-item InlineList-item--bordered hidden"><div><span><span class="js-view-count view-count u-mr2x" data-work-id="12565062"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 12565062; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=12565062]").text(description); $(".js-view-count-work_12565062").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_12565062").removeClass('hidden') })</script></div></li><li class="InlineList-item u-positionRelative" style="max-width: 250px"><div class="u-positionAbsolute" data-has-card-for-ri-list="12565062"><i class="fa fa-tag InlineList-item-icon u-positionRelative"></i>  <a class="InlineList-item-text u-positionRelative">5</a>  </div><span class="InlineList-item-text u-textTruncate u-pl9x"><a class="InlineList-item-text" data-has-card-for-ri="2963" href="https://www.academia.edu/Documents/in/Mathematical_Biology">Mathematical Biology</a>, <script data-card-contents-for-ri="2963" type="text/json">{"id":2963,"name":"Mathematical Biology","url":"https://www.academia.edu/Documents/in/Mathematical_Biology?f_ri=2963","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="4967" href="https://www.academia.edu/Documents/in/Molecular_Evolution">Molecular Evolution</a>, <script data-card-contents-for-ri="4967" type="text/json">{"id":4967,"name":"Molecular Evolution","url":"https://www.academia.edu/Documents/in/Molecular_Evolution?f_ri=2963","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="47884" href="https://www.academia.edu/Documents/in/Biological_Sciences">Biological Sciences</a>, <script data-card-contents-for-ri="47884" type="text/json">{"id":47884,"name":"Biological Sciences","url":"https://www.academia.edu/Documents/in/Biological_Sciences?f_ri=2963","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="80414" href="https://www.academia.edu/Documents/in/Mathematical_Sciences">Mathematical Sciences</a><script data-card-contents-for-ri="80414" type="text/json">{"id":80414,"name":"Mathematical Sciences","url":"https://www.academia.edu/Documents/in/Mathematical_Sciences?f_ri=2963","nofollow":false}</script></span></li><script>(function(){ if (true) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=12565062]'), work: {"id":12565062,"title":"Combinatorial vector fields and the valley structure of fitness landscapes","created_at":"2015-05-24T13:58:11.265-07:00","url":"https://www.academia.edu/12565062/Combinatorial_vector_fields_and_the_valley_structure_of_fitness_landscapes?f_ri=2963","dom_id":"work_12565062","summary":null,"downloadable_attachments":[{"id":46084782,"asset_id":12565062,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":31482800,"first_name":"Peter","last_name":"Stadler","domain_name":"independent","page_name":"PeterStadler","display_name":"Peter F . Stadler","profile_url":"https://independent.academia.edu/PeterStadler?f_ri=2963","photo":"/images/s65_no_pic.png"}],"research_interests":[{"id":2963,"name":"Mathematical Biology","url":"https://www.academia.edu/Documents/in/Mathematical_Biology?f_ri=2963","nofollow":false},{"id":4967,"name":"Molecular Evolution","url":"https://www.academia.edu/Documents/in/Molecular_Evolution?f_ri=2963","nofollow":false},{"id":47884,"name":"Biological Sciences","url":"https://www.academia.edu/Documents/in/Biological_Sciences?f_ri=2963","nofollow":false},{"id":80414,"name":"Mathematical Sciences","url":"https://www.academia.edu/Documents/in/Mathematical_Sciences?f_ri=2963","nofollow":false},{"id":86034,"name":"Mathematical Analysis","url":"https://www.academia.edu/Documents/in/Mathematical_Analysis?f_ri=2963"}]}, }) } })();</script></ul></li></ul></div></div><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_14839384" data-work_id="14839384" itemscope="itemscope" itemtype="https://schema.org/ScholarlyArticle"><div class="header"><div class="title u-fontSerif u-fs22 u-lineHeight1_3"><a class="u-tcGrayDarkest js-work-link" href="https://www.academia.edu/14839384/Global_Stability_Results_in_a_SVIR_Epidemic_Model_with_Immunity_Loss_Rate_Depending_on_the_Vaccine_Age">Global Stability Results in a SVIR Epidemic Model with Immunity Loss Rate Depending on the Vaccine-Age</a></div></div><div class="u-pb4x u-mt3x"></div><ul class="InlineList u-ph0x u-fs13"><li class="InlineList-item logged_in_only"><div class="share_on_academia_work_button"><a class="academia_share Button Button--inverseBlue Button--sm js-bookmark-button" data-academia-share="Work/14839384" data-share-source="work_strip" data-spinner="small_white_hide_contents"><i class="fa fa-plus"></i><span class="work-strip-link-text u-ml1x" data-content="button_text">Bookmark</span></a></div></li><li class="InlineList-item"><div class="download"><a id="c4dc846630fb3d068f7050842c193df9" rel="nofollow" data-download="{"attachment_id":43856064,"asset_id":14839384,"asset_type":"Work","always_allow_download":false,"track":null,"button_location":"work_strip","source":null,"hide_modal":null}" class="Button Button--sm Button--inverseGreen js-download-button prompt_button doc_download" href="https://www.academia.edu/attachments/43856064/download_file?st=MTczMjk4MzU1Miw4LjIyMi4yMDguMTQ2&s=work_strip"><i class="fa fa-arrow-circle-o-down fa-lg"></i><span class="u-textUppercase u-ml1x" data-content="button_text">Download</span></a></div></li><li class="InlineList-item"><ul class="InlineList InlineList--bordered u-ph0x"><li class="InlineList-item InlineList-item--bordered"><span class="InlineList-item-text">by <span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a class="u-tcGrayDark u-fw700" data-has-card-for-user="33803769" href="https://independent.academia.edu/PedroMiramontes">Pedro Miramontes</a><script data-card-contents-for-user="33803769" type="text/json">{"id":33803769,"first_name":"Pedro","last_name":"Miramontes","domain_name":"independent","page_name":"PedroMiramontes","display_name":"Pedro Miramontes","profile_url":"https://independent.academia.edu/PedroMiramontes?f_ri=2963","photo":"/images/s65_no_pic.png"}</script></span></span></li><li class="js-paper-rank-work_14839384 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="14839384"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 14839384, container: ".js-paper-rank-work_14839384", }); });</script></li><li class="js-percentile-work_14839384 InlineList-item InlineList-item--bordered hidden u-tcGrayDark"><span class="percentile-widget hidden"><span class="u-mr2x percentile-widget" style="display: none">•</span><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 14839384; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-percentile-work_14839384"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></li><li class="js-view-count-work_14839384 InlineList-item InlineList-item--bordered hidden"><div><span><span class="js-view-count view-count u-mr2x" data-work-id="14839384"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 14839384; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=14839384]").text(description); $(".js-view-count-work_14839384").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_14839384").removeClass('hidden') })</script></div></li><li class="InlineList-item u-positionRelative" style="max-width: 250px"><div class="u-positionAbsolute" data-has-card-for-ri-list="14839384"><i class="fa fa-tag InlineList-item-icon u-positionRelative"></i>  <a class="InlineList-item-text u-positionRelative">9</a>  </div><span class="InlineList-item-text u-textTruncate u-pl9x"><a class="InlineList-item-text" data-has-card-for-ri="2963" href="https://www.academia.edu/Documents/in/Mathematical_Biology">Mathematical Biology</a>, <script data-card-contents-for-ri="2963" type="text/json">{"id":2963,"name":"Mathematical Biology","url":"https://www.academia.edu/Documents/in/Mathematical_Biology?f_ri=2963","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="13398" href="https://www.academia.edu/Documents/in/Mathematical_Epidemiology">Mathematical Epidemiology</a>, <script data-card-contents-for-ri="13398" type="text/json">{"id":13398,"name":"Mathematical Epidemiology","url":"https://www.academia.edu/Documents/in/Mathematical_Epidemiology?f_ri=2963","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="16521" href="https://www.academia.edu/Documents/in/Mathematical_biology_Mathematics_">Mathematical biology (Mathematics)</a>, <script data-card-contents-for-ri="16521" type="text/json">{"id":16521,"name":"Mathematical biology (Mathematics)","url":"https://www.academia.edu/Documents/in/Mathematical_biology_Mathematics_?f_ri=2963","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="67038" href="https://www.academia.edu/Documents/in/Lyapunov_Stability_Theory">Lyapunov Stability Theory</a><script data-card-contents-for-ri="67038" type="text/json">{"id":67038,"name":"Lyapunov Stability Theory","url":"https://www.academia.edu/Documents/in/Lyapunov_Stability_Theory?f_ri=2963","nofollow":false}</script></span></li><script>(function(){ if (true) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=14839384]'), work: {"id":14839384,"title":"Global Stability Results in a SVIR Epidemic Model with Immunity Loss Rate Depending on the Vaccine-Age","created_at":"2015-08-10T22:40:46.985-07:00","url":"https://www.academia.edu/14839384/Global_Stability_Results_in_a_SVIR_Epidemic_Model_with_Immunity_Loss_Rate_Depending_on_the_Vaccine_Age?f_ri=2963","dom_id":"work_14839384","summary":null,"downloadable_attachments":[{"id":43856064,"asset_id":14839384,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":33803769,"first_name":"Pedro","last_name":"Miramontes","domain_name":"independent","page_name":"PedroMiramontes","display_name":"Pedro Miramontes","profile_url":"https://independent.academia.edu/PedroMiramontes?f_ri=2963","photo":"/images/s65_no_pic.png"}],"research_interests":[{"id":2963,"name":"Mathematical Biology","url":"https://www.academia.edu/Documents/in/Mathematical_Biology?f_ri=2963","nofollow":false},{"id":13398,"name":"Mathematical Epidemiology","url":"https://www.academia.edu/Documents/in/Mathematical_Epidemiology?f_ri=2963","nofollow":false},{"id":16521,"name":"Mathematical biology (Mathematics)","url":"https://www.academia.edu/Documents/in/Mathematical_biology_Mathematics_?f_ri=2963","nofollow":false},{"id":67038,"name":"Lyapunov Stability Theory","url":"https://www.academia.edu/Documents/in/Lyapunov_Stability_Theory?f_ri=2963","nofollow":false},{"id":420906,"name":"Lyapunov functions","url":"https://www.academia.edu/Documents/in/Lyapunov_functions?f_ri=2963"},{"id":543165,"name":"direct Lyapunov method","url":"https://www.academia.edu/Documents/in/direct_Lyapunov_method?f_ri=2963"},{"id":543171,"name":"Lyapunov function","url":"https://www.academia.edu/Documents/in/Lyapunov_function?f_ri=2963"},{"id":543197,"name":"Second Method of Lyapunov","url":"https://www.academia.edu/Documents/in/Second_Method_of_Lyapunov?f_ri=2963"},{"id":544875,"name":"Lyapunov techniques","url":"https://www.academia.edu/Documents/in/Lyapunov_techniques?f_ri=2963"}]}, }) } })();</script></ul></li></ul></div></div><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_6141676" data-work_id="6141676" itemscope="itemscope" itemtype="https://schema.org/ScholarlyArticle"><div class="header"><div class="title u-fontSerif u-fs22 u-lineHeight1_3"><a class="u-tcGrayDarkest js-work-link" href="https://www.academia.edu/6141676/A_graph_theoretic_method_for_the_basic_reproduction_number_in_continuous_time_epidemiological_models">A graph-theoretic method for the basic reproduction number in continuous time epidemiological models</a></div></div><div class="u-pb4x u-mt3x"><div class="summary u-fs14 u-fw300 u-lineHeight1_5 u-tcGrayDarkest"><div class="summarized">In epidemiological models of infectious diseases the basic reproduction number ${\mathcal{R}_0}$ is used as a threshold parameter to determine the threshold between disease extinction and outbreak. A graph-theoretic form of Gaussian... <a class="more_link u-tcGrayDark u-linkUnstyled" data-container=".work_6141676" data-show=".complete" data-hide=".summarized" data-more-link-behavior="true" href="#">more</a></div><div class="complete hidden">In epidemiological models of infectious diseases the basic reproduction number ${\mathcal{R}_0}$ is used as a threshold parameter to determine the threshold between disease extinction and outbreak. A graph-theoretic form of Gaussian elimination using digraph reduction is derived and an algorithm given for calculating the basic reproduction number in continuous time epidemiological models. Examples illustrate how this method can be applied to compartmental models of infectious diseases modelled by a system of ordinary differential equations. We also show with these examples how lower bounds for ${\mathcal{R}_0}$ can be obtained from the digraphs in the reduction process.</div></div></div><ul class="InlineList u-ph0x u-fs13"><li class="InlineList-item logged_in_only"><div class="share_on_academia_work_button"><a class="academia_share Button Button--inverseBlue Button--sm js-bookmark-button" data-academia-share="Work/6141676" data-share-source="work_strip" data-spinner="small_white_hide_contents"><i class="fa fa-plus"></i><span class="work-strip-link-text u-ml1x" data-content="button_text">Bookmark</span></a></div></li><li class="InlineList-item"><div class="download"><a id="a4795d92b249e24794f259d7bed4c963" rel="nofollow" data-download="{"attachment_id":49001577,"asset_id":6141676,"asset_type":"Work","always_allow_download":false,"track":null,"button_location":"work_strip","source":null,"hide_modal":null}" class="Button Button--sm Button--inverseGreen js-download-button prompt_button doc_download" href="https://www.academia.edu/attachments/49001577/download_file?st=MTczMjk4MzU1Miw4LjIyMi4yMDguMTQ2&s=work_strip"><i class="fa fa-arrow-circle-o-down fa-lg"></i><span class="u-textUppercase u-ml1x" data-content="button_text">Download</span></a></div></li><li class="InlineList-item"><ul class="InlineList InlineList--bordered u-ph0x"><li class="InlineList-item InlineList-item--bordered"><span class="InlineList-item-text">by <span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a class="u-tcGrayDark u-fw700" data-has-card-for-user="9324630" href="https://ucr.academia.edu/TomasdeCamino">Tomas de Camino</a><script data-card-contents-for-user="9324630" type="text/json">{"id":9324630,"first_name":"Tomas","last_name":"de Camino","domain_name":"ucr","page_name":"TomasdeCamino","display_name":"Tomas de Camino","profile_url":"https://ucr.academia.edu/TomasdeCamino?f_ri=2963","photo":"/images/s65_no_pic.png"}</script></span></span></li><li class="js-paper-rank-work_6141676 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="6141676"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 6141676, container: ".js-paper-rank-work_6141676", }); });</script></li><li class="js-percentile-work_6141676 InlineList-item InlineList-item--bordered hidden u-tcGrayDark"><span class="percentile-widget hidden"><span class="u-mr2x percentile-widget" style="display: none">•</span><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 6141676; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-percentile-work_6141676"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></li><li class="js-view-count-work_6141676 InlineList-item InlineList-item--bordered hidden"><div><span><span class="js-view-count view-count u-mr2x" data-work-id="6141676"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 6141676; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=6141676]").text(description); $(".js-view-count-work_6141676").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_6141676").removeClass('hidden') })</script></div></li><li class="InlineList-item u-positionRelative" style="max-width: 250px"><div class="u-positionAbsolute" data-has-card-for-ri-list="6141676"><i class="fa fa-tag InlineList-item-icon u-positionRelative"></i>  <a class="InlineList-item-text u-positionRelative">11</a>  </div><span class="InlineList-item-text u-textTruncate u-pl10x"><a class="InlineList-item-text" data-has-card-for-ri="428" href="https://www.academia.edu/Documents/in/Algorithms">Algorithms</a>, <script data-card-contents-for-ri="428" type="text/json">{"id":428,"name":"Algorithms","url":"https://www.academia.edu/Documents/in/Algorithms?f_ri=2963","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="2963" href="https://www.academia.edu/Documents/in/Mathematical_Biology">Mathematical Biology</a>, <script data-card-contents-for-ri="2963" type="text/json">{"id":2963,"name":"Mathematical Biology","url":"https://www.academia.edu/Documents/in/Mathematical_Biology?f_ri=2963","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="13734" href="https://www.academia.edu/Documents/in/Communicable_Diseases">Communicable Diseases</a>, <script data-card-contents-for-ri="13734" type="text/json">{"id":13734,"name":"Communicable Diseases","url":"https://www.academia.edu/Documents/in/Communicable_Diseases?f_ri=2963","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="47884" href="https://www.academia.edu/Documents/in/Biological_Sciences">Biological Sciences</a><script data-card-contents-for-ri="47884" type="text/json">{"id":47884,"name":"Biological Sciences","url":"https://www.academia.edu/Documents/in/Biological_Sciences?f_ri=2963","nofollow":false}</script></span></li><script>(function(){ if (true) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=6141676]'), work: {"id":6141676,"title":"A graph-theoretic method for the basic reproduction number in continuous time epidemiological models","created_at":"2014-02-19T20:35:23.538-08:00","url":"https://www.academia.edu/6141676/A_graph_theoretic_method_for_the_basic_reproduction_number_in_continuous_time_epidemiological_models?f_ri=2963","dom_id":"work_6141676","summary":"In epidemiological models of infectious diseases the basic reproduction number ${\\mathcal{R}_0}$ is used as a threshold parameter to determine the threshold between disease extinction and outbreak. A graph-theoretic form of Gaussian elimination using digraph reduction is derived and an algorithm given for calculating the basic reproduction number in continuous time epidemiological models. Examples illustrate how this method can be applied to compartmental models of infectious diseases modelled by a system of ordinary differential equations. We also show with these examples how lower bounds for ${\\mathcal{R}_0}$ can be obtained from the digraphs in the reduction process.","downloadable_attachments":[{"id":49001577,"asset_id":6141676,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":9324630,"first_name":"Tomas","last_name":"de Camino","domain_name":"ucr","page_name":"TomasdeCamino","display_name":"Tomas de Camino","profile_url":"https://ucr.academia.edu/TomasdeCamino?f_ri=2963","photo":"/images/s65_no_pic.png"}],"research_interests":[{"id":428,"name":"Algorithms","url":"https://www.academia.edu/Documents/in/Algorithms?f_ri=2963","nofollow":false},{"id":2963,"name":"Mathematical Biology","url":"https://www.academia.edu/Documents/in/Mathematical_Biology?f_ri=2963","nofollow":false},{"id":13734,"name":"Communicable Diseases","url":"https://www.academia.edu/Documents/in/Communicable_Diseases?f_ri=2963","nofollow":false},{"id":47884,"name":"Biological Sciences","url":"https://www.academia.edu/Documents/in/Biological_Sciences?f_ri=2963","nofollow":false},{"id":80414,"name":"Mathematical Sciences","url":"https://www.academia.edu/Documents/in/Mathematical_Sciences?f_ri=2963"},{"id":389519,"name":"Gaussian Elimination","url":"https://www.academia.edu/Documents/in/Gaussian_Elimination?f_ri=2963"},{"id":521862,"name":"West Nile Fever","url":"https://www.academia.edu/Documents/in/West_Nile_Fever?f_ri=2963"},{"id":543163,"name":"Basic Reproduction Number","url":"https://www.academia.edu/Documents/in/Basic_Reproduction_Number?f_ri=2963"},{"id":571143,"name":"Lower Bound","url":"https://www.academia.edu/Documents/in/Lower_Bound?f_ri=2963"},{"id":991097,"name":"Continuous Time Systems","url":"https://www.academia.edu/Documents/in/Continuous_Time_Systems?f_ri=2963"},{"id":1770555,"name":"Ordinary Differential Equation","url":"https://www.academia.edu/Documents/in/Ordinary_Differential_Equation?f_ri=2963"}]}, }) } })();</script></ul></li></ul></div></div><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_12052037" data-work_id="12052037" itemscope="itemscope" itemtype="https://schema.org/ScholarlyArticle"><div class="header"><div class="title u-fontSerif u-fs22 u-lineHeight1_3"><a class="u-tcGrayDarkest js-work-link" href="https://www.academia.edu/12052037/Computing_the_length_of_the_shortest_telomeres">Computing the length of the shortest telomeres</a></div></div><div class="u-pb4x u-mt3x"><div class="summary u-fs14 u-fw300 u-lineHeight1_5 u-tcGrayDarkest"><div class="summarized">The telomere length can either be shortened or elongated by an enzyme called telomerase after each cell division. Interestingly, the shortest telomere is involved in controlling the ability of a cell to divide. Yet, its dynamics remains... <a class="more_link u-tcGrayDark u-linkUnstyled" data-container=".work_12052037" data-show=".complete" data-hide=".summarized" data-more-link-behavior="true" href="#">more</a></div><div class="complete hidden">The telomere length can either be shortened or elongated by an enzyme called telomerase after each cell <br />division. Interestingly, the shortest telomere is involved in controlling the ability of a cell to divide. Yet, its <br />dynamics remains elusive. We present here a stochastic approach where we model this dynamics using a <br />Markov jump process.We solve the forward Fokker-Planck equation to obtain the steady state distribution <br />and the statistical moments of telomere lengths. We focus specifically on the shortest one and we estimate <br />its length difference with the second shortest telomere. After extracting key parameters such as elongation <br />and shortening dynamics from experimental data, we compute the length of telomeres in yeast and obtain <br />as a possible prediction the minimum concentration of telomerase required to ensure a proper cell <br />division.</div></div></div><ul class="InlineList u-ph0x u-fs13"><li class="InlineList-item logged_in_only"><div class="share_on_academia_work_button"><a class="academia_share Button Button--inverseBlue Button--sm js-bookmark-button" data-academia-share="Work/12052037" data-share-source="work_strip" data-spinner="small_white_hide_contents"><i class="fa fa-plus"></i><span class="work-strip-link-text u-ml1x" data-content="button_text">Bookmark</span></a></div></li><li class="InlineList-item"><div class="download"><a id="984f7c0e0b84b01b0adf90010a5b83eb" rel="nofollow" data-download="{"attachment_id":37380615,"asset_id":12052037,"asset_type":"Work","always_allow_download":false,"track":null,"button_location":"work_strip","source":null,"hide_modal":null}" class="Button Button--sm Button--inverseGreen js-download-button prompt_button doc_download" href="https://www.academia.edu/attachments/37380615/download_file?st=MTczMjk4MzU1Miw4LjIyMi4yMDguMTQ2&s=work_strip"><i class="fa fa-arrow-circle-o-down fa-lg"></i><span class="u-textUppercase u-ml1x" data-content="button_text">Download</span></a></div></li><li class="InlineList-item"><ul class="InlineList InlineList--bordered u-ph0x"><li class="InlineList-item InlineList-item--bordered"><span class="InlineList-item-text">by <span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a class="u-tcGrayDark u-fw700" data-has-card-for-user="21403871" href="https://berkeley.academia.edu/KhanhDaoDuc">Khanh Dao Duc</a><script data-card-contents-for-user="21403871" type="text/json">{"id":21403871,"first_name":"Khanh","last_name":"Dao Duc","domain_name":"berkeley","page_name":"KhanhDaoDuc","display_name":"Khanh Dao Duc","profile_url":"https://berkeley.academia.edu/KhanhDaoDuc?f_ri=2963","photo":"/images/s65_no_pic.png"}</script></span></span></li><li class="js-paper-rank-work_12052037 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="12052037"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 12052037, container: ".js-paper-rank-work_12052037", }); });</script></li><li class="js-percentile-work_12052037 InlineList-item InlineList-item--bordered hidden u-tcGrayDark"><span class="percentile-widget hidden"><span class="u-mr2x percentile-widget" style="display: none">•</span><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 12052037; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-percentile-work_12052037"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></li><li class="js-view-count-work_12052037 InlineList-item InlineList-item--bordered hidden"><div><span><span class="js-view-count view-count u-mr2x" data-work-id="12052037"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 12052037; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=12052037]").text(description); $(".js-view-count-work_12052037").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_12052037").removeClass('hidden') })</script></div></li><li class="InlineList-item u-positionRelative" style="max-width: 250px"><div class="u-positionAbsolute" data-has-card-for-ri-list="12052037"><i class="fa fa-tag InlineList-item-icon u-positionRelative"></i>  <a class="InlineList-item-text u-positionRelative">7</a>  </div><span class="InlineList-item-text u-textTruncate u-pl9x"><a class="InlineList-item-text" data-has-card-for-ri="347" href="https://www.academia.edu/Documents/in/Stochastic_Process">Stochastic Process</a>, <script data-card-contents-for-ri="347" type="text/json">{"id":347,"name":"Stochastic Process","url":"https://www.academia.edu/Documents/in/Stochastic_Process?f_ri=2963","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="2963" href="https://www.academia.edu/Documents/in/Mathematical_Biology">Mathematical Biology</a>, <script data-card-contents-for-ri="2963" type="text/json">{"id":2963,"name":"Mathematical Biology","url":"https://www.academia.edu/Documents/in/Mathematical_Biology?f_ri=2963","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="3775" href="https://www.academia.edu/Documents/in/Senescence">Senescence</a>, <script data-card-contents-for-ri="3775" type="text/json">{"id":3775,"name":"Senescence","url":"https://www.academia.edu/Documents/in/Senescence?f_ri=2963","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="4218" href="https://www.academia.edu/Documents/in/Telomeres">Telomeres</a><script data-card-contents-for-ri="4218" type="text/json">{"id":4218,"name":"Telomeres","url":"https://www.academia.edu/Documents/in/Telomeres?f_ri=2963","nofollow":false}</script></span></li><script>(function(){ if (true) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=12052037]'), work: {"id":12052037,"title":"Computing the length of the shortest telomeres","created_at":"2015-04-21T11:23:11.283-07:00","url":"https://www.academia.edu/12052037/Computing_the_length_of_the_shortest_telomeres?f_ri=2963","dom_id":"work_12052037","summary":"The telomere length can either be shortened or elongated by an enzyme called telomerase after each cell\r\ndivision. Interestingly, the shortest telomere is involved in controlling the ability of a cell to divide. Yet, its\r\ndynamics remains elusive. We present here a stochastic approach where we model this dynamics using a\r\nMarkov jump process.We solve the forward Fokker-Planck equation to obtain the steady state distribution\r\nand the statistical moments of telomere lengths. We focus specifically on the shortest one and we estimate\r\nits length difference with the second shortest telomere. After extracting key parameters such as elongation\r\nand shortening dynamics from experimental data, we compute the length of telomeres in yeast and obtain\r\nas a possible prediction the minimum concentration of telomerase required to ensure a proper cell\r\ndivision.","downloadable_attachments":[{"id":37380615,"asset_id":12052037,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":21403871,"first_name":"Khanh","last_name":"Dao Duc","domain_name":"berkeley","page_name":"KhanhDaoDuc","display_name":"Khanh Dao Duc","profile_url":"https://berkeley.academia.edu/KhanhDaoDuc?f_ri=2963","photo":"/images/s65_no_pic.png"}],"research_interests":[{"id":347,"name":"Stochastic Process","url":"https://www.academia.edu/Documents/in/Stochastic_Process?f_ri=2963","nofollow":false},{"id":2963,"name":"Mathematical Biology","url":"https://www.academia.edu/Documents/in/Mathematical_Biology?f_ri=2963","nofollow":false},{"id":3775,"name":"Senescence","url":"https://www.academia.edu/Documents/in/Senescence?f_ri=2963","nofollow":false},{"id":4218,"name":"Telomeres","url":"https://www.academia.edu/Documents/in/Telomeres?f_ri=2963","nofollow":false},{"id":4233,"name":"Computational Biology","url":"https://www.academia.edu/Documents/in/Computational_Biology?f_ri=2963"},{"id":39865,"name":"Telomerase","url":"https://www.academia.edu/Documents/in/Telomerase?f_ri=2963"},{"id":159886,"name":"TELOMERE LENGTH","url":"https://www.academia.edu/Documents/in/TELOMERE_LENGTH?f_ri=2963"}]}, }) } })();</script></ul></li></ul></div></div><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_76384794" data-work_id="76384794" itemscope="itemscope" itemtype="https://schema.org/ScholarlyArticle"><div class="header"><div class="title u-fontSerif u-fs22 u-lineHeight1_3"><a class="u-tcGrayDarkest js-work-link" href="https://www.academia.edu/76384794/Reliable_analysis_for_delay_differential_equations_arising_in_mathematical_biology">Reliable analysis for delay differential equations arising in mathematical biology</a></div></div><div class="u-pb4x u-mt3x"></div><ul class="InlineList u-ph0x u-fs13"><li class="InlineList-item logged_in_only"><div class="share_on_academia_work_button"><a class="academia_share Button Button--inverseBlue Button--sm js-bookmark-button" data-academia-share="Work/76384794" data-share-source="work_strip" data-spinner="small_white_hide_contents"><i class="fa fa-plus"></i><span class="work-strip-link-text u-ml1x" data-content="button_text">Bookmark</span></a></div></li><li class="InlineList-item"><div class="download"><a id="19c1bfa29bb7e3343bfc5723a8fb6f53" rel="nofollow" data-download="{"attachment_id":84110151,"asset_id":76384794,"asset_type":"Work","always_allow_download":false,"track":null,"button_location":"work_strip","source":null,"hide_modal":null}" class="Button Button--sm Button--inverseGreen js-download-button prompt_button doc_download" href="https://www.academia.edu/attachments/84110151/download_file?st=MTczMjk4MzU1Miw4LjIyMi4yMDguMTQ2&s=work_strip"><i class="fa fa-arrow-circle-o-down fa-lg"></i><span class="u-textUppercase u-ml1x" data-content="button_text">Download</span></a></div></li><li class="InlineList-item"><ul class="InlineList InlineList--bordered u-ph0x"><li class="InlineList-item InlineList-item--bordered"><span class="InlineList-item-text">by <span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a class="u-tcGrayDark u-fw700" data-has-card-for-user="23332195" href="https://independent.academia.edu/AhmetYILDIRIM6">Ahmet YILDIRIM</a><script data-card-contents-for-user="23332195" type="text/json">{"id":23332195,"first_name":"Ahmet","last_name":"YILDIRIM","domain_name":"independent","page_name":"AhmetYILDIRIM6","display_name":"Ahmet YILDIRIM","profile_url":"https://independent.academia.edu/AhmetYILDIRIM6?f_ri=2963","photo":"/images/s65_no_pic.png"}</script></span></span></li><li class="js-paper-rank-work_76384794 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="76384794"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 76384794, container: ".js-paper-rank-work_76384794", }); });</script></li><li class="js-percentile-work_76384794 InlineList-item InlineList-item--bordered hidden u-tcGrayDark"><span class="percentile-widget hidden"><span class="u-mr2x percentile-widget" style="display: none">•</span><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 76384794; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-percentile-work_76384794"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></li><li class="js-view-count-work_76384794 InlineList-item InlineList-item--bordered hidden"><div><span><span class="js-view-count view-count u-mr2x" data-work-id="76384794"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 76384794; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=76384794]").text(description); $(".js-view-count-work_76384794").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_76384794").removeClass('hidden') })</script></div></li><li class="InlineList-item u-positionRelative" style="max-width: 250px"><div class="u-positionAbsolute" data-has-card-for-ri-list="76384794"><i class="fa fa-tag InlineList-item-icon u-positionRelative"></i>  <a class="InlineList-item-text u-positionRelative">8</a>  </div><span class="InlineList-item-text u-textTruncate u-pl9x"><a class="InlineList-item-text" data-has-card-for-ri="2963" href="https://www.academia.edu/Documents/in/Mathematical_Biology">Mathematical Biology</a>, <script data-card-contents-for-ri="2963" type="text/json">{"id":2963,"name":"Mathematical Biology","url":"https://www.academia.edu/Documents/in/Mathematical_Biology?f_ri=2963","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="28235" href="https://www.academia.edu/Documents/in/Multidisciplinary">Multidisciplinary</a>, <script data-card-contents-for-ri="28235" type="text/json">{"id":28235,"name":"Multidisciplinary","url":"https://www.academia.edu/Documents/in/Multidisciplinary?f_ri=2963","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="84487" href="https://www.academia.edu/Documents/in/Delay_Differential_Equation">Delay Differential Equation</a>, <script data-card-contents-for-ri="84487" type="text/json">{"id":84487,"name":"Delay Differential Equation","url":"https://www.academia.edu/Documents/in/Delay_Differential_Equation?f_ri=2963","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="122983" href="https://www.academia.edu/Documents/in/Reliability_Analysis">Reliability Analysis</a><script data-card-contents-for-ri="122983" type="text/json">{"id":122983,"name":"Reliability Analysis","url":"https://www.academia.edu/Documents/in/Reliability_Analysis?f_ri=2963","nofollow":false}</script></span></li><script>(function(){ if (true) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=76384794]'), work: {"id":76384794,"title":"Reliable analysis for delay differential equations arising in mathematical biology","created_at":"2022-04-13T23:02:02.740-07:00","url":"https://www.academia.edu/76384794/Reliable_analysis_for_delay_differential_equations_arising_in_mathematical_biology?f_ri=2963","dom_id":"work_76384794","summary":null,"downloadable_attachments":[{"id":84110151,"asset_id":76384794,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":23332195,"first_name":"Ahmet","last_name":"YILDIRIM","domain_name":"independent","page_name":"AhmetYILDIRIM6","display_name":"Ahmet YILDIRIM","profile_url":"https://independent.academia.edu/AhmetYILDIRIM6?f_ri=2963","photo":"/images/s65_no_pic.png"}],"research_interests":[{"id":2963,"name":"Mathematical Biology","url":"https://www.academia.edu/Documents/in/Mathematical_Biology?f_ri=2963","nofollow":false},{"id":28235,"name":"Multidisciplinary","url":"https://www.academia.edu/Documents/in/Multidisciplinary?f_ri=2963","nofollow":false},{"id":84487,"name":"Delay Differential Equation","url":"https://www.academia.edu/Documents/in/Delay_Differential_Equation?f_ri=2963","nofollow":false},{"id":122983,"name":"Reliability Analysis","url":"https://www.academia.edu/Documents/in/Reliability_Analysis?f_ri=2963","nofollow":false},{"id":136174,"name":"Delay Differential Equations","url":"https://www.academia.edu/Documents/in/Delay_Differential_Equations?f_ri=2963"},{"id":291387,"name":"Mathematical Model","url":"https://www.academia.edu/Documents/in/Mathematical_Model?f_ri=2963"},{"id":394477,"name":"Time Dependent","url":"https://www.academia.edu/Documents/in/Time_Dependent?f_ri=2963"},{"id":3771578,"name":"variational iteration method","url":"https://www.academia.edu/Documents/in/variational_iteration_method?f_ri=2963"}]}, }) } })();</script></ul></li></ul></div></div><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_37491545 coauthored" data-work_id="37491545" itemscope="itemscope" itemtype="https://schema.org/ScholarlyArticle"><div class="header"><div class="title u-fontSerif u-fs22 u-lineHeight1_3"><a class="u-tcGrayDarkest js-work-link" href="https://www.academia.edu/37491545/Burden_of_tuberculosis_disease_in_South_East_Asia_A_statistical_analysis">Burden of tuberculosis disease in South-East Asia: A statistical analysis</a></div></div><div class="u-pb4x u-mt3x"><div class="summary u-fs14 u-fw300 u-lineHeight1_5 u-tcGrayDarkest"><div class="summarized">The reports published by WHO on a daily basis suggest that tuberculosis (TB) remains the top infectious killer as in 2016 in SouthEast Asia, and hence considered a " burden " in these countries. Very few studies on the burden of TB in... <a class="more_link u-tcGrayDark u-linkUnstyled" data-container=".work_37491545" data-show=".complete" data-hide=".summarized" data-more-link-behavior="true" href="#">more</a></div><div class="complete hidden">The reports published by WHO on a daily basis suggest that tuberculosis (TB) remains the top infectious killer as in 2016 in SouthEast Asia, and hence considered a " burden " in these countries. Very few studies on the burden of TB in SouthEast Asia have been done. One cannot only hypothesize the causes of TB, but also try to venture what forms of medications have been implemented to eradicate the disease. Some of these possibilities have been looked into and analysed in the study of the patients suffering from TB in SouthEast Asian countries (as demarcated by WHO). It has been approximated that there is a total of 95602 TB suffering patients and among them just 1500 of them took different clinical tests to detect for the actual presence of the disease so that they can adopt treatment at the earliest. These patients were either immune to rifampicin or multi-drug treatment. Also, HIV test was done with their dried blood samples, but just a handful of them tested positive for HIV. So there was no reason to treat the HIV+ patients separately while carrying out the analysis. It is seen that women are more prone to running the risk of TB as compared to men. Further, we observe that the disease is not equally distributed in all the countries considered. For, instance there is hardly any new incidence of TB case in Singapore. At the same time, there is an unequal distribution among all the countries with respect to the processing of effective test detection for TB. Moreover, extensively drug-resistant TB has also been reported in Indonesia, Myanmar and Thailand.</div></div></div><ul class="InlineList u-ph0x u-fs13"><li class="InlineList-item logged_in_only"><div class="share_on_academia_work_button"><a class="academia_share Button Button--inverseBlue Button--sm js-bookmark-button" data-academia-share="Work/37491545" data-share-source="work_strip" data-spinner="small_white_hide_contents"><i class="fa fa-plus"></i><span class="work-strip-link-text u-ml1x" data-content="button_text">Bookmark</span></a></div></li><li class="InlineList-item"><div class="download"><a id="ca10b4613a0994d42f3d0c49c26d8c85" rel="nofollow" data-download="{"attachment_id":57462191,"asset_id":37491545,"asset_type":"Work","always_allow_download":false,"track":null,"button_location":"work_strip","source":null,"hide_modal":null}" class="Button Button--sm Button--inverseGreen js-download-button prompt_button doc_download" href="https://www.academia.edu/attachments/57462191/download_file?st=MTczMjk4MzU1Miw4LjIyMi4yMDguMTQ2&s=work_strip"><i class="fa fa-arrow-circle-o-down fa-lg"></i><span class="u-textUppercase u-ml1x" data-content="button_text">Download</span></a></div></li><li class="InlineList-item"><ul class="InlineList InlineList--bordered u-ph0x"><li class="InlineList-item InlineList-item--bordered"><span class="InlineList-item-text">by <span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a class="u-tcGrayDark u-fw700" data-has-card-for-user="807504" href="https://niftem.academia.edu/KalyanDas">Kalyan Das</a><script data-card-contents-for-user="807504" type="text/json">{"id":807504,"first_name":"Kalyan","last_name":"Das","domain_name":"niftem","page_name":"KalyanDas","display_name":"Kalyan Das","profile_url":"https://niftem.academia.edu/KalyanDas?f_ri=2963","photo":"https://0.academia-photos.com/807504/280944/19209742/s65_kalyan.das.jpg"}</script></span></span><span class="u-displayInlineBlock InlineList-item-text"> and <span class="u-textDecorationUnderline u-clickable InlineList-item-text js-work-more-authors-37491545">+1</span><div class="hidden js-additional-users-37491545"><div><span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a href="https://independent.academia.edu/AnishaDas8">Anisha Das</a></span></div></div></span><script>(function(){ var popoverSettings = { el: $('.js-work-more-authors-37491545'), placement: 'bottom', hide_delay: 200, html: true, content: function(){ return $('.js-additional-users-37491545').html(); } } new HoverPopover(popoverSettings); })();</script></li><li class="js-paper-rank-work_37491545 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="37491545"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 37491545, container: ".js-paper-rank-work_37491545", }); });</script></li><li class="js-percentile-work_37491545 InlineList-item InlineList-item--bordered hidden u-tcGrayDark"><span class="percentile-widget hidden"><span class="u-mr2x percentile-widget" style="display: none">•</span><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 37491545; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-percentile-work_37491545"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></li><li class="js-view-count-work_37491545 InlineList-item InlineList-item--bordered hidden"><div><span><span class="js-view-count view-count u-mr2x" data-work-id="37491545"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 37491545; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=37491545]").text(description); $(".js-view-count-work_37491545").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_37491545").removeClass('hidden') })</script></div></li><li class="InlineList-item u-positionRelative" style="max-width: 250px"><div class="u-positionAbsolute" data-has-card-for-ri-list="37491545"><i class="fa fa-tag InlineList-item-icon u-positionRelative"></i></div><span class="InlineList-item-text u-textTruncate u-pl6x"><a class="InlineList-item-text" data-has-card-for-ri="2963" href="https://www.academia.edu/Documents/in/Mathematical_Biology">Mathematical Biology</a><script data-card-contents-for-ri="2963" type="text/json">{"id":2963,"name":"Mathematical Biology","url":"https://www.academia.edu/Documents/in/Mathematical_Biology?f_ri=2963","nofollow":false}</script></span></li><script>(function(){ if (false) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=37491545]'), work: {"id":37491545,"title":"Burden of tuberculosis disease in South-East Asia: A statistical analysis","created_at":"2018-09-27T22:21:47.005-07:00","url":"https://www.academia.edu/37491545/Burden_of_tuberculosis_disease_in_South_East_Asia_A_statistical_analysis?f_ri=2963","dom_id":"work_37491545","summary":"The reports published by WHO on a daily basis suggest that tuberculosis (TB) remains the top infectious killer as in 2016 in SouthEast Asia, and hence considered a \" burden \" in these countries. Very few studies on the burden of TB in SouthEast Asia have been done. One cannot only hypothesize the causes of TB, but also try to venture what forms of medications have been implemented to eradicate the disease. Some of these possibilities have been looked into and analysed in the study of the patients suffering from TB in SouthEast Asian countries (as demarcated by WHO). It has been approximated that there is a total of 95602 TB suffering patients and among them just 1500 of them took different clinical tests to detect for the actual presence of the disease so that they can adopt treatment at the earliest. These patients were either immune to rifampicin or multi-drug treatment. Also, HIV test was done with their dried blood samples, but just a handful of them tested positive for HIV. So there was no reason to treat the HIV+ patients separately while carrying out the analysis. It is seen that women are more prone to running the risk of TB as compared to men. Further, we observe that the disease is not equally distributed in all the countries considered. For, instance there is hardly any new incidence of TB case in Singapore. At the same time, there is an unequal distribution among all the countries with respect to the processing of effective test detection for TB. Moreover, extensively drug-resistant TB has also been reported in Indonesia, Myanmar and Thailand.","downloadable_attachments":[{"id":57462191,"asset_id":37491545,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":807504,"first_name":"Kalyan","last_name":"Das","domain_name":"niftem","page_name":"KalyanDas","display_name":"Kalyan Das","profile_url":"https://niftem.academia.edu/KalyanDas?f_ri=2963","photo":"https://0.academia-photos.com/807504/280944/19209742/s65_kalyan.das.jpg"},{"id":83333538,"first_name":"Anisha","last_name":"Das","domain_name":"independent","page_name":"AnishaDas8","display_name":"Anisha Das","profile_url":"https://independent.academia.edu/AnishaDas8?f_ri=2963","photo":"/images/s65_no_pic.png"}],"research_interests":[{"id":2963,"name":"Mathematical Biology","url":"https://www.academia.edu/Documents/in/Mathematical_Biology?f_ri=2963","nofollow":false}]}, }) } })();</script></ul></li></ul></div></div><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_7593164" data-work_id="7593164" itemscope="itemscope" itemtype="https://schema.org/ScholarlyArticle"><div class="header"><div class="title u-fontSerif u-fs22 u-lineHeight1_3"><a class="u-tcGrayDarkest js-work-link" href="https://www.academia.edu/7593164/Modeling_Neural_Development">Modeling Neural Development</a></div></div><div class="u-pb4x u-mt3x"><div class="summary u-fs14 u-fw300 u-lineHeight1_5 u-tcGrayDarkest"><div class="summarized">This is one of the first books to study neural development using computational and mathematical modeling. Modeling provides precise and exact ways of expression, which allow us to go beyond the insights that intuitive or commonsense... <a class="more_link u-tcGrayDark u-linkUnstyled" data-container=".work_7593164" data-show=".complete" data-hide=".summarized" data-more-link-behavior="true" href="#">more</a></div><div class="complete hidden">This is one of the first books to study neural development using computational and mathematical modeling. Modeling provides precise and exact ways of expression, which allow us to go beyond the insights that intuitive or commonsense reasoning alone can yield. Most neural modeling focuses on information processing in the adult nervous system; Modeling Neural Development shows how models can be used to study the development of the nervous system at different levels of organization and at different phases of development, from molecule to system and from neurulation to cognition. The book's fourteen chapters follow loosely the chronology of neural development. Chapters 1 and 2 study the very early development of the nervous system, discussing gene networks, cell differentiation, and neural tube development. Chapters 3-5 examine neuronal morphogenesis and neurite outgrowth. Chapters 6-8 study different aspects of the self-organization of neurons into networks. Chapters 9-12 cover refinement of connectivity and the development of specific connectivity patterns. Chapters 13 and 14 focus on some of the functional implications of morphology and development. Each chapter contains an overview of the biology of the topic in question, a review of the modeling efforts in the field, a discussion in more detail of some of the models, and some perspectives on future theoretical and experimental work. The science of studying neural development by computational and mathematical modeling is relatively new; this book, as Dale Purves writes in the foreword, "serves as an important progress report" in the effort to understand the complexities of neural development.</div></div></div><ul class="InlineList u-ph0x u-fs13"><li class="InlineList-item logged_in_only"><div class="share_on_academia_work_button"><a class="academia_share Button Button--inverseBlue Button--sm js-bookmark-button" data-academia-share="Work/7593164" data-share-source="work_strip" data-spinner="small_white_hide_contents"><i class="fa fa-plus"></i><span class="work-strip-link-text u-ml1x" data-content="button_text">Bookmark</span></a></div></li><li class="InlineList-item"><div class="download"><a id="d21b091e19ffbf6ba055fbfb1b664242" rel="nofollow" data-download="{"attachment_id":51016357,"asset_id":7593164,"asset_type":"Work","always_allow_download":false,"track":null,"button_location":"work_strip","source":null,"hide_modal":null}" class="Button Button--sm Button--inverseGreen js-download-button prompt_button doc_download" href="https://www.academia.edu/attachments/51016357/download_file?st=MTczMjk4MzU1Miw4LjIyMi4yMDguMTQ2&s=work_strip"><i class="fa fa-arrow-circle-o-down fa-lg"></i><span class="u-textUppercase u-ml1x" data-content="button_text">Download</span></a></div></li><li class="InlineList-item"><ul class="InlineList InlineList--bordered u-ph0x"><li class="InlineList-item InlineList-item--bordered"><span class="InlineList-item-text">by <span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a class="u-tcGrayDark u-fw700" data-has-card-for-user="13197303" href="https://independent.academia.edu/ArjenvanOoyen">Arjen van Ooyen</a><script data-card-contents-for-user="13197303" type="text/json">{"id":13197303,"first_name":"Arjen","last_name":"van Ooyen","domain_name":"independent","page_name":"ArjenvanOoyen","display_name":"Arjen van Ooyen","profile_url":"https://independent.academia.edu/ArjenvanOoyen?f_ri=2963","photo":"https://0.academia-photos.com/13197303/3721252/4360030/s65_arjen.van_ooyen.jpg"}</script></span></span></li><li class="js-paper-rank-work_7593164 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="7593164"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 7593164, container: ".js-paper-rank-work_7593164", }); });</script></li><li class="js-percentile-work_7593164 InlineList-item InlineList-item--bordered hidden u-tcGrayDark"><span class="percentile-widget hidden"><span class="u-mr2x percentile-widget" style="display: none">•</span><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 7593164; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-percentile-work_7593164"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></li><li class="js-view-count-work_7593164 InlineList-item InlineList-item--bordered hidden"><div><span><span class="js-view-count view-count u-mr2x" data-work-id="7593164"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 7593164; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=7593164]").text(description); $(".js-view-count-work_7593164").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_7593164").removeClass('hidden') })</script></div></li><li class="InlineList-item u-positionRelative" style="max-width: 250px"><div class="u-positionAbsolute" data-has-card-for-ri-list="7593164"><i class="fa fa-tag InlineList-item-icon u-positionRelative"></i>  <a class="InlineList-item-text u-positionRelative">10</a>  </div><span class="InlineList-item-text u-textTruncate u-pl10x"><a class="InlineList-item-text" data-has-card-for-ri="161" href="https://www.academia.edu/Documents/in/Neuroscience">Neuroscience</a>, <script data-card-contents-for-ri="161" type="text/json">{"id":161,"name":"Neuroscience","url":"https://www.academia.edu/Documents/in/Neuroscience?f_ri=2963","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="1084" href="https://www.academia.edu/Documents/in/Developmental_Neurobiology">Developmental Neurobiology</a>, <script data-card-contents-for-ri="1084" type="text/json">{"id":1084,"name":"Developmental Neurobiology","url":"https://www.academia.edu/Documents/in/Developmental_Neurobiology?f_ri=2963","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="2963" href="https://www.academia.edu/Documents/in/Mathematical_Biology">Mathematical Biology</a>, <script data-card-contents-for-ri="2963" type="text/json">{"id":2963,"name":"Mathematical Biology","url":"https://www.academia.edu/Documents/in/Mathematical_Biology?f_ri=2963","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="5451" href="https://www.academia.edu/Documents/in/Computational_Neuroscience">Computational Neuroscience</a><script data-card-contents-for-ri="5451" type="text/json">{"id":5451,"name":"Computational Neuroscience","url":"https://www.academia.edu/Documents/in/Computational_Neuroscience?f_ri=2963","nofollow":false}</script></span></li><script>(function(){ if (true) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=7593164]'), work: {"id":7593164,"title":"Modeling Neural Development","created_at":"2014-07-07T22:24:39.124-07:00","url":"https://www.academia.edu/7593164/Modeling_Neural_Development?f_ri=2963","dom_id":"work_7593164","summary":"This is one of the first books to study neural development using computational and mathematical modeling. Modeling provides precise and exact ways of expression, which allow us to go beyond the insights that intuitive or commonsense reasoning alone can yield. Most neural modeling focuses on information processing in the adult nervous system; Modeling Neural Development shows how models can be used to study the development of the nervous system at different levels of organization and at different phases of development, from molecule to system and from neurulation to cognition. The book's fourteen chapters follow loosely the chronology of neural development. Chapters 1 and 2 study the very early development of the nervous system, discussing gene networks, cell differentiation, and neural tube development. Chapters 3-5 examine neuronal morphogenesis and neurite outgrowth. Chapters 6-8 study different aspects of the self-organization of neurons into networks. Chapters 9-12 cover refinement of connectivity and the development of specific connectivity patterns. Chapters 13 and 14 focus on some of the functional implications of morphology and development. Each chapter contains an overview of the biology of the topic in question, a review of the modeling efforts in the field, a discussion in more detail of some of the models, and some perspectives on future theoretical and experimental work. The science of studying neural development by computational and mathematical modeling is relatively new; this book, as Dale Purves writes in the foreword, \"serves as an important progress report\" in the effort to understand the complexities of neural development.","downloadable_attachments":[{"id":51016357,"asset_id":7593164,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":13197303,"first_name":"Arjen","last_name":"van Ooyen","domain_name":"independent","page_name":"ArjenvanOoyen","display_name":"Arjen van Ooyen","profile_url":"https://independent.academia.edu/ArjenvanOoyen?f_ri=2963","photo":"https://0.academia-photos.com/13197303/3721252/4360030/s65_arjen.van_ooyen.jpg"}],"research_interests":[{"id":161,"name":"Neuroscience","url":"https://www.academia.edu/Documents/in/Neuroscience?f_ri=2963","nofollow":false},{"id":1084,"name":"Developmental Neurobiology","url":"https://www.academia.edu/Documents/in/Developmental_Neurobiology?f_ri=2963","nofollow":false},{"id":2963,"name":"Mathematical Biology","url":"https://www.academia.edu/Documents/in/Mathematical_Biology?f_ri=2963","nofollow":false},{"id":5451,"name":"Computational Neuroscience","url":"https://www.academia.edu/Documents/in/Computational_Neuroscience?f_ri=2963","nofollow":false},{"id":8322,"name":"Developmental neuroscience","url":"https://www.academia.edu/Documents/in/Developmental_neuroscience?f_ri=2963"},{"id":26977,"name":"Theoretical biology","url":"https://www.academia.edu/Documents/in/Theoretical_biology?f_ri=2963"},{"id":40540,"name":"Neural Development","url":"https://www.academia.edu/Documents/in/Neural_Development?f_ri=2963"},{"id":49731,"name":"Mathematical Neuroscience","url":"https://www.academia.edu/Documents/in/Mathematical_Neuroscience?f_ri=2963"},{"id":55356,"name":"Theoretical Neuroscience","url":"https://www.academia.edu/Documents/in/Theoretical_Neuroscience?f_ri=2963"},{"id":424012,"name":"Human Nervous System","url":"https://www.academia.edu/Documents/in/Human_Nervous_System?f_ri=2963"}]}, }) } })();</script></ul></li></ul></div></div><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_68173600" data-work_id="68173600" itemscope="itemscope" itemtype="https://schema.org/ScholarlyArticle"><div class="header"><div class="title u-fontSerif u-fs22 u-lineHeight1_3"><a class="u-tcGrayDarkest js-work-link" href="https://www.academia.edu/68173600/Development_of_a_computational_model_of_glucose_toxicity_in_the_progression_of_diabetes_mellitus">Development of a computational model of glucose toxicity in the progression of diabetes mellitus</a></div></div><div class="u-pb4x u-mt3x"><div class="summary u-fs14 u-fw300 u-lineHeight1_5 u-tcGrayDarkest"><div class="summarized">Diabetes mellitus is a disease characterized by a range of metabolic complications involving an individual&amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;#39;s blood glucose levels, and its main regulator, insulin. These... <a class="more_link u-tcGrayDark u-linkUnstyled" data-container=".work_68173600" data-show=".complete" data-hide=".summarized" data-more-link-behavior="true" href="#">more</a></div><div class="complete hidden">Diabetes mellitus is a disease characterized by a range of metabolic complications involving an individual&amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;#39;s blood glucose levels, and its main regulator, insulin. These complications can vary largely from person to person depending on their current biophysical state. Biomedical research day-by-day makes strides to impact the lives of patients of a variety of diseases, including diabetes. One large stride that is being made is the generation of techniques to assist physicians to ``personalize medicine&amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;#39;&amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;#39;. From available physiological data, biological understanding of the system, and dimensional analysis, a differential equation-based mathematical model was built in a sequential matter, to be able to elucidate clearly how each parameter correlates to the patient&amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;#39;s current physiological state. We developed a simple mathematical model that accurately simulates the dynamics between glucose, insulin, and pancreatic $\beta$-cells throughout disease progression with constraints to maintain biological relevance. The current framework is clearly capable of tracking the patient&amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;#39;s current progress through the disease, dependent on factors such as latent insulin resistance or an attrite $\beta$-cell population. Further interests would be to develop tools that allow the direct and feasible testing of how effective a given plan of treatment would be at returning the patient to a desirable biophysical state.</div></div></div><ul class="InlineList u-ph0x u-fs13"><li class="InlineList-item logged_in_only"><div class="share_on_academia_work_button"><a class="academia_share Button Button--inverseBlue Button--sm js-bookmark-button" data-academia-share="Work/68173600" data-share-source="work_strip" data-spinner="small_white_hide_contents"><i class="fa fa-plus"></i><span class="work-strip-link-text u-ml1x" data-content="button_text">Bookmark</span></a></div></li><li class="InlineList-item"><ul class="InlineList InlineList--bordered u-ph0x"><li class="InlineList-item InlineList-item--bordered"><span class="InlineList-item-text">by <span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a class="u-tcGrayDark u-fw700" data-has-card-for-user="175566957" href="https://independent.academia.edu/Danilorivera19">Danilo rivera</a><script data-card-contents-for-user="175566957" type="text/json">{"id":175566957,"first_name":"Danilo","last_name":"rivera","domain_name":"independent","page_name":"Danilorivera19","display_name":"Danilo rivera","profile_url":"https://independent.academia.edu/Danilorivera19?f_ri=2963","photo":"/images/s65_no_pic.png"}</script></span></span></li><li class="js-paper-rank-work_68173600 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="68173600"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 68173600, container: ".js-paper-rank-work_68173600", }); });</script></li><li class="js-percentile-work_68173600 InlineList-item InlineList-item--bordered hidden u-tcGrayDark"><span class="percentile-widget hidden"><span class="u-mr2x percentile-widget" style="display: none">•</span><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 68173600; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-percentile-work_68173600"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></li><li class="js-view-count-work_68173600 InlineList-item InlineList-item--bordered hidden"><div><span><span class="js-view-count view-count u-mr2x" data-work-id="68173600"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 68173600; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=68173600]").text(description); $(".js-view-count-work_68173600").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_68173600").removeClass('hidden') })</script></div></li><li class="InlineList-item u-positionRelative" style="max-width: 250px"><div class="u-positionAbsolute" data-has-card-for-ri-list="68173600"><i class="fa fa-tag InlineList-item-icon u-positionRelative"></i>  <a class="InlineList-item-text u-positionRelative">15</a>  </div><span class="InlineList-item-text u-textTruncate u-pl10x"><a class="InlineList-item-text" data-has-card-for-ri="72" href="https://www.academia.edu/Documents/in/Chemical_Engineering">Chemical Engineering</a>, <script data-card-contents-for-ri="72" type="text/json">{"id":72,"name":"Chemical Engineering","url":"https://www.academia.edu/Documents/in/Chemical_Engineering?f_ri=2963","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="305" href="https://www.academia.edu/Documents/in/Applied_Mathematics">Applied Mathematics</a>, <script data-card-contents-for-ri="305" type="text/json">{"id":305,"name":"Applied Mathematics","url":"https://www.academia.edu/Documents/in/Applied_Mathematics?f_ri=2963","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="1080" href="https://www.academia.edu/Documents/in/Dynamical_Systems">Dynamical Systems</a>, <script data-card-contents-for-ri="1080" type="text/json">{"id":1080,"name":"Dynamical Systems","url":"https://www.academia.edu/Documents/in/Dynamical_Systems?f_ri=2963","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="1131" href="https://www.academia.edu/Documents/in/Biomedical_Engineering">Biomedical Engineering</a><script data-card-contents-for-ri="1131" type="text/json">{"id":1131,"name":"Biomedical Engineering","url":"https://www.academia.edu/Documents/in/Biomedical_Engineering?f_ri=2963","nofollow":false}</script></span></li><script>(function(){ if (true) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=68173600]'), work: {"id":68173600,"title":"Development of a computational model of glucose toxicity in the progression of diabetes mellitus","created_at":"2022-01-14T14:37:46.193-08:00","url":"https://www.academia.edu/68173600/Development_of_a_computational_model_of_glucose_toxicity_in_the_progression_of_diabetes_mellitus?f_ri=2963","dom_id":"work_68173600","summary":"Diabetes mellitus is a disease characterized by a range of metabolic complications involving an individual\u0026amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;#39;s blood glucose levels, and its main regulator, insulin. These complications can vary largely from person to person depending on their current biophysical state. Biomedical research day-by-day makes strides to impact the lives of patients of a variety of diseases, including diabetes. One large stride that is being made is the generation of techniques to assist physicians to ``personalize medicine\u0026amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;#39;\u0026amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;#39;. From available physiological data, biological understanding of the system, and dimensional analysis, a differential equation-based mathematical model was built in a sequential matter, to be able to elucidate clearly how each parameter correlates to the patient\u0026amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;#39;s current physiological state. We developed a simple mathematical model that accurately simulates the dynamics between glucose, insulin, and pancreatic $\\beta$-cells throughout disease progression with constraints to maintain biological relevance. The current framework is clearly capable of tracking the patient\u0026amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;#39;s current progress through the disease, dependent on factors such as latent insulin resistance or an attrite $\\beta$-cell population. Further interests would be to develop tools that allow the direct and feasible testing of how effective a given plan of treatment would be at returning the patient to a desirable biophysical state.","downloadable_attachments":[],"ordered_authors":[{"id":175566957,"first_name":"Danilo","last_name":"rivera","domain_name":"independent","page_name":"Danilorivera19","display_name":"Danilo rivera","profile_url":"https://independent.academia.edu/Danilorivera19?f_ri=2963","photo":"/images/s65_no_pic.png"}],"research_interests":[{"id":72,"name":"Chemical Engineering","url":"https://www.academia.edu/Documents/in/Chemical_Engineering?f_ri=2963","nofollow":false},{"id":305,"name":"Applied Mathematics","url":"https://www.academia.edu/Documents/in/Applied_Mathematics?f_ri=2963","nofollow":false},{"id":1080,"name":"Dynamical Systems","url":"https://www.academia.edu/Documents/in/Dynamical_Systems?f_ri=2963","nofollow":false},{"id":1131,"name":"Biomedical Engineering","url":"https://www.academia.edu/Documents/in/Biomedical_Engineering?f_ri=2963","nofollow":false},{"id":2963,"name":"Mathematical Biology","url":"https://www.academia.edu/Documents/in/Mathematical_Biology?f_ri=2963"},{"id":4581,"name":"Diabetes","url":"https://www.academia.edu/Documents/in/Diabetes?f_ri=2963"},{"id":16221,"name":"Mathematical Modeling","url":"https://www.academia.edu/Documents/in/Mathematical_Modeling?f_ri=2963"},{"id":16521,"name":"Mathematical biology (Mathematics)","url":"https://www.academia.edu/Documents/in/Mathematical_biology_Mathematics_?f_ri=2963"},{"id":71289,"name":"Glucose","url":"https://www.academia.edu/Documents/in/Glucose?f_ri=2963"},{"id":71300,"name":"Blood Glucose","url":"https://www.academia.edu/Documents/in/Blood_Glucose?f_ri=2963"},{"id":71400,"name":"Insulin","url":"https://www.academia.edu/Documents/in/Insulin?f_ri=2963"},{"id":71511,"name":"Diabetes mellitus","url":"https://www.academia.edu/Documents/in/Diabetes_mellitus?f_ri=2963"},{"id":343667,"name":"Theoretical Models","url":"https://www.academia.edu/Documents/in/Theoretical_Models?f_ri=2963"},{"id":842794,"name":"Applied Mathematics and Mathematical Biology","url":"https://www.academia.edu/Documents/in/Applied_Mathematics_and_Mathematical_Biology?f_ri=2963"},{"id":1274741,"name":"Beta Cells","url":"https://www.academia.edu/Documents/in/Beta_Cells?f_ri=2963"}]}, }) } })();</script></ul></li></ul></div></div><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_13362612 coauthored" data-work_id="13362612" itemscope="itemscope" itemtype="https://schema.org/ScholarlyArticle"><div class="header"><div class="title u-fontSerif u-fs22 u-lineHeight1_3"><a class="u-tcGrayDarkest js-work-link" href="https://www.academia.edu/13362612/Optimal_strategies_in_immunology_III_The_IgM_IgG_switch">Optimal strategies in immunology III. The IgM-IgG switch</a></div></div><div class="u-pb4x u-mt3x"></div><ul class="InlineList u-ph0x u-fs13"><li class="InlineList-item logged_in_only"><div class="share_on_academia_work_button"><a class="academia_share Button Button--inverseBlue Button--sm js-bookmark-button" data-academia-share="Work/13362612" data-share-source="work_strip" data-spinner="small_white_hide_contents"><i class="fa fa-plus"></i><span class="work-strip-link-text u-ml1x" data-content="button_text">Bookmark</span></a></div></li><li class="InlineList-item"><div class="download"><a id="fc402590b61c3a791a91b317a627851a" rel="nofollow" data-download="{"attachment_id":45431329,"asset_id":13362612,"asset_type":"Work","always_allow_download":false,"track":null,"button_location":"work_strip","source":null,"hide_modal":null}" class="Button Button--sm Button--inverseGreen js-download-button prompt_button doc_download" href="https://www.academia.edu/attachments/45431329/download_file?st=MTczMjk4MzU1Miw4LjIyMi4yMDguMTQ2&s=work_strip"><i class="fa fa-arrow-circle-o-down fa-lg"></i><span class="u-textUppercase u-ml1x" data-content="button_text">Download</span></a></div></li><li class="InlineList-item"><ul class="InlineList InlineList--bordered u-ph0x"><li class="InlineList-item InlineList-item--bordered"><span class="InlineList-item-text">by <span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a class="u-tcGrayDark u-fw700" data-has-card-for-user="32841145" href="https://independent.academia.edu/GoldsteinByron">Byron Goldstein</a><script data-card-contents-for-user="32841145" type="text/json">{"id":32841145,"first_name":"Byron","last_name":"Goldstein","domain_name":"independent","page_name":"GoldsteinByron","display_name":"Byron Goldstein","profile_url":"https://independent.academia.edu/GoldsteinByron?f_ri=2963","photo":"/images/s65_no_pic.png"}</script></span></span><span class="u-displayInlineBlock InlineList-item-text"> and <span class="u-textDecorationUnderline u-clickable InlineList-item-text js-work-more-authors-13362612">+1</span><div class="hidden js-additional-users-13362612"><div><span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a href="https://lanl.academia.edu/AlanPerelson">Alan Perelson</a></span></div></div></span><script>(function(){ var popoverSettings = { el: $('.js-work-more-authors-13362612'), placement: 'bottom', hide_delay: 200, html: true, content: function(){ return $('.js-additional-users-13362612').html(); } } new HoverPopover(popoverSettings); })();</script></li><li class="js-paper-rank-work_13362612 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="13362612"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 13362612, container: ".js-paper-rank-work_13362612", }); });</script></li><li class="js-percentile-work_13362612 InlineList-item InlineList-item--bordered hidden u-tcGrayDark"><span class="percentile-widget hidden"><span class="u-mr2x percentile-widget" style="display: none">•</span><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 13362612; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-percentile-work_13362612"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></li><li class="js-view-count-work_13362612 InlineList-item InlineList-item--bordered hidden"><div><span><span class="js-view-count view-count u-mr2x" data-work-id="13362612"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 13362612; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=13362612]").text(description); $(".js-view-count-work_13362612").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_13362612").removeClass('hidden') })</script></div></li><li class="InlineList-item u-positionRelative" style="max-width: 250px"><div class="u-positionAbsolute" data-has-card-for-ri-list="13362612"><i class="fa fa-tag InlineList-item-icon u-positionRelative"></i>  <a class="InlineList-item-text u-positionRelative">9</a>  </div><span class="InlineList-item-text u-textTruncate u-pl9x"><a class="InlineList-item-text" data-has-card-for-ri="2702" href="https://www.academia.edu/Documents/in/Immune_response">Immune response</a>, <script data-card-contents-for-ri="2702" type="text/json">{"id":2702,"name":"Immune response","url":"https://www.academia.edu/Documents/in/Immune_response?f_ri=2963","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="2963" href="https://www.academia.edu/Documents/in/Mathematical_Biology">Mathematical Biology</a>, <script data-card-contents-for-ri="2963" type="text/json">{"id":2963,"name":"Mathematical Biology","url":"https://www.academia.edu/Documents/in/Mathematical_Biology?f_ri=2963","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="4987" href="https://www.academia.edu/Documents/in/Kinetics">Kinetics</a>, <script data-card-contents-for-ri="4987" type="text/json">{"id":4987,"name":"Kinetics","url":"https://www.academia.edu/Documents/in/Kinetics?f_ri=2963","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="47884" href="https://www.academia.edu/Documents/in/Biological_Sciences">Biological Sciences</a><script data-card-contents-for-ri="47884" type="text/json">{"id":47884,"name":"Biological Sciences","url":"https://www.academia.edu/Documents/in/Biological_Sciences?f_ri=2963","nofollow":false}</script></span></li><script>(function(){ if (true) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=13362612]'), work: {"id":13362612,"title":"Optimal strategies in immunology III. The IgM-IgG switch","created_at":"2015-06-27T14:23:33.745-07:00","url":"https://www.academia.edu/13362612/Optimal_strategies_in_immunology_III_The_IgM_IgG_switch?f_ri=2963","dom_id":"work_13362612","summary":null,"downloadable_attachments":[{"id":45431329,"asset_id":13362612,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":32841145,"first_name":"Byron","last_name":"Goldstein","domain_name":"independent","page_name":"GoldsteinByron","display_name":"Byron Goldstein","profile_url":"https://independent.academia.edu/GoldsteinByron?f_ri=2963","photo":"/images/s65_no_pic.png"},{"id":32593695,"first_name":"Alan","last_name":"Perelson","domain_name":"lanl","page_name":"AlanPerelson","display_name":"Alan Perelson","profile_url":"https://lanl.academia.edu/AlanPerelson?f_ri=2963","photo":"/images/s65_no_pic.png"}],"research_interests":[{"id":2702,"name":"Immune response","url":"https://www.academia.edu/Documents/in/Immune_response?f_ri=2963","nofollow":false},{"id":2963,"name":"Mathematical Biology","url":"https://www.academia.edu/Documents/in/Mathematical_Biology?f_ri=2963","nofollow":false},{"id":4987,"name":"Kinetics","url":"https://www.academia.edu/Documents/in/Kinetics?f_ri=2963","nofollow":false},{"id":47884,"name":"Biological Sciences","url":"https://www.academia.edu/Documents/in/Biological_Sciences?f_ri=2963","nofollow":false},{"id":70355,"name":"Optimal Control theory","url":"https://www.academia.edu/Documents/in/Optimal_Control_theory?f_ri=2963"},{"id":80414,"name":"Mathematical Sciences","url":"https://www.academia.edu/Documents/in/Mathematical_Sciences?f_ri=2963"},{"id":868560,"name":"Lymphocytes","url":"https://www.academia.edu/Documents/in/Lymphocytes?f_ri=2963"},{"id":1274458,"name":"Antigens","url":"https://www.academia.edu/Documents/in/Antigens?f_ri=2963"},{"id":1716403,"name":"immunoglobulin G","url":"https://www.academia.edu/Documents/in/immunoglobulin_G?f_ri=2963"}]}, }) } })();</script></ul></li></ul></div></div><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_58952530" data-work_id="58952530" itemscope="itemscope" itemtype="https://schema.org/ScholarlyArticle"><div class="header"><div class="title u-fontSerif u-fs22 u-lineHeight1_3"><a class="u-tcGrayDarkest js-work-link" href="https://www.academia.edu/58952530/A_theoretical_model_for_studying_the_rate_of_oxygenation_of_blood_in_pulmonary_capillaries">A theoretical model for studying the rate of oxygenation of blood in pulmonary capillaries</a></div></div><div class="u-pb4x u-mt3x"></div><ul class="InlineList u-ph0x u-fs13"><li class="InlineList-item logged_in_only"><div class="share_on_academia_work_button"><a class="academia_share Button Button--inverseBlue Button--sm js-bookmark-button" data-academia-share="Work/58952530" data-share-source="work_strip" data-spinner="small_white_hide_contents"><i class="fa fa-plus"></i><span class="work-strip-link-text u-ml1x" data-content="button_text">Bookmark</span></a></div></li><li class="InlineList-item"><div class="download"><a id="93b33d5a16bce85d356eeb8a61aa28d8" rel="nofollow" data-download="{"attachment_id":73113860,"asset_id":58952530,"asset_type":"Work","always_allow_download":false,"track":null,"button_location":"work_strip","source":null,"hide_modal":null}" class="Button Button--sm Button--inverseGreen js-download-button prompt_button doc_download" href="https://www.academia.edu/attachments/73113860/download_file?st=MTczMjk4MzU1Miw4LjIyMi4yMDguMTQ2&s=work_strip"><i class="fa fa-arrow-circle-o-down fa-lg"></i><span class="u-textUppercase u-ml1x" data-content="button_text">Download</span></a></div></li><li class="InlineList-item"><ul class="InlineList InlineList--bordered u-ph0x"><li class="InlineList-item InlineList-item--bordered"><span class="InlineList-item-text">by <span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a class="u-tcGrayDark u-fw700" data-has-card-for-user="45310998" href="https://independent.academia.edu/SharanMaithili">Maithili Sharan</a><script data-card-contents-for-user="45310998" type="text/json">{"id":45310998,"first_name":"Maithili","last_name":"Sharan","domain_name":"independent","page_name":"SharanMaithili","display_name":"Maithili Sharan","profile_url":"https://independent.academia.edu/SharanMaithili?f_ri=2963","photo":"/images/s65_no_pic.png"}</script></span></span></li><li class="js-paper-rank-work_58952530 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="58952530"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 58952530, container: ".js-paper-rank-work_58952530", }); });</script></li><li class="js-percentile-work_58952530 InlineList-item InlineList-item--bordered hidden u-tcGrayDark"><span class="percentile-widget hidden"><span class="u-mr2x percentile-widget" style="display: none">•</span><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 58952530; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-percentile-work_58952530"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></li><li class="js-view-count-work_58952530 InlineList-item InlineList-item--bordered hidden"><div><span><span class="js-view-count view-count u-mr2x" data-work-id="58952530"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 58952530; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=58952530]").text(description); $(".js-view-count-work_58952530").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_58952530").removeClass('hidden') })</script></div></li><li class="InlineList-item u-positionRelative" style="max-width: 250px"><div class="u-positionAbsolute" data-has-card-for-ri-list="58952530"><i class="fa fa-tag InlineList-item-icon u-positionRelative"></i>  <a class="InlineList-item-text u-positionRelative">14</a>  </div><span class="InlineList-item-text u-textTruncate u-pl10x"><a class="InlineList-item-text" data-has-card-for-ri="300" href="https://www.academia.edu/Documents/in/Mathematics">Mathematics</a>, <script data-card-contents-for-ri="300" type="text/json">{"id":300,"name":"Mathematics","url":"https://www.academia.edu/Documents/in/Mathematics?f_ri=2963","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="2963" href="https://www.academia.edu/Documents/in/Mathematical_Biology">Mathematical Biology</a>, <script data-card-contents-for-ri="2963" type="text/json">{"id":2963,"name":"Mathematical Biology","url":"https://www.academia.edu/Documents/in/Mathematical_Biology?f_ri=2963","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="4594" href="https://www.academia.edu/Documents/in/Carbon_Dioxide">Carbon Dioxide</a>, <script data-card-contents-for-ri="4594" type="text/json">{"id":4594,"name":"Carbon Dioxide","url":"https://www.academia.edu/Documents/in/Carbon_Dioxide?f_ri=2963","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="47884" href="https://www.academia.edu/Documents/in/Biological_Sciences">Biological Sciences</a><script data-card-contents-for-ri="47884" type="text/json">{"id":47884,"name":"Biological Sciences","url":"https://www.academia.edu/Documents/in/Biological_Sciences?f_ri=2963","nofollow":false}</script></span></li><script>(function(){ if (true) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=58952530]'), work: {"id":58952530,"title":"A theoretical model for studying the rate of oxygenation of blood in pulmonary capillaries","created_at":"2021-10-18T22:20:15.787-07:00","url":"https://www.academia.edu/58952530/A_theoretical_model_for_studying_the_rate_of_oxygenation_of_blood_in_pulmonary_capillaries?f_ri=2963","dom_id":"work_58952530","summary":null,"downloadable_attachments":[{"id":73113860,"asset_id":58952530,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":45310998,"first_name":"Maithili","last_name":"Sharan","domain_name":"independent","page_name":"SharanMaithili","display_name":"Maithili Sharan","profile_url":"https://independent.academia.edu/SharanMaithili?f_ri=2963","photo":"/images/s65_no_pic.png"}],"research_interests":[{"id":300,"name":"Mathematics","url":"https://www.academia.edu/Documents/in/Mathematics?f_ri=2963","nofollow":false},{"id":2963,"name":"Mathematical Biology","url":"https://www.academia.edu/Documents/in/Mathematical_Biology?f_ri=2963","nofollow":false},{"id":4594,"name":"Carbon Dioxide","url":"https://www.academia.edu/Documents/in/Carbon_Dioxide?f_ri=2963","nofollow":false},{"id":47884,"name":"Biological Sciences","url":"https://www.academia.edu/Documents/in/Biological_Sciences?f_ri=2963","nofollow":false},{"id":71421,"name":"Capillaries","url":"https://www.academia.edu/Documents/in/Capillaries?f_ri=2963"},{"id":80414,"name":"Mathematical Sciences","url":"https://www.academia.edu/Documents/in/Mathematical_Sciences?f_ri=2963"},{"id":86034,"name":"Mathematical Analysis","url":"https://www.academia.edu/Documents/in/Mathematical_Analysis?f_ri=2963"},{"id":215075,"name":"Experimental Study","url":"https://www.academia.edu/Documents/in/Experimental_Study?f_ri=2963"},{"id":380825,"name":"Oxygen","url":"https://www.academia.edu/Documents/in/Oxygen?f_ri=2963"},{"id":1154248,"name":"Theoretical Model","url":"https://www.academia.edu/Documents/in/Theoretical_Model?f_ri=2963"},{"id":1311261,"name":"Hemoglobins","url":"https://www.academia.edu/Documents/in/Hemoglobins?f_ri=2963"},{"id":1778694,"name":"Pulmonary diffusing capacity","url":"https://www.academia.edu/Documents/in/Pulmonary_diffusing_capacity?f_ri=2963"},{"id":1787781,"name":"Gas Exchange","url":"https://www.academia.edu/Documents/in/Gas_Exchange?f_ri=2963"},{"id":2226523,"name":"Pulmonary circulation","url":"https://www.academia.edu/Documents/in/Pulmonary_circulation?f_ri=2963"}]}, }) } })();</script></ul></li></ul></div></div><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_12069013" data-work_id="12069013" itemscope="itemscope" itemtype="https://schema.org/ScholarlyArticle"><div class="header"><div class="title u-fontSerif u-fs22 u-lineHeight1_3"><a class="u-tcGrayDarkest js-work-link" href="https://www.academia.edu/12069013/On_the_maintenance_of_bird_song_dialects">On the maintenance of bird song dialects</a></div></div><div class="u-pb4x u-mt3x"></div><ul class="InlineList u-ph0x u-fs13"><li class="InlineList-item logged_in_only"><div class="share_on_academia_work_button"><a class="academia_share Button Button--inverseBlue Button--sm js-bookmark-button" data-academia-share="Work/12069013" data-share-source="work_strip" data-spinner="small_white_hide_contents"><i class="fa fa-plus"></i><span class="work-strip-link-text u-ml1x" data-content="button_text">Bookmark</span></a></div></li><li class="InlineList-item"><div class="download"><a id="622041d790c89dcd0dd8667a4f9caff4" rel="nofollow" data-download="{"attachment_id":46389824,"asset_id":12069013,"asset_type":"Work","always_allow_download":false,"track":null,"button_location":"work_strip","source":null,"hide_modal":null}" class="Button Button--sm Button--inverseGreen js-download-button prompt_button doc_download" href="https://www.academia.edu/attachments/46389824/download_file?st=MTczMjk4MzU1Miw4LjIyMi4yMDguMTQ2&s=work_strip"><i class="fa fa-arrow-circle-o-down fa-lg"></i><span class="u-textUppercase u-ml1x" data-content="button_text">Download</span></a></div></li><li class="InlineList-item"><ul class="InlineList InlineList--bordered u-ph0x"><li class="InlineList-item InlineList-item--bordered"><span class="InlineList-item-text">by <span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a class="u-tcGrayDark u-fw700" data-has-card-for-user="4884219" href="https://independent.academia.edu/NickBritton">Nick Britton</a><script data-card-contents-for-user="4884219" type="text/json">{"id":4884219,"first_name":"Nick","last_name":"Britton","domain_name":"independent","page_name":"NickBritton","display_name":"Nick Britton","profile_url":"https://independent.academia.edu/NickBritton?f_ri=2963","photo":"/images/s65_no_pic.png"}</script></span></span></li><li class="js-paper-rank-work_12069013 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="12069013"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 12069013, container: ".js-paper-rank-work_12069013", }); });</script></li><li class="js-percentile-work_12069013 InlineList-item InlineList-item--bordered hidden u-tcGrayDark"><span class="percentile-widget hidden"><span class="u-mr2x percentile-widget" style="display: none">•</span><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 12069013; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-percentile-work_12069013"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></li><li class="js-view-count-work_12069013 InlineList-item InlineList-item--bordered hidden"><div><span><span class="js-view-count view-count u-mr2x" data-work-id="12069013"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 12069013; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=12069013]").text(description); $(".js-view-count-work_12069013").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_12069013").removeClass('hidden') })</script></div></li><li class="InlineList-item u-positionRelative" style="max-width: 250px"><div class="u-positionAbsolute" data-has-card-for-ri-list="12069013"><i class="fa fa-tag InlineList-item-icon u-positionRelative"></i>  <a class="InlineList-item-text u-positionRelative">9</a>  </div><span class="InlineList-item-text u-textTruncate u-pl9x"><a class="InlineList-item-text" data-has-card-for-ri="499" href="https://www.academia.edu/Documents/in/Acoustics">Acoustics</a>, <script data-card-contents-for-ri="499" type="text/json">{"id":499,"name":"Acoustics","url":"https://www.academia.edu/Documents/in/Acoustics?f_ri=2963","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="2963" href="https://www.academia.edu/Documents/in/Mathematical_Biology">Mathematical Biology</a>, <script data-card-contents-for-ri="2963" type="text/json">{"id":2963,"name":"Mathematical Biology","url":"https://www.academia.edu/Documents/in/Mathematical_Biology?f_ri=2963","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="28378" href="https://www.academia.edu/Documents/in/Animal_communication">Animal communication</a>, <script data-card-contents-for-ri="28378" type="text/json">{"id":28378,"name":"Animal communication","url":"https://www.academia.edu/Documents/in/Animal_communication?f_ri=2963","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="43774" href="https://www.academia.edu/Documents/in/Learning">Learning</a><script data-card-contents-for-ri="43774" type="text/json">{"id":43774,"name":"Learning","url":"https://www.academia.edu/Documents/in/Learning?f_ri=2963","nofollow":false}</script></span></li><script>(function(){ if (true) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=12069013]'), work: {"id":12069013,"title":"On the maintenance of bird song dialects","created_at":"2015-04-22T09:22:55.397-07:00","url":"https://www.academia.edu/12069013/On_the_maintenance_of_bird_song_dialects?f_ri=2963","dom_id":"work_12069013","summary":null,"downloadable_attachments":[{"id":46389824,"asset_id":12069013,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":4884219,"first_name":"Nick","last_name":"Britton","domain_name":"independent","page_name":"NickBritton","display_name":"Nick Britton","profile_url":"https://independent.academia.edu/NickBritton?f_ri=2963","photo":"/images/s65_no_pic.png"}],"research_interests":[{"id":499,"name":"Acoustics","url":"https://www.academia.edu/Documents/in/Acoustics?f_ri=2963","nofollow":false},{"id":2963,"name":"Mathematical Biology","url":"https://www.academia.edu/Documents/in/Mathematical_Biology?f_ri=2963","nofollow":false},{"id":28378,"name":"Animal communication","url":"https://www.academia.edu/Documents/in/Animal_communication?f_ri=2963","nofollow":false},{"id":43774,"name":"Learning","url":"https://www.academia.edu/Documents/in/Learning?f_ri=2963","nofollow":false},{"id":47884,"name":"Biological Sciences","url":"https://www.academia.edu/Documents/in/Biological_Sciences?f_ri=2963"},{"id":80414,"name":"Mathematical Sciences","url":"https://www.academia.edu/Documents/in/Mathematical_Sciences?f_ri=2963"},{"id":151693,"name":"Songbirds","url":"https://www.academia.edu/Documents/in/Songbirds?f_ri=2963"},{"id":343667,"name":"Theoretical Models","url":"https://www.academia.edu/Documents/in/Theoretical_Models?f_ri=2963"},{"id":1208706,"name":"Environment","url":"https://www.academia.edu/Documents/in/Environment?f_ri=2963"}]}, }) } })();</script></ul></li></ul></div></div><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_30753588" data-work_id="30753588" itemscope="itemscope" itemtype="https://schema.org/ScholarlyArticle"><div class="header"><div class="title u-fontSerif u-fs22 u-lineHeight1_3"><a class="u-tcGrayDarkest js-work-link" href="https://www.academia.edu/30753588/The_effect_of_ureteric_stents_on_urine_flow_Reflux">The effect of ureteric stents on urine flow: Reflux</a></div></div><div class="u-pb4x u-mt3x"></div><ul class="InlineList u-ph0x u-fs13"><li class="InlineList-item logged_in_only"><div class="share_on_academia_work_button"><a class="academia_share Button Button--inverseBlue Button--sm js-bookmark-button" data-academia-share="Work/30753588" data-share-source="work_strip" data-spinner="small_white_hide_contents"><i class="fa fa-plus"></i><span class="work-strip-link-text u-ml1x" data-content="button_text">Bookmark</span></a></div></li><li class="InlineList-item"><div class="download"><a id="e74e3633082ef5886f124a3766282ec2" rel="nofollow" data-download="{"attachment_id":51193310,"asset_id":30753588,"asset_type":"Work","always_allow_download":false,"track":null,"button_location":"work_strip","source":null,"hide_modal":null}" class="Button Button--sm Button--inverseGreen js-download-button prompt_button doc_download" href="https://www.academia.edu/attachments/51193310/download_file?st=MTczMjk4MzU1Miw4LjIyMi4yMDguMTQ2&s=work_strip"><i class="fa fa-arrow-circle-o-down fa-lg"></i><span class="u-textUppercase u-ml1x" data-content="button_text">Download</span></a></div></li><li class="InlineList-item"><ul class="InlineList InlineList--bordered u-ph0x"><li class="InlineList-item InlineList-item--bordered"><span class="InlineList-item-text">by <span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a class="u-tcGrayDark u-fw700" data-has-card-for-user="58556947" href="https://njit.academia.edu/LindaCummings">Linda Cummings</a><script data-card-contents-for-user="58556947" type="text/json">{"id":58556947,"first_name":"Linda","last_name":"Cummings","domain_name":"njit","page_name":"LindaCummings","display_name":"Linda Cummings","profile_url":"https://njit.academia.edu/LindaCummings?f_ri=2963","photo":"/images/s65_no_pic.png"}</script></span></span></li><li class="js-paper-rank-work_30753588 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="30753588"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 30753588, container: ".js-paper-rank-work_30753588", }); });</script></li><li class="js-percentile-work_30753588 InlineList-item InlineList-item--bordered hidden u-tcGrayDark"><span class="percentile-widget hidden"><span class="u-mr2x percentile-widget" style="display: none">•</span><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 30753588; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-percentile-work_30753588"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></li><li class="js-view-count-work_30753588 InlineList-item InlineList-item--bordered hidden"><div><span><span class="js-view-count view-count u-mr2x" data-work-id="30753588"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 30753588; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=30753588]").text(description); $(".js-view-count-work_30753588").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_30753588").removeClass('hidden') })</script></div></li><li class="InlineList-item u-positionRelative" style="max-width: 250px"><div class="u-positionAbsolute" data-has-card-for-ri-list="30753588"><i class="fa fa-tag InlineList-item-icon u-positionRelative"></i>  <a class="InlineList-item-text u-positionRelative">6</a>  </div><span class="InlineList-item-text u-textTruncate u-pl9x"><a class="InlineList-item-text" data-has-card-for-ri="2963" href="https://www.academia.edu/Documents/in/Mathematical_Biology">Mathematical Biology</a>, <script data-card-contents-for-ri="2963" type="text/json">{"id":2963,"name":"Mathematical Biology","url":"https://www.academia.edu/Documents/in/Mathematical_Biology?f_ri=2963","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="27521" href="https://www.academia.edu/Documents/in/Stents">Stents</a>, <script data-card-contents-for-ri="27521" type="text/json">{"id":27521,"name":"Stents","url":"https://www.academia.edu/Documents/in/Stents?f_ri=2963","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="47884" href="https://www.academia.edu/Documents/in/Biological_Sciences">Biological Sciences</a>, <script data-card-contents-for-ri="47884" type="text/json">{"id":47884,"name":"Biological Sciences","url":"https://www.academia.edu/Documents/in/Biological_Sciences?f_ri=2963","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="80414" href="https://www.academia.edu/Documents/in/Mathematical_Sciences">Mathematical Sciences</a><script data-card-contents-for-ri="80414" type="text/json">{"id":80414,"name":"Mathematical Sciences","url":"https://www.academia.edu/Documents/in/Mathematical_Sciences?f_ri=2963","nofollow":false}</script></span></li><script>(function(){ if (true) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=30753588]'), work: {"id":30753588,"title":"The effect of ureteric stents on urine flow: Reflux","created_at":"2017-01-04T19:30:22.258-08:00","url":"https://www.academia.edu/30753588/The_effect_of_ureteric_stents_on_urine_flow_Reflux?f_ri=2963","dom_id":"work_30753588","summary":null,"downloadable_attachments":[{"id":51193310,"asset_id":30753588,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":58556947,"first_name":"Linda","last_name":"Cummings","domain_name":"njit","page_name":"LindaCummings","display_name":"Linda Cummings","profile_url":"https://njit.academia.edu/LindaCummings?f_ri=2963","photo":"/images/s65_no_pic.png"}],"research_interests":[{"id":2963,"name":"Mathematical Biology","url":"https://www.academia.edu/Documents/in/Mathematical_Biology?f_ri=2963","nofollow":false},{"id":27521,"name":"Stents","url":"https://www.academia.edu/Documents/in/Stents?f_ri=2963","nofollow":false},{"id":47884,"name":"Biological Sciences","url":"https://www.academia.edu/Documents/in/Biological_Sciences?f_ri=2963","nofollow":false},{"id":80414,"name":"Mathematical Sciences","url":"https://www.academia.edu/Documents/in/Mathematical_Sciences?f_ri=2963","nofollow":false},{"id":213709,"name":"Mathematical","url":"https://www.academia.edu/Documents/in/Mathematical?f_ri=2963"},{"id":2497729,"name":"Ureter","url":"https://www.academia.edu/Documents/in/Ureter?f_ri=2963"}]}, }) } })();</script></ul></li></ul></div></div><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_75367254" data-work_id="75367254" itemscope="itemscope" itemtype="https://schema.org/ScholarlyArticle"><div class="header"><div class="title u-fontSerif u-fs22 u-lineHeight1_3"><a class="u-tcGrayDarkest js-work-link" href="https://www.academia.edu/75367254/Simulating_the_spread_of_COVID_19_via_a_spatially_resolved_susceptible_exposed_infected_recovered_deceased_SEIRD_model_with_heterogeneous_diffusion">Simulating the spread of COVID-19 via a spatially-resolved susceptible–exposed–infected–recovered–deceased (SEIRD) model with heterogeneous diffusion</a></div></div><div class="u-pb4x u-mt3x"></div><ul class="InlineList u-ph0x u-fs13"><li class="InlineList-item logged_in_only"><div class="share_on_academia_work_button"><a class="academia_share Button Button--inverseBlue Button--sm js-bookmark-button" data-academia-share="Work/75367254" data-share-source="work_strip" data-spinner="small_white_hide_contents"><i class="fa fa-plus"></i><span class="work-strip-link-text u-ml1x" data-content="button_text">Bookmark</span></a></div></li><li class="InlineList-item"><div class="download"><a id="6371c7946e2874c4ea5f02fc45f88bfb" rel="nofollow" data-download="{"attachment_id":83163947,"asset_id":75367254,"asset_type":"Work","always_allow_download":false,"track":null,"button_location":"work_strip","source":null,"hide_modal":null}" class="Button Button--sm Button--inverseGreen js-download-button prompt_button doc_download" href="https://www.academia.edu/attachments/83163947/download_file?st=MTczMjk4MzU1Miw4LjIyMi4yMDguMTQ2&s=work_strip"><i class="fa fa-arrow-circle-o-down fa-lg"></i><span class="u-textUppercase u-ml1x" data-content="button_text">Download</span></a></div></li><li class="InlineList-item"><ul class="InlineList InlineList--bordered u-ph0x"><li class="InlineList-item InlineList-item--bordered"><span class="InlineList-item-text">by <span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a class="u-tcGrayDark u-fw700" data-has-card-for-user="135038711" href="https://independent.academia.edu/AlessandroVeneziani">Alessandro Veneziani</a><script data-card-contents-for-user="135038711" type="text/json">{"id":135038711,"first_name":"Alessandro","last_name":"Veneziani","domain_name":"independent","page_name":"AlessandroVeneziani","display_name":"Alessandro Veneziani","profile_url":"https://independent.academia.edu/AlessandroVeneziani?f_ri=2963","photo":"https://gravatar.com/avatar/b6a2f965b3ad3f8a77c1fae18566a28b?s=65"}</script></span></span></li><li class="js-paper-rank-work_75367254 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="75367254"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 75367254, container: ".js-paper-rank-work_75367254", }); });</script></li><li class="js-percentile-work_75367254 InlineList-item InlineList-item--bordered hidden u-tcGrayDark"><span class="percentile-widget hidden"><span class="u-mr2x percentile-widget" style="display: none">•</span><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 75367254; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-percentile-work_75367254"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></li><li class="js-view-count-work_75367254 InlineList-item InlineList-item--bordered hidden"><div><span><span class="js-view-count view-count u-mr2x" data-work-id="75367254"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 75367254; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=75367254]").text(description); $(".js-view-count-work_75367254").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_75367254").removeClass('hidden') })</script></div></li><li class="InlineList-item u-positionRelative" style="max-width: 250px"><div class="u-positionAbsolute" data-has-card-for-ri-list="75367254"><i class="fa fa-tag InlineList-item-icon u-positionRelative"></i>  <a class="InlineList-item-text u-positionRelative">12</a>  </div><span class="InlineList-item-text u-textTruncate u-pl10x"><a class="InlineList-item-text" data-has-card-for-ri="300" href="https://www.academia.edu/Documents/in/Mathematics">Mathematics</a>, <script data-card-contents-for-ri="300" type="text/json">{"id":300,"name":"Mathematics","url":"https://www.academia.edu/Documents/in/Mathematics?f_ri=2963","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="305" href="https://www.academia.edu/Documents/in/Applied_Mathematics">Applied Mathematics</a>, <script data-card-contents-for-ri="305" type="text/json">{"id":305,"name":"Applied Mathematics","url":"https://www.academia.edu/Documents/in/Applied_Mathematics?f_ri=2963","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="377" href="https://www.academia.edu/Documents/in/Partial_Differential_Equations">Partial Differential Equations</a>, <script data-card-contents-for-ri="377" type="text/json">{"id":377,"name":"Partial Differential Equations","url":"https://www.academia.edu/Documents/in/Partial_Differential_Equations?f_ri=2963","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="422" href="https://www.academia.edu/Documents/in/Computer_Science">Computer Science</a><script data-card-contents-for-ri="422" type="text/json">{"id":422,"name":"Computer Science","url":"https://www.academia.edu/Documents/in/Computer_Science?f_ri=2963","nofollow":false}</script></span></li><script>(function(){ if (true) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=75367254]'), work: {"id":75367254,"title":"Simulating the spread of COVID-19 via a spatially-resolved susceptible–exposed–infected–recovered–deceased (SEIRD) model with heterogeneous diffusion","created_at":"2022-04-03T20:34:06.918-07:00","url":"https://www.academia.edu/75367254/Simulating_the_spread_of_COVID_19_via_a_spatially_resolved_susceptible_exposed_infected_recovered_deceased_SEIRD_model_with_heterogeneous_diffusion?f_ri=2963","dom_id":"work_75367254","summary":null,"downloadable_attachments":[{"id":83163947,"asset_id":75367254,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":135038711,"first_name":"Alessandro","last_name":"Veneziani","domain_name":"independent","page_name":"AlessandroVeneziani","display_name":"Alessandro Veneziani","profile_url":"https://independent.academia.edu/AlessandroVeneziani?f_ri=2963","photo":"https://gravatar.com/avatar/b6a2f965b3ad3f8a77c1fae18566a28b?s=65"}],"research_interests":[{"id":300,"name":"Mathematics","url":"https://www.academia.edu/Documents/in/Mathematics?f_ri=2963","nofollow":false},{"id":305,"name":"Applied Mathematics","url":"https://www.academia.edu/Documents/in/Applied_Mathematics?f_ri=2963","nofollow":false},{"id":377,"name":"Partial Differential Equations","url":"https://www.academia.edu/Documents/in/Partial_Differential_Equations?f_ri=2963","nofollow":false},{"id":422,"name":"Computer Science","url":"https://www.academia.edu/Documents/in/Computer_Science?f_ri=2963","nofollow":false},{"id":498,"name":"Physics","url":"https://www.academia.edu/Documents/in/Physics?f_ri=2963"},{"id":2963,"name":"Mathematical Biology","url":"https://www.academia.edu/Documents/in/Mathematical_Biology?f_ri=2963"},{"id":7710,"name":"Biology","url":"https://www.academia.edu/Documents/in/Biology?f_ri=2963"},{"id":13398,"name":"Mathematical Epidemiology","url":"https://www.academia.edu/Documents/in/Mathematical_Epidemiology?f_ri=2963"},{"id":16682,"name":"Mathematical Modelling","url":"https://www.academia.edu/Documents/in/Mathematical_Modelling?f_ri=2963"},{"id":26327,"name":"Medicine","url":"https://www.academia.edu/Documents/in/Medicine?f_ri=2963"},{"id":214192,"name":"Compartmental Models","url":"https://www.academia.edu/Documents/in/Compartmental_Models?f_ri=2963"},{"id":1133506,"name":"Epidemic Model","url":"https://www.academia.edu/Documents/in/Epidemic_Model?f_ri=2963"}]}, }) } })();</script></ul></li></ul></div></div><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_40351361" data-work_id="40351361" itemscope="itemscope" itemtype="https://schema.org/ScholarlyArticle"><div class="header"><div class="title u-fontSerif u-fs22 u-lineHeight1_3"><a class="u-tcGrayDarkest js-work-link" href="https://www.academia.edu/40351361/2017_Pub_Med_Mathematical_Models_of_College_Myopia_Greene_Grill_Medina">2017 Pub Med, "Mathematical Models of College Myopia", Greene, Grill, Medina</a></div></div><div class="u-pb4x u-mt3x"><div class="summary u-fs14 u-fw300 u-lineHeight1_5 u-tcGrayDarkest"><div class="summarized">Experimental design phase of a pilot study at Annapolis is described, using reading glasses, +1.5 D. to +3.0 D. to alleviate college myopia. College students often become 1.0 to 2.0 diopters more myopic, so reading glasses were explored... <a class="more_link u-tcGrayDark u-linkUnstyled" data-container=".work_40351361" data-show=".complete" data-hide=".summarized" data-more-link-behavior="true" href="#">more</a></div><div class="complete hidden">Experimental design phase of a pilot study at Annapolis is described, using reading glasses, +1.5 D. to +3.0 D. to alleviate college myopia. College students often become 1.0 to 2.0 diopters more myopic, so reading glasses were explored to partially cancel the effects of the study environment. N = 25 different sets of (+)Add lenses are evaluated, for required adjustment period and reading comfort. Three computer models are developed to predict refraction versus time. Basic control system equations predict exponential myopia shift of refractive state R(t) with time constant t0 = 100 days. Linear, exponential and Gompertz computer results are compared calculating refraction R(t) during the college years, showing correlation coefficients |r| = 0.96 to 0.97, accurate +/−0.31 D. over a 14 year interval. Typical college myopia rate is −0.3 to −0.4 D/yr. Reading glasses may be a simple, practical solution to stabilize college myopia.</div></div></div><ul class="InlineList u-ph0x u-fs13"><li class="InlineList-item logged_in_only"><div class="share_on_academia_work_button"><a class="academia_share Button Button--inverseBlue Button--sm js-bookmark-button" data-academia-share="Work/40351361" data-share-source="work_strip" data-spinner="small_white_hide_contents"><i class="fa fa-plus"></i><span class="work-strip-link-text u-ml1x" data-content="button_text">Bookmark</span></a></div></li><li class="InlineList-item"><div class="download"><a id="e050771c1690edeae499a4d4cf5463e8" rel="nofollow" data-download="{"attachment_id":60596849,"asset_id":40351361,"asset_type":"Work","always_allow_download":false,"track":null,"button_location":"work_strip","source":null,"hide_modal":null}" class="Button Button--sm Button--inverseGreen js-download-button prompt_button doc_download" href="https://www.academia.edu/attachments/60596849/download_file?st=MTczMjk4MzU1Miw4LjIyMi4yMDguMTQ2&s=work_strip"><i class="fa fa-arrow-circle-o-down fa-lg"></i><span class="u-textUppercase u-ml1x" data-content="button_text">Download</span></a></div></li><li class="InlineList-item"><ul class="InlineList InlineList--bordered u-ph0x"><li class="InlineList-item InlineList-item--bordered"><span class="InlineList-item-text">by <span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a class="u-tcGrayDark u-fw700" data-has-card-for-user="33849221" href="https://greene.academia.edu/PeterGreene">Peter R Greene</a><script data-card-contents-for-user="33849221" type="text/json">{"id":33849221,"first_name":"Peter","last_name":"Greene","domain_name":"greene","page_name":"PeterGreene","display_name":"Peter R Greene","profile_url":"https://greene.academia.edu/PeterGreene?f_ri=2963","photo":"https://0.academia-photos.com/33849221/9961656/11108775/s65_peter.greene.jpg"}</script></span></span></li><li class="js-paper-rank-work_40351361 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="40351361"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 40351361, container: ".js-paper-rank-work_40351361", }); });</script></li><li class="js-percentile-work_40351361 InlineList-item InlineList-item--bordered hidden u-tcGrayDark"><span class="percentile-widget hidden"><span class="u-mr2x percentile-widget" style="display: none">•</span><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 40351361; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-percentile-work_40351361"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></li><li class="js-view-count-work_40351361 InlineList-item InlineList-item--bordered hidden"><div><span><span class="js-view-count view-count u-mr2x" data-work-id="40351361"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 40351361; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=40351361]").text(description); $(".js-view-count-work_40351361").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_40351361").removeClass('hidden') })</script></div></li><li class="InlineList-item u-positionRelative" style="max-width: 250px"><div class="u-positionAbsolute" data-has-card-for-ri-list="40351361"><i class="fa fa-tag InlineList-item-icon u-positionRelative"></i>  <a class="InlineList-item-text u-positionRelative">3</a>  </div><span class="InlineList-item-text u-textTruncate u-pl9x"><a class="InlineList-item-text" data-has-card-for-ri="68" href="https://www.academia.edu/Documents/in/Bioengineering">Bioengineering</a>, <script data-card-contents-for-ri="68" type="text/json">{"id":68,"name":"Bioengineering","url":"https://www.academia.edu/Documents/in/Bioengineering?f_ri=2963","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="2963" href="https://www.academia.edu/Documents/in/Mathematical_Biology">Mathematical Biology</a>, <script data-card-contents-for-ri="2963" type="text/json">{"id":2963,"name":"Mathematical Biology","url":"https://www.academia.edu/Documents/in/Mathematical_Biology?f_ri=2963","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="11284" href="https://www.academia.edu/Documents/in/Myopia">Myopia</a><script data-card-contents-for-ri="11284" type="text/json">{"id":11284,"name":"Myopia","url":"https://www.academia.edu/Documents/in/Myopia?f_ri=2963","nofollow":false}</script></span></li><script>(function(){ if (true) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=40351361]'), work: {"id":40351361,"title":"2017 Pub Med, \"Mathematical Models of College Myopia\", Greene, Grill, Medina","created_at":"2019-09-14T17:37:46.359-07:00","url":"https://www.academia.edu/40351361/2017_Pub_Med_Mathematical_Models_of_College_Myopia_Greene_Grill_Medina?f_ri=2963","dom_id":"work_40351361","summary":"Experimental design phase of a pilot study at Annapolis is described, using reading glasses, +1.5 D. to +3.0 D. to alleviate college myopia. College students often become 1.0 to 2.0 diopters more myopic, so reading glasses were explored to partially cancel the effects of the study environment. N = 25 different sets of (+)Add lenses are evaluated, for required adjustment period and reading comfort. Three computer models are developed to predict refraction versus time. Basic control system equations predict exponential myopia shift of refractive state R(t) with time constant t0 = 100 days. Linear, exponential and Gompertz computer results are compared calculating refraction R(t) during the college years, showing correlation coefficients |r| = 0.96 to 0.97, accurate +/−0.31 D. over a 14 year interval. Typical college myopia rate is −0.3 to −0.4 D/yr. Reading glasses may be a simple, practical solution to stabilize college myopia.","downloadable_attachments":[{"id":60596849,"asset_id":40351361,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":33849221,"first_name":"Peter","last_name":"Greene","domain_name":"greene","page_name":"PeterGreene","display_name":"Peter R Greene","profile_url":"https://greene.academia.edu/PeterGreene?f_ri=2963","photo":"https://0.academia-photos.com/33849221/9961656/11108775/s65_peter.greene.jpg"}],"research_interests":[{"id":68,"name":"Bioengineering","url":"https://www.academia.edu/Documents/in/Bioengineering?f_ri=2963","nofollow":false},{"id":2963,"name":"Mathematical Biology","url":"https://www.academia.edu/Documents/in/Mathematical_Biology?f_ri=2963","nofollow":false},{"id":11284,"name":"Myopia","url":"https://www.academia.edu/Documents/in/Myopia?f_ri=2963","nofollow":false}]}, }) } })();</script></ul></li></ul></div></div><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_8753641" data-work_id="8753641" itemscope="itemscope" itemtype="https://schema.org/ScholarlyArticle"><div class="header"><div class="title u-fontSerif u-fs22 u-lineHeight1_3"><a class="u-tcGrayDarkest js-work-link" href="https://www.academia.edu/8753641/A_New_Approach_to_Generalized_Fractional_Derivatives">A New Approach to Generalized Fractional Derivatives</a></div></div><div class="u-pb4x u-mt3x"><div class="summary u-fs14 u-fw300 u-lineHeight1_5 u-tcGrayDarkest"><div class="summarized">The author \mbox{(Appl. Math. Comput. 218(3):860-865, 2011)} introduced a new fractional integral operator given by, \[ \big({}^\rho \mathcal{I}^\alpha_{a+}f\big)(x) = \frac{\rho^{1- \alpha }}{\Gamma({\alpha})} \int^x_a... <a class="more_link u-tcGrayDark u-linkUnstyled" data-container=".work_8753641" data-show=".complete" data-hide=".summarized" data-more-link-behavior="true" href="#">more</a></div><div class="complete hidden">The author \mbox{(Appl. Math. Comput. 218(3):860-865, 2011)} introduced a new fractional integral operator given by, <br />\[ <br />\big({}^\rho \mathcal{I}^\alpha_{a+}f\big)(x) = \frac{\rho^{1- \alpha }}{\Gamma({\alpha})} \int^x_a \frac{\tau^{\rho-1} f(\tau) }{(x^\rho - \tau^\rho)^{1-\alpha}}\, d\tau, <br />\] <br />which generalizes the well-known Riemann-Liouville and the Hadamard fractional integrals. In this paper we present a new fractional derivative which generalizes the familiar Riemann-Liouville and the Hadamard fractional derivatives to a single form. We also obtain two representations of the generalized derivative in question. An example is given to illustrate the results.</div></div></div><ul class="InlineList u-ph0x u-fs13"><li class="InlineList-item logged_in_only"><div class="share_on_academia_work_button"><a class="academia_share Button Button--inverseBlue Button--sm js-bookmark-button" data-academia-share="Work/8753641" data-share-source="work_strip" data-spinner="small_white_hide_contents"><i class="fa fa-plus"></i><span class="work-strip-link-text u-ml1x" data-content="button_text">Bookmark</span></a></div></li><li class="InlineList-item"><div class="download"><a id="f1a3a69301fe1eabb6d8e035f11debe0" rel="nofollow" data-download="{"attachment_id":35108235,"asset_id":8753641,"asset_type":"Work","always_allow_download":false,"track":null,"button_location":"work_strip","source":null,"hide_modal":null}" class="Button Button--sm Button--inverseGreen js-download-button prompt_button doc_download" href="https://www.academia.edu/attachments/35108235/download_file?st=MTczMjk4MzU1Miw4LjIyMi4yMDguMTQ2&s=work_strip"><i class="fa fa-arrow-circle-o-down fa-lg"></i><span class="u-textUppercase u-ml1x" data-content="button_text">Download</span></a></div></li><li class="InlineList-item"><ul class="InlineList InlineList--bordered u-ph0x"><li class="InlineList-item InlineList-item--bordered"><span class="InlineList-item-text">by <span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a class="u-tcGrayDark u-fw700" data-has-card-for-user="1193935" href="https://indianatech.academia.edu/UditaKatugampola">Udita Katugampola</a><script data-card-contents-for-user="1193935" type="text/json">{"id":1193935,"first_name":"Udita","last_name":"Katugampola","domain_name":"indianatech","page_name":"UditaKatugampola","display_name":"Udita Katugampola","profile_url":"https://indianatech.academia.edu/UditaKatugampola?f_ri=2963","photo":"https://0.academia-photos.com/1193935/427459/18264398/s65_udita.katugampola.jpg"}</script></span></span></li><li class="js-paper-rank-work_8753641 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="8753641"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 8753641, container: ".js-paper-rank-work_8753641", }); });</script></li><li class="js-percentile-work_8753641 InlineList-item InlineList-item--bordered hidden u-tcGrayDark"><span class="percentile-widget hidden"><span class="u-mr2x percentile-widget" style="display: none">•</span><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 8753641; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-percentile-work_8753641"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></li><li class="js-view-count-work_8753641 InlineList-item InlineList-item--bordered hidden"><div><span><span class="js-view-count view-count u-mr2x" data-work-id="8753641"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 8753641; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=8753641]").text(description); $(".js-view-count-work_8753641").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_8753641").removeClass('hidden') })</script></div></li><li class="InlineList-item u-positionRelative" style="max-width: 250px"><div class="u-positionAbsolute" data-has-card-for-ri-list="8753641"><i class="fa fa-tag InlineList-item-icon u-positionRelative"></i>  <a class="InlineList-item-text u-positionRelative">4</a>  </div><span class="InlineList-item-text u-textTruncate u-pl9x"><a class="InlineList-item-text" data-has-card-for-ri="2963" href="https://www.academia.edu/Documents/in/Mathematical_Biology">Mathematical Biology</a>, <script data-card-contents-for-ri="2963" type="text/json">{"id":2963,"name":"Mathematical Biology","url":"https://www.academia.edu/Documents/in/Mathematical_Biology?f_ri=2963","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="5436" href="https://www.academia.edu/Documents/in/Combinatorics">Combinatorics</a>, <script data-card-contents-for-ri="5436" type="text/json">{"id":5436,"name":"Combinatorics","url":"https://www.academia.edu/Documents/in/Combinatorics?f_ri=2963","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="16682" href="https://www.academia.edu/Documents/in/Mathematical_Modelling">Mathematical Modelling</a>, <script data-card-contents-for-ri="16682" type="text/json">{"id":16682,"name":"Mathematical Modelling","url":"https://www.academia.edu/Documents/in/Mathematical_Modelling?f_ri=2963","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="56624" href="https://www.academia.edu/Documents/in/Fractional_calculus_and_its_applications">Fractional calculus and its applications</a><script data-card-contents-for-ri="56624" type="text/json">{"id":56624,"name":"Fractional calculus and its applications","url":"https://www.academia.edu/Documents/in/Fractional_calculus_and_its_applications?f_ri=2963","nofollow":false}</script></span></li><script>(function(){ if (true) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=8753641]'), work: {"id":8753641,"title":"A New Approach to Generalized Fractional Derivatives","created_at":"2014-10-13T06:21:43.183-07:00","url":"https://www.academia.edu/8753641/A_New_Approach_to_Generalized_Fractional_Derivatives?f_ri=2963","dom_id":"work_8753641","summary":"The author \\mbox{(Appl. Math. Comput. 218(3):860-865, 2011)} introduced a new fractional integral operator given by, \r\n\\[\r\n\\big({}^\\rho \\mathcal{I}^\\alpha_{a+}f\\big)(x) = \\frac{\\rho^{1- \\alpha }}{\\Gamma({\\alpha})} \\int^x_a \\frac{\\tau^{\\rho-1} f(\\tau) }{(x^\\rho - \\tau^\\rho)^{1-\\alpha}}\\, d\\tau, \r\n\\] \r\nwhich generalizes the well-known Riemann-Liouville and the Hadamard fractional integrals. In this paper we present a new fractional derivative which generalizes the familiar Riemann-Liouville and the Hadamard fractional derivatives to a single form. We also obtain two representations of the generalized derivative in question. An example is given to illustrate the results.","downloadable_attachments":[{"id":35108235,"asset_id":8753641,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":1193935,"first_name":"Udita","last_name":"Katugampola","domain_name":"indianatech","page_name":"UditaKatugampola","display_name":"Udita Katugampola","profile_url":"https://indianatech.academia.edu/UditaKatugampola?f_ri=2963","photo":"https://0.academia-photos.com/1193935/427459/18264398/s65_udita.katugampola.jpg"}],"research_interests":[{"id":2963,"name":"Mathematical Biology","url":"https://www.academia.edu/Documents/in/Mathematical_Biology?f_ri=2963","nofollow":false},{"id":5436,"name":"Combinatorics","url":"https://www.academia.edu/Documents/in/Combinatorics?f_ri=2963","nofollow":false},{"id":16682,"name":"Mathematical Modelling","url":"https://www.academia.edu/Documents/in/Mathematical_Modelling?f_ri=2963","nofollow":false},{"id":56624,"name":"Fractional calculus and its applications","url":"https://www.academia.edu/Documents/in/Fractional_calculus_and_its_applications?f_ri=2963","nofollow":false}]}, }) } })();</script></ul></li></ul></div></div><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_27987575" data-work_id="27987575" itemscope="itemscope" itemtype="https://schema.org/ScholarlyArticle"><div class="header"><div class="title u-fontSerif u-fs22 u-lineHeight1_3"><a class="u-tcGrayDarkest js-work-link" href="https://www.academia.edu/27987575/Temperature_dependent_predator_prey_mite_ecosystem_on_apple_tree_foliage">Temperature-dependent predator-prey mite ecosystem on apple tree foliage</a></div></div><div class="u-pb4x u-mt3x"></div><ul class="InlineList u-ph0x u-fs13"><li class="InlineList-item logged_in_only"><div class="share_on_academia_work_button"><a class="academia_share Button Button--inverseBlue Button--sm js-bookmark-button" data-academia-share="Work/27987575" data-share-source="work_strip" data-spinner="small_white_hide_contents"><i class="fa fa-plus"></i><span class="work-strip-link-text u-ml1x" data-content="button_text">Bookmark</span></a></div></li><li class="InlineList-item"><div class="download"><a id="8ed8b250f43c36b56573f507c0d3772a" rel="nofollow" data-download="{"attachment_id":48290829,"asset_id":27987575,"asset_type":"Work","always_allow_download":false,"track":null,"button_location":"work_strip","source":null,"hide_modal":null}" class="Button Button--sm Button--inverseGreen js-download-button prompt_button doc_download" href="https://www.academia.edu/attachments/48290829/download_file?st=MTczMjk4MzU1Miw4LjIyMi4yMDguMTQ2&s=work_strip"><i class="fa fa-arrow-circle-o-down fa-lg"></i><span class="u-textUppercase u-ml1x" data-content="button_text">Download</span></a></div></li><li class="InlineList-item"><ul class="InlineList InlineList--bordered u-ph0x"><li class="InlineList-item InlineList-item--bordered"><span class="InlineList-item-text">by <span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a class="u-tcGrayDark u-fw700" data-has-card-for-user="52474113" href="https://independent.academia.edu/DWollkind">D. Wollkind</a><script data-card-contents-for-user="52474113" type="text/json">{"id":52474113,"first_name":"D.","last_name":"Wollkind","domain_name":"independent","page_name":"DWollkind","display_name":"D. Wollkind","profile_url":"https://independent.academia.edu/DWollkind?f_ri=2963","photo":"/images/s65_no_pic.png"}</script></span></span></li><li class="js-paper-rank-work_27987575 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="27987575"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 27987575, container: ".js-paper-rank-work_27987575", }); });</script></li><li class="js-percentile-work_27987575 InlineList-item InlineList-item--bordered hidden u-tcGrayDark"><span class="percentile-widget hidden"><span class="u-mr2x percentile-widget" style="display: none">•</span><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 27987575; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-percentile-work_27987575"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></li><li class="js-view-count-work_27987575 InlineList-item InlineList-item--bordered hidden"><div><span><span class="js-view-count view-count u-mr2x" data-work-id="27987575"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 27987575; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=27987575]").text(description); $(".js-view-count-work_27987575").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_27987575").removeClass('hidden') })</script></div></li><li class="InlineList-item u-positionRelative" style="max-width: 250px"><div class="u-positionAbsolute" data-has-card-for-ri-list="27987575"><i class="fa fa-tag InlineList-item-icon u-positionRelative"></i>  <a class="InlineList-item-text u-positionRelative">4</a>  </div><span class="InlineList-item-text u-textTruncate u-pl9x"><a class="InlineList-item-text" data-has-card-for-ri="2963" href="https://www.academia.edu/Documents/in/Mathematical_Biology">Mathematical Biology</a>, <script data-card-contents-for-ri="2963" type="text/json">{"id":2963,"name":"Mathematical Biology","url":"https://www.academia.edu/Documents/in/Mathematical_Biology?f_ri=2963","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="47884" href="https://www.academia.edu/Documents/in/Biological_Sciences">Biological Sciences</a>, <script data-card-contents-for-ri="47884" type="text/json">{"id":47884,"name":"Biological Sciences","url":"https://www.academia.edu/Documents/in/Biological_Sciences?f_ri=2963","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="80414" href="https://www.academia.edu/Documents/in/Mathematical_Sciences">Mathematical Sciences</a>, <script data-card-contents-for-ri="80414" type="text/json">{"id":80414,"name":"Mathematical Sciences","url":"https://www.academia.edu/Documents/in/Mathematical_Sciences?f_ri=2963","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="175992" href="https://www.academia.edu/Documents/in/Singular_perturbation_problems">Singular perturbation problems</a><script data-card-contents-for-ri="175992" type="text/json">{"id":175992,"name":"Singular perturbation problems","url":"https://www.academia.edu/Documents/in/Singular_perturbation_problems?f_ri=2963","nofollow":false}</script></span></li><script>(function(){ if (true) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=27987575]'), work: {"id":27987575,"title":"Temperature-dependent predator-prey mite ecosystem on apple tree foliage","created_at":"2016-08-24T13:32:16.927-07:00","url":"https://www.academia.edu/27987575/Temperature_dependent_predator_prey_mite_ecosystem_on_apple_tree_foliage?f_ri=2963","dom_id":"work_27987575","summary":null,"downloadable_attachments":[{"id":48290829,"asset_id":27987575,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":52474113,"first_name":"D.","last_name":"Wollkind","domain_name":"independent","page_name":"DWollkind","display_name":"D. Wollkind","profile_url":"https://independent.academia.edu/DWollkind?f_ri=2963","photo":"/images/s65_no_pic.png"}],"research_interests":[{"id":2963,"name":"Mathematical Biology","url":"https://www.academia.edu/Documents/in/Mathematical_Biology?f_ri=2963","nofollow":false},{"id":47884,"name":"Biological Sciences","url":"https://www.academia.edu/Documents/in/Biological_Sciences?f_ri=2963","nofollow":false},{"id":80414,"name":"Mathematical Sciences","url":"https://www.academia.edu/Documents/in/Mathematical_Sciences?f_ri=2963","nofollow":false},{"id":175992,"name":"Singular perturbation problems","url":"https://www.academia.edu/Documents/in/Singular_perturbation_problems?f_ri=2963","nofollow":false}]}, }) } })();</script></ul></li></ul></div></div><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_61340068" data-work_id="61340068" itemscope="itemscope" itemtype="https://schema.org/ScholarlyArticle"><div class="header"><div class="title u-fontSerif u-fs22 u-lineHeight1_3"><a class="u-tcGrayDarkest js-work-link" href="https://www.academia.edu/61340068/Individual_based_and_continuum_models_of_growing_cell_populations_a_comparison">Individual-based and continuum models of growing cell populations: a comparison</a></div></div><div class="u-pb4x u-mt3x"></div><ul class="InlineList u-ph0x u-fs13"><li class="InlineList-item logged_in_only"><div class="share_on_academia_work_button"><a class="academia_share Button Button--inverseBlue Button--sm js-bookmark-button" data-academia-share="Work/61340068" data-share-source="work_strip" data-spinner="small_white_hide_contents"><i class="fa fa-plus"></i><span class="work-strip-link-text u-ml1x" data-content="button_text">Bookmark</span></a></div></li><li class="InlineList-item"><div class="download"><a id="e4274d9f5a38c75da31744431fd816b4" rel="nofollow" data-download="{"attachment_id":74398196,"asset_id":61340068,"asset_type":"Work","always_allow_download":false,"track":null,"button_location":"work_strip","source":null,"hide_modal":null}" class="Button Button--sm Button--inverseGreen js-download-button prompt_button doc_download" href="https://www.academia.edu/attachments/74398196/download_file?st=MTczMjk4MzU1Miw4LjIyMi4yMDguMTQ2&s=work_strip"><i class="fa fa-arrow-circle-o-down fa-lg"></i><span class="u-textUppercase u-ml1x" data-content="button_text">Download</span></a></div></li><li class="InlineList-item"><ul class="InlineList InlineList--bordered u-ph0x"><li class="InlineList-item InlineList-item--bordered"><span class="InlineList-item-text">by <span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a class="u-tcGrayDark u-fw700" data-has-card-for-user="32440763" href="https://independent.academia.edu/DirkDrasdo">Dirk Drasdo</a><script data-card-contents-for-user="32440763" type="text/json">{"id":32440763,"first_name":"Dirk","last_name":"Drasdo","domain_name":"independent","page_name":"DirkDrasdo","display_name":"Dirk Drasdo","profile_url":"https://independent.academia.edu/DirkDrasdo?f_ri=2963","photo":"/images/s65_no_pic.png"}</script></span></span></li><li class="js-paper-rank-work_61340068 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="61340068"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 61340068, container: ".js-paper-rank-work_61340068", }); });</script></li><li class="js-percentile-work_61340068 InlineList-item InlineList-item--bordered hidden u-tcGrayDark"><span class="percentile-widget hidden"><span class="u-mr2x percentile-widget" style="display: none">•</span><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 61340068; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-percentile-work_61340068"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></li><li class="js-view-count-work_61340068 InlineList-item InlineList-item--bordered hidden"><div><span><span class="js-view-count view-count u-mr2x" data-work-id="61340068"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 61340068; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=61340068]").text(description); $(".js-view-count-work_61340068").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_61340068").removeClass('hidden') })</script></div></li><li class="InlineList-item u-positionRelative" style="max-width: 250px"><div class="u-positionAbsolute" data-has-card-for-ri-list="61340068"><i class="fa fa-tag InlineList-item-icon u-positionRelative"></i>  <a class="InlineList-item-text u-positionRelative">18</a>  </div><span class="InlineList-item-text u-textTruncate u-pl10x"><a class="InlineList-item-text" data-has-card-for-ri="2963" href="https://www.academia.edu/Documents/in/Mathematical_Biology">Mathematical Biology</a>, <script data-card-contents-for-ri="2963" type="text/json">{"id":2963,"name":"Mathematical Biology","url":"https://www.academia.edu/Documents/in/Mathematical_Biology?f_ri=2963","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="7406" href="https://www.academia.edu/Documents/in/Agent_Based">Agent Based</a>, <script data-card-contents-for-ri="7406" type="text/json">{"id":7406,"name":"Agent Based","url":"https://www.academia.edu/Documents/in/Agent_Based?f_ri=2963","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="8863" href="https://www.academia.edu/Documents/in/Cell_Migration">Cell Migration</a>, <script data-card-contents-for-ri="8863" type="text/json">{"id":8863,"name":"Cell Migration","url":"https://www.academia.edu/Documents/in/Cell_Migration?f_ri=2963","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="10055" href="https://www.academia.edu/Documents/in/Cell_Adhesion">Cell Adhesion</a><script data-card-contents-for-ri="10055" type="text/json">{"id":10055,"name":"Cell Adhesion","url":"https://www.academia.edu/Documents/in/Cell_Adhesion?f_ri=2963","nofollow":false}</script></span></li><script>(function(){ if (true) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=61340068]'), work: {"id":61340068,"title":"Individual-based and continuum models of growing cell populations: a comparison","created_at":"2021-11-08T11:06:47.939-08:00","url":"https://www.academia.edu/61340068/Individual_based_and_continuum_models_of_growing_cell_populations_a_comparison?f_ri=2963","dom_id":"work_61340068","summary":null,"downloadable_attachments":[{"id":74398196,"asset_id":61340068,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":32440763,"first_name":"Dirk","last_name":"Drasdo","domain_name":"independent","page_name":"DirkDrasdo","display_name":"Dirk Drasdo","profile_url":"https://independent.academia.edu/DirkDrasdo?f_ri=2963","photo":"/images/s65_no_pic.png"}],"research_interests":[{"id":2963,"name":"Mathematical Biology","url":"https://www.academia.edu/Documents/in/Mathematical_Biology?f_ri=2963","nofollow":false},{"id":7406,"name":"Agent Based","url":"https://www.academia.edu/Documents/in/Agent_Based?f_ri=2963","nofollow":false},{"id":8863,"name":"Cell Migration","url":"https://www.academia.edu/Documents/in/Cell_Migration?f_ri=2963","nofollow":false},{"id":10055,"name":"Cell Adhesion","url":"https://www.academia.edu/Documents/in/Cell_Adhesion?f_ri=2963","nofollow":false},{"id":10959,"name":"Continuum Mechanics","url":"https://www.academia.edu/Documents/in/Continuum_Mechanics?f_ri=2963"},{"id":35865,"name":"Growth Kinetics","url":"https://www.academia.edu/Documents/in/Growth_Kinetics?f_ri=2963"},{"id":47884,"name":"Biological Sciences","url":"https://www.academia.edu/Documents/in/Biological_Sciences?f_ri=2963"},{"id":80414,"name":"Mathematical Sciences","url":"https://www.academia.edu/Documents/in/Mathematical_Sciences?f_ri=2963"},{"id":350931,"name":"Mechanical Stress","url":"https://www.academia.edu/Documents/in/Mechanical_Stress?f_ri=2963"},{"id":363691,"name":"Mathematical Concepts","url":"https://www.academia.edu/Documents/in/Mathematical_Concepts?f_ri=2963"},{"id":511994,"name":"Exponential Growth","url":"https://www.academia.edu/Documents/in/Exponential_Growth?f_ri=2963"},{"id":741144,"name":"Agent Based Model","url":"https://www.academia.edu/Documents/in/Agent_Based_Model?f_ri=2963"},{"id":782251,"name":"Cell Proliferation","url":"https://www.academia.edu/Documents/in/Cell_Proliferation?f_ri=2963"},{"id":1202082,"name":"Critical Parameter","url":"https://www.academia.edu/Documents/in/Critical_Parameter?f_ri=2963"},{"id":1745766,"name":"Cellular automaton","url":"https://www.academia.edu/Documents/in/Cellular_automaton?f_ri=2963"},{"id":2524494,"name":"Cell Aggregation","url":"https://www.academia.edu/Documents/in/Cell_Aggregation?f_ri=2963"},{"id":2796077,"name":"Cell count","url":"https://www.academia.edu/Documents/in/Cell_count?f_ri=2963"},{"id":3889899,"name":"Growth pattern","url":"https://www.academia.edu/Documents/in/Growth_pattern?f_ri=2963"}]}, }) } })();</script></ul></li></ul></div></div><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_4793358" data-work_id="4793358" itemscope="itemscope" itemtype="https://schema.org/ScholarlyArticle"><div class="header"><div class="title u-fontSerif u-fs22 u-lineHeight1_3"><a class="u-tcGrayDarkest js-work-link" href="https://www.academia.edu/4793358/A_study_on_mucus_trasport_in_human_lung_airways">A study on mucus trasport in human lung airways</a></div></div><div class="u-pb4x u-mt3x"></div><ul class="InlineList u-ph0x u-fs13"><li class="InlineList-item logged_in_only"><div class="share_on_academia_work_button"><a class="academia_share Button Button--inverseBlue Button--sm js-bookmark-button" data-academia-share="Work/4793358" data-share-source="work_strip" data-spinner="small_white_hide_contents"><i class="fa fa-plus"></i><span class="work-strip-link-text u-ml1x" data-content="button_text">Bookmark</span></a></div></li><li class="InlineList-item"><div class="download"><a id="0a612d79f0dc7b16731bfd30bc6739e4" rel="nofollow" data-download="{"attachment_id":32094639,"asset_id":4793358,"asset_type":"Work","always_allow_download":false,"track":null,"button_location":"work_strip","source":null,"hide_modal":null}" class="Button Button--sm Button--inverseGreen js-download-button prompt_button doc_download" href="https://www.academia.edu/attachments/32094639/download_file?st=MTczMjk4MzU1Miw4LjIyMi4yMDguMTQ2&s=work_strip"><i class="fa fa-arrow-circle-o-down fa-lg"></i><span class="u-textUppercase u-ml1x" data-content="button_text">Download</span></a></div></li><li class="InlineList-item"><ul class="InlineList InlineList--bordered u-ph0x"><li class="InlineList-item InlineList-item--bordered"><span class="InlineList-item-text">by <span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a class="u-tcGrayDark u-fw700" data-has-card-for-user="5301455" href="https://ddugkp.academia.edu/ShiveshManiTripathi">Shivesh Mani Tripathi</a><script data-card-contents-for-user="5301455" type="text/json">{"id":5301455,"first_name":"Shivesh","last_name":"Mani Tripathi","domain_name":"ddugkp","page_name":"ShiveshManiTripathi","display_name":"Shivesh Mani Tripathi","profile_url":"https://ddugkp.academia.edu/ShiveshManiTripathi?f_ri=2963","photo":"https://0.academia-photos.com/5301455/2330424/18491980/s65_shivesh.mani_tripathi.jpg"}</script></span></span></li><li class="js-paper-rank-work_4793358 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="4793358"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 4793358, container: ".js-paper-rank-work_4793358", }); });</script></li><li class="js-percentile-work_4793358 InlineList-item InlineList-item--bordered hidden u-tcGrayDark"><span class="percentile-widget hidden"><span class="u-mr2x percentile-widget" style="display: none">•</span><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 4793358; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-percentile-work_4793358"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></li><li class="js-view-count-work_4793358 InlineList-item InlineList-item--bordered hidden"><div><span><span class="js-view-count view-count u-mr2x" data-work-id="4793358"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 4793358; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=4793358]").text(description); $(".js-view-count-work_4793358").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_4793358").removeClass('hidden') })</script></div></li><li class="InlineList-item u-positionRelative" style="max-width: 250px"><div class="u-positionAbsolute" data-has-card-for-ri-list="4793358"><i class="fa fa-tag InlineList-item-icon u-positionRelative"></i></div><span class="InlineList-item-text u-textTruncate u-pl6x"><a class="InlineList-item-text" data-has-card-for-ri="2963" href="https://www.academia.edu/Documents/in/Mathematical_Biology">Mathematical Biology</a><script data-card-contents-for-ri="2963" type="text/json">{"id":2963,"name":"Mathematical Biology","url":"https://www.academia.edu/Documents/in/Mathematical_Biology?f_ri=2963","nofollow":false}</script></span></li><script>(function(){ if (false) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=4793358]'), work: {"id":4793358,"title":"A study on mucus trasport in human lung airways","created_at":"2013-10-16T19:37:55.852-07:00","url":"https://www.academia.edu/4793358/A_study_on_mucus_trasport_in_human_lung_airways?f_ri=2963","dom_id":"work_4793358","summary":null,"downloadable_attachments":[{"id":32094639,"asset_id":4793358,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":5301455,"first_name":"Shivesh","last_name":"Mani Tripathi","domain_name":"ddugkp","page_name":"ShiveshManiTripathi","display_name":"Shivesh Mani Tripathi","profile_url":"https://ddugkp.academia.edu/ShiveshManiTripathi?f_ri=2963","photo":"https://0.academia-photos.com/5301455/2330424/18491980/s65_shivesh.mani_tripathi.jpg"}],"research_interests":[{"id":2963,"name":"Mathematical Biology","url":"https://www.academia.edu/Documents/in/Mathematical_Biology?f_ri=2963","nofollow":false}]}, }) } })();</script></ul></li></ul></div></div><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_26090836" data-work_id="26090836" itemscope="itemscope" itemtype="https://schema.org/ScholarlyArticle"><div class="header"><div class="title u-fontSerif u-fs22 u-lineHeight1_3"><a class="u-tcGrayDarkest js-work-link" href="https://www.academia.edu/26090836/Hierarchies_The_Core_Argument_for_a_Naturalistic_Christian_Faith">Hierarchies: The Core Argument for a Naturalistic Christian Faith</a></div></div><div class="u-pb4x u-mt3x"></div><ul class="InlineList u-ph0x u-fs13"><li class="InlineList-item logged_in_only"><div class="share_on_academia_work_button"><a class="academia_share Button Button--inverseBlue Button--sm js-bookmark-button" data-academia-share="Work/26090836" data-share-source="work_strip" data-spinner="small_white_hide_contents"><i class="fa fa-plus"></i><span class="work-strip-link-text u-ml1x" data-content="button_text">Bookmark</span></a></div></li><li class="InlineList-item"><div class="download"><a id="118c710970795d3a179d5faaa05d8fc3" rel="nofollow" data-download="{"attachment_id":46443961,"asset_id":26090836,"asset_type":"Work","always_allow_download":false,"track":null,"button_location":"work_strip","source":null,"hide_modal":null}" class="Button Button--sm Button--inverseGreen js-download-button prompt_button doc_download" href="https://www.academia.edu/attachments/46443961/download_file?st=MTczMjk4MzU1Miw4LjIyMi4yMDguMTQ2&s=work_strip"><i class="fa fa-arrow-circle-o-down fa-lg"></i><span class="u-textUppercase u-ml1x" data-content="button_text">Download</span></a></div></li><li class="InlineList-item"><ul class="InlineList InlineList--bordered u-ph0x"><li class="InlineList-item InlineList-item--bordered"><span class="InlineList-item-text">by <span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a class="u-tcGrayDark u-fw700" data-has-card-for-user="44310" href="https://cst.academia.edu/PhilipClayton">Philip Clayton</a><script data-card-contents-for-user="44310" type="text/json">{"id":44310,"first_name":"Philip","last_name":"Clayton","domain_name":"cst","page_name":"PhilipClayton","display_name":"Philip Clayton","profile_url":"https://cst.academia.edu/PhilipClayton?f_ri=2963","photo":"https://0.academia-photos.com/44310/14158/13235/s65_philip.clayton.jpeg"}</script></span></span></li><li class="js-paper-rank-work_26090836 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="26090836"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 26090836, container: ".js-paper-rank-work_26090836", }); });</script></li><li class="js-percentile-work_26090836 InlineList-item InlineList-item--bordered hidden u-tcGrayDark"><span class="percentile-widget hidden"><span class="u-mr2x percentile-widget" style="display: none">•</span><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 26090836; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-percentile-work_26090836"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></li><li class="js-view-count-work_26090836 InlineList-item InlineList-item--bordered hidden"><div><span><span class="js-view-count view-count u-mr2x" data-work-id="26090836"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 26090836; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=26090836]").text(description); $(".js-view-count-work_26090836").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_26090836").removeClass('hidden') })</script></div></li><li class="InlineList-item u-positionRelative" style="max-width: 250px"><div class="u-positionAbsolute" data-has-card-for-ri-list="26090836"><i class="fa fa-tag InlineList-item-icon u-positionRelative"></i>  <a class="InlineList-item-text u-positionRelative">7</a>  </div><span class="InlineList-item-text u-textTruncate u-pl9x"><a class="InlineList-item-text" data-has-card-for-ri="184" href="https://www.academia.edu/Documents/in/Sociology">Sociology</a>, <script data-card-contents-for-ri="184" type="text/json">{"id":184,"name":"Sociology","url":"https://www.academia.edu/Documents/in/Sociology?f_ri=2963","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="803" href="https://www.academia.edu/Documents/in/Philosophy">Philosophy</a>, <script data-card-contents-for-ri="803" type="text/json">{"id":803,"name":"Philosophy","url":"https://www.academia.edu/Documents/in/Philosophy?f_ri=2963","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="806" href="https://www.academia.edu/Documents/in/Philosophy_of_Mind">Philosophy of Mind</a>, <script data-card-contents-for-ri="806" type="text/json">{"id":806,"name":"Philosophy of Mind","url":"https://www.academia.edu/Documents/in/Philosophy_of_Mind?f_ri=2963","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="2963" href="https://www.academia.edu/Documents/in/Mathematical_Biology">Mathematical Biology</a><script data-card-contents-for-ri="2963" type="text/json">{"id":2963,"name":"Mathematical Biology","url":"https://www.academia.edu/Documents/in/Mathematical_Biology?f_ri=2963","nofollow":false}</script></span></li><script>(function(){ if (true) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=26090836]'), work: {"id":26090836,"title":"Hierarchies: The Core Argument for a Naturalistic Christian Faith","created_at":"2016-06-13T10:50:42.483-07:00","url":"https://www.academia.edu/26090836/Hierarchies_The_Core_Argument_for_a_Naturalistic_Christian_Faith?f_ri=2963","dom_id":"work_26090836","summary":null,"downloadable_attachments":[{"id":46443961,"asset_id":26090836,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":44310,"first_name":"Philip","last_name":"Clayton","domain_name":"cst","page_name":"PhilipClayton","display_name":"Philip Clayton","profile_url":"https://cst.academia.edu/PhilipClayton?f_ri=2963","photo":"https://0.academia-photos.com/44310/14158/13235/s65_philip.clayton.jpeg"}],"research_interests":[{"id":184,"name":"Sociology","url":"https://www.academia.edu/Documents/in/Sociology?f_ri=2963","nofollow":false},{"id":803,"name":"Philosophy","url":"https://www.academia.edu/Documents/in/Philosophy?f_ri=2963","nofollow":false},{"id":806,"name":"Philosophy of Mind","url":"https://www.academia.edu/Documents/in/Philosophy_of_Mind?f_ri=2963","nofollow":false},{"id":2963,"name":"Mathematical Biology","url":"https://www.academia.edu/Documents/in/Mathematical_Biology?f_ri=2963","nofollow":false},{"id":3155,"name":"Complexity Theory","url":"https://www.academia.edu/Documents/in/Complexity_Theory?f_ri=2963"},{"id":19744,"name":"System Biology","url":"https://www.academia.edu/Documents/in/System_Biology?f_ri=2963"},{"id":1424532,"name":"Zygon","url":"https://www.academia.edu/Documents/in/Zygon?f_ri=2963"}]}, }) } })();</script></ul></li></ul></div></div><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_73106905" data-work_id="73106905" itemscope="itemscope" itemtype="https://schema.org/ScholarlyArticle"><div class="header"><div class="title u-fontSerif u-fs22 u-lineHeight1_3"><a class="u-tcGrayDarkest js-work-link" href="https://www.academia.edu/73106905/Mathematical_models_and_population_cycles_A_critical_evaluation_of_a_recent_modeling_effort">Mathematical models and population cycles: A critical evaluation of a recent modeling effort</a></div></div><div class="u-pb4x u-mt3x"></div><ul class="InlineList u-ph0x u-fs13"><li class="InlineList-item logged_in_only"><div class="share_on_academia_work_button"><a class="academia_share Button Button--inverseBlue Button--sm js-bookmark-button" data-academia-share="Work/73106905" data-share-source="work_strip" data-spinner="small_white_hide_contents"><i class="fa fa-plus"></i><span class="work-strip-link-text u-ml1x" data-content="button_text">Bookmark</span></a></div></li><li class="InlineList-item"><div class="download"><a id="f508d9d16e586e8c7b00f49f88db3326" rel="nofollow" data-download="{"attachment_id":81758412,"asset_id":73106905,"asset_type":"Work","always_allow_download":false,"track":null,"button_location":"work_strip","source":null,"hide_modal":null}" class="Button Button--sm Button--inverseGreen js-download-button prompt_button doc_download" href="https://www.academia.edu/attachments/81758412/download_file?st=MTczMjk4MzU1Miw4LjIyMi4yMDguMTQ2&s=work_strip"><i class="fa fa-arrow-circle-o-down fa-lg"></i><span class="u-textUppercase u-ml1x" data-content="button_text">Download</span></a></div></li><li class="InlineList-item"><ul class="InlineList InlineList--bordered u-ph0x"><li class="InlineList-item InlineList-item--bordered"><span class="InlineList-item-text">by <span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a class="u-tcGrayDark u-fw700" data-has-card-for-user="45253844" href="https://independent.academia.edu/JamesNichols9">James Nichols</a><script data-card-contents-for-user="45253844" type="text/json">{"id":45253844,"first_name":"James","last_name":"Nichols","domain_name":"independent","page_name":"JamesNichols9","display_name":"James Nichols","profile_url":"https://independent.academia.edu/JamesNichols9?f_ri=2963","photo":"/images/s65_no_pic.png"}</script></span></span></li><li class="js-paper-rank-work_73106905 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="73106905"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 73106905, container: ".js-paper-rank-work_73106905", }); });</script></li><li class="js-percentile-work_73106905 InlineList-item InlineList-item--bordered hidden u-tcGrayDark"><span class="percentile-widget hidden"><span class="u-mr2x percentile-widget" style="display: none">•</span><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 73106905; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-percentile-work_73106905"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></li><li class="js-view-count-work_73106905 InlineList-item InlineList-item--bordered hidden"><div><span><span class="js-view-count view-count u-mr2x" data-work-id="73106905"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 73106905; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=73106905]").text(description); $(".js-view-count-work_73106905").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_73106905").removeClass('hidden') })</script></div></li><li class="InlineList-item u-positionRelative" style="max-width: 250px"><div class="u-positionAbsolute" data-has-card-for-ri-list="73106905"><i class="fa fa-tag InlineList-item-icon u-positionRelative"></i>  <a class="InlineList-item-text u-positionRelative">6</a>  </div><span class="InlineList-item-text u-textTruncate u-pl9x"><a class="InlineList-item-text" data-has-card-for-ri="422" href="https://www.academia.edu/Documents/in/Computer_Science">Computer Science</a>, <script data-card-contents-for-ri="422" type="text/json">{"id":422,"name":"Computer Science","url":"https://www.academia.edu/Documents/in/Computer_Science?f_ri=2963","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="2963" href="https://www.academia.edu/Documents/in/Mathematical_Biology">Mathematical Biology</a>, <script data-card-contents-for-ri="2963" type="text/json">{"id":2963,"name":"Mathematical Biology","url":"https://www.academia.edu/Documents/in/Mathematical_Biology?f_ri=2963","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="47884" href="https://www.academia.edu/Documents/in/Biological_Sciences">Biological Sciences</a>, <script data-card-contents-for-ri="47884" type="text/json">{"id":47884,"name":"Biological Sciences","url":"https://www.academia.edu/Documents/in/Biological_Sciences?f_ri=2963","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="80414" href="https://www.academia.edu/Documents/in/Mathematical_Sciences">Mathematical Sciences</a><script data-card-contents-for-ri="80414" type="text/json">{"id":80414,"name":"Mathematical Sciences","url":"https://www.academia.edu/Documents/in/Mathematical_Sciences?f_ri=2963","nofollow":false}</script></span></li><script>(function(){ if (true) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=73106905]'), work: {"id":73106905,"title":"Mathematical models and population cycles: A critical evaluation of a recent modeling effort","created_at":"2022-03-05T05:50:35.544-08:00","url":"https://www.academia.edu/73106905/Mathematical_models_and_population_cycles_A_critical_evaluation_of_a_recent_modeling_effort?f_ri=2963","dom_id":"work_73106905","summary":null,"downloadable_attachments":[{"id":81758412,"asset_id":73106905,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":45253844,"first_name":"James","last_name":"Nichols","domain_name":"independent","page_name":"JamesNichols9","display_name":"James Nichols","profile_url":"https://independent.academia.edu/JamesNichols9?f_ri=2963","photo":"/images/s65_no_pic.png"}],"research_interests":[{"id":422,"name":"Computer Science","url":"https://www.academia.edu/Documents/in/Computer_Science?f_ri=2963","nofollow":false},{"id":2963,"name":"Mathematical Biology","url":"https://www.academia.edu/Documents/in/Mathematical_Biology?f_ri=2963","nofollow":false},{"id":47884,"name":"Biological Sciences","url":"https://www.academia.edu/Documents/in/Biological_Sciences?f_ri=2963","nofollow":false},{"id":80414,"name":"Mathematical Sciences","url":"https://www.academia.edu/Documents/in/Mathematical_Sciences?f_ri=2963","nofollow":false},{"id":291387,"name":"Mathematical Model","url":"https://www.academia.edu/Documents/in/Mathematical_Model?f_ri=2963"},{"id":393606,"name":"Population Cycles","url":"https://www.academia.edu/Documents/in/Population_Cycles?f_ri=2963"}]}, }) } })();</script></ul></li></ul></div></div><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_36045131" data-work_id="36045131" itemscope="itemscope" itemtype="https://schema.org/ScholarlyArticle"><div class="header"><div class="title u-fontSerif u-fs22 u-lineHeight1_3"><a class="u-tcGrayDarkest js-work-link" href="https://www.academia.edu/36045131/Protective_effect_of_garlic_extract_against_maternal_and_fetal_cerebellar_damage_induced_by_lead_administration_during_pregnancy_in_rats">Protective effect of garlic extract against maternal and fetal cerebellar damage induced by lead administration during pregnancy in rats</a></div></div><div class="u-pb4x u-mt3x"><div class="summary u-fs14 u-fw300 u-lineHeight1_5 u-tcGrayDarkest"><div class="summarized">BACKGROUND: In spite of its indusrial usefulness and varied daily uses, lead (Pb) pollution is a widespread ecological problem that faces the humans in the 21th century. Pb was found to produces a wide range of toxic effects including... <a class="more_link u-tcGrayDark u-linkUnstyled" data-container=".work_36045131" data-show=".complete" data-hide=".summarized" data-more-link-behavior="true" href="#">more</a></div><div class="complete hidden">BACKGROUND:<br />In spite of its indusrial usefulness and varied daily uses, lead (Pb) pollution is a widespread ecological problem that faces the humans in the 21th century. Pb was found to produces a wide range of toxic effects including neurotoxicity especially to the developing and young offspring. Recently, the utilization of herbal plants has received a significant attention where there has been rising awareness in their therapeutic use; among these is the garlic.<br />AIM OF THE WORK:<br />In light of the above, the current study is designed experimentally in female pregnant rats in order to investigate the beneficial role of garlic extract in the protection from the maternal and fetal cerebellar damage that produced by administration of different doses of Pb during pregnancy.<br />MATERIALS AND METHODS:<br />Positively pregnant female rats were divided into five groups; one control group, two Pb-treated groups (exposed to 160 and 320 mg/kg b.wt. of Pb, respectively) and two groups treated with both Pb and garlic (exposed to Pb as previous groups together with 250 mg/ kg b.wt. /day of garlic extract). Treatments started from day 1 till day 20 of pregnancy, where the mother rats of different experimental groups were sacrified to obtain the fetuses. Pb level in the maternal nd fetal blood and cerebellum was estimated by spectrophotometry. Specimens of the cerebellum of different mother and fetal groups were processed to histological and immunohistochemical staining for microscopic examination.<br />RESULTS:<br />The results showed that administration of Pb to pregnant rats resulted in a dose-dependent toxicity for both mothers and fetuses in the form of decrease of maternal weight gain, placental and fetal weights, brain weight and diminished fetal growth parameters, which were prominent in rat's group treated with larger dose of Pb. In Pb-treated rats, Pb level in blood and cerebellum was high when compared to the control. The histopathological examination of the cerebellum of treated dams and fetuses showed marked alterations mainly in the form of Purkinje cell degeneration and lack of deveopmet of fetal cerebellum. Co-treatment of garlic extract along with Pb resulted in a significant decrease in Pb levels as compared with those treated with Pb alone with improvement of the histopathological changes.<br />CONCLUSIONS:<br />This study was useful in evaluating the hazardous effects of uncontrolled use of Pb in general and in assessing the developmental and neurotoxicity of fetuses due to exposure during pregnancy in particular. Co-administration of garlic has beneficial effects in amelioration of Pb-induced neurotoxicity and reversing the histopathological changes of the cerebellum of mother rats and fetuses.<br />KEYWORDS:<br />garlic; glial fibrillary acidic protein; lead; purkinje cells</div></div></div><ul class="InlineList u-ph0x u-fs13"><li class="InlineList-item logged_in_only"><div class="share_on_academia_work_button"><a class="academia_share Button Button--inverseBlue Button--sm js-bookmark-button" data-academia-share="Work/36045131" data-share-source="work_strip" data-spinner="small_white_hide_contents"><i class="fa fa-plus"></i><span class="work-strip-link-text u-ml1x" data-content="button_text">Bookmark</span></a></div></li><li class="InlineList-item"><div class="download"><a id="165cc29bc8e599bbfe3e61541d9d8266" rel="nofollow" data-download="{"attachment_id":55931132,"asset_id":36045131,"asset_type":"Work","always_allow_download":false,"track":null,"button_location":"work_strip","source":null,"hide_modal":null}" class="Button Button--sm Button--inverseGreen js-download-button prompt_button doc_download" href="https://www.academia.edu/attachments/55931132/download_file?st=MTczMjk4MzU1Miw4LjIyMi4yMDguMTQ2&s=work_strip"><i class="fa fa-arrow-circle-o-down fa-lg"></i><span class="u-textUppercase u-ml1x" data-content="button_text">Download</span></a></div></li><li class="InlineList-item"><ul class="InlineList InlineList--bordered u-ph0x"><li class="InlineList-item InlineList-item--bordered"><span class="InlineList-item-text">by <span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a class="u-tcGrayDark u-fw700" data-has-card-for-user="21972122" href="https://kau.academia.edu/HMustafa">Prof. Hesham N Mustafa</a><script data-card-contents-for-user="21972122" type="text/json">{"id":21972122,"first_name":"Prof. Hesham","last_name":"Mustafa","domain_name":"kau","page_name":"HMustafa","display_name":"Prof. Hesham N Mustafa","profile_url":"https://kau.academia.edu/HMustafa?f_ri=2963","photo":"https://0.academia-photos.com/21972122/6015802/7471085/s65_hesham.mustafa.jpg"}</script></span></span></li><li class="js-paper-rank-work_36045131 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="36045131"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 36045131, container: ".js-paper-rank-work_36045131", }); });</script></li><li class="js-percentile-work_36045131 InlineList-item InlineList-item--bordered hidden u-tcGrayDark"><span class="percentile-widget hidden"><span class="u-mr2x percentile-widget" style="display: none">•</span><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 36045131; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-percentile-work_36045131"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></li><li class="js-view-count-work_36045131 InlineList-item InlineList-item--bordered hidden"><div><span><span class="js-view-count view-count u-mr2x" data-work-id="36045131"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 36045131; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=36045131]").text(description); $(".js-view-count-work_36045131").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_36045131").removeClass('hidden') })</script></div></li><li class="InlineList-item u-positionRelative" style="max-width: 250px"><div class="u-positionAbsolute" data-has-card-for-ri-list="36045131"><i class="fa fa-tag InlineList-item-icon u-positionRelative"></i>  <a class="InlineList-item-text u-positionRelative">156</a>  </div><span class="InlineList-item-text u-textTruncate u-pl11x"><a class="InlineList-item-text" data-has-card-for-ri="143" href="https://www.academia.edu/Documents/in/Comparative_Anatomy">Comparative Anatomy</a>, <script data-card-contents-for-ri="143" type="text/json">{"id":143,"name":"Comparative Anatomy","url":"https://www.academia.edu/Documents/in/Comparative_Anatomy?f_ri=2963","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="144" href="https://www.academia.edu/Documents/in/Human_Anatomy_Biology_">Human Anatomy (Biology)</a>, <script data-card-contents-for-ri="144" type="text/json">{"id":144,"name":"Human Anatomy (Biology)","url":"https://www.academia.edu/Documents/in/Human_Anatomy_Biology_?f_ri=2963","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="155" href="https://www.academia.edu/Documents/in/Evolutionary_Biology">Evolutionary Biology</a>, <script data-card-contents-for-ri="155" type="text/json">{"id":155,"name":"Evolutionary Biology","url":"https://www.academia.edu/Documents/in/Evolutionary_Biology?f_ri=2963","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="158" href="https://www.academia.edu/Documents/in/Marine_Biology">Marine Biology</a><script data-card-contents-for-ri="158" type="text/json">{"id":158,"name":"Marine Biology","url":"https://www.academia.edu/Documents/in/Marine_Biology?f_ri=2963","nofollow":false}</script></span></li><script>(function(){ if (true) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=36045131]'), work: {"id":36045131,"title":"Protective effect of garlic extract against maternal and fetal cerebellar damage induced by lead administration during pregnancy in rats","created_at":"2018-02-28T13:39:33.137-08:00","url":"https://www.academia.edu/36045131/Protective_effect_of_garlic_extract_against_maternal_and_fetal_cerebellar_damage_induced_by_lead_administration_during_pregnancy_in_rats?f_ri=2963","dom_id":"work_36045131","summary":"BACKGROUND:\nIn spite of its indusrial usefulness and varied daily uses, lead (Pb) pollution is a widespread ecological problem that faces the humans in the 21th century. Pb was found to produces a wide range of toxic effects including neurotoxicity especially to the developing and young offspring. Recently, the utilization of herbal plants has received a significant attention where there has been rising awareness in their therapeutic use; among these is the garlic.\nAIM OF THE WORK:\nIn light of the above, the current study is designed experimentally in female pregnant rats in order to investigate the beneficial role of garlic extract in the protection from the maternal and fetal cerebellar damage that produced by administration of different doses of Pb during pregnancy.\nMATERIALS AND METHODS:\nPositively pregnant female rats were divided into five groups; one control group, two Pb-treated groups (exposed to 160 and 320 mg/kg b.wt. of Pb, respectively) and two groups treated with both Pb and garlic (exposed to Pb as previous groups together with 250 mg/ kg b.wt. /day of garlic extract). Treatments started from day 1 till day 20 of pregnancy, where the mother rats of different experimental groups were sacrified to obtain the fetuses. Pb level in the maternal nd fetal blood and cerebellum was estimated by spectrophotometry. Specimens of the cerebellum of different mother and fetal groups were processed to histological and immunohistochemical staining for microscopic examination.\nRESULTS:\nThe results showed that administration of Pb to pregnant rats resulted in a dose-dependent toxicity for both mothers and fetuses in the form of decrease of maternal weight gain, placental and fetal weights, brain weight and diminished fetal growth parameters, which were prominent in rat's group treated with larger dose of Pb. In Pb-treated rats, Pb level in blood and cerebellum was high when compared to the control. The histopathological examination of the cerebellum of treated dams and fetuses showed marked alterations mainly in the form of Purkinje cell degeneration and lack of deveopmet of fetal cerebellum. Co-treatment of garlic extract along with Pb resulted in a significant decrease in Pb levels as compared with those treated with Pb alone with improvement of the histopathological changes.\nCONCLUSIONS:\nThis study was useful in evaluating the hazardous effects of uncontrolled use of Pb in general and in assessing the developmental and neurotoxicity of fetuses due to exposure during pregnancy in particular. Co-administration of garlic has beneficial effects in amelioration of Pb-induced neurotoxicity and reversing the histopathological changes of the cerebellum of mother rats and fetuses.\nKEYWORDS:\ngarlic; glial fibrillary acidic protein; lead; purkinje cells","downloadable_attachments":[{"id":55931132,"asset_id":36045131,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":21972122,"first_name":"Prof. Hesham","last_name":"Mustafa","domain_name":"kau","page_name":"HMustafa","display_name":"Prof. Hesham N Mustafa","profile_url":"https://kau.academia.edu/HMustafa?f_ri=2963","photo":"https://0.academia-photos.com/21972122/6015802/7471085/s65_hesham.mustafa.jpg"}],"research_interests":[{"id":143,"name":"Comparative Anatomy","url":"https://www.academia.edu/Documents/in/Comparative_Anatomy?f_ri=2963","nofollow":false},{"id":144,"name":"Human Anatomy (Biology)","url":"https://www.academia.edu/Documents/in/Human_Anatomy_Biology_?f_ri=2963","nofollow":false},{"id":155,"name":"Evolutionary Biology","url":"https://www.academia.edu/Documents/in/Evolutionary_Biology?f_ri=2963","nofollow":false},{"id":158,"name":"Marine Biology","url":"https://www.academia.edu/Documents/in/Marine_Biology?f_ri=2963","nofollow":false},{"id":161,"name":"Neuroscience","url":"https://www.academia.edu/Documents/in/Neuroscience?f_ri=2963"},{"id":165,"name":"Pathology","url":"https://www.academia.edu/Documents/in/Pathology?f_ri=2963"},{"id":594,"name":"Speech Language Pathology","url":"https://www.academia.edu/Documents/in/Speech_Language_Pathology?f_ri=2963"},{"id":657,"name":"Veterinary Medicine","url":"https://www.academia.edu/Documents/in/Veterinary_Medicine?f_ri=2963"},{"id":823,"name":"Philosophy of Biology","url":"https://www.academia.edu/Documents/in/Philosophy_of_Biology?f_ri=2963"},{"id":1083,"name":"Developmental Biology","url":"https://www.academia.edu/Documents/in/Developmental_Biology?f_ri=2963"},{"id":1906,"name":"Veterinary Pathology","url":"https://www.academia.edu/Documents/in/Veterinary_Pathology?f_ri=2963"},{"id":2075,"name":"Speech Pathology","url":"https://www.academia.edu/Documents/in/Speech_Pathology?f_ri=2963"},{"id":2183,"name":"Cellular Biology","url":"https://www.academia.edu/Documents/in/Cellular_Biology?f_ri=2963"},{"id":2184,"name":"Electron Microscopy","url":"https://www.academia.edu/Documents/in/Electron_Microscopy?f_ri=2963"},{"id":2230,"name":"Bone Biology","url":"https://www.academia.edu/Documents/in/Bone_Biology?f_ri=2963"},{"id":2273,"name":"History of Medicine","url":"https://www.academia.edu/Documents/in/History_of_Medicine?f_ri=2963"},{"id":2361,"name":"Skeletal Biology","url":"https://www.academia.edu/Documents/in/Skeletal_Biology?f_ri=2963"},{"id":2447,"name":"Speech-Language Pathology/ Communication Disorders","url":"https://www.academia.edu/Documents/in/Speech-Language_Pathology_Communication_Disorders?f_ri=2963"},{"id":2467,"name":"Conservation Biology","url":"https://www.academia.edu/Documents/in/Conservation_Biology?f_ri=2963"},{"id":2513,"name":"Molecular Biology","url":"https://www.academia.edu/Documents/in/Molecular_Biology?f_ri=2963"},{"id":2541,"name":"Structural Biology","url":"https://www.academia.edu/Documents/in/Structural_Biology?f_ri=2963"},{"id":2748,"name":"Sensory Neuroscience","url":"https://www.academia.edu/Documents/in/Sensory_Neuroscience?f_ri=2963"},{"id":2894,"name":"Evolution of cooperation (Evolutionary Biology)","url":"https://www.academia.edu/Documents/in/Evolution_of_cooperation_Evolutionary_Biology_?f_ri=2963"},{"id":2963,"name":"Mathematical Biology","url":"https://www.academia.edu/Documents/in/Mathematical_Biology?f_ri=2963"},{"id":3091,"name":"Microscopy","url":"https://www.academia.edu/Documents/in/Microscopy?f_ri=2963"},{"id":3313,"name":"Cultural Transmission (Evolutionary Biology)","url":"https://www.academia.edu/Documents/in/Cultural_Transmission_Evolutionary_Biology_?f_ri=2963"},{"id":3363,"name":"Systematic Biology","url":"https://www.academia.edu/Documents/in/Systematic_Biology?f_ri=2963"},{"id":3629,"name":"Synthetic Biology","url":"https://www.academia.edu/Documents/in/Synthetic_Biology?f_ri=2963"},{"id":3699,"name":"Stem cell and Regenerative medicine","url":"https://www.academia.edu/Documents/in/Stem_cell_and_Regenerative_medicine?f_ri=2963"},{"id":3939,"name":"History and Philosophy of Biology","url":"https://www.academia.edu/Documents/in/History_and_Philosophy_of_Biology?f_ri=2963"},{"id":3940,"name":"Evolutionary Developmental Biology","url":"https://www.academia.edu/Documents/in/Evolutionary_Developmental_Biology?f_ri=2963"},{"id":4228,"name":"Skeletal muscle biology","url":"https://www.academia.edu/Documents/in/Skeletal_muscle_biology?f_ri=2963"},{"id":4233,"name":"Computational Biology","url":"https://www.academia.edu/Documents/in/Computational_Biology?f_ri=2963"},{"id":4246,"name":"Learning and Memory (Neurosciences)","url":"https://www.academia.edu/Documents/in/Learning_and_Memory_Neurosciences_?f_ri=2963"},{"id":4258,"name":"Embryology","url":"https://www.academia.edu/Documents/in/Embryology?f_ri=2963"},{"id":4266,"name":"Wildlife Biology","url":"https://www.academia.edu/Documents/in/Wildlife_Biology?f_ri=2963"},{"id":4558,"name":"Invertebrate Biology","url":"https://www.academia.edu/Documents/in/Invertebrate_Biology?f_ri=2963"},{"id":4926,"name":"Functional Anatomy","url":"https://www.academia.edu/Documents/in/Functional_Anatomy?f_ri=2963"},{"id":5400,"name":"Systems Biology","url":"https://www.academia.edu/Documents/in/Systems_Biology?f_ri=2963"},{"id":5451,"name":"Computational Neuroscience","url":"https://www.academia.edu/Documents/in/Computational_Neuroscience?f_ri=2963"},{"id":5525,"name":"Clinical Neuroscience","url":"https://www.academia.edu/Documents/in/Clinical_Neuroscience?f_ri=2963"},{"id":5541,"name":"Plant Biology","url":"https://www.academia.edu/Documents/in/Plant_Biology?f_ri=2963"},{"id":5692,"name":"Visual Neuroscience","url":"https://www.academia.edu/Documents/in/Visual_Neuroscience?f_ri=2963"},{"id":5971,"name":"Human Anatomy (Biological Anthropology)","url":"https://www.academia.edu/Documents/in/Human_Anatomy_Biological_Anthropology_?f_ri=2963"},{"id":7080,"name":"Freshwater Biology","url":"https://www.academia.edu/Documents/in/Freshwater_Biology?f_ri=2963"},{"id":7436,"name":"Population Biology","url":"https://www.academia.edu/Documents/in/Population_Biology?f_ri=2963"},{"id":7700,"name":"Fluorescence Microscopy","url":"https://www.academia.edu/Documents/in/Fluorescence_Microscopy?f_ri=2963"},{"id":7701,"name":"Membrane Biology","url":"https://www.academia.edu/Documents/in/Membrane_Biology?f_ri=2963"},{"id":7710,"name":"Biology","url":"https://www.academia.edu/Documents/in/Biology?f_ri=2963"},{"id":7859,"name":"Scanning Probe Microscopy","url":"https://www.academia.edu/Documents/in/Scanning_Probe_Microscopy?f_ri=2963"},{"id":7874,"name":"Educational Neuroscience","url":"https://www.academia.edu/Documents/in/Educational_Neuroscience?f_ri=2963"},{"id":7987,"name":"Radiation Biology","url":"https://www.academia.edu/Documents/in/Radiation_Biology?f_ri=2963"},{"id":8241,"name":"Tropical Medicine","url":"https://www.academia.edu/Documents/in/Tropical_Medicine?f_ri=2963"},{"id":8322,"name":"Developmental neuroscience","url":"https://www.academia.edu/Documents/in/Developmental_neuroscience?f_ri=2963"},{"id":9088,"name":"Affective Neuroscience","url":"https://www.academia.edu/Documents/in/Affective_Neuroscience?f_ri=2963"},{"id":9506,"name":"History of Neuroscience","url":"https://www.academia.edu/Documents/in/History_of_Neuroscience?f_ri=2963"},{"id":10024,"name":"Population genetics (Biology)","url":"https://www.academia.edu/Documents/in/Population_genetics_Biology_?f_ri=2963"},{"id":10102,"name":"Social Neuroscience","url":"https://www.academia.edu/Documents/in/Social_Neuroscience?f_ri=2963"},{"id":10154,"name":"Environmental Microbiology (Biology)","url":"https://www.academia.edu/Documents/in/Environmental_Microbiology_Biology_?f_ri=2963"},{"id":10574,"name":"Auditory Neuroscience","url":"https://www.academia.edu/Documents/in/Auditory_Neuroscience?f_ri=2963"},{"id":10655,"name":"Scanning Electron Microscopy","url":"https://www.academia.edu/Documents/in/Scanning_Electron_Microscopy?f_ri=2963"},{"id":11228,"name":"Mycology and Plant pathology","url":"https://www.academia.edu/Documents/in/Mycology_and_Plant_pathology?f_ri=2963"},{"id":11267,"name":"Wood Anatomy","url":"https://www.academia.edu/Documents/in/Wood_Anatomy?f_ri=2963"},{"id":11632,"name":"Executive Functions (Cognitive Neuroscience)","url":"https://www.academia.edu/Documents/in/Executive_Functions_Cognitive_Neuroscience_?f_ri=2963"},{"id":11873,"name":"Fish Biology","url":"https://www.academia.edu/Documents/in/Fish_Biology?f_ri=2963"},{"id":12069,"name":"Histology","url":"https://www.academia.edu/Documents/in/Histology?f_ri=2963"},{"id":12808,"name":"Climate change biology","url":"https://www.academia.edu/Documents/in/Climate_change_biology?f_ri=2963"},{"id":13075,"name":"History of Biology","url":"https://www.academia.edu/Documents/in/History_of_Biology?f_ri=2963"},{"id":13827,"name":"Cell Biology","url":"https://www.academia.edu/Documents/in/Cell_Biology?f_ri=2963"},{"id":13828,"name":"Cancer Cell Biology","url":"https://www.academia.edu/Documents/in/Cancer_Cell_Biology?f_ri=2963"},{"id":14076,"name":"Transmission Electron Microscopy","url":"https://www.academia.edu/Documents/in/Transmission_Electron_Microscopy?f_ri=2963"},{"id":14195,"name":"Cancer Biology","url":"https://www.academia.edu/Documents/in/Cancer_Biology?f_ri=2963"},{"id":14490,"name":"Fisheries Biology","url":"https://www.academia.edu/Documents/in/Fisheries_Biology?f_ri=2963"},{"id":14927,"name":"Agriculture (Biology)","url":"https://www.academia.edu/Documents/in/Agriculture_Biology_?f_ri=2963"},{"id":15594,"name":"Systems Neuroscience","url":"https://www.academia.edu/Documents/in/Systems_Neuroscience?f_ri=2963"},{"id":16580,"name":"Plant Physiology (Biology)","url":"https://www.academia.edu/Documents/in/Plant_Physiology_Biology_?f_ri=2963"},{"id":17605,"name":"Malacology (Biology)","url":"https://www.academia.edu/Documents/in/Malacology_Biology_?f_ri=2963"},{"id":17706,"name":"Molluscan Biology","url":"https://www.academia.edu/Documents/in/Molluscan_Biology?f_ri=2963"},{"id":17843,"name":"Landscape ecology (Biology)","url":"https://www.academia.edu/Documents/in/Landscape_ecology_Biology_?f_ri=2963"},{"id":18014,"name":"History of Anatomy","url":"https://www.academia.edu/Documents/in/History_of_Anatomy?f_ri=2963"},{"id":18147,"name":"Bioenergy (Biology)","url":"https://www.academia.edu/Documents/in/Bioenergy_Biology_?f_ri=2963"},{"id":18533,"name":"Confocal Microscopy","url":"https://www.academia.edu/Documents/in/Confocal_Microscopy?f_ri=2963"},{"id":21099,"name":"Cognitive Neuroscience (in Cognition/Cognitive Development)","url":"https://www.academia.edu/Documents/in/Cognitive_Neuroscience_in_Cognition_Cognitive_Development_?f_ri=2963"},{"id":21180,"name":"Chemical Biology","url":"https://www.academia.edu/Documents/in/Chemical_Biology?f_ri=2963"},{"id":21548,"name":"Cognitive Neuroscience","url":"https://www.academia.edu/Documents/in/Cognitive_Neuroscience?f_ri=2963"},{"id":21717,"name":"Forensic Pathology","url":"https://www.academia.edu/Documents/in/Forensic_Pathology?f_ri=2963"},{"id":22308,"name":"Marine Larval Biology \u0026 Ecology","url":"https://www.academia.edu/Documents/in/Marine_Larval_Biology_and_Ecology?f_ri=2963"},{"id":22844,"name":"Insect Molecular Biology","url":"https://www.academia.edu/Documents/in/Insect_Molecular_Biology?f_ri=2963"},{"id":23773,"name":"Avian Biology","url":"https://www.academia.edu/Documents/in/Avian_Biology?f_ri=2963"},{"id":23779,"name":"Population Ecology (Biology)","url":"https://www.academia.edu/Documents/in/Population_Ecology_Biology_?f_ri=2963"},{"id":24373,"name":"Atomic Force Microscopy","url":"https://www.academia.edu/Documents/in/Atomic_Force_Microscopy?f_ri=2963"},{"id":25067,"name":"Neuroscience (Psychology)","url":"https://www.academia.edu/Documents/in/Neuroscience_Psychology_?f_ri=2963"},{"id":25657,"name":"Plant Molecular Biology","url":"https://www.academia.edu/Documents/in/Plant_Molecular_Biology?f_ri=2963"},{"id":25872,"name":"Oral pathology","url":"https://www.academia.edu/Documents/in/Oral_pathology?f_ri=2963"},{"id":26282,"name":"Vascular biology","url":"https://www.academia.edu/Documents/in/Vascular_biology?f_ri=2963"},{"id":26327,"name":"Medicine","url":"https://www.academia.edu/Documents/in/Medicine?f_ri=2963"},{"id":26977,"name":"Theoretical biology","url":"https://www.academia.edu/Documents/in/Theoretical_biology?f_ri=2963"},{"id":27552,"name":"Reproductive Biology","url":"https://www.academia.edu/Documents/in/Reproductive_Biology?f_ri=2963"},{"id":30296,"name":"Cladistics (Systematic Biology)","url":"https://www.academia.edu/Documents/in/Cladistics_Systematic_Biology_?f_ri=2963"},{"id":30601,"name":"Behavioral Neuroscience","url":"https://www.academia.edu/Documents/in/Behavioral_Neuroscience?f_ri=2963"},{"id":31053,"name":"Philosophy of cognitive neuroscience","url":"https://www.academia.edu/Documents/in/Philosophy_of_cognitive_neuroscience?f_ri=2963"},{"id":32511,"name":"Evo-Devo (Developmental Biology)","url":"https://www.academia.edu/Documents/in/Evo-Devo_Developmental_Biology_?f_ri=2963"},{"id":35581,"name":"Clinical Pathology","url":"https://www.academia.edu/Documents/in/Clinical_Pathology?f_ri=2963"},{"id":36325,"name":"Social Cognitive Neuroscience","url":"https://www.academia.edu/Documents/in/Social_Cognitive_Neuroscience?f_ri=2963"},{"id":36520,"name":"Philosophy of Neuroscience","url":"https://www.academia.edu/Documents/in/Philosophy_of_Neuroscience?f_ri=2963"},{"id":37270,"name":"Biology Education","url":"https://www.academia.edu/Documents/in/Biology_Education?f_ri=2963"},{"id":37870,"name":"Organismal Biology","url":"https://www.academia.edu/Documents/in/Organismal_Biology?f_ri=2963"},{"id":37871,"name":"Integrative Biology","url":"https://www.academia.edu/Documents/in/Integrative_Biology?f_ri=2963"},{"id":38408,"name":"Phycology (Biology)","url":"https://www.academia.edu/Documents/in/Phycology_Biology_?f_ri=2963"},{"id":41023,"name":"Social Cognitive Affective Neuroscience","url":"https://www.academia.edu/Documents/in/Social_Cognitive_Affective_Neuroscience?f_ri=2963"},{"id":44297,"name":"Herbal Medicine","url":"https://www.academia.edu/Documents/in/Herbal_Medicine?f_ri=2963"},{"id":45223,"name":"Crustacean Biology","url":"https://www.academia.edu/Documents/in/Crustacean_Biology?f_ri=2963"},{"id":45615,"name":"Plant Anatomy","url":"https://www.academia.edu/Documents/in/Plant_Anatomy?f_ri=2963"},{"id":46578,"name":"Cell and Molecular Biology","url":"https://www.academia.edu/Documents/in/Cell_and_Molecular_Biology?f_ri=2963"},{"id":46901,"name":"Human Biology","url":"https://www.academia.edu/Documents/in/Human_Biology?f_ri=2963"},{"id":46992,"name":"Molecular Biology Cancer","url":"https://www.academia.edu/Documents/in/Molecular_Biology_Cancer?f_ri=2963"},{"id":50531,"name":"Clinical Anatomy","url":"https://www.academia.edu/Documents/in/Clinical_Anatomy?f_ri=2963"},{"id":54381,"name":"Molecular Biology and genetics","url":"https://www.academia.edu/Documents/in/Molecular_Biology_and_genetics?f_ri=2963"},{"id":54589,"name":"Anatomy","url":"https://www.academia.edu/Documents/in/Anatomy?f_ri=2963"},{"id":63067,"name":"Molecular and cellular biology","url":"https://www.academia.edu/Documents/in/Molecular_and_cellular_biology?f_ri=2963"},{"id":64801,"name":"Text-book of Biology","url":"https://www.academia.edu/Documents/in/Text-book_of_Biology?f_ri=2963"},{"id":68927,"name":"Anatomy and Physiology","url":"https://www.academia.edu/Documents/in/Anatomy_and_Physiology?f_ri=2963"},{"id":71260,"name":"Molecular plant pathology","url":"https://www.academia.edu/Documents/in/Molecular_plant_pathology?f_ri=2963"},{"id":76054,"name":"Histology and Cell Biology","url":"https://www.academia.edu/Documents/in/Histology_and_Cell_Biology?f_ri=2963"},{"id":95842,"name":"Ecology and Evolutionary Biology","url":"https://www.academia.edu/Documents/in/Ecology_and_Evolutionary_Biology-1?f_ri=2963"},{"id":96853,"name":"Human Anatomy","url":"https://www.academia.edu/Documents/in/Human_Anatomy?f_ri=2963"},{"id":97142,"name":"Environmental Biology","url":"https://www.academia.edu/Documents/in/Environmental_Biology?f_ri=2963"},{"id":101834,"name":"Cave Biology","url":"https://www.academia.edu/Documents/in/Cave_Biology?f_ri=2963"},{"id":103011,"name":"Plant Biotechnology and Molecular Biology","url":"https://www.academia.edu/Documents/in/Plant_Biotechnology_and_Molecular_Biology?f_ri=2963"},{"id":132282,"name":"Biochemistry and Molecular Biology of Lipids","url":"https://www.academia.edu/Documents/in/Biochemistry_and_Molecular_Biology_of_Lipids?f_ri=2963"},{"id":172797,"name":"Plant morphology and anatomy","url":"https://www.academia.edu/Documents/in/Plant_morphology_and_anatomy?f_ri=2963"},{"id":205560,"name":"Molecular Cell Biology","url":"https://www.academia.edu/Documents/in/Molecular_Cell_Biology?f_ri=2963"},{"id":206504,"name":"General Biology","url":"https://www.academia.edu/Documents/in/General_Biology?f_ri=2963"},{"id":218599,"name":"Plant metabolomics and molecular biology","url":"https://www.academia.edu/Documents/in/Plant_metabolomics_and_molecular_biology?f_ri=2963"},{"id":254762,"name":"Marine Biology and Oceanography","url":"https://www.academia.edu/Documents/in/Marine_Biology_and_Oceanography?f_ri=2963"},{"id":254815,"name":"Freshwater Biology and Limnology","url":"https://www.academia.edu/Documents/in/Freshwater_Biology_and_Limnology?f_ri=2963"},{"id":259191,"name":"Psychology and Neuroscience","url":"https://www.academia.edu/Documents/in/Psychology_and_Neuroscience-1?f_ri=2963"},{"id":285891,"name":"Animal Biology","url":"https://www.academia.edu/Documents/in/Animal_Biology?f_ri=2963"},{"id":290215,"name":"Molecular biology and/or Plant breeding and Genetics of Stress Tolerence","url":"https://www.academia.edu/Documents/in/Molecular_biology_and_or_Plant_breeding_and_Genetics_of_Stress_Tolerence?f_ri=2963"},{"id":362037,"name":"Veterinary Clinical Pathology","url":"https://www.academia.edu/Documents/in/Veterinary_Clinical_Pathology?f_ri=2963"},{"id":365106,"name":"Biology Teacher Education","url":"https://www.academia.edu/Documents/in/Biology_Teacher_Education?f_ri=2963"},{"id":382325,"name":"Internasional Journal of Biology Education","url":"https://www.academia.edu/Documents/in/Internasional_Journal_of_Biology_Education?f_ri=2963"},{"id":473228,"name":"Oral and Maxillofacial Pathology and Microbiology","url":"https://www.academia.edu/Documents/in/Oral_and_Maxillofacial_Pathology_and_Microbiology?f_ri=2963"},{"id":487156,"name":"Critical Neuroscience","url":"https://www.academia.edu/Documents/in/Critical_Neuroscience?f_ri=2963"},{"id":510297,"name":"Neuroscience and brain research","url":"https://www.academia.edu/Documents/in/Neuroscience_and_brain_research?f_ri=2963"},{"id":602219,"name":"Biochemistry and molecular biology","url":"https://www.academia.edu/Documents/in/Biochemistry_and_molecular_biology?f_ri=2963"},{"id":624980,"name":"Plant Pathology","url":"https://www.academia.edu/Documents/in/Plant_Pathology?f_ri=2963"},{"id":643749,"name":"Human Anatomy and Physiology Teaching Methodologies","url":"https://www.academia.edu/Documents/in/Human_Anatomy_and_Physiology_Teaching_Methodologies?f_ri=2963"},{"id":685785,"name":"Science process skill in Biology at Secondary Education","url":"https://www.academia.edu/Documents/in/Science_process_skill_in_Biology_at_Secondary_Education?f_ri=2963"},{"id":741684,"name":"Biology and Educational Sciences","url":"https://www.academia.edu/Documents/in/Biology_and_Educational_Sciences?f_ri=2963"},{"id":902713,"name":"Speech Language Pathology and Audiology","url":"https://www.academia.edu/Documents/in/Speech_Language_Pathology_and_Audiology?f_ri=2963"},{"id":1112835,"name":"E.g. Biology","url":"https://www.academia.edu/Documents/in/E.g._Biology?f_ri=2963"},{"id":1115412,"name":"Vector Biology \u0026 Control","url":"https://www.academia.edu/Documents/in/Vector_Biology_and_Control-1?f_ri=2963"},{"id":1152892,"name":"Speech-language Pathology","url":"https://www.academia.edu/Documents/in/Speech-language_Pathology?f_ri=2963"},{"id":1239755,"name":"Neurosciences","url":"https://www.academia.edu/Documents/in/Neurosciences?f_ri=2963"},{"id":1681026,"name":"Biochemistry and cell biology","url":"https://www.academia.edu/Documents/in/Biochemistry_and_cell_biology?f_ri=2963"}]}, }) } })();</script></ul></li></ul></div></div><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_30857399" data-work_id="30857399" itemscope="itemscope" itemtype="https://schema.org/ScholarlyArticle"><div class="header"><div class="title u-fontSerif u-fs22 u-lineHeight1_3"><a class="u-tcGrayDarkest js-work-link" href="https://www.academia.edu/30857399/The_educational_experiences_of_young_people_with_sickle_cell_disorder_a_commentary_on_the_existing_literature">The educational experiences of young people with sickle cell disorder: a commentary on the existing literature</a></div></div><div class="u-pb4x u-mt3x"><div class="summary u-fs14 u-fw300 u-lineHeight1_5 u-tcGrayDarkest"><div class="summarized">Sickle cell disorder (SCD) is a chronic illness that in England disproportionately affects marginalized ethnic groups, but has yet to feature extensively within educational or disability research. This review of existing literature makes... <a class="more_link u-tcGrayDark u-linkUnstyled" data-container=".work_30857399" data-show=".complete" data-hide=".summarized" data-more-link-behavior="true" href="#">more</a></div><div class="complete hidden">Sickle cell disorder (SCD) is a chronic illness that in England disproportionately affects marginalized ethnic groups, but has yet to feature extensively within educational or disability research. This review of existing literature makes the case for a sustained developmental research programme around SCD, disability and education. There are potentially life‐saving decisions that could be made by teachers in caring for</div></div></div><ul class="InlineList u-ph0x u-fs13"><li class="InlineList-item logged_in_only"><div class="share_on_academia_work_button"><a class="academia_share Button Button--inverseBlue Button--sm js-bookmark-button" data-academia-share="Work/30857399" data-share-source="work_strip" data-spinner="small_white_hide_contents"><i class="fa fa-plus"></i><span class="work-strip-link-text u-ml1x" data-content="button_text">Bookmark</span></a></div></li><li class="InlineList-item"><div class="download"><a id="324b7f7200bb7d7fc009ca4ae818ad06" rel="nofollow" data-download="{"attachment_id":51283866,"asset_id":30857399,"asset_type":"Work","always_allow_download":false,"track":null,"button_location":"work_strip","source":null,"hide_modal":null}" class="Button Button--sm Button--inverseGreen js-download-button prompt_button doc_download" href="https://www.academia.edu/attachments/51283866/download_file?st=MTczMjk4MzU1Miw4LjIyMi4yMDguMTQ2&s=work_strip"><i class="fa fa-arrow-circle-o-down fa-lg"></i><span class="u-textUppercase u-ml1x" data-content="button_text">Download</span></a></div></li><li class="InlineList-item"><ul class="InlineList InlineList--bordered u-ph0x"><li class="InlineList-item InlineList-item--bordered"><span class="InlineList-item-text">by <span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a class="u-tcGrayDark u-fw700" data-has-card-for-user="58729460" href="https://independent.academia.edu/KarlAtkin">Karl Atkin</a><script data-card-contents-for-user="58729460" type="text/json">{"id":58729460,"first_name":"Karl","last_name":"Atkin","domain_name":"independent","page_name":"KarlAtkin","display_name":"Karl Atkin","profile_url":"https://independent.academia.edu/KarlAtkin?f_ri=2963","photo":"/images/s65_no_pic.png"}</script></span></span></li><li class="js-paper-rank-work_30857399 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="30857399"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 30857399, container: ".js-paper-rank-work_30857399", }); });</script></li><li class="js-percentile-work_30857399 InlineList-item InlineList-item--bordered hidden u-tcGrayDark"><span class="percentile-widget hidden"><span class="u-mr2x percentile-widget" style="display: none">•</span><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 30857399; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-percentile-work_30857399"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></li><li class="js-view-count-work_30857399 InlineList-item InlineList-item--bordered hidden"><div><span><span class="js-view-count view-count u-mr2x" data-work-id="30857399"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 30857399; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=30857399]").text(description); $(".js-view-count-work_30857399").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_30857399").removeClass('hidden') })</script></div></li><li class="InlineList-item u-positionRelative" style="max-width: 250px"><div class="u-positionAbsolute" data-has-card-for-ri-list="30857399"><i class="fa fa-tag InlineList-item-icon u-positionRelative"></i>  <a class="InlineList-item-text u-positionRelative">12</a>  </div><span class="InlineList-item-text u-textTruncate u-pl10x"><a class="InlineList-item-text" data-has-card-for-ri="184" href="https://www.academia.edu/Documents/in/Sociology">Sociology</a>, <script data-card-contents-for-ri="184" type="text/json">{"id":184,"name":"Sociology","url":"https://www.academia.edu/Documents/in/Sociology?f_ri=2963","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="940" href="https://www.academia.edu/Documents/in/Social_Work">Social Work</a>, <script data-card-contents-for-ri="940" type="text/json">{"id":940,"name":"Social Work","url":"https://www.academia.edu/Documents/in/Social_Work?f_ri=2963","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="2963" href="https://www.academia.edu/Documents/in/Mathematical_Biology">Mathematical Biology</a>, <script data-card-contents-for-ri="2963" type="text/json">{"id":2963,"name":"Mathematical Biology","url":"https://www.academia.edu/Documents/in/Mathematical_Biology?f_ri=2963","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="7428" href="https://www.academia.edu/Documents/in/Health_Education">Health Education</a><script data-card-contents-for-ri="7428" type="text/json">{"id":7428,"name":"Health Education","url":"https://www.academia.edu/Documents/in/Health_Education?f_ri=2963","nofollow":false}</script></span></li><script>(function(){ if (true) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=30857399]'), work: {"id":30857399,"title":"The educational experiences of young people with sickle cell disorder: a commentary on the existing literature","created_at":"2017-01-10T07:05:44.947-08:00","url":"https://www.academia.edu/30857399/The_educational_experiences_of_young_people_with_sickle_cell_disorder_a_commentary_on_the_existing_literature?f_ri=2963","dom_id":"work_30857399","summary":"Sickle cell disorder (SCD) is a chronic illness that in England disproportionately affects marginalized ethnic groups, but has yet to feature extensively within educational or disability research. This review of existing literature makes the case for a sustained developmental research programme around SCD, disability and education. There are potentially life‐saving decisions that could be made by teachers in caring for","downloadable_attachments":[{"id":51283866,"asset_id":30857399,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":58729460,"first_name":"Karl","last_name":"Atkin","domain_name":"independent","page_name":"KarlAtkin","display_name":"Karl Atkin","profile_url":"https://independent.academia.edu/KarlAtkin?f_ri=2963","photo":"/images/s65_no_pic.png"}],"research_interests":[{"id":184,"name":"Sociology","url":"https://www.academia.edu/Documents/in/Sociology?f_ri=2963","nofollow":false},{"id":940,"name":"Social Work","url":"https://www.academia.edu/Documents/in/Social_Work?f_ri=2963","nofollow":false},{"id":2963,"name":"Mathematical Biology","url":"https://www.academia.edu/Documents/in/Mathematical_Biology?f_ri=2963","nofollow":false},{"id":7428,"name":"Health Education","url":"https://www.academia.edu/Documents/in/Health_Education?f_ri=2963","nofollow":false},{"id":18512,"name":"Inclusive Education","url":"https://www.academia.edu/Documents/in/Inclusive_Education?f_ri=2963"},{"id":22927,"name":"Chronic illness","url":"https://www.academia.edu/Documents/in/Chronic_illness?f_ri=2963"},{"id":25953,"name":"Young People","url":"https://www.academia.edu/Documents/in/Young_People?f_ri=2963"},{"id":98560,"name":"Sickle Cell Disease","url":"https://www.academia.edu/Documents/in/Sickle_Cell_Disease?f_ri=2963"},{"id":413189,"name":"Ethnic Group","url":"https://www.academia.edu/Documents/in/Ethnic_Group?f_ri=2963"},{"id":469110,"name":"Dental Care","url":"https://www.academia.edu/Documents/in/Dental_Care?f_ri=2963"},{"id":811651,"name":"School policy","url":"https://www.academia.edu/Documents/in/School_policy?f_ri=2963"},{"id":1608323,"name":"Disability and Society","url":"https://www.academia.edu/Documents/in/Disability_and_Society?f_ri=2963"}]}, }) } })();</script></ul></li></ul></div></div><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_63131244" data-work_id="63131244" itemscope="itemscope" itemtype="https://schema.org/ScholarlyArticle"><div class="header"><div class="title u-fontSerif u-fs22 u-lineHeight1_3"><a class="u-tcGrayDarkest js-work-link" href="https://www.academia.edu/63131244/Cell_Mechanics">Cell Mechanics</a></div></div><div class="u-pb4x u-mt3x"></div><ul class="InlineList u-ph0x u-fs13"><li class="InlineList-item logged_in_only"><div class="share_on_academia_work_button"><a class="academia_share Button Button--inverseBlue Button--sm js-bookmark-button" data-academia-share="Work/63131244" data-share-source="work_strip" data-spinner="small_white_hide_contents"><i class="fa fa-plus"></i><span class="work-strip-link-text u-ml1x" data-content="button_text">Bookmark</span></a></div></li><li class="InlineList-item"><div class="download"><a id="194d2223a6cb3d64047d964fccf04313" rel="nofollow" data-download="{"attachment_id":75656413,"asset_id":63131244,"asset_type":"Work","always_allow_download":false,"track":null,"button_location":"work_strip","source":null,"hide_modal":null}" class="Button Button--sm Button--inverseGreen js-download-button prompt_button doc_download" href="https://www.academia.edu/attachments/75656413/download_file?st=MTczMjk4MzU1Miw4LjIyMi4yMDguMTQ2&s=work_strip"><i class="fa fa-arrow-circle-o-down fa-lg"></i><span class="u-textUppercase u-ml1x" data-content="button_text">Download</span></a></div></li><li class="InlineList-item"><ul class="InlineList InlineList--bordered u-ph0x"><li class="InlineList-item InlineList-item--bordered"><span class="InlineList-item-text">by <span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a class="u-tcGrayDark u-fw700" data-has-card-for-user="41975132" href="https://polito.academia.edu/lpreziosi">luigi preziosi</a><script data-card-contents-for-user="41975132" type="text/json">{"id":41975132,"first_name":"luigi","last_name":"preziosi","domain_name":"polito","page_name":"lpreziosi","display_name":"luigi preziosi","profile_url":"https://polito.academia.edu/lpreziosi?f_ri=2963","photo":"https://0.academia-photos.com/41975132/11566700/12899679/s65_luigi.preziosi.jpg"}</script></span></span></li><li class="js-paper-rank-work_63131244 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="63131244"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 63131244, container: ".js-paper-rank-work_63131244", }); });</script></li><li class="js-percentile-work_63131244 InlineList-item InlineList-item--bordered hidden u-tcGrayDark"><span class="percentile-widget hidden"><span class="u-mr2x percentile-widget" style="display: none">•</span><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 63131244; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-percentile-work_63131244"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></li><li class="js-view-count-work_63131244 InlineList-item InlineList-item--bordered hidden"><div><span><span class="js-view-count view-count u-mr2x" data-work-id="63131244"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 63131244; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=63131244]").text(description); $(".js-view-count-work_63131244").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_63131244").removeClass('hidden') })</script></div></li><li class="InlineList-item u-positionRelative" style="max-width: 250px"><div class="u-positionAbsolute" data-has-card-for-ri-list="63131244"><i class="fa fa-tag InlineList-item-icon u-positionRelative"></i>  <a class="InlineList-item-text u-positionRelative">7</a>  </div><span class="InlineList-item-text u-textTruncate u-pl9x"><a class="InlineList-item-text" data-has-card-for-ri="502" href="https://www.academia.edu/Documents/in/Biophysics">Biophysics</a>, <script data-card-contents-for-ri="502" type="text/json">{"id":502,"name":"Biophysics","url":"https://www.academia.edu/Documents/in/Biophysics?f_ri=2963","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="1131" href="https://www.academia.edu/Documents/in/Biomedical_Engineering">Biomedical Engineering</a>, <script data-card-contents-for-ri="1131" type="text/json">{"id":1131,"name":"Biomedical Engineering","url":"https://www.academia.edu/Documents/in/Biomedical_Engineering?f_ri=2963","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="2963" href="https://www.academia.edu/Documents/in/Mathematical_Biology">Mathematical Biology</a>, <script data-card-contents-for-ri="2963" type="text/json">{"id":2963,"name":"Mathematical Biology","url":"https://www.academia.edu/Documents/in/Mathematical_Biology?f_ri=2963","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="47884" href="https://www.academia.edu/Documents/in/Biological_Sciences">Biological Sciences</a><script data-card-contents-for-ri="47884" type="text/json">{"id":47884,"name":"Biological Sciences","url":"https://www.academia.edu/Documents/in/Biological_Sciences?f_ri=2963","nofollow":false}</script></span></li><script>(function(){ if (true) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=63131244]'), work: {"id":63131244,"title":"Cell Mechanics","created_at":"2021-12-03T08:47:10.581-08:00","url":"https://www.academia.edu/63131244/Cell_Mechanics?f_ri=2963","dom_id":"work_63131244","summary":null,"downloadable_attachments":[{"id":75656413,"asset_id":63131244,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":41975132,"first_name":"luigi","last_name":"preziosi","domain_name":"polito","page_name":"lpreziosi","display_name":"luigi preziosi","profile_url":"https://polito.academia.edu/lpreziosi?f_ri=2963","photo":"https://0.academia-photos.com/41975132/11566700/12899679/s65_luigi.preziosi.jpg"}],"research_interests":[{"id":502,"name":"Biophysics","url":"https://www.academia.edu/Documents/in/Biophysics?f_ri=2963","nofollow":false},{"id":1131,"name":"Biomedical Engineering","url":"https://www.academia.edu/Documents/in/Biomedical_Engineering?f_ri=2963","nofollow":false},{"id":2963,"name":"Mathematical Biology","url":"https://www.academia.edu/Documents/in/Mathematical_Biology?f_ri=2963","nofollow":false},{"id":47884,"name":"Biological Sciences","url":"https://www.academia.edu/Documents/in/Biological_Sciences?f_ri=2963","nofollow":false},{"id":80414,"name":"Mathematical Sciences","url":"https://www.academia.edu/Documents/in/Mathematical_Sciences?f_ri=2963"},{"id":161240,"name":"Recherche","url":"https://www.academia.edu/Documents/in/Recherche?f_ri=2963"},{"id":3763225,"name":"Medical and Health Sciences","url":"https://www.academia.edu/Documents/in/Medical_and_Health_Sciences?f_ri=2963"}]}, }) } })();</script></ul></li></ul></div></div><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_1611666" data-work_id="1611666" itemscope="itemscope" itemtype="https://schema.org/ScholarlyArticle"><div class="header"><div class="title u-fontSerif u-fs22 u-lineHeight1_3"><a class="u-tcGrayDarkest js-work-link" href="https://www.academia.edu/1611666/Social_Insects_as_Models_in_Epidemiology_Establishing_the_Foundation_for_an_Interdisciplinary_Approach_to_Disease_and_Sociality">Social Insects as Models in Epidemiology: Establishing the Foundation for an Interdisciplinary Approach to Disease and Sociality</a></div></div><div class="u-pb4x u-mt3x"></div><ul class="InlineList u-ph0x u-fs13"><li class="InlineList-item logged_in_only"><div class="share_on_academia_work_button"><a class="academia_share Button Button--inverseBlue Button--sm js-bookmark-button" data-academia-share="Work/1611666" data-share-source="work_strip" data-spinner="small_white_hide_contents"><i class="fa fa-plus"></i><span class="work-strip-link-text u-ml1x" data-content="button_text">Bookmark</span></a></div></li><li class="InlineList-item"><div class="download"><a id="5ec7dadedbbd2a7cbe50316ae41d9124" rel="nofollow" data-download="{"attachment_id":15708246,"asset_id":1611666,"asset_type":"Work","always_allow_download":false,"track":null,"button_location":"work_strip","source":null,"hide_modal":null}" class="Button Button--sm Button--inverseGreen js-download-button prompt_button doc_download" href="https://www.academia.edu/attachments/15708246/download_file?st=MTczMjk4MzU1Miw4LjIyMi4yMDguMTQ2&s=work_strip"><i class="fa fa-arrow-circle-o-down fa-lg"></i><span class="u-textUppercase u-ml1x" data-content="button_text">Download</span></a></div></li><li class="InlineList-item"><ul class="InlineList InlineList--bordered u-ph0x"><li class="InlineList-item InlineList-item--bordered"><span class="InlineList-item-text">by <span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a class="u-tcGrayDark u-fw700" data-has-card-for-user="42174" href="https://rutgers.academia.edu/NinaHFefferman">Nina H. Fefferman</a><script data-card-contents-for-user="42174" type="text/json">{"id":42174,"first_name":"Nina H.","last_name":"Fefferman","domain_name":"rutgers","page_name":"NinaHFefferman","display_name":"Nina H. Fefferman","profile_url":"https://rutgers.academia.edu/NinaHFefferman?f_ri=2963","photo":"https://0.academia-photos.com/42174/13686/12804/s65_nina_h..fefferman.jpg"}</script></span></span></li><li class="js-paper-rank-work_1611666 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="1611666"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 1611666, container: ".js-paper-rank-work_1611666", }); });</script></li><li class="js-percentile-work_1611666 InlineList-item InlineList-item--bordered hidden u-tcGrayDark"><span class="percentile-widget hidden"><span class="u-mr2x percentile-widget" style="display: none">•</span><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 1611666; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-percentile-work_1611666"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></li><li class="js-view-count-work_1611666 InlineList-item InlineList-item--bordered hidden"><div><span><span class="js-view-count view-count u-mr2x" data-work-id="1611666"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 1611666; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=1611666]").text(description); $(".js-view-count-work_1611666").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_1611666").removeClass('hidden') })</script></div></li><li class="InlineList-item u-positionRelative" style="max-width: 250px"><div class="u-positionAbsolute" data-has-card-for-ri-list="1611666"><i class="fa fa-tag InlineList-item-icon u-positionRelative"></i>  <a class="InlineList-item-text u-positionRelative">4</a>  </div><span class="InlineList-item-text u-textTruncate u-pl9x"><a class="InlineList-item-text" data-has-card-for-ri="1088" href="https://www.academia.edu/Documents/in/Infectious_disease_epidemiology">Infectious disease epidemiology</a>, <script data-card-contents-for-ri="1088" type="text/json">{"id":1088,"name":"Infectious disease epidemiology","url":"https://www.academia.edu/Documents/in/Infectious_disease_epidemiology?f_ri=2963","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="1089" href="https://www.academia.edu/Documents/in/Social_epidemiology">Social epidemiology</a>, <script data-card-contents-for-ri="1089" type="text/json">{"id":1089,"name":"Social epidemiology","url":"https://www.academia.edu/Documents/in/Social_epidemiology?f_ri=2963","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="2963" href="https://www.academia.edu/Documents/in/Mathematical_Biology">Mathematical Biology</a>, <script data-card-contents-for-ri="2963" type="text/json">{"id":2963,"name":"Mathematical Biology","url":"https://www.academia.edu/Documents/in/Mathematical_Biology?f_ri=2963","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="9066" href="https://www.academia.edu/Documents/in/Social_insects">Social insects</a><script data-card-contents-for-ri="9066" type="text/json">{"id":9066,"name":"Social insects","url":"https://www.academia.edu/Documents/in/Social_insects?f_ri=2963","nofollow":false}</script></span></li><script>(function(){ if (true) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=1611666]'), work: {"id":1611666,"title":"Social Insects as Models in Epidemiology: Establishing the Foundation for an Interdisciplinary Approach to Disease and Sociality","created_at":"2012-06-01T14:19:51.577-07:00","url":"https://www.academia.edu/1611666/Social_Insects_as_Models_in_Epidemiology_Establishing_the_Foundation_for_an_Interdisciplinary_Approach_to_Disease_and_Sociality?f_ri=2963","dom_id":"work_1611666","summary":null,"downloadable_attachments":[{"id":15708246,"asset_id":1611666,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":42174,"first_name":"Nina H.","last_name":"Fefferman","domain_name":"rutgers","page_name":"NinaHFefferman","display_name":"Nina H. Fefferman","profile_url":"https://rutgers.academia.edu/NinaHFefferman?f_ri=2963","photo":"https://0.academia-photos.com/42174/13686/12804/s65_nina_h..fefferman.jpg"}],"research_interests":[{"id":1088,"name":"Infectious disease epidemiology","url":"https://www.academia.edu/Documents/in/Infectious_disease_epidemiology?f_ri=2963","nofollow":false},{"id":1089,"name":"Social epidemiology","url":"https://www.academia.edu/Documents/in/Social_epidemiology?f_ri=2963","nofollow":false},{"id":2963,"name":"Mathematical Biology","url":"https://www.academia.edu/Documents/in/Mathematical_Biology?f_ri=2963","nofollow":false},{"id":9066,"name":"Social insects","url":"https://www.academia.edu/Documents/in/Social_insects?f_ri=2963","nofollow":false}]}, }) } })();</script></ul></li></ul></div></div><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_4232110" data-work_id="4232110" itemscope="itemscope" itemtype="https://schema.org/ScholarlyArticle"><div class="header"><div class="title u-fontSerif u-fs22 u-lineHeight1_3"><a class="u-tcGrayDarkest js-work-link" href="https://www.academia.edu/4232110/Global_stability_in_some_ecological_models_of_commensalism_between_two_species">Global stability in some ecological models of commensalism between two species</a></div></div><div class="u-pb4x u-mt3x"><div class="summary u-fs14 u-fw300 u-lineHeight1_5 u-tcGrayDarkest"><div class="summarized">"""Lyapunov functions for some mathematical models of ecological commensalism between two species are introduced. Global stability of the unique positive equilibrium is thereby established. Keyword: Models of ecological commensalism;... <a class="more_link u-tcGrayDark u-linkUnstyled" data-container=".work_4232110" data-show=".complete" data-hide=".summarized" data-more-link-behavior="true" href="#">more</a></div><div class="complete hidden">"""Lyapunov functions for some mathematical models of ecological commensalism between two species are introduced. Global stability of the unique positive equilibrium is thereby established. <br /> <br />Keyword: Models of ecological commensalism; Lyapunov's asymptotic stability theorem; Global stability"""</div></div></div><ul class="InlineList u-ph0x u-fs13"><li class="InlineList-item logged_in_only"><div class="share_on_academia_work_button"><a class="academia_share Button Button--inverseBlue Button--sm js-bookmark-button" data-academia-share="Work/4232110" data-share-source="work_strip" data-spinner="small_white_hide_contents"><i class="fa fa-plus"></i><span class="work-strip-link-text u-ml1x" data-content="button_text">Bookmark</span></a></div></li><li class="InlineList-item"><div class="download"><a id="be06a4fb2d20f749c32302a52d9a7862" rel="nofollow" data-download="{"attachment_id":31745622,"asset_id":4232110,"asset_type":"Work","always_allow_download":false,"track":null,"button_location":"work_strip","source":null,"hide_modal":null}" class="Button Button--sm Button--inverseGreen js-download-button prompt_button doc_download" href="https://www.academia.edu/attachments/31745622/download_file?st=MTczMjk4MzU1Miw4LjIyMi4yMDguMTQ2&s=work_strip"><i class="fa fa-arrow-circle-o-down fa-lg"></i><span class="u-textUppercase u-ml1x" data-content="button_text">Download</span></a></div></li><li class="InlineList-item"><ul class="InlineList InlineList--bordered u-ph0x"><li class="InlineList-item InlineList-item--bordered"><span class="InlineList-item-text">by <span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a class="u-tcGrayDark u-fw700" data-has-card-for-user="2121744" href="https://independent.academia.edu/leoncruz82">Cruz Vargas-De-León</a><script data-card-contents-for-user="2121744" type="text/json">{"id":2121744,"first_name":"Cruz","last_name":"Vargas-De-León","domain_name":"independent","page_name":"leoncruz82","display_name":"Cruz Vargas-De-León","profile_url":"https://independent.academia.edu/leoncruz82?f_ri=2963","photo":"https://0.academia-photos.com/2121744/688983/19867024/s65_cruz.vargas-de-le_n.png"}</script></span></span></li><li class="js-paper-rank-work_4232110 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="4232110"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 4232110, container: ".js-paper-rank-work_4232110", }); });</script></li><li class="js-percentile-work_4232110 InlineList-item InlineList-item--bordered hidden u-tcGrayDark"><span class="percentile-widget hidden"><span class="u-mr2x percentile-widget" style="display: none">•</span><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 4232110; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-percentile-work_4232110"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></li><li class="js-view-count-work_4232110 InlineList-item InlineList-item--bordered hidden"><div><span><span class="js-view-count view-count u-mr2x" data-work-id="4232110"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 4232110; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=4232110]").text(description); $(".js-view-count-work_4232110").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_4232110").removeClass('hidden') })</script></div></li><li class="InlineList-item u-positionRelative" style="max-width: 250px"><div class="u-positionAbsolute" data-has-card-for-ri-list="4232110"><i class="fa fa-tag InlineList-item-icon u-positionRelative"></i>  <a class="InlineList-item-text u-positionRelative">12</a>  </div><span class="InlineList-item-text u-textTruncate u-pl10x"><a class="InlineList-item-text" data-has-card-for-ri="2963" href="https://www.academia.edu/Documents/in/Mathematical_Biology">Mathematical Biology</a>, <script data-card-contents-for-ri="2963" type="text/json">{"id":2963,"name":"Mathematical Biology","url":"https://www.academia.edu/Documents/in/Mathematical_Biology?f_ri=2963","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="5590" href="https://www.academia.edu/Documents/in/Biomathematics">Biomathematics</a>, <script data-card-contents-for-ri="5590" type="text/json">{"id":5590,"name":"Biomathematics","url":"https://www.academia.edu/Documents/in/Biomathematics?f_ri=2963","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="15396" href="https://www.academia.edu/Documents/in/Mathematical_Ecology">Mathematical Ecology</a>, <script data-card-contents-for-ri="15396" type="text/json">{"id":15396,"name":"Mathematical Ecology","url":"https://www.academia.edu/Documents/in/Mathematical_Ecology?f_ri=2963","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="16521" href="https://www.academia.edu/Documents/in/Mathematical_biology_Mathematics_">Mathematical biology (Mathematics)</a><script data-card-contents-for-ri="16521" type="text/json">{"id":16521,"name":"Mathematical biology (Mathematics)","url":"https://www.academia.edu/Documents/in/Mathematical_biology_Mathematics_?f_ri=2963","nofollow":false}</script></span></li><script>(function(){ if (true) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=4232110]'), work: {"id":4232110,"title":"Global stability in some ecological models of commensalism between two species","created_at":"2013-08-13T09:14:11.516-07:00","url":"https://www.academia.edu/4232110/Global_stability_in_some_ecological_models_of_commensalism_between_two_species?f_ri=2963","dom_id":"work_4232110","summary":"\"\"\"Lyapunov functions for some mathematical models of ecological commensalism between two species are introduced. Global stability of the unique positive equilibrium is thereby established.\r\n\r\nKeyword: Models of ecological commensalism; Lyapunov's asymptotic stability theorem; Global stability\"\"\"","downloadable_attachments":[{"id":31745622,"asset_id":4232110,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":2121744,"first_name":"Cruz","last_name":"Vargas-De-León","domain_name":"independent","page_name":"leoncruz82","display_name":"Cruz Vargas-De-León","profile_url":"https://independent.academia.edu/leoncruz82?f_ri=2963","photo":"https://0.academia-photos.com/2121744/688983/19867024/s65_cruz.vargas-de-le_n.png"}],"research_interests":[{"id":2963,"name":"Mathematical Biology","url":"https://www.academia.edu/Documents/in/Mathematical_Biology?f_ri=2963","nofollow":false},{"id":5590,"name":"Biomathematics","url":"https://www.academia.edu/Documents/in/Biomathematics?f_ri=2963","nofollow":false},{"id":15396,"name":"Mathematical Ecology","url":"https://www.academia.edu/Documents/in/Mathematical_Ecology?f_ri=2963","nofollow":false},{"id":16521,"name":"Mathematical biology (Mathematics)","url":"https://www.academia.edu/Documents/in/Mathematical_biology_Mathematics_?f_ri=2963","nofollow":false},{"id":67038,"name":"Lyapunov Stability Theory","url":"https://www.academia.edu/Documents/in/Lyapunov_Stability_Theory?f_ri=2963"},{"id":103214,"name":"Lotka Volterra","url":"https://www.academia.edu/Documents/in/Lotka_Volterra?f_ri=2963"},{"id":141894,"name":"Lotka-Volterra","url":"https://www.academia.edu/Documents/in/Lotka-Volterra?f_ri=2963"},{"id":420906,"name":"Lyapunov functions","url":"https://www.academia.edu/Documents/in/Lyapunov_functions?f_ri=2963"},{"id":543165,"name":"direct Lyapunov method","url":"https://www.academia.edu/Documents/in/direct_Lyapunov_method?f_ri=2963"},{"id":543171,"name":"Lyapunov function","url":"https://www.academia.edu/Documents/in/Lyapunov_function?f_ri=2963"},{"id":543197,"name":"Second Method of Lyapunov","url":"https://www.academia.edu/Documents/in/Second_Method_of_Lyapunov?f_ri=2963"},{"id":544875,"name":"Lyapunov techniques","url":"https://www.academia.edu/Documents/in/Lyapunov_techniques?f_ri=2963"}]}, }) } })();</script></ul></li></ul></div></div><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_26166123" data-work_id="26166123" itemscope="itemscope" itemtype="https://schema.org/ScholarlyArticle"><div class="header"><div class="title u-fontSerif u-fs22 u-lineHeight1_3"><a class="u-tcGrayDarkest js-work-link" href="https://www.academia.edu/26166123/Richard_Levins">Richard Levins</a></div></div><div class="u-pb4x u-mt3x"><div class="summary u-fs14 u-fw300 u-lineHeight1_5 u-tcGrayDarkest"><div class="summarized">Richard "Dick" Levins (June 1, 1930 – January 19, 2016) was an ex-tropical farmer turned ecologist, a population geneticist, biomathematician, mathematical ecologist, and philosopher of science who had researched diversity in human... <a class="more_link u-tcGrayDark u-linkUnstyled" data-container=".work_26166123" data-show=".complete" data-hide=".summarized" data-more-link-behavior="true" href="#">more</a></div><div class="complete hidden">Richard "Dick" Levins (June 1, 1930 – January 19, 2016) was an ex-tropical farmer turned ecologist, a population geneticist, biomathematician, mathematical ecologist, and philosopher of science who had researched diversity in human populations. Until his death, Levins was a university professor at the Harvard T.H. Chan School of Public Health and a long-time political activist. He was best known for his work on evolution and complexity in changing environments and on metapopulations.<br /><br />Levins' writing and speaking is extremely condensed.  This, combined with his Marxism, has made his analyses less well-known than those of some other ecologists and evolutionists who were adept at popularization.  One story of his Chicago years is that, in order to understand his lectures, his graduate students each needed to attend Levins' courses three times: the first time to acclimate themselves to the speed of his delivery and the difficulty of his mathematics; the second to get the basic ideas down; and the third to pick up his subtleties and profundities.<br /><br />Levins also had written on philosophical issues in biology and modelling. One of his influential articles is "The Strategy of Model Building in Population Biology". He has influenced a number of contemporary philosophers of biology.[citation needed] Levins often boasted publicly that he was a 'fourth generation Marxist' and often had said that the methodology in his Evolution in Changing Environments was based upon the introduction to Marx's Grundrisse, the rough draft of Das Kapital. With the evolutionary geneticist Richard Lewontin (1929–), Levins had written a number of articles on methodology, philosophy, and social implications of biology. Many of these are collected in The Dialectical Biologist. In 2007, the duo published a second thematic collection of essays titled Biology Under the Influence: Dialectical Essays on Ecology, Agriculture, and Health.<br /><br />Also with Lewontin, Levins had co-authored a number of satirical articles criticizing sociobiology, systems modeling in ecology, and other topics under the pseudonym Isadore Nabi. Levins and Lewontin managed to place a ridiculous biography of Nabi and his achievements in American Men of Science, thereby showing how little editorial care and fact-checking work went on in that respected reference work.</div></div></div><ul class="InlineList u-ph0x u-fs13"><li class="InlineList-item logged_in_only"><div class="share_on_academia_work_button"><a class="academia_share Button Button--inverseBlue Button--sm js-bookmark-button" data-academia-share="Work/26166123" data-share-source="work_strip" data-spinner="small_white_hide_contents"><i class="fa fa-plus"></i><span class="work-strip-link-text u-ml1x" data-content="button_text">Bookmark</span></a></div></li><li class="InlineList-item"><div class="download"><a id="87727b037c73eba4bde9bd86df4e30e1" rel="nofollow" data-download="{"attachment_id":46493733,"asset_id":26166123,"asset_type":"Work","always_allow_download":false,"track":null,"button_location":"work_strip","source":null,"hide_modal":null}" class="Button Button--sm Button--inverseGreen js-download-button prompt_button doc_download" href="https://www.academia.edu/attachments/46493733/download_file?st=MTczMjk4MzU1Miw4LjIyMi4yMDguMTQ2&s=work_strip"><i class="fa fa-arrow-circle-o-down fa-lg"></i><span class="u-textUppercase u-ml1x" data-content="button_text">Download</span></a></div></li><li class="InlineList-item"><ul class="InlineList InlineList--bordered u-ph0x"><li class="InlineList-item InlineList-item--bordered"><span class="InlineList-item-text">by <span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a class="u-tcGrayDark u-fw700" data-has-card-for-user="94942" href="https://hsph-harvard.academia.edu/MaynardClark">Maynard S Clark</a><script data-card-contents-for-user="94942" type="text/json">{"id":94942,"first_name":"Maynard","last_name":"Clark","domain_name":"hsph-harvard","page_name":"MaynardClark","display_name":"Maynard S Clark","profile_url":"https://hsph-harvard.academia.edu/MaynardClark?f_ri=2963","photo":"https://0.academia-photos.com/94942/26308/24263/s65_maynard.clark.jpeg"}</script></span></span></li><li class="js-paper-rank-work_26166123 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="26166123"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 26166123, container: ".js-paper-rank-work_26166123", }); });</script></li><li class="js-percentile-work_26166123 InlineList-item InlineList-item--bordered hidden u-tcGrayDark"><span class="percentile-widget hidden"><span class="u-mr2x percentile-widget" style="display: none">•</span><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 26166123; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-percentile-work_26166123"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></li><li class="js-view-count-work_26166123 InlineList-item InlineList-item--bordered hidden"><div><span><span class="js-view-count view-count u-mr2x" data-work-id="26166123"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 26166123; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=26166123]").text(description); $(".js-view-count-work_26166123").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_26166123").removeClass('hidden') })</script></div></li><li class="InlineList-item u-positionRelative" style="max-width: 250px"><div class="u-positionAbsolute" data-has-card-for-ri-list="26166123"><i class="fa fa-tag InlineList-item-icon u-positionRelative"></i>  <a class="InlineList-item-text u-positionRelative">14</a>  </div><span class="InlineList-item-text u-textTruncate u-pl10x"><a class="InlineList-item-text" data-has-card-for-ri="1698" href="https://www.academia.edu/Documents/in/Marxism">Marxism</a>, <script data-card-contents-for-ri="1698" type="text/json">{"id":1698,"name":"Marxism","url":"https://www.academia.edu/Documents/in/Marxism?f_ri=2963","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="2963" href="https://www.academia.edu/Documents/in/Mathematical_Biology">Mathematical Biology</a>, <script data-card-contents-for-ri="2963" type="text/json">{"id":2963,"name":"Mathematical Biology","url":"https://www.academia.edu/Documents/in/Mathematical_Biology?f_ri=2963","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="10806" href="https://www.academia.edu/Documents/in/Marxist_theory">Marxist theory</a>, <script data-card-contents-for-ri="10806" type="text/json">{"id":10806,"name":"Marxist theory","url":"https://www.academia.edu/Documents/in/Marxist_theory?f_ri=2963","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="16521" href="https://www.academia.edu/Documents/in/Mathematical_biology_Mathematics_">Mathematical biology (Mathematics)</a><script data-card-contents-for-ri="16521" type="text/json">{"id":16521,"name":"Mathematical biology (Mathematics)","url":"https://www.academia.edu/Documents/in/Mathematical_biology_Mathematics_?f_ri=2963","nofollow":false}</script></span></li><script>(function(){ if (true) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=26166123]'), work: {"id":26166123,"title":"Richard Levins","created_at":"2016-06-14T19:52:22.321-07:00","url":"https://www.academia.edu/26166123/Richard_Levins?f_ri=2963","dom_id":"work_26166123","summary":"Richard \"Dick\" Levins (June 1, 1930 – January 19, 2016) was an ex-tropical farmer turned ecologist, a population geneticist, biomathematician, mathematical ecologist, and philosopher of science who had researched diversity in human populations. Until his death, Levins was a university professor at the Harvard T.H. Chan School of Public Health and a long-time political activist. He was best known for his work on evolution and complexity in changing environments and on metapopulations.\n\nLevins' writing and speaking is extremely condensed. This, combined with his Marxism, has made his analyses less well-known than those of some other ecologists and evolutionists who were adept at popularization. One story of his Chicago years is that, in order to understand his lectures, his graduate students each needed to attend Levins' courses three times: the first time to acclimate themselves to the speed of his delivery and the difficulty of his mathematics; the second to get the basic ideas down; and the third to pick up his subtleties and profundities.\n\nLevins also had written on philosophical issues in biology and modelling. One of his influential articles is \"The Strategy of Model Building in Population Biology\". He has influenced a number of contemporary philosophers of biology.[citation needed] Levins often boasted publicly that he was a 'fourth generation Marxist' and often had said that the methodology in his Evolution in Changing Environments was based upon the introduction to Marx's Grundrisse, the rough draft of Das Kapital. With the evolutionary geneticist Richard Lewontin (1929–), Levins had written a number of articles on methodology, philosophy, and social implications of biology. Many of these are collected in The Dialectical Biologist. In 2007, the duo published a second thematic collection of essays titled Biology Under the Influence: Dialectical Essays on Ecology, Agriculture, and Health.\n\nAlso with Lewontin, Levins had co-authored a number of satirical articles criticizing sociobiology, systems modeling in ecology, and other topics under the pseudonym Isadore Nabi. Levins and Lewontin managed to place a ridiculous biography of Nabi and his achievements in American Men of Science, thereby showing how little editorial care and fact-checking work went on in that respected reference work.","downloadable_attachments":[{"id":46493733,"asset_id":26166123,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":94942,"first_name":"Maynard","last_name":"Clark","domain_name":"hsph-harvard","page_name":"MaynardClark","display_name":"Maynard S Clark","profile_url":"https://hsph-harvard.academia.edu/MaynardClark?f_ri=2963","photo":"https://0.academia-photos.com/94942/26308/24263/s65_maynard.clark.jpeg"}],"research_interests":[{"id":1698,"name":"Marxism","url":"https://www.academia.edu/Documents/in/Marxism?f_ri=2963","nofollow":false},{"id":2963,"name":"Mathematical Biology","url":"https://www.academia.edu/Documents/in/Mathematical_Biology?f_ri=2963","nofollow":false},{"id":10806,"name":"Marxist theory","url":"https://www.academia.edu/Documents/in/Marxist_theory?f_ri=2963","nofollow":false},{"id":16521,"name":"Mathematical biology (Mathematics)","url":"https://www.academia.edu/Documents/in/Mathematical_biology_Mathematics_?f_ri=2963","nofollow":false},{"id":19653,"name":"History of Political Activism","url":"https://www.academia.edu/Documents/in/History_of_Political_Activism?f_ri=2963"},{"id":43923,"name":"Social Movements and Political Action","url":"https://www.academia.edu/Documents/in/Social_Movements_and_Political_Action?f_ri=2963"},{"id":70724,"name":"Neo-Marxism","url":"https://www.academia.edu/Documents/in/Neo-Marxism?f_ri=2963"},{"id":101663,"name":"Mathematical Modelling of Biological Systems","url":"https://www.academia.edu/Documents/in/Mathematical_Modelling_of_Biological_Systems?f_ri=2963"},{"id":135891,"name":"Political activism","url":"https://www.academia.edu/Documents/in/Political_activism?f_ri=2963"},{"id":182165,"name":"Cultural and Political Activism of the 1960s and 1970s","url":"https://www.academia.edu/Documents/in/Cultural_and_Political_Activism_of_the_1960s_and_1970s?f_ri=2963"},{"id":240473,"name":"Mathematical Modelling in Biology, Ecology \u0026 Epidemics","url":"https://www.academia.edu/Documents/in/Mathematical_Modelling_in_Biology_Ecology_and_Epidemics?f_ri=2963"},{"id":842794,"name":"Applied Mathematics and Mathematical Biology","url":"https://www.academia.edu/Documents/in/Applied_Mathematics_and_Mathematical_Biology?f_ri=2963"},{"id":2480258,"name":"Harvard School of Public Health","url":"https://www.academia.edu/Documents/in/Harvard_School_of_Public_Health?f_ri=2963"},{"id":2480259,"name":"Harvard T.H. Chan School of Public Health","url":"https://www.academia.edu/Documents/in/Harvard_T.H._Chan_School_of_Public_Health?f_ri=2963"}]}, }) } })();</script></ul></li></ul></div></div><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_72861143 coauthored" data-work_id="72861143" itemscope="itemscope" itemtype="https://schema.org/ScholarlyArticle"><div class="header"><div class="title u-fontSerif u-fs22 u-lineHeight1_3"><a class="u-tcGrayDarkest js-work-link" href="https://www.academia.edu/72861143/Analysis_and_optimal_control_of_an_HIV_model_based_on_CD4_count">Analysis and optimal control of an HIV model based on CD4 count</a></div></div><div class="u-pb4x u-mt3x"><div class="summary u-fs14 u-fw300 u-lineHeight1_5 u-tcGrayDarkest"><div class="summarized">A non-linear mechanistic model for the transmission dynamics of HIV/AIDS is developed and analyzed. The model classified the infected individuals based on their CD4 count level. Furthermore, education campaign, voluntary testing and... <a class="more_link u-tcGrayDark u-linkUnstyled" data-container=".work_72861143" data-show=".complete" data-hide=".summarized" data-more-link-behavior="true" href="#">more</a></div><div class="complete hidden">A non-linear mechanistic model for the transmission dynamics of HIV/AIDS is developed and analyzed. The model classified the infected individuals based on their CD4 count level. Furthermore, education campaign, voluntary testing and counseling and treatment are considered as intervention strategies for controlling the disease. The analysis of the model reveals that imperfect public enlightenment campaign can induce backward bifurcation. It has been shown that when public enlightenment campaign is [Formula: see text] effective, the disease free equilibrium is globally asymptotically stable for [Formula: see text], whereas for [Formula: see text] the global stability of the endemic equilibrium is proved only in a special case. Time dependent controls of the intervention strategies mentioned above are incorporated into the model and the optimal control strategies with minimal implementation cost are identified. In addition, cost effectiveness analysis in the form of incremental cost effectiveness ratio is carried-out to identify the most cost effective strategies. The results suggest that out of the three non dominated strategies, the strategy of educating the newly entrants only or combination of newly entrants and susceptible individuals is very cost effective using per capita GDP of Nigeria as at 2018. However, the choice of which strategy to implement depends on budgetary allocation and resource availability.</div></div></div><ul class="InlineList u-ph0x u-fs13"><li class="InlineList-item logged_in_only"><div class="share_on_academia_work_button"><a class="academia_share Button Button--inverseBlue Button--sm js-bookmark-button" data-academia-share="Work/72861143" data-share-source="work_strip" data-spinner="small_white_hide_contents"><i class="fa fa-plus"></i><span class="work-strip-link-text u-ml1x" data-content="button_text">Bookmark</span></a></div></li><li class="InlineList-item"><ul class="InlineList InlineList--bordered u-ph0x"><li class="InlineList-item InlineList-item--bordered"><span class="InlineList-item-text">by <span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a class="u-tcGrayDark u-fw700" data-has-card-for-user="132556717" href="https://gomsu.academia.edu/ADAMUISHAKU">ADAMU ISHAKU</a><script data-card-contents-for-user="132556717" type="text/json">{"id":132556717,"first_name":"ADAMU","last_name":"ISHAKU","domain_name":"gomsu","page_name":"ADAMUISHAKU","display_name":"ADAMU ISHAKU","profile_url":"https://gomsu.academia.edu/ADAMUISHAKU?f_ri=2963","photo":"/images/s65_no_pic.png"}</script></span></span><span class="u-displayInlineBlock InlineList-item-text"> and <span class="u-textDecorationUnderline u-clickable InlineList-item-text js-work-more-authors-72861143">+2</span><div class="hidden js-additional-users-72861143"><div><span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a href="https://independent.academia.edu/ShuaibuAbdullahi10">Shuaibu Abdullahi</a></span></div><div><span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a href="https://independent.academia.edu/NafiuHussaini1">Nafiu Hussaini</a></span></div></div></span><script>(function(){ var popoverSettings = { el: $('.js-work-more-authors-72861143'), placement: 'bottom', hide_delay: 200, html: true, content: function(){ return $('.js-additional-users-72861143').html(); } } new HoverPopover(popoverSettings); })();</script></li><li class="js-paper-rank-work_72861143 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="72861143"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 72861143, container: ".js-paper-rank-work_72861143", }); });</script></li><li class="js-percentile-work_72861143 InlineList-item InlineList-item--bordered hidden u-tcGrayDark"><span class="percentile-widget hidden"><span class="u-mr2x percentile-widget" style="display: none">•</span><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 72861143; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-percentile-work_72861143"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></li><li class="js-view-count-work_72861143 InlineList-item InlineList-item--bordered hidden"><div><span><span class="js-view-count view-count u-mr2x" data-work-id="72861143"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 72861143; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=72861143]").text(description); $(".js-view-count-work_72861143").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_72861143").removeClass('hidden') })</script></div></li><li class="InlineList-item u-positionRelative" style="max-width: 250px"><div class="u-positionAbsolute" data-has-card-for-ri-list="72861143"><i class="fa fa-tag InlineList-item-icon u-positionRelative"></i>  <a class="InlineList-item-text u-positionRelative">3</a>  </div><span class="InlineList-item-text u-textTruncate u-pl9x"><a class="InlineList-item-text" data-has-card-for-ri="2963" href="https://www.academia.edu/Documents/in/Mathematical_Biology">Mathematical Biology</a>, <script data-card-contents-for-ri="2963" type="text/json">{"id":2963,"name":"Mathematical Biology","url":"https://www.academia.edu/Documents/in/Mathematical_Biology?f_ri=2963","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="47884" href="https://www.academia.edu/Documents/in/Biological_Sciences">Biological Sciences</a>, <script data-card-contents-for-ri="47884" type="text/json">{"id":47884,"name":"Biological Sciences","url":"https://www.academia.edu/Documents/in/Biological_Sciences?f_ri=2963","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="80414" href="https://www.academia.edu/Documents/in/Mathematical_Sciences">Mathematical Sciences</a><script data-card-contents-for-ri="80414" type="text/json">{"id":80414,"name":"Mathematical Sciences","url":"https://www.academia.edu/Documents/in/Mathematical_Sciences?f_ri=2963","nofollow":false}</script></span></li><script>(function(){ if (true) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=72861143]'), work: {"id":72861143,"title":"Analysis and optimal control of an HIV model based on CD4 count","created_at":"2022-03-02T21:25:19.499-08:00","url":"https://www.academia.edu/72861143/Analysis_and_optimal_control_of_an_HIV_model_based_on_CD4_count?f_ri=2963","dom_id":"work_72861143","summary":"A non-linear mechanistic model for the transmission dynamics of HIV/AIDS is developed and analyzed. The model classified the infected individuals based on their CD4 count level. Furthermore, education campaign, voluntary testing and counseling and treatment are considered as intervention strategies for controlling the disease. The analysis of the model reveals that imperfect public enlightenment campaign can induce backward bifurcation. It has been shown that when public enlightenment campaign is [Formula: see text] effective, the disease free equilibrium is globally asymptotically stable for [Formula: see text], whereas for [Formula: see text] the global stability of the endemic equilibrium is proved only in a special case. Time dependent controls of the intervention strategies mentioned above are incorporated into the model and the optimal control strategies with minimal implementation cost are identified. In addition, cost effectiveness analysis in the form of incremental cost effectiveness ratio is carried-out to identify the most cost effective strategies. The results suggest that out of the three non dominated strategies, the strategy of educating the newly entrants only or combination of newly entrants and susceptible individuals is very cost effective using per capita GDP of Nigeria as at 2018. However, the choice of which strategy to implement depends on budgetary allocation and resource availability.","downloadable_attachments":[],"ordered_authors":[{"id":132556717,"first_name":"ADAMU","last_name":"ISHAKU","domain_name":"gomsu","page_name":"ADAMUISHAKU","display_name":"ADAMU ISHAKU","profile_url":"https://gomsu.academia.edu/ADAMUISHAKU?f_ri=2963","photo":"/images/s65_no_pic.png"},{"id":97595651,"first_name":"Shuaibu","last_name":"Abdullahi","domain_name":"independent","page_name":"ShuaibuAbdullahi10","display_name":"Shuaibu Abdullahi","profile_url":"https://independent.academia.edu/ShuaibuAbdullahi10?f_ri=2963","photo":"/images/s65_no_pic.png"},{"id":329183727,"first_name":"Nafiu","last_name":"Hussaini","domain_name":"independent","page_name":"NafiuHussaini1","display_name":"Nafiu Hussaini","profile_url":"https://independent.academia.edu/NafiuHussaini1?f_ri=2963","photo":"/images/s65_no_pic.png"}],"research_interests":[{"id":2963,"name":"Mathematical Biology","url":"https://www.academia.edu/Documents/in/Mathematical_Biology?f_ri=2963","nofollow":false},{"id":47884,"name":"Biological Sciences","url":"https://www.academia.edu/Documents/in/Biological_Sciences?f_ri=2963","nofollow":false},{"id":80414,"name":"Mathematical Sciences","url":"https://www.academia.edu/Documents/in/Mathematical_Sciences?f_ri=2963","nofollow":false}]}, }) } })();</script></ul></li></ul></div></div><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_11966862" data-work_id="11966862" itemscope="itemscope" itemtype="https://schema.org/ScholarlyArticle"><div class="header"><div class="title u-fontSerif u-fs22 u-lineHeight1_3"><a class="u-tcGrayDarkest js-work-link" href="https://www.academia.edu/11966862/Adaptive_dynamics_a_framework_to_model_evolution_in_the_ecological_theatre">Adaptive dynamics: a framework to model evolution in the ecological theatre</a></div></div><div class="u-pb4x u-mt3x"></div><ul class="InlineList u-ph0x u-fs13"><li class="InlineList-item logged_in_only"><div class="share_on_academia_work_button"><a class="academia_share Button Button--inverseBlue Button--sm js-bookmark-button" data-academia-share="Work/11966862" data-share-source="work_strip" data-spinner="small_white_hide_contents"><i class="fa fa-plus"></i><span class="work-strip-link-text u-ml1x" data-content="button_text">Bookmark</span></a></div></li><li class="InlineList-item"><div class="download"><a id="8491cca189e805b35e33faeb7047f44d" rel="nofollow" data-download="{"attachment_id":46419420,"asset_id":11966862,"asset_type":"Work","always_allow_download":false,"track":null,"button_location":"work_strip","source":null,"hide_modal":null}" class="Button Button--sm Button--inverseGreen js-download-button prompt_button doc_download" href="https://www.academia.edu/attachments/46419420/download_file?st=MTczMjk4MzU1Miw4LjIyMi4yMDguMTQ2&s=work_strip"><i class="fa fa-arrow-circle-o-down fa-lg"></i><span class="u-textUppercase u-ml1x" data-content="button_text">Download</span></a></div></li><li class="InlineList-item"><ul class="InlineList InlineList--bordered u-ph0x"><li class="InlineList-item InlineList-item--bordered"><span class="InlineList-item-text">by <span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a class="u-tcGrayDark u-fw700" data-has-card-for-user="29704184" href="https://elte-hu.academia.edu/GezaMeszena">Géza Meszéna</a><script data-card-contents-for-user="29704184" type="text/json">{"id":29704184,"first_name":"Géza","last_name":"Meszéna","domain_name":"elte-hu","page_name":"GezaMeszena","display_name":"Géza Meszéna","profile_url":"https://elte-hu.academia.edu/GezaMeszena?f_ri=2963","photo":"/images/s65_no_pic.png"}</script></span></span></li><li class="js-paper-rank-work_11966862 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="11966862"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 11966862, container: ".js-paper-rank-work_11966862", }); });</script></li><li class="js-percentile-work_11966862 InlineList-item InlineList-item--bordered hidden u-tcGrayDark"><span class="percentile-widget hidden"><span class="u-mr2x percentile-widget" style="display: none">•</span><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 11966862; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-percentile-work_11966862"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></li><li class="js-view-count-work_11966862 InlineList-item InlineList-item--bordered hidden"><div><span><span class="js-view-count view-count u-mr2x" data-work-id="11966862"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 11966862; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=11966862]").text(description); $(".js-view-count-work_11966862").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_11966862").removeClass('hidden') })</script></div></li><li class="InlineList-item u-positionRelative" style="max-width: 250px"><div class="u-positionAbsolute" data-has-card-for-ri-list="11966862"><i class="fa fa-tag InlineList-item-icon u-positionRelative"></i>  <a class="InlineList-item-text u-positionRelative">8</a>  </div><span class="InlineList-item-text u-textTruncate u-pl9x"><a class="InlineList-item-text" data-has-card-for-ri="2963" href="https://www.academia.edu/Documents/in/Mathematical_Biology">Mathematical Biology</a>, <script data-card-contents-for-ri="2963" type="text/json">{"id":2963,"name":"Mathematical Biology","url":"https://www.academia.edu/Documents/in/Mathematical_Biology?f_ri=2963","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="9846" href="https://www.academia.edu/Documents/in/Ecology">Ecology</a>, <script data-card-contents-for-ri="9846" type="text/json">{"id":9846,"name":"Ecology","url":"https://www.academia.edu/Documents/in/Ecology?f_ri=2963","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="47884" href="https://www.academia.edu/Documents/in/Biological_Sciences">Biological Sciences</a>, <script data-card-contents-for-ri="47884" type="text/json">{"id":47884,"name":"Biological Sciences","url":"https://www.academia.edu/Documents/in/Biological_Sciences?f_ri=2963","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="70123" href="https://www.academia.edu/Documents/in/Adaptive_Dynamics">Adaptive Dynamics</a><script data-card-contents-for-ri="70123" type="text/json">{"id":70123,"name":"Adaptive Dynamics","url":"https://www.academia.edu/Documents/in/Adaptive_Dynamics?f_ri=2963","nofollow":false}</script></span></li><script>(function(){ if (true) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=11966862]'), work: {"id":11966862,"title":"Adaptive dynamics: a framework to model evolution in the ecological theatre","created_at":"2015-04-15T23:03:53.582-07:00","url":"https://www.academia.edu/11966862/Adaptive_dynamics_a_framework_to_model_evolution_in_the_ecological_theatre?f_ri=2963","dom_id":"work_11966862","summary":null,"downloadable_attachments":[{"id":46419420,"asset_id":11966862,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":29704184,"first_name":"Géza","last_name":"Meszéna","domain_name":"elte-hu","page_name":"GezaMeszena","display_name":"Géza Meszéna","profile_url":"https://elte-hu.academia.edu/GezaMeszena?f_ri=2963","photo":"/images/s65_no_pic.png"}],"research_interests":[{"id":2963,"name":"Mathematical Biology","url":"https://www.academia.edu/Documents/in/Mathematical_Biology?f_ri=2963","nofollow":false},{"id":9846,"name":"Ecology","url":"https://www.academia.edu/Documents/in/Ecology?f_ri=2963","nofollow":false},{"id":47884,"name":"Biological Sciences","url":"https://www.academia.edu/Documents/in/Biological_Sciences?f_ri=2963","nofollow":false},{"id":70123,"name":"Adaptive Dynamics","url":"https://www.academia.edu/Documents/in/Adaptive_Dynamics?f_ri=2963","nofollow":false},{"id":80414,"name":"Mathematical Sciences","url":"https://www.academia.edu/Documents/in/Mathematical_Sciences?f_ri=2963"},{"id":191815,"name":"Biological evolution","url":"https://www.academia.edu/Documents/in/Biological_evolution?f_ri=2963"},{"id":577933,"name":"Genetic variation","url":"https://www.academia.edu/Documents/in/Genetic_variation?f_ri=2963"},{"id":702621,"name":"Genetic Fitness","url":"https://www.academia.edu/Documents/in/Genetic_Fitness?f_ri=2963"}]}, }) } })();</script></ul></li></ul></div></div><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_4088859" data-work_id="4088859" itemscope="itemscope" itemtype="https://schema.org/ScholarlyArticle"><div class="header"><div class="title u-fontSerif u-fs22 u-lineHeight1_3"><a class="u-tcGrayDarkest js-work-link" href="https://www.academia.edu/4088859/Elementary_Arithmetic_in_Base_7">Elementary Arithmetic in Base 7</a></div></div><div class="u-pb4x u-mt3x"></div><ul class="InlineList u-ph0x u-fs13"><li class="InlineList-item logged_in_only"><div class="share_on_academia_work_button"><a class="academia_share Button Button--inverseBlue Button--sm js-bookmark-button" data-academia-share="Work/4088859" data-share-source="work_strip" data-spinner="small_white_hide_contents"><i class="fa fa-plus"></i><span class="work-strip-link-text u-ml1x" data-content="button_text">Bookmark</span></a></div></li><li class="InlineList-item"><div class="download"><a id="8ce618ba1387b43afe53ef3237c9a3bc" rel="nofollow" data-download="{"attachment_id":33805141,"asset_id":4088859,"asset_type":"Work","always_allow_download":false,"track":null,"button_location":"work_strip","source":null,"hide_modal":null}" class="Button Button--sm Button--inverseGreen js-download-button prompt_button doc_download" href="https://www.academia.edu/attachments/33805141/download_file?st=MTczMjk4MzU1Miw4LjIyMi4yMDguMTQ2&s=work_strip"><i class="fa fa-arrow-circle-o-down fa-lg"></i><span class="u-textUppercase u-ml1x" data-content="button_text">Download</span></a></div></li><li class="InlineList-item"><ul class="InlineList InlineList--bordered u-ph0x"><li class="InlineList-item InlineList-item--bordered"><span class="InlineList-item-text">by <span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a class="u-tcGrayDark u-fw700" data-has-card-for-user="1930006" href="https://independent.academia.edu/paolodipasquale">Paolo Di Pasquale</a><script data-card-contents-for-user="1930006" type="text/json">{"id":1930006,"first_name":"Paolo","last_name":"Di Pasquale","domain_name":"independent","page_name":"paolodipasquale","display_name":"Paolo Di Pasquale","profile_url":"https://independent.academia.edu/paolodipasquale?f_ri=2963","photo":"https://0.academia-photos.com/1930006/651321/807219/s65_paolo.di_pasquale.jpg"}</script></span></span></li><li class="js-paper-rank-work_4088859 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="4088859"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 4088859, container: ".js-paper-rank-work_4088859", }); });</script></li><li class="js-percentile-work_4088859 InlineList-item InlineList-item--bordered hidden u-tcGrayDark"><span class="percentile-widget hidden"><span class="u-mr2x percentile-widget" style="display: none">•</span><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 4088859; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-percentile-work_4088859"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></li><li class="js-view-count-work_4088859 InlineList-item InlineList-item--bordered hidden"><div><span><span class="js-view-count view-count u-mr2x" data-work-id="4088859"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 4088859; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=4088859]").text(description); $(".js-view-count-work_4088859").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_4088859").removeClass('hidden') })</script></div></li><li class="InlineList-item u-positionRelative" style="max-width: 250px"><div class="u-positionAbsolute" data-has-card-for-ri-list="4088859"><i class="fa fa-tag InlineList-item-icon u-positionRelative"></i>  <a class="InlineList-item-text u-positionRelative">123</a>  </div><span class="InlineList-item-text u-textTruncate u-pl11x"><a class="InlineList-item-text" data-has-card-for-ri="48" href="https://www.academia.edu/Documents/in/Engineering">Engineering</a>, <script data-card-contents-for-ri="48" type="text/json">{"id":48,"name":"Engineering","url":"https://www.academia.edu/Documents/in/Engineering?f_ri=2963","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="72" href="https://www.academia.edu/Documents/in/Chemical_Engineering">Chemical Engineering</a>, <script data-card-contents-for-ri="72" type="text/json">{"id":72,"name":"Chemical Engineering","url":"https://www.academia.edu/Documents/in/Chemical_Engineering?f_ri=2963","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="237" href="https://www.academia.edu/Documents/in/Cognitive_Science">Cognitive Science</a>, <script data-card-contents-for-ri="237" type="text/json">{"id":237,"name":"Cognitive Science","url":"https://www.academia.edu/Documents/in/Cognitive_Science?f_ri=2963","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="300" href="https://www.academia.edu/Documents/in/Mathematics">Mathematics</a><script data-card-contents-for-ri="300" type="text/json">{"id":300,"name":"Mathematics","url":"https://www.academia.edu/Documents/in/Mathematics?f_ri=2963","nofollow":false}</script></span></li><script>(function(){ if (true) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=4088859]'), work: {"id":4088859,"title":"Elementary Arithmetic in Base 7","created_at":"2013-07-23T02:49:41.099-07:00","url":"https://www.academia.edu/4088859/Elementary_Arithmetic_in_Base_7?f_ri=2963","dom_id":"work_4088859","summary":null,"downloadable_attachments":[{"id":33805141,"asset_id":4088859,"asset_type":"Work","always_allow_download":false},{"id":31614237,"asset_id":4088859,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":1930006,"first_name":"Paolo","last_name":"Di Pasquale","domain_name":"independent","page_name":"paolodipasquale","display_name":"Paolo Di Pasquale","profile_url":"https://independent.academia.edu/paolodipasquale?f_ri=2963","photo":"https://0.academia-photos.com/1930006/651321/807219/s65_paolo.di_pasquale.jpg"}],"research_interests":[{"id":48,"name":"Engineering","url":"https://www.academia.edu/Documents/in/Engineering?f_ri=2963","nofollow":false},{"id":72,"name":"Chemical Engineering","url":"https://www.academia.edu/Documents/in/Chemical_Engineering?f_ri=2963","nofollow":false},{"id":237,"name":"Cognitive Science","url":"https://www.academia.edu/Documents/in/Cognitive_Science?f_ri=2963","nofollow":false},{"id":300,"name":"Mathematics","url":"https://www.academia.edu/Documents/in/Mathematics?f_ri=2963","nofollow":false},{"id":301,"name":"Number Theory","url":"https://www.academia.edu/Documents/in/Number_Theory?f_ri=2963"},{"id":302,"name":"Analytic Number Theory","url":"https://www.academia.edu/Documents/in/Analytic_Number_Theory?f_ri=2963"},{"id":303,"name":"Algebraic Number Theory","url":"https://www.academia.edu/Documents/in/Algebraic_Number_Theory?f_ri=2963"},{"id":305,"name":"Applied Mathematics","url":"https://www.academia.edu/Documents/in/Applied_Mathematics?f_ri=2963"},{"id":310,"name":"Demography","url":"https://www.academia.edu/Documents/in/Demography?f_ri=2963"},{"id":312,"name":"Optimization (Mathematical Programming)","url":"https://www.academia.edu/Documents/in/Optimization_Mathematical_Programming_?f_ri=2963"},{"id":318,"name":"Mathematical Physics","url":"https://www.academia.edu/Documents/in/Mathematical_Physics?f_ri=2963"},{"id":323,"name":"Information Theory (Mathematics)","url":"https://www.academia.edu/Documents/in/Information_Theory_Mathematics_?f_ri=2963"},{"id":324,"name":"Mathematics of Cryptography","url":"https://www.academia.edu/Documents/in/Mathematics_of_Cryptography?f_ri=2963"},{"id":329,"name":"Algebra","url":"https://www.academia.edu/Documents/in/Algebra?f_ri=2963"},{"id":360,"name":"Logic And Foundations Of Mathematics","url":"https://www.academia.edu/Documents/in/Logic_And_Foundations_Of_Mathematics?f_ri=2963"},{"id":367,"name":"Analysis (Mathematics)","url":"https://www.academia.edu/Documents/in/Analysis_Mathematics_?f_ri=2963"},{"id":400,"name":"Earth Sciences","url":"https://www.academia.edu/Documents/in/Earth_Sciences?f_ri=2963"},{"id":422,"name":"Computer Science","url":"https://www.academia.edu/Documents/in/Computer_Science?f_ri=2963"},{"id":465,"name":"Artificial Intelligence","url":"https://www.academia.edu/Documents/in/Artificial_Intelligence?f_ri=2963"},{"id":475,"name":"Algebraic (Symbolic) Computation","url":"https://www.academia.edu/Documents/in/Algebraic_Symbolic_Computation?f_ri=2963"},{"id":498,"name":"Physics","url":"https://www.academia.edu/Documents/in/Physics?f_ri=2963"},{"id":503,"name":"Theoretical Physics","url":"https://www.academia.edu/Documents/in/Theoretical_Physics?f_ri=2963"},{"id":511,"name":"Materials Science","url":"https://www.academia.edu/Documents/in/Materials_Science?f_ri=2963"},{"id":518,"name":"Quantum Physics","url":"https://www.academia.edu/Documents/in/Quantum_Physics?f_ri=2963"},{"id":523,"name":"Chemistry","url":"https://www.academia.edu/Documents/in/Chemistry?f_ri=2963"},{"id":524,"name":"Analytical Chemistry","url":"https://www.academia.edu/Documents/in/Analytical_Chemistry?f_ri=2963"},{"id":532,"name":"Physical Chemistry","url":"https://www.academia.edu/Documents/in/Physical_Chemistry?f_ri=2963"},{"id":586,"name":"Health Sciences","url":"https://www.academia.edu/Documents/in/Health_Sciences?f_ri=2963"},{"id":595,"name":"Medical Sciences","url":"https://www.academia.edu/Documents/in/Medical_Sciences?f_ri=2963"},{"id":671,"name":"Music","url":"https://www.academia.edu/Documents/in/Music?f_ri=2963"},{"id":724,"name":"Economics","url":"https://www.academia.edu/Documents/in/Economics?f_ri=2963"},{"id":803,"name":"Philosophy","url":"https://www.academia.edu/Documents/in/Philosophy?f_ri=2963"},{"id":806,"name":"Philosophy of Mind","url":"https://www.academia.edu/Documents/in/Philosophy_of_Mind?f_ri=2963"},{"id":807,"name":"Philosophy Of Language","url":"https://www.academia.edu/Documents/in/Philosophy_Of_Language?f_ri=2963"},{"id":821,"name":"Philosophy of Science","url":"https://www.academia.edu/Documents/in/Philosophy_of_Science?f_ri=2963"},{"id":855,"name":"Philosophy of Technology","url":"https://www.academia.edu/Documents/in/Philosophy_of_Technology?f_ri=2963"},{"id":888,"name":"Cosmology (Physics)","url":"https://www.academia.edu/Documents/in/Cosmology_Physics_?f_ri=2963"},{"id":892,"name":"Statistics","url":"https://www.academia.edu/Documents/in/Statistics?f_ri=2963"},{"id":915,"name":"Art History","url":"https://www.academia.edu/Documents/in/Art_History?f_ri=2963"},{"id":922,"name":"Education","url":"https://www.academia.edu/Documents/in/Education?f_ri=2963"},{"id":1011,"name":"Library Science","url":"https://www.academia.edu/Documents/in/Library_Science?f_ri=2963"},{"id":1018,"name":"Music Technology","url":"https://www.academia.edu/Documents/in/Music_Technology?f_ri=2963"},{"id":1085,"name":"Epidemiology","url":"https://www.academia.edu/Documents/in/Epidemiology?f_ri=2963"},{"id":1236,"name":"Art","url":"https://www.academia.edu/Documents/in/Art?f_ri=2963"},{"id":1237,"name":"Social Sciences","url":"https://www.academia.edu/Documents/in/Social_Sciences?f_ri=2963"},{"id":1386,"name":"Art Theory","url":"https://www.academia.edu/Documents/in/Art_Theory?f_ri=2963"},{"id":1736,"name":"Science Education","url":"https://www.academia.edu/Documents/in/Science_Education?f_ri=2963"},{"id":2019,"name":"Aristotle","url":"https://www.academia.edu/Documents/in/Aristotle?f_ri=2963"},{"id":2084,"name":"History of Mathematics","url":"https://www.academia.edu/Documents/in/History_of_Mathematics?f_ri=2963"},{"id":2418,"name":"Literature","url":"https://www.academia.edu/Documents/in/Literature?f_ri=2963"},{"id":2509,"name":"Philosophy Of Mathematics","url":"https://www.academia.edu/Documents/in/Philosophy_Of_Mathematics?f_ri=2963"},{"id":2559,"name":"Philosophy of Education","url":"https://www.academia.edu/Documents/in/Philosophy_of_Education?f_ri=2963"},{"id":2731,"name":"Mathematics Education","url":"https://www.academia.edu/Documents/in/Mathematics_Education?f_ri=2963"},{"id":2963,"name":"Mathematical Biology","url":"https://www.academia.edu/Documents/in/Mathematical_Biology?f_ri=2963"},{"id":3051,"name":"Contemporary Art","url":"https://www.academia.edu/Documents/in/Contemporary_Art?f_ri=2963"},{"id":3058,"name":"Biostatistics","url":"https://www.academia.edu/Documents/in/Biostatistics?f_ri=2963"},{"id":3723,"name":"History of Science","url":"https://www.academia.edu/Documents/in/History_of_Science?f_ri=2963"},{"id":3853,"name":"Optimization (Mathematics)","url":"https://www.academia.edu/Documents/in/Optimization_Mathematics_?f_ri=2963"},{"id":4486,"name":"Political Science","url":"https://www.academia.edu/Documents/in/Political_Science?f_ri=2963"},{"id":4950,"name":"Modern Art","url":"https://www.academia.edu/Documents/in/Modern_Art?f_ri=2963"},{"id":5290,"name":"Philosophy of Art","url":"https://www.academia.edu/Documents/in/Philosophy_of_Art?f_ri=2963"},{"id":5292,"name":"Teaching Middle-Years Math Methods","url":"https://www.academia.edu/Documents/in/Teaching_Middle-Years_Math_Methods?f_ri=2963"},{"id":5463,"name":"Performance Art","url":"https://www.academia.edu/Documents/in/Performance_Art?f_ri=2963"},{"id":5960,"name":"Continental Philosophy","url":"https://www.academia.edu/Documents/in/Continental_Philosophy?f_ri=2963"},{"id":6177,"name":"Modeling","url":"https://www.academia.edu/Documents/in/Modeling?f_ri=2963"},{"id":6728,"name":"Philosophy Of Law","url":"https://www.academia.edu/Documents/in/Philosophy_Of_Law?f_ri=2963"},{"id":6779,"name":"Science","url":"https://www.academia.edu/Documents/in/Science?f_ri=2963"},{"id":8014,"name":"Life Sciences","url":"https://www.academia.edu/Documents/in/Life_Sciences?f_ri=2963"},{"id":8694,"name":"Science Fiction","url":"https://www.academia.edu/Documents/in/Science_Fiction?f_ri=2963"},{"id":8927,"name":"Art and Science","url":"https://www.academia.edu/Documents/in/Art_and_Science?f_ri=2963"},{"id":9038,"name":"Digital Signal Processing","url":"https://www.academia.edu/Documents/in/Digital_Signal_Processing?f_ri=2963"},{"id":9721,"name":"Music Aesthetics","url":"https://www.academia.edu/Documents/in/Music_Aesthetics?f_ri=2963"},{"id":10598,"name":"String Theory","url":"https://www.academia.edu/Documents/in/String_Theory?f_ri=2963"},{"id":12022,"name":"Numerical Analysis","url":"https://www.academia.edu/Documents/in/Numerical_Analysis?f_ri=2963"},{"id":12474,"name":"Algebraic Combinatorics","url":"https://www.academia.edu/Documents/in/Algebraic_Combinatorics?f_ri=2963"},{"id":13640,"name":"Computer Arithmetic","url":"https://www.academia.edu/Documents/in/Computer_Arithmetic?f_ri=2963"},{"id":13966,"name":"History of Art","url":"https://www.academia.edu/Documents/in/History_of_Art?f_ri=2963"},{"id":16682,"name":"Mathematical Modelling","url":"https://www.academia.edu/Documents/in/Mathematical_Modelling?f_ri=2963"},{"id":17442,"name":"Mathematical Logic","url":"https://www.academia.edu/Documents/in/Mathematical_Logic?f_ri=2963"},{"id":17546,"name":"Contemporary Music","url":"https://www.academia.edu/Documents/in/Contemporary_Music?f_ri=2963"},{"id":17969,"name":"Health Policy","url":"https://www.academia.edu/Documents/in/Health_Policy?f_ri=2963"},{"id":18494,"name":"Metaphysics Of Number","url":"https://www.academia.edu/Documents/in/Metaphysics_Of_Number?f_ri=2963"},{"id":19997,"name":"Pure Mathematics","url":"https://www.academia.edu/Documents/in/Pure_Mathematics?f_ri=2963"},{"id":20178,"name":"Conceptual Art","url":"https://www.academia.edu/Documents/in/Conceptual_Art?f_ri=2963"},{"id":20254,"name":"Elementary Number Theory","url":"https://www.academia.edu/Documents/in/Elementary_Number_Theory?f_ri=2963"},{"id":20372,"name":"Neurology of giftedness in art/music comb.w/science \u0026/or math","url":"https://www.academia.edu/Documents/in/Neurology_of_giftedness_in_art_music_comb.w_science_and_or_math?f_ri=2963"},{"id":22878,"name":"Ancient Greek History","url":"https://www.academia.edu/Documents/in/Ancient_Greek_History?f_ri=2963"},{"id":27305,"name":"Computational Mathematics","url":"https://www.academia.edu/Documents/in/Computational_Mathematics?f_ri=2963"},{"id":27801,"name":"Mathematics Teacher Education","url":"https://www.academia.edu/Documents/in/Mathematics_Teacher_Education?f_ri=2963"},{"id":29972,"name":"Linear Algebra","url":"https://www.academia.edu/Documents/in/Linear_Algebra?f_ri=2963"},{"id":37345,"name":"Discrete Mathematics","url":"https://www.academia.edu/Documents/in/Discrete_Mathematics?f_ri=2963"},{"id":37606,"name":"Arithmetic Geometry","url":"https://www.academia.edu/Documents/in/Arithmetic_Geometry?f_ri=2963"},{"id":40259,"name":"Writing in Mathematics Education: Writing to Learn Approach, Writing Activities for Learning MAth","url":"https://www.academia.edu/Documents/in/Writing_in_Mathematics_Education_Writing_to_Learn_Approach_Writing_Activities_for_Learning_MAth?f_ri=2963"},{"id":48636,"name":"Simulation","url":"https://www.academia.edu/Documents/in/Simulation?f_ri=2963"},{"id":53292,"name":"Programming","url":"https://www.academia.edu/Documents/in/Programming?f_ri=2963"},{"id":67525,"name":"Existentialism","url":"https://www.academia.edu/Documents/in/Existentialism?f_ri=2963"},{"id":70951,"name":"K-12 STEM (Science, Technology, Engineering and Math) education and outreach","url":"https://www.academia.edu/Documents/in/K-12_STEM_Science_Technology_Engineering_and_Math_education_and_outreach?f_ri=2963"},{"id":83471,"name":"Health Services","url":"https://www.academia.edu/Documents/in/Health_Services?f_ri=2963"},{"id":113473,"name":"Art and Design","url":"https://www.academia.edu/Documents/in/Art_and_Design?f_ri=2963"},{"id":131903,"name":"Arithmetic","url":"https://www.academia.edu/Documents/in/Arithmetic?f_ri=2963"},{"id":157353,"name":"Communications theory, signal processing, applied mathematics to communications systems, control theory, electromagnetism, microwave theory, electronics, computings and operational systems, antenna theory","url":"https://www.academia.edu/Documents/in/Communications_theory_signal_processing_applied_mathematics_to_communications_systems_control_the?f_ri=2963"},{"id":166529,"name":"Tutoring Math and Science","url":"https://www.academia.edu/Documents/in/Tutoring_Math_and_Science?f_ri=2963"},{"id":193513,"name":"Computer Assisted Composition","url":"https://www.academia.edu/Documents/in/Computer_Assisted_Composition?f_ri=2963"},{"id":204903,"name":"Music and Mathematics","url":"https://www.academia.edu/Documents/in/Music_and_Mathematics?f_ri=2963"},{"id":215769,"name":"Math and Science","url":"https://www.academia.edu/Documents/in/Math_and_Science?f_ri=2963"},{"id":256867,"name":"Computer Security, Cryptography, Number theory","url":"https://www.academia.edu/Documents/in/Computer_Security_Cryptography_Number_theory?f_ri=2963"},{"id":258324,"name":"Applied Math, Cryptology","url":"https://www.academia.edu/Documents/in/Applied_Math_Cryptology?f_ri=2963"},{"id":280461,"name":"Higgs physics","url":"https://www.academia.edu/Documents/in/Higgs_physics?f_ri=2963"},{"id":321147,"name":"Self Concept","url":"https://www.academia.edu/Documents/in/Self_Concept?f_ri=2963"},{"id":354417,"name":"Dynamic Systems and Control","url":"https://www.academia.edu/Documents/in/Dynamic_Systems_and_Control?f_ri=2963"},{"id":444238,"name":"Music and philosophy","url":"https://www.academia.edu/Documents/in/Music_and_philosophy?f_ri=2963"},{"id":522782,"name":"Information Technology and System Integration","url":"https://www.academia.edu/Documents/in/Information_Technology_and_System_Integration?f_ri=2963"},{"id":613846,"name":"Optimization Technology","url":"https://www.academia.edu/Documents/in/Optimization_Technology?f_ri=2963"},{"id":680257,"name":"System Modeling and Simulation","url":"https://www.academia.edu/Documents/in/System_Modeling_and_Simulation?f_ri=2963"},{"id":922047,"name":"Sound Spatialization","url":"https://www.academia.edu/Documents/in/Sound_Spatialization?f_ri=2963"},{"id":931375,"name":"Integration Technology of Automation Systems","url":"https://www.academia.edu/Documents/in/Integration_Technology_of_Automation_Systems?f_ri=2963"},{"id":971438,"name":"Impact of Factors Like OF GENDER","url":"https://www.academia.edu/Documents/in/Impact_of_Factors_Like_OF_GENDER?f_ri=2963"},{"id":971442,"name":"SOCIO ECONOMIC BACK GROUND OF PARENTS","url":"https://www.academia.edu/Documents/in/SOCIO_ECONOMIC_BACK_GROUND_OF_PARENTS?f_ri=2963"},{"id":971444,"name":"ATTITUDE TOWARDS MATH","url":"https://www.academia.edu/Documents/in/ATTITUDE_TOWARDS_MATH?f_ri=2963"},{"id":971446,"name":"CURRICULUM AND MATH ANXIETY ON ACHIEVEMENT OF MATHEMATICS IN MIDDLE AND SENIOR SCHOOL CHILDREN","url":"https://www.academia.edu/Documents/in/CURRICULUM_AND_MATH_ANXIETY_ON_ACHIEVEMENT_OF_MATHEMATICS_IN_MIDDLE_AND_SENIOR_SCHOOL_CHILDREN?f_ri=2963"},{"id":1007649,"name":"Theoretical High Energy Physics : Supersymmetry","url":"https://www.academia.edu/Documents/in/Theoretical_High_Energy_Physics_Supersymmetry?f_ri=2963"},{"id":1007652,"name":"Cosmological Phase Transition","url":"https://www.academia.edu/Documents/in/Cosmological_Phase_Transition?f_ri=2963"},{"id":2214362,"name":"Math","url":"https://www.academia.edu/Documents/in/Math?f_ri=2963"}]}, }) } })();</script></ul></li></ul></div></div><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_4568574" data-work_id="4568574" itemscope="itemscope" itemtype="https://schema.org/ScholarlyArticle"><div class="header"><div class="title u-fontSerif u-fs22 u-lineHeight1_3"><a class="u-tcGrayDarkest js-work-link" href="https://www.academia.edu/4568574/Computational_methods_in_noncoding_RNA_research">Computational methods in noncoding RNA research</a></div></div><div class="u-pb4x u-mt3x"><div class="summary u-fs14 u-fw300 u-lineHeight1_5 u-tcGrayDarkest"><div class="summarized">Non protein-coding RNAs (ncRNAs) are a research hotspot in bioinformatics. Recent discoveries have revealed new ncRNA families performing a variety of roles, from gene expression regulation to catalytic activities. It is also believed... <a class="more_link u-tcGrayDark u-linkUnstyled" data-container=".work_4568574" data-show=".complete" data-hide=".summarized" data-more-link-behavior="true" href="#">more</a></div><div class="complete hidden">Non protein-coding RNAs (ncRNAs) are a research hotspot in bioinformatics. Recent discoveries have revealed new ncRNA families performing a variety of roles, from gene expression regulation to catalytic activities. It is also believed that other families are still to be unveiled. Computational methods developed for protein coding genes often fail when searching for ncRNAs. Noncoding RNAs functionality is often heavily dependent on their secondary structure, which makes gene discovery very different from protein coding RNA genes. This motivated the development of specific methods for ncRNA research. This article reviews the main approaches used to identify ncRNAs and predict secondary structure.</div></div></div><ul class="InlineList u-ph0x u-fs13"><li class="InlineList-item logged_in_only"><div class="share_on_academia_work_button"><a class="academia_share Button Button--inverseBlue Button--sm js-bookmark-button" data-academia-share="Work/4568574" data-share-source="work_strip" data-spinner="small_white_hide_contents"><i class="fa fa-plus"></i><span class="work-strip-link-text u-ml1x" data-content="button_text">Bookmark</span></a></div></li><li class="InlineList-item"><div class="download"><a id="b8ae82d09d72d3619bf27cba75a091c9" rel="nofollow" data-download="{"attachment_id":49783252,"asset_id":4568574,"asset_type":"Work","always_allow_download":false,"track":null,"button_location":"work_strip","source":null,"hide_modal":null}" class="Button Button--sm Button--inverseGreen js-download-button prompt_button doc_download" href="https://www.academia.edu/attachments/49783252/download_file?st=MTczMjk4MzU1Miw4LjIyMi4yMDguMTQ2&s=work_strip"><i class="fa fa-arrow-circle-o-down fa-lg"></i><span class="u-textUppercase u-ml1x" data-content="button_text">Download</span></a></div></li><li class="InlineList-item"><ul class="InlineList InlineList--bordered u-ph0x"><li class="InlineList-item InlineList-item--bordered"><span class="InlineList-item-text">by <span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a class="u-tcGrayDark u-fw700" data-has-card-for-user="5719926" href="https://usp-br.academia.edu/ArianeMachadoLima">Ariane Machado Lima</a><script data-card-contents-for-user="5719926" type="text/json">{"id":5719926,"first_name":"Ariane","last_name":"Machado Lima","domain_name":"usp-br","page_name":"ArianeMachadoLima","display_name":"Ariane Machado Lima","profile_url":"https://usp-br.academia.edu/ArianeMachadoLima?f_ri=2963","photo":"https://0.academia-photos.com/5719926/30949795/28623252/s65_ariane.machado_lima.jpg"}</script></span></span></li><li class="js-paper-rank-work_4568574 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="4568574"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 4568574, container: ".js-paper-rank-work_4568574", }); });</script></li><li class="js-percentile-work_4568574 InlineList-item InlineList-item--bordered hidden u-tcGrayDark"><span class="percentile-widget hidden"><span class="u-mr2x percentile-widget" style="display: none">•</span><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 4568574; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-percentile-work_4568574"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></li><li class="js-view-count-work_4568574 InlineList-item InlineList-item--bordered hidden"><div><span><span class="js-view-count view-count u-mr2x" data-work-id="4568574"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 4568574; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=4568574]").text(description); $(".js-view-count-work_4568574").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_4568574").removeClass('hidden') })</script></div></li><li class="InlineList-item u-positionRelative" style="max-width: 250px"><div class="u-positionAbsolute" data-has-card-for-ri-list="4568574"><i class="fa fa-tag InlineList-item-icon u-positionRelative"></i>  <a class="InlineList-item-text u-positionRelative">15</a>  </div><span class="InlineList-item-text u-textTruncate u-pl10x"><a class="InlineList-item-text" data-has-card-for-ri="428" href="https://www.academia.edu/Documents/in/Algorithms">Algorithms</a>, <script data-card-contents-for-ri="428" type="text/json">{"id":428,"name":"Algorithms","url":"https://www.academia.edu/Documents/in/Algorithms?f_ri=2963","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="522" href="https://www.academia.edu/Documents/in/Thermodynamics">Thermodynamics</a>, <script data-card-contents-for-ri="522" type="text/json">{"id":522,"name":"Thermodynamics","url":"https://www.academia.edu/Documents/in/Thermodynamics?f_ri=2963","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="2963" href="https://www.academia.edu/Documents/in/Mathematical_Biology">Mathematical Biology</a>, <script data-card-contents-for-ri="2963" type="text/json">{"id":2963,"name":"Mathematical Biology","url":"https://www.academia.edu/Documents/in/Mathematical_Biology?f_ri=2963","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="4233" href="https://www.academia.edu/Documents/in/Computational_Biology">Computational Biology</a><script data-card-contents-for-ri="4233" type="text/json">{"id":4233,"name":"Computational Biology","url":"https://www.academia.edu/Documents/in/Computational_Biology?f_ri=2963","nofollow":false}</script></span></li><script>(function(){ if (true) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=4568574]'), work: {"id":4568574,"title":"Computational methods in noncoding RNA research","created_at":"2013-09-23T21:57:01.494-07:00","url":"https://www.academia.edu/4568574/Computational_methods_in_noncoding_RNA_research?f_ri=2963","dom_id":"work_4568574","summary":"Non protein-coding RNAs (ncRNAs) are a research hotspot in bioinformatics. Recent discoveries have revealed new ncRNA families performing a variety of roles, from gene expression regulation to catalytic activities. It is also believed that other families are still to be unveiled. Computational methods developed for protein coding genes often fail when searching for ncRNAs. Noncoding RNAs functionality is often heavily dependent on their secondary structure, which makes gene discovery very different from protein coding RNA genes. This motivated the development of specific methods for ncRNA research. This article reviews the main approaches used to identify ncRNAs and predict secondary structure.","downloadable_attachments":[{"id":49783252,"asset_id":4568574,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":5719926,"first_name":"Ariane","last_name":"Machado Lima","domain_name":"usp-br","page_name":"ArianeMachadoLima","display_name":"Ariane Machado Lima","profile_url":"https://usp-br.academia.edu/ArianeMachadoLima?f_ri=2963","photo":"https://0.academia-photos.com/5719926/30949795/28623252/s65_ariane.machado_lima.jpg"}],"research_interests":[{"id":428,"name":"Algorithms","url":"https://www.academia.edu/Documents/in/Algorithms?f_ri=2963","nofollow":false},{"id":522,"name":"Thermodynamics","url":"https://www.academia.edu/Documents/in/Thermodynamics?f_ri=2963","nofollow":false},{"id":2963,"name":"Mathematical Biology","url":"https://www.academia.edu/Documents/in/Mathematical_Biology?f_ri=2963","nofollow":false},{"id":4233,"name":"Computational Biology","url":"https://www.academia.edu/Documents/in/Computational_Biology?f_ri=2963","nofollow":false},{"id":47884,"name":"Biological Sciences","url":"https://www.academia.edu/Documents/in/Biological_Sciences?f_ri=2963"},{"id":80414,"name":"Mathematical Sciences","url":"https://www.academia.edu/Documents/in/Mathematical_Sciences?f_ri=2963"},{"id":213709,"name":"Mathematical","url":"https://www.academia.edu/Documents/in/Mathematical?f_ri=2963"},{"id":337175,"name":"Secondary Structure","url":"https://www.academia.edu/Documents/in/Secondary_Structure?f_ri=2963"},{"id":809882,"name":"Base Sequence","url":"https://www.academia.edu/Documents/in/Base_Sequence?f_ri=2963"},{"id":1277798,"name":"Catalytic Activity","url":"https://www.academia.edu/Documents/in/Catalytic_Activity?f_ri=2963"},{"id":1362652,"name":"Nucleic Acid Conformation","url":"https://www.academia.edu/Documents/in/Nucleic_Acid_Conformation?f_ri=2963"},{"id":1449632,"name":"Computational Method","url":"https://www.academia.edu/Documents/in/Computational_Method?f_ri=2963"},{"id":1763968,"name":"Gene Expression Regulation","url":"https://www.academia.edu/Documents/in/Gene_Expression_Regulation?f_ri=2963"},{"id":2292505,"name":"noncoding RNA","url":"https://www.academia.edu/Documents/in/noncoding_RNA?f_ri=2963"},{"id":2518536,"name":"Secondary structure prediction","url":"https://www.academia.edu/Documents/in/Secondary_structure_prediction?f_ri=2963"}]}, }) } })();</script></ul></li></ul></div></div><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_3158697 coauthored" data-work_id="3158697" itemscope="itemscope" itemtype="https://schema.org/ScholarlyArticle"><div class="header"><div class="title u-fontSerif u-fs22 u-lineHeight1_3"><a class="u-tcGrayDarkest js-work-link" href="https://www.academia.edu/3158697/Network_Biology_ISSN_2220_8879_">Network Biology (ISSN 2220-8879)</a></div></div><div class="u-pb4x u-mt3x"><div class="summary u-fs14 u-fw300 u-lineHeight1_5 u-tcGrayDarkest"><div class="summarized">"Networks are mathematically directed (in practical applications also undirected) graphs and a graph is a one-dimensional abstract complex, i.e., a topological space. Network theory focuses on various topological structures and... <a class="more_link u-tcGrayDark u-linkUnstyled" data-container=".work_3158697" data-show=".complete" data-hide=".summarized" data-more-link-behavior="true" href="#">more</a></div><div class="complete hidden">"Networks are mathematically directed (in practical applications also undirected) graphs and a graph is a one-dimensional abstract complex, i.e., a topological space. Network theory focuses on various topological structures and properties, dynamic properties, and functionality-topology relationship, etc. There are some common mathematical foundations, theories and methodology for network analysis, in which graph theory, statistics, and operational research, etc., are the fundamental sciences of network analysis. Various emerging biological networks, at both micro- and macro- levels, will provide numerous sources for the development of general network theory and methodology and also facilitate the development of theory and methodology of biological networks.<br /><br />Biological network analysis is a fast moving science. Many core scientific issues, for example, ecological structure, co-evolution, co-extinction and biodiversity conservation in ecology, and cancer development and metabolic regulation in health science, etc., are expected to be addressed by network approaches and network analysis. Network analysis is becoming the core methodology to treat complex biological systems. As the fast development of this area, more and more papers on biological networks are published. <br /><br />At present explosive numbers of quality papers on biological networks are being published each year. The initiation of the journal, Network Biology, will provide a public and unified platform for the publication of these studies. From this integrated and unique journal, researchers, university teachers and students will thoroughly have an in-depth and complete insight on knowledge, methodology and recent advances of biological networks.<br /><br />In the view of system dynamics, biological networks are always self-organized systems with emergent, autonomous and adaptive properties. Their dynamics can be represented by agent-based modeling, individual-based modeling and some other methodologies like neural network modeling. Therefore, agent-based modeling, individual-based modeling, self-organization of biological systems, and neural network modeling, etc., fall into the aims and scope of the journal, Network Biology. <br /><br />The NETWORK BIOLOGY (ISSN 2220-8879) is an open access, peer-reviewed online journal that considers scientific articles in all different areas of network biology. It is the transactions of the International Society of Network Biology.It dedicates to the latest advances in network biology. The goal of this journal is to keep a record of the state-of-the-art research and promote the research work in these fast moving areas. The topics to be covered by Network Biology include, but are not limited to: <br /><br />•Theories, algorithms and programs of network analysis<br />•Innovations and applications of biological networks<br />•Dynamics, optimization and control of biological networks<br />•Ecological networks, food webs and natural equilibrium<br />•Co-evolution, co-extinction, biodiversity conservation<br />•Metabolic networks, protein-protein interaction networks, biochemical reaction networks, gene networks, transcriptional regulatory networks, cell cycle networks, phylogenetic networks, network motifs<br />•Physiological networks<br />•Network regulation of metabolic processes, human diseases and ecological systems<br />•Social networks, epidemiological networks<br />•System complexity, self-organized systems, emergence of biological systems, agent-based modeling, individual-based modeling, neural network modeling, and other network-based modeling, etc.<br />We are also interested in short communications that clearly address a specific issue or completely present a new ecological network, food web, or metabolic or gene network, etc. <br /><br />Authors can submit their works to the email box of this journal, <a href="mailto:networkbiology@iaees.org" rel="nofollow">networkbiology@iaees.org</a>. All manuscripts submitted to this journal must be previously unpublished and may not be considered for publication elsewhere at any time during review period of this journal. Authors are asked to read Author Guidelines before submitting manuscripts.<br /><br />In addition to free submissions from authors around the world, special issues are also accepted. The organizer of a special issue can collect submissions (yielded from a research project, a research group, etc.) on a specific research topic, or submissions of a scientific conference for publication of special issue. <br /><br />Network Biology  <br />ISSN 2220-8879 <br />URL: <a href="http://www.iaees.org/publications/journals/nb/online-version.asp" rel="nofollow">http://www.iaees.org/publications/journals/nb/online-version.asp</a><br />RSS feed: <a href="http://www.iaees.org/publications/journals/nb/rss.xml" rel="nofollow">http://www.iaees.org/publications/journals/nb/rss.xml</a><br />E-mail: <a href="mailto:networkbiology@iaees.org" rel="nofollow">networkbiology@iaees.org</a><br />Editor-in-Chief: WenJun Zhang"</div></div></div><ul class="InlineList u-ph0x u-fs13"><li class="InlineList-item logged_in_only"><div class="share_on_academia_work_button"><a class="academia_share Button Button--inverseBlue Button--sm js-bookmark-button" data-academia-share="Work/3158697" data-share-source="work_strip" data-spinner="small_white_hide_contents"><i class="fa fa-plus"></i><span class="work-strip-link-text u-ml1x" data-content="button_text">Bookmark</span></a></div></li><li class="InlineList-item"><div class="download"><a id="54c9f3df2d9f0d4325645c90e531ecd9" rel="nofollow" data-download="{"attachment_id":41547697,"asset_id":3158697,"asset_type":"Work","always_allow_download":false,"track":null,"button_location":"work_strip","source":null,"hide_modal":null}" class="Button Button--sm Button--inverseGreen js-download-button prompt_button doc_download" href="https://www.academia.edu/attachments/41547697/download_file?st=MTczMjk4MzU1Miw4LjIyMi4yMDguMTQ2&s=work_strip"><i class="fa fa-arrow-circle-o-down fa-lg"></i><span class="u-textUppercase u-ml1x" data-content="button_text">Download</span></a></div></li><li class="InlineList-item"><ul class="InlineList InlineList--bordered u-ph0x"><li class="InlineList-item InlineList-item--bordered"><span class="InlineList-item-text">by <span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a class="u-tcGrayDark u-fw700" data-has-card-for-user="3573924" href="https://iaees.academia.edu/IAEESPublications">IAEES Publications</a><script data-card-contents-for-user="3573924" type="text/json">{"id":3573924,"first_name":"IAEES","last_name":"Publications","domain_name":"iaees","page_name":"IAEESPublications","display_name":"IAEES Publications","profile_url":"https://iaees.academia.edu/IAEESPublications?f_ri=2963","photo":"https://0.academia-photos.com/3573924/5016887/37919633/s65_iaees.publications.png"}</script></span></span><span class="u-displayInlineBlock InlineList-item-text"> and <span class="u-textDecorationUnderline u-clickable InlineList-item-text js-work-more-authors-3158697">+2</span><div class="hidden js-additional-users-3158697"><div><span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a href="https://newengland.academia.edu/CarrieByron">Carrie Byron</a></span></div><div><span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a href="https://independent.academia.edu/CraigTennenhouse">Craig Tennenhouse</a></span></div></div></span><script>(function(){ var popoverSettings = { el: $('.js-work-more-authors-3158697'), placement: 'bottom', hide_delay: 200, html: true, content: function(){ return $('.js-additional-users-3158697').html(); } } new HoverPopover(popoverSettings); })();</script></li><li class="js-paper-rank-work_3158697 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="3158697"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 3158697, container: ".js-paper-rank-work_3158697", }); });</script></li><li class="js-percentile-work_3158697 InlineList-item InlineList-item--bordered hidden u-tcGrayDark"><span class="percentile-widget hidden"><span class="u-mr2x percentile-widget" style="display: none">•</span><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 3158697; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-percentile-work_3158697"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></li><li class="js-view-count-work_3158697 InlineList-item InlineList-item--bordered hidden"><div><span><span class="js-view-count view-count u-mr2x" data-work-id="3158697"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 3158697; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=3158697]").text(description); $(".js-view-count-work_3158697").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_3158697").removeClass('hidden') })</script></div></li><li class="InlineList-item u-positionRelative" style="max-width: 250px"><div class="u-positionAbsolute" data-has-card-for-ri-list="3158697"><i class="fa fa-tag InlineList-item-icon u-positionRelative"></i>  <a class="InlineList-item-text u-positionRelative">182</a>  </div><span class="InlineList-item-text u-textTruncate u-pl11x"><a class="InlineList-item-text" data-has-card-for-ri="146" href="https://www.academia.edu/Documents/in/Bioinformatics">Bioinformatics</a>, <script data-card-contents-for-ri="146" type="text/json">{"id":146,"name":"Bioinformatics","url":"https://www.academia.edu/Documents/in/Bioinformatics?f_ri=2963","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="155" href="https://www.academia.edu/Documents/in/Evolutionary_Biology">Evolutionary Biology</a>, <script data-card-contents-for-ri="155" type="text/json">{"id":155,"name":"Evolutionary Biology","url":"https://www.academia.edu/Documents/in/Evolutionary_Biology?f_ri=2963","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="300" href="https://www.academia.edu/Documents/in/Mathematics">Mathematics</a>, <script data-card-contents-for-ri="300" type="text/json">{"id":300,"name":"Mathematics","url":"https://www.academia.edu/Documents/in/Mathematics?f_ri=2963","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="312" href="https://www.academia.edu/Documents/in/Optimization_Mathematical_Programming_">Optimization (Mathematical Programming)</a><script data-card-contents-for-ri="312" type="text/json">{"id":312,"name":"Optimization (Mathematical Programming)","url":"https://www.academia.edu/Documents/in/Optimization_Mathematical_Programming_?f_ri=2963","nofollow":false}</script></span></li><script>(function(){ if (true) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=3158697]'), work: {"id":3158697,"title":"Network Biology (ISSN 2220-8879)","created_at":"2013-03-29T13:59:50.279-07:00","url":"https://www.academia.edu/3158697/Network_Biology_ISSN_2220_8879_?f_ri=2963","dom_id":"work_3158697","summary":"\"Networks are mathematically directed (in practical applications also undirected) graphs and a graph is a one-dimensional abstract complex, i.e., a topological space. Network theory focuses on various topological structures and properties, dynamic properties, and functionality-topology relationship, etc. There are some common mathematical foundations, theories and methodology for network analysis, in which graph theory, statistics, and operational research, etc., are the fundamental sciences of network analysis. Various emerging biological networks, at both micro- and macro- levels, will provide numerous sources for the development of general network theory and methodology and also facilitate the development of theory and methodology of biological networks.\n\nBiological network analysis is a fast moving science. Many core scientific issues, for example, ecological structure, co-evolution, co-extinction and biodiversity conservation in ecology, and cancer development and metabolic regulation in health science, etc., are expected to be addressed by network approaches and network analysis. Network analysis is becoming the core methodology to treat complex biological systems. As the fast development of this area, more and more papers on biological networks are published. \n\nAt present explosive numbers of quality papers on biological networks are being published each year. The initiation of the journal, Network Biology, will provide a public and unified platform for the publication of these studies. From this integrated and unique journal, researchers, university teachers and students will thoroughly have an in-depth and complete insight on knowledge, methodology and recent advances of biological networks.\n\nIn the view of system dynamics, biological networks are always self-organized systems with emergent, autonomous and adaptive properties. Their dynamics can be represented by agent-based modeling, individual-based modeling and some other methodologies like neural network modeling. Therefore, agent-based modeling, individual-based modeling, self-organization of biological systems, and neural network modeling, etc., fall into the aims and scope of the journal, Network Biology. \n\nThe NETWORK BIOLOGY (ISSN 2220-8879) is an open access, peer-reviewed online journal that considers scientific articles in all different areas of network biology. It is the transactions of the International Society of Network Biology.It dedicates to the latest advances in network biology. The goal of this journal is to keep a record of the state-of-the-art research and promote the research work in these fast moving areas. The topics to be covered by Network Biology include, but are not limited to: \n\n•Theories, algorithms and programs of network analysis\n•Innovations and applications of biological networks\n•Dynamics, optimization and control of biological networks\n•Ecological networks, food webs and natural equilibrium\n•Co-evolution, co-extinction, biodiversity conservation\n•Metabolic networks, protein-protein interaction networks, biochemical reaction networks, gene networks, transcriptional regulatory networks, cell cycle networks, phylogenetic networks, network motifs\n•Physiological networks\n•Network regulation of metabolic processes, human diseases and ecological systems\n•Social networks, epidemiological networks\n•System complexity, self-organized systems, emergence of biological systems, agent-based modeling, individual-based modeling, neural network modeling, and other network-based modeling, etc.\nWe are also interested in short communications that clearly address a specific issue or completely present a new ecological network, food web, or metabolic or gene network, etc. \n\nAuthors can submit their works to the email box of this journal, networkbiology@iaees.org. All manuscripts submitted to this journal must be previously unpublished and may not be considered for publication elsewhere at any time during review period of this journal. Authors are asked to read Author Guidelines before submitting manuscripts.\n\nIn addition to free submissions from authors around the world, special issues are also accepted. The organizer of a special issue can collect submissions (yielded from a research project, a research group, etc.) on a specific research topic, or submissions of a scientific conference for publication of special issue. \n\nNetwork Biology \nISSN 2220-8879 \nURL: http://www.iaees.org/publications/journals/nb/online-version.asp\nRSS feed: http://www.iaees.org/publications/journals/nb/rss.xml\nE-mail: networkbiology@iaees.org\nEditor-in-Chief: WenJun Zhang\"","downloadable_attachments":[{"id":41547697,"asset_id":3158697,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":3573924,"first_name":"IAEES","last_name":"Publications","domain_name":"iaees","page_name":"IAEESPublications","display_name":"IAEES Publications","profile_url":"https://iaees.academia.edu/IAEESPublications?f_ri=2963","photo":"https://0.academia-photos.com/3573924/5016887/37919633/s65_iaees.publications.png"},{"id":34585032,"first_name":"Carrie","last_name":"Byron","domain_name":"newengland","page_name":"CarrieByron","display_name":"Carrie Byron","profile_url":"https://newengland.academia.edu/CarrieByron?f_ri=2963","photo":"https://0.academia-photos.com/34585032/12333907/13731191/s65_carrie.byron.jpg"},{"id":150060624,"first_name":"Craig","last_name":"Tennenhouse","domain_name":"independent","page_name":"CraigTennenhouse","display_name":"Craig Tennenhouse","profile_url":"https://independent.academia.edu/CraigTennenhouse?f_ri=2963","photo":"/images/s65_no_pic.png"}],"research_interests":[{"id":146,"name":"Bioinformatics","url":"https://www.academia.edu/Documents/in/Bioinformatics?f_ri=2963","nofollow":false},{"id":155,"name":"Evolutionary Biology","url":"https://www.academia.edu/Documents/in/Evolutionary_Biology?f_ri=2963","nofollow":false},{"id":300,"name":"Mathematics","url":"https://www.academia.edu/Documents/in/Mathematics?f_ri=2963","nofollow":false},{"id":312,"name":"Optimization (Mathematical Programming)","url":"https://www.academia.edu/Documents/in/Optimization_Mathematical_Programming_?f_ri=2963","nofollow":false},{"id":377,"name":"Partial Differential Equations","url":"https://www.academia.edu/Documents/in/Partial_Differential_Equations?f_ri=2963"},{"id":444,"name":"Quantum Computing","url":"https://www.academia.edu/Documents/in/Quantum_Computing?f_ri=2963"},{"id":465,"name":"Artificial Intelligence","url":"https://www.academia.edu/Documents/in/Artificial_Intelligence?f_ri=2963"},{"id":472,"name":"Human Computer Interaction","url":"https://www.academia.edu/Documents/in/Human_Computer_Interaction?f_ri=2963"},{"id":1088,"name":"Infectious disease epidemiology","url":"https://www.academia.edu/Documents/in/Infectious_disease_epidemiology?f_ri=2963"},{"id":1233,"name":"Social Networks","url":"https://www.academia.edu/Documents/in/Social_Networks?f_ri=2963"},{"id":1252,"name":"Remote Sensing","url":"https://www.academia.edu/Documents/in/Remote_Sensing?f_ri=2963"},{"id":1432,"name":"Natural Language Processing","url":"https://www.academia.edu/Documents/in/Natural_Language_Processing?f_ri=2963"},{"id":1615,"name":"Usability","url":"https://www.academia.edu/Documents/in/Usability?f_ri=2963"},{"id":2008,"name":"Machine Learning","url":"https://www.academia.edu/Documents/in/Machine_Learning?f_ri=2963"},{"id":2009,"name":"Data Mining","url":"https://www.academia.edu/Documents/in/Data_Mining?f_ri=2963"},{"id":2141,"name":"Signal Processing","url":"https://www.academia.edu/Documents/in/Signal_Processing?f_ri=2963"},{"id":2189,"name":"Computational Complexity","url":"https://www.academia.edu/Documents/in/Computational_Complexity?f_ri=2963"},{"id":2298,"name":"Computational Fluid Dynamics","url":"https://www.academia.edu/Documents/in/Computational_Fluid_Dynamics?f_ri=2963"},{"id":2553,"name":"Social Networking","url":"https://www.academia.edu/Documents/in/Social_Networking?f_ri=2963"},{"id":2616,"name":"Graph Theory","url":"https://www.academia.edu/Documents/in/Graph_Theory?f_ri=2963"},{"id":2630,"name":"Numerical Modeling","url":"https://www.academia.edu/Documents/in/Numerical_Modeling?f_ri=2963"},{"id":2736,"name":"Molecular Dynamics Simulation","url":"https://www.academia.edu/Documents/in/Molecular_Dynamics_Simulation?f_ri=2963"},{"id":2919,"name":"Organizational Culture","url":"https://www.academia.edu/Documents/in/Organizational_Culture?f_ri=2963"},{"id":2963,"name":"Mathematical Biology","url":"https://www.academia.edu/Documents/in/Mathematical_Biology?f_ri=2963"},{"id":3155,"name":"Complexity Theory","url":"https://www.academia.edu/Documents/in/Complexity_Theory?f_ri=2963"},{"id":3216,"name":"Genomics","url":"https://www.academia.edu/Documents/in/Genomics?f_ri=2963"},{"id":3521,"name":"Computational Intelligence","url":"https://www.academia.edu/Documents/in/Computational_Intelligence?f_ri=2963"},{"id":3523,"name":"Evolutionary Computation","url":"https://www.academia.edu/Documents/in/Evolutionary_Computation?f_ri=2963"},{"id":3703,"name":"Network Security","url":"https://www.academia.edu/Documents/in/Network_Security?f_ri=2963"},{"id":3717,"name":"Geotechnical Engineering","url":"https://www.academia.edu/Documents/in/Geotechnical_Engineering?f_ri=2963"},{"id":4165,"name":"Fuzzy Logic","url":"https://www.academia.edu/Documents/in/Fuzzy_Logic?f_ri=2963"},{"id":4206,"name":"Phylogeography","url":"https://www.academia.edu/Documents/in/Phylogeography?f_ri=2963"},{"id":4222,"name":"Hybrid Systems","url":"https://www.academia.edu/Documents/in/Hybrid_Systems?f_ri=2963"},{"id":4233,"name":"Computational Biology","url":"https://www.academia.edu/Documents/in/Computational_Biology?f_ri=2963"},{"id":4306,"name":"Pest Management","url":"https://www.academia.edu/Documents/in/Pest_Management?f_ri=2963"},{"id":4455,"name":"Medical Education","url":"https://www.academia.edu/Documents/in/Medical_Education?f_ri=2963"},{"id":4600,"name":"Protein Structure Prediction","url":"https://www.academia.edu/Documents/in/Protein_Structure_Prediction?f_ri=2963"},{"id":4955,"name":"Computational Modelling","url":"https://www.academia.edu/Documents/in/Computational_Modelling?f_ri=2963"},{"id":5025,"name":"Genetic Programming","url":"https://www.academia.edu/Documents/in/Genetic_Programming?f_ri=2963"},{"id":5026,"name":"Genetic Algorithms","url":"https://www.academia.edu/Documents/in/Genetic_Algorithms?f_ri=2963"},{"id":5400,"name":"Systems Biology","url":"https://www.academia.edu/Documents/in/Systems_Biology?f_ri=2963"},{"id":5542,"name":"Plant-pathogen interactions","url":"https://www.academia.edu/Documents/in/Plant-pathogen_interactions?f_ri=2963"},{"id":5639,"name":"Text Mining","url":"https://www.academia.edu/Documents/in/Text_Mining?f_ri=2963"},{"id":6021,"name":"Cancer","url":"https://www.academia.edu/Documents/in/Cancer?f_ri=2963"},{"id":6132,"name":"Soft Computing","url":"https://www.academia.edu/Documents/in/Soft_Computing?f_ri=2963"},{"id":6791,"name":"Aging","url":"https://www.academia.edu/Documents/in/Aging?f_ri=2963"},{"id":7293,"name":"Market Microstructure","url":"https://www.academia.edu/Documents/in/Market_Microstructure?f_ri=2963"},{"id":7649,"name":"Traditional Ecological Knowledge","url":"https://www.academia.edu/Documents/in/Traditional_Ecological_Knowledge?f_ri=2963"},{"id":7710,"name":"Biology","url":"https://www.academia.edu/Documents/in/Biology?f_ri=2963"},{"id":7799,"name":"Environmental modeling","url":"https://www.academia.edu/Documents/in/Environmental_modeling?f_ri=2963"},{"id":7823,"name":"Malaria","url":"https://www.academia.edu/Documents/in/Malaria?f_ri=2963"},{"id":9136,"name":"Wireless Sensor Networks","url":"https://www.academia.edu/Documents/in/Wireless_Sensor_Networks?f_ri=2963"},{"id":9780,"name":"Insect-Plant Interactions","url":"https://www.academia.edu/Documents/in/Insect-Plant_Interactions?f_ri=2963"},{"id":9846,"name":"Ecology","url":"https://www.academia.edu/Documents/in/Ecology?f_ri=2963"},{"id":10225,"name":"Agriculture","url":"https://www.academia.edu/Documents/in/Agriculture?f_ri=2963"},{"id":10408,"name":"Support Vector Machines","url":"https://www.academia.edu/Documents/in/Support_Vector_Machines?f_ri=2963"},{"id":10662,"name":"Algebra and Topology","url":"https://www.academia.edu/Documents/in/Algebra_and_Topology?f_ri=2963"},{"id":10977,"name":"Intelligent Systems","url":"https://www.academia.edu/Documents/in/Intelligent_Systems?f_ri=2963"},{"id":11191,"name":"Plant-Animal Interactions","url":"https://www.academia.edu/Documents/in/Plant-Animal_Interactions?f_ri=2963"},{"id":11681,"name":"Environmental Informatics","url":"https://www.academia.edu/Documents/in/Environmental_Informatics?f_ri=2963"},{"id":11750,"name":"Environmental Design","url":"https://www.academia.edu/Documents/in/Environmental_Design?f_ri=2963"},{"id":11801,"name":"Environmental Monitoring","url":"https://www.academia.edu/Documents/in/Environmental_Monitoring?f_ri=2963"},{"id":11820,"name":"Modeling and Simulation","url":"https://www.academia.edu/Documents/in/Modeling_and_Simulation?f_ri=2963"},{"id":12022,"name":"Numerical Analysis","url":"https://www.academia.edu/Documents/in/Numerical_Analysis?f_ri=2963"},{"id":12516,"name":"Predator-Prey Interactions","url":"https://www.academia.edu/Documents/in/Predator-Prey_Interactions?f_ri=2963"},{"id":13104,"name":"Cellular Reprogramming","url":"https://www.academia.edu/Documents/in/Cellular_Reprogramming?f_ri=2963"},{"id":13276,"name":"Soil Dynamics","url":"https://www.academia.edu/Documents/in/Soil_Dynamics?f_ri=2963"},{"id":13739,"name":"Social Network Analysis (SNA)","url":"https://www.academia.edu/Documents/in/Social_Network_Analysis_SNA_?f_ri=2963"},{"id":13827,"name":"Cell Biology","url":"https://www.academia.edu/Documents/in/Cell_Biology?f_ri=2963"},{"id":13923,"name":"Computer Security","url":"https://www.academia.edu/Documents/in/Computer_Security?f_ri=2963"},{"id":14054,"name":"Chemical","url":"https://www.academia.edu/Documents/in/Chemical?f_ri=2963"},{"id":14195,"name":"Cancer Biology","url":"https://www.academia.edu/Documents/in/Cancer_Biology?f_ri=2963"},{"id":14292,"name":"Oxidative Stress","url":"https://www.academia.edu/Documents/in/Oxidative_Stress?f_ri=2963"},{"id":15118,"name":"Topology","url":"https://www.academia.edu/Documents/in/Topology?f_ri=2963"},{"id":15118,"name":"Topology","url":"https://www.academia.edu/Documents/in/Topology?f_ri=2963"},{"id":16682,"name":"Mathematical Modelling","url":"https://www.academia.edu/Documents/in/Mathematical_Modelling?f_ri=2963"},{"id":17823,"name":"Biogeography","url":"https://www.academia.edu/Documents/in/Biogeography?f_ri=2963"},{"id":18594,"name":"Evolutionary Ecology","url":"https://www.academia.edu/Documents/in/Evolutionary_Ecology?f_ri=2963"},{"id":21117,"name":"Earthquake Geotechnical Engineering","url":"https://www.academia.edu/Documents/in/Earthquake_Geotechnical_Engineering?f_ri=2963"},{"id":23323,"name":"Transcription Factors","url":"https://www.academia.edu/Documents/in/Transcription_Factors?f_ri=2963"},{"id":23515,"name":"Biological Control","url":"https://www.academia.edu/Documents/in/Biological_Control?f_ri=2963"},{"id":25122,"name":"Energy efficiency","url":"https://www.academia.edu/Documents/in/Energy_efficiency?f_ri=2963"},{"id":25596,"name":"Network Dynamics and Stability","url":"https://www.academia.edu/Documents/in/Network_Dynamics_and_Stability?f_ri=2963"},{"id":25955,"name":"Emergent Quantum Gravity","url":"https://www.academia.edu/Documents/in/Emergent_Quantum_Gravity?f_ri=2963"},{"id":26681,"name":"Inference of Regulatory Networks","url":"https://www.academia.edu/Documents/in/Inference_of_Regulatory_Networks?f_ri=2963"},{"id":26825,"name":"Mobile Computing","url":"https://www.academia.edu/Documents/in/Mobile_Computing?f_ri=2963"},{"id":27305,"name":"Computational Mathematics","url":"https://www.academia.edu/Documents/in/Computational_Mathematics?f_ri=2963"},{"id":29223,"name":"Graphical Models","url":"https://www.academia.edu/Documents/in/Graphical_Models?f_ri=2963"},{"id":30329,"name":"Genetic Algorithm","url":"https://www.academia.edu/Documents/in/Genetic_Algorithm?f_ri=2963"},{"id":30888,"name":"Differential Equations","url":"https://www.academia.edu/Documents/in/Differential_Equations?f_ri=2963"},{"id":31812,"name":"Fuzzy Control","url":"https://www.academia.edu/Documents/in/Fuzzy_Control?f_ri=2963"},{"id":32703,"name":"Graph/Network Algorithms","url":"https://www.academia.edu/Documents/in/Graph_Network_Algorithms?f_ri=2963"},{"id":32991,"name":"Optimization Methods","url":"https://www.academia.edu/Documents/in/Optimization_Methods?f_ri=2963"},{"id":35938,"name":"Digital Image Processing","url":"https://www.academia.edu/Documents/in/Digital_Image_Processing?f_ri=2963"},{"id":35996,"name":"Differential Equations Theory and Dynamical Systems","url":"https://www.academia.edu/Documents/in/Differential_Equations_Theory_and_Dynamical_Systems?f_ri=2963"},{"id":39682,"name":"Graph Data Mining","url":"https://www.academia.edu/Documents/in/Graph_Data_Mining?f_ri=2963"},{"id":39704,"name":"Network Biology","url":"https://www.academia.edu/Documents/in/Network_Biology?f_ri=2963"},{"id":40727,"name":"Next generation sequencing","url":"https://www.academia.edu/Documents/in/Next_generation_sequencing?f_ri=2963"},{"id":41407,"name":"Marine and Fisheries Policy","url":"https://www.academia.edu/Documents/in/Marine_and_Fisheries_Policy?f_ri=2963"},{"id":41408,"name":"Ecosystem-Based Fisheries Management","url":"https://www.academia.edu/Documents/in/Ecosystem-Based_Fisheries_Management?f_ri=2963"},{"id":41409,"name":"Climate Impacts to Fisheries","url":"https://www.academia.edu/Documents/in/Climate_Impacts_to_Fisheries?f_ri=2963"},{"id":41410,"name":"Ecosystem Modelling","url":"https://www.academia.edu/Documents/in/Ecosystem_Modelling?f_ri=2963"},{"id":41559,"name":"Network","url":"https://www.academia.edu/Documents/in/Network?f_ri=2963"},{"id":41613,"name":"Java","url":"https://www.academia.edu/Documents/in/Java?f_ri=2963"},{"id":46185,"name":"Algorithmic Trading","url":"https://www.academia.edu/Documents/in/Algorithmic_Trading?f_ri=2963"},{"id":46580,"name":"Live-cell imaging","url":"https://www.academia.edu/Documents/in/Live-cell_imaging?f_ri=2963"},{"id":48636,"name":"Simulation","url":"https://www.academia.edu/Documents/in/Simulation?f_ri=2963"},{"id":49833,"name":"Protein-protein interactions","url":"https://www.academia.edu/Documents/in/Protein-protein_interactions?f_ri=2963"},{"id":53606,"name":"Cytogenetics, Cancer Molecular Biology, Apoptosis and Molecular Signaling","url":"https://www.academia.edu/Documents/in/Cytogenetics_Cancer_Molecular_Biology_Apoptosis_and_Molecular_Signaling?f_ri=2963"},{"id":54123,"name":"Artificial Neural Networks","url":"https://www.academia.edu/Documents/in/Artificial_Neural_Networks?f_ri=2963"},{"id":55009,"name":"Cognitive training","url":"https://www.academia.edu/Documents/in/Cognitive_training?f_ri=2963"},{"id":55620,"name":"Systems thinking, complexity science, emergence and organisational development, the application of knowledge from Quakerism to public policy to achieve social enterprise and sustainable development","url":"https://www.academia.edu/Documents/in/Systems_thinking_complexity_science_emergence_and_organisational_development_the_application_of_k?f_ri=2963"},{"id":61709,"name":"Computational Fluid Dynamics (CFD) modelling and simulation","url":"https://www.academia.edu/Documents/in/Computational_Fluid_Dynamics_CFD_modelling_and_simulation?f_ri=2963"},{"id":63224,"name":"Mobile Communications","url":"https://www.academia.edu/Documents/in/Mobile_Communications?f_ri=2963"},{"id":68231,"name":"Agent-Based Modelling","url":"https://www.academia.edu/Documents/in/Agent-Based_Modelling?f_ri=2963"},{"id":70773,"name":"Multi Agent Systems and Technologies","url":"https://www.academia.edu/Documents/in/Multi_Agent_Systems_and_Technologies?f_ri=2963"},{"id":71987,"name":"Connectedness","url":"https://www.academia.edu/Documents/in/Connectedness?f_ri=2963"},{"id":75647,"name":"Interactions","url":"https://www.academia.edu/Documents/in/Interactions?f_ri=2963"},{"id":97585,"name":"User interfaces","url":"https://www.academia.edu/Documents/in/User_interfaces?f_ri=2963"},{"id":102847,"name":"Digital mapping","url":"https://www.academia.edu/Documents/in/Digital_mapping?f_ri=2963"},{"id":110645,"name":"Biological Networks","url":"https://www.academia.edu/Documents/in/Biological_Networks?f_ri=2963"},{"id":115807,"name":"Limnology, Periphyton, Zooplankton, Phytoplankton, Fish, Macroinvertebrates, Submerged Aquatic Vegetation, Food Web Dynamics","url":"https://www.academia.edu/Documents/in/Limnology_Periphyton_Zooplankton_Phytoplankton_Fish_Macroinvertebrates_Submerged_Aquatic_Veget?f_ri=2963"},{"id":121527,"name":"Soil Behavior","url":"https://www.academia.edu/Documents/in/Soil_Behavior?f_ri=2963"},{"id":125784,"name":"Cell Signalling","url":"https://www.academia.edu/Documents/in/Cell_Signalling?f_ri=2963"},{"id":126903,"name":"Moleculer Biology and Genetics","url":"https://www.academia.edu/Documents/in/Moleculer_Biology_and_Genetics?f_ri=2963"},{"id":142522,"name":"Domestication","url":"https://www.academia.edu/Documents/in/Domestication?f_ri=2963"},{"id":163095,"name":"Practice Based Learning","url":"https://www.academia.edu/Documents/in/Practice_Based_Learning?f_ri=2963"},{"id":169699,"name":"Isomorphism","url":"https://www.academia.edu/Documents/in/Isomorphism?f_ri=2963"},{"id":170816,"name":"Neighborhood","url":"https://www.academia.edu/Documents/in/Neighborhood?f_ri=2963"},{"id":205560,"name":"Molecular Cell Biology","url":"https://www.academia.edu/Documents/in/Molecular_Cell_Biology?f_ri=2963"},{"id":210852,"name":"Gene Regulatory Networks","url":"https://www.academia.edu/Documents/in/Gene_Regulatory_Networks?f_ri=2963"},{"id":239811,"name":"\tLiver Cancer \tTumor Microenvironment \tMolecular Mechanisms of Fibrogenesis \tDisease Modifying Genes in Chronic Liver Disease","url":"https://www.academia.edu/Documents/in/_Liver_Cancer_Tumor_Microenvironment_Molecular_Mechanisms_of_Fibrogenesis_Disease_Mod?f_ri=2963"},{"id":251187,"name":"Environmental Design of Buildings","url":"https://www.academia.edu/Documents/in/Environmental_Design_of_Buildings?f_ri=2963"},{"id":252815,"name":"Grammatical Evolution","url":"https://www.academia.edu/Documents/in/Grammatical_Evolution?f_ri=2963"},{"id":277776,"name":"Quantum and classical statistical mechanics","url":"https://www.academia.edu/Documents/in/Quantum_and_classical_statistical_mechanics?f_ri=2963"},{"id":280478,"name":"Quantum Phase Transitions","url":"https://www.academia.edu/Documents/in/Quantum_Phase_Transitions?f_ri=2963"},{"id":281029,"name":"Chronic Kidney Diease, Diabetes, Anaemia, Metabolic Syndrome, and Obesity, Oxidative Stress, Electrolyte Metabolism, Cance R Research","url":"https://www.academia.edu/Documents/in/Chronic_Kidney_Diease_Diabetes_Anaemia_Metabolic_Syndrome_and_Obesity_Oxidative_Stress_Electro?f_ri=2963"},{"id":342382,"name":"Syntactic and Semantic Knowledge","url":"https://www.academia.edu/Documents/in/Syntactic_and_Semantic_Knowledge?f_ri=2963"},{"id":354417,"name":"Dynamic Systems and Control","url":"https://www.academia.edu/Documents/in/Dynamic_Systems_and_Control?f_ri=2963"},{"id":419498,"name":"Covering Arrays","url":"https://www.academia.edu/Documents/in/Covering_Arrays?f_ri=2963"},{"id":468656,"name":"Insect","url":"https://www.academia.edu/Documents/in/Insect?f_ri=2963"},{"id":468675,"name":"Thermal comfort \u0026 Energy efficiency in hot climates","url":"https://www.academia.edu/Documents/in/Thermal_comfort_and_Energy_efficiency_in_hot_climates?f_ri=2963"},{"id":468676,"name":"Natural ventilation as a passive cooling strategy","url":"https://www.academia.edu/Documents/in/Natural_ventilation_as_a_passive_cooling_strategy?f_ri=2963"},{"id":470469,"name":"Biomolecular Modeling","url":"https://www.academia.edu/Documents/in/Biomolecular_Modeling?f_ri=2963"},{"id":474730,"name":"Membrane biochemistry","url":"https://www.academia.edu/Documents/in/Membrane_biochemistry?f_ri=2963"},{"id":500925,"name":"Excavations","url":"https://www.academia.edu/Documents/in/Excavations?f_ri=2963"},{"id":507705,"name":"Traditional Fisheries","url":"https://www.academia.edu/Documents/in/Traditional_Fisheries?f_ri=2963"},{"id":515729,"name":"Stem cells and Regenerative Medicine","url":"https://www.academia.edu/Documents/in/Stem_cells_and_Regenerative_Medicine?f_ri=2963"},{"id":522782,"name":"Information Technology and System Integration","url":"https://www.academia.edu/Documents/in/Information_Technology_and_System_Integration?f_ri=2963"},{"id":554376,"name":"Finite Element Simulations","url":"https://www.academia.edu/Documents/in/Finite_Element_Simulations?f_ri=2963"},{"id":613846,"name":"Optimization Technology","url":"https://www.academia.edu/Documents/in/Optimization_Technology?f_ri=2963"},{"id":680257,"name":"System Modeling and Simulation","url":"https://www.academia.edu/Documents/in/System_Modeling_and_Simulation?f_ri=2963"},{"id":782626,"name":"Directed Graph","url":"https://www.academia.edu/Documents/in/Directed_Graph?f_ri=2963"},{"id":782630,"name":"Simple Graph","url":"https://www.academia.edu/Documents/in/Simple_Graph?f_ri=2963"},{"id":782638,"name":"Topological Space","url":"https://www.academia.edu/Documents/in/Topological_Space?f_ri=2963"},{"id":782648,"name":"Dual Graph","url":"https://www.academia.edu/Documents/in/Dual_Graph?f_ri=2963"},{"id":782649,"name":"Path Optimization","url":"https://www.academia.edu/Documents/in/Path_Optimization?f_ri=2963"},{"id":880402,"name":"Encryption Algorithms","url":"https://www.academia.edu/Documents/in/Encryption_Algorithms?f_ri=2963"},{"id":931375,"name":"Integration Technology of Automation Systems","url":"https://www.academia.edu/Documents/in/Integration_Technology_of_Automation_Systems?f_ri=2963"},{"id":931947,"name":"Self assembly of Macromolecules","url":"https://www.academia.edu/Documents/in/Self_assembly_of_Macromolecules?f_ri=2963"},{"id":931948,"name":"Gene expression and regulation","url":"https://www.academia.edu/Documents/in/Gene_expression_and_regulation?f_ri=2963"},{"id":939407,"name":"Buildings’ Monitoring","url":"https://www.academia.edu/Documents/in/Buildings_Monitoring-1?f_ri=2963"},{"id":939415,"name":"Illegal, Unreported and Unregulated (IUU) Fishing","url":"https://www.academia.edu/Documents/in/Illegal_Unreported_and_Unregulated_IUU_Fishing?f_ri=2963"},{"id":939612,"name":"Geodesy and Global Positioning System (GPS) and Their Applications In Earth Sciences","url":"https://www.academia.edu/Documents/in/Geodesy_and_Global_Positioning_System_GPS_and_Their_Applications_In_Earth_Sciences?f_ri=2963"},{"id":939809,"name":"Soil Foundations","url":"https://www.academia.edu/Documents/in/Soil_Foundations?f_ri=2963"},{"id":953403,"name":"Diabetes \u0026 Metabolic Syndrome","url":"https://www.academia.edu/Documents/in/Diabetes_and_Metabolic_Syndrome?f_ri=2963"},{"id":957164,"name":"Artificial Financial Markets","url":"https://www.academia.edu/Documents/in/Artificial_Financial_Markets?f_ri=2963"},{"id":963036,"name":"Subgraph","url":"https://www.academia.edu/Documents/in/Subgraph?f_ri=2963"},{"id":963042,"name":"Spanning Subgraph","url":"https://www.academia.edu/Documents/in/Spanning_Subgraph?f_ri=2963"},{"id":964639,"name":"Probe Design for Diagnosis of Diseases","url":"https://www.academia.edu/Documents/in/Probe_Design_for_Diagnosis_of_Diseases?f_ri=2963"},{"id":964641,"name":"Open Source Technologies","url":"https://www.academia.edu/Documents/in/Open_Source_Technologies?f_ri=2963"},{"id":988946,"name":"Traditional Agriculture","url":"https://www.academia.edu/Documents/in/Traditional_Agriculture?f_ri=2963"},{"id":992303,"name":"Theory of Entanglement","url":"https://www.academia.edu/Documents/in/Theory_of_Entanglement?f_ri=2963"},{"id":992306,"name":"Topological Quantum Computing","url":"https://www.academia.edu/Documents/in/Topological_Quantum_Computing?f_ri=2963"},{"id":992308,"name":"Quantum Information In Open Systems","url":"https://www.academia.edu/Documents/in/Quantum_Information_In_Open_Systems?f_ri=2963"},{"id":992309,"name":"Theory of Topological Order","url":"https://www.academia.edu/Documents/in/Theory_of_Topological_Order?f_ri=2963"},{"id":1009312,"name":"Geographic Information Systems (GIS)","url":"https://www.academia.edu/Documents/in/Geographic_Information_Systems_GIS_?f_ri=2963"},{"id":1019292,"name":"Packet Analysis","url":"https://www.academia.edu/Documents/in/Packet_Analysis?f_ri=2963"},{"id":1019293,"name":"Server Operating Systems","url":"https://www.academia.edu/Documents/in/Server_Operating_Systems?f_ri=2963"},{"id":1019294,"name":"NET Software Development","url":"https://www.academia.edu/Documents/in/NET_Software_Development?f_ri=2963"},{"id":1033738,"name":"Systems Based Practice","url":"https://www.academia.edu/Documents/in/Systems_Based_Practice?f_ri=2963"},{"id":2254216,"name":"Closed Set","url":"https://www.academia.edu/Documents/in/Closed_Set?f_ri=2963"}]}, }) } })();</script></ul></li></ul></div></div><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_35979267" data-work_id="35979267" itemscope="itemscope" itemtype="https://schema.org/ScholarlyArticle"><div class="header"><div class="title u-fontSerif u-fs22 u-lineHeight1_3"><a class="u-tcGrayDarkest js-work-link" href="https://www.academia.edu/35979267/Folia_Morphologica_Reviewers_2017">Folia Morphologica Reviewers 2017</a></div></div><div class="u-pb4x u-mt3x"></div><ul class="InlineList u-ph0x u-fs13"><li class="InlineList-item logged_in_only"><div class="share_on_academia_work_button"><a class="academia_share Button Button--inverseBlue Button--sm js-bookmark-button" data-academia-share="Work/35979267" data-share-source="work_strip" data-spinner="small_white_hide_contents"><i class="fa fa-plus"></i><span class="work-strip-link-text u-ml1x" data-content="button_text">Bookmark</span></a></div></li><li class="InlineList-item"><div class="download"><a id="efa69a2240aff9fde4fe77dab587ac47" rel="nofollow" data-download="{"attachment_id":55863649,"asset_id":35979267,"asset_type":"Work","always_allow_download":false,"track":null,"button_location":"work_strip","source":null,"hide_modal":null}" class="Button Button--sm Button--inverseGreen js-download-button prompt_button doc_download" href="https://www.academia.edu/attachments/55863649/download_file?st=MTczMjk4MzU1Miw4LjIyMi4yMDguMTQ2&s=work_strip"><i class="fa fa-arrow-circle-o-down fa-lg"></i><span class="u-textUppercase u-ml1x" data-content="button_text">Download</span></a></div></li><li class="InlineList-item"><ul class="InlineList InlineList--bordered u-ph0x"><li class="InlineList-item InlineList-item--bordered"><span class="InlineList-item-text">by <span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a class="u-tcGrayDark u-fw700" data-has-card-for-user="21972122" href="https://kau.academia.edu/HMustafa">Prof. Hesham N Mustafa</a><script data-card-contents-for-user="21972122" type="text/json">{"id":21972122,"first_name":"Prof. Hesham","last_name":"Mustafa","domain_name":"kau","page_name":"HMustafa","display_name":"Prof. Hesham N Mustafa","profile_url":"https://kau.academia.edu/HMustafa?f_ri=2963","photo":"https://0.academia-photos.com/21972122/6015802/7471085/s65_hesham.mustafa.jpg"}</script></span></span></li><li class="js-paper-rank-work_35979267 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="35979267"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 35979267, container: ".js-paper-rank-work_35979267", }); });</script></li><li class="js-percentile-work_35979267 InlineList-item InlineList-item--bordered hidden u-tcGrayDark"><span class="percentile-widget hidden"><span class="u-mr2x percentile-widget" style="display: none">•</span><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 35979267; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-percentile-work_35979267"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></li><li class="js-view-count-work_35979267 InlineList-item InlineList-item--bordered hidden"><div><span><span class="js-view-count view-count u-mr2x" data-work-id="35979267"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 35979267; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=35979267]").text(description); $(".js-view-count-work_35979267").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_35979267").removeClass('hidden') })</script></div></li><li class="InlineList-item u-positionRelative" style="max-width: 250px"><div class="u-positionAbsolute" data-has-card-for-ri-list="35979267"><i class="fa fa-tag InlineList-item-icon u-positionRelative"></i>  <a class="InlineList-item-text u-positionRelative">164</a>  </div><span class="InlineList-item-text u-textTruncate u-pl11x"><a class="InlineList-item-text" data-has-card-for-ri="143" href="https://www.academia.edu/Documents/in/Comparative_Anatomy">Comparative Anatomy</a>, <script data-card-contents-for-ri="143" type="text/json">{"id":143,"name":"Comparative Anatomy","url":"https://www.academia.edu/Documents/in/Comparative_Anatomy?f_ri=2963","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="144" href="https://www.academia.edu/Documents/in/Human_Anatomy_Biology_">Human Anatomy (Biology)</a>, <script data-card-contents-for-ri="144" type="text/json">{"id":144,"name":"Human Anatomy (Biology)","url":"https://www.academia.edu/Documents/in/Human_Anatomy_Biology_?f_ri=2963","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="155" href="https://www.academia.edu/Documents/in/Evolutionary_Biology">Evolutionary Biology</a>, <script data-card-contents-for-ri="155" type="text/json">{"id":155,"name":"Evolutionary Biology","url":"https://www.academia.edu/Documents/in/Evolutionary_Biology?f_ri=2963","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="158" href="https://www.academia.edu/Documents/in/Marine_Biology">Marine Biology</a><script data-card-contents-for-ri="158" type="text/json">{"id":158,"name":"Marine Biology","url":"https://www.academia.edu/Documents/in/Marine_Biology?f_ri=2963","nofollow":false}</script></span></li><script>(function(){ if (true) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=35979267]'), work: {"id":35979267,"title":"Folia Morphologica Reviewers 2017","created_at":"2018-02-21T08:22:57.934-08:00","url":"https://www.academia.edu/35979267/Folia_Morphologica_Reviewers_2017?f_ri=2963","dom_id":"work_35979267","summary":null,"downloadable_attachments":[{"id":55863649,"asset_id":35979267,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":21972122,"first_name":"Prof. Hesham","last_name":"Mustafa","domain_name":"kau","page_name":"HMustafa","display_name":"Prof. Hesham N Mustafa","profile_url":"https://kau.academia.edu/HMustafa?f_ri=2963","photo":"https://0.academia-photos.com/21972122/6015802/7471085/s65_hesham.mustafa.jpg"}],"research_interests":[{"id":143,"name":"Comparative Anatomy","url":"https://www.academia.edu/Documents/in/Comparative_Anatomy?f_ri=2963","nofollow":false},{"id":144,"name":"Human Anatomy (Biology)","url":"https://www.academia.edu/Documents/in/Human_Anatomy_Biology_?f_ri=2963","nofollow":false},{"id":155,"name":"Evolutionary Biology","url":"https://www.academia.edu/Documents/in/Evolutionary_Biology?f_ri=2963","nofollow":false},{"id":158,"name":"Marine Biology","url":"https://www.academia.edu/Documents/in/Marine_Biology?f_ri=2963","nofollow":false},{"id":165,"name":"Pathology","url":"https://www.academia.edu/Documents/in/Pathology?f_ri=2963"},{"id":594,"name":"Speech Language Pathology","url":"https://www.academia.edu/Documents/in/Speech_Language_Pathology?f_ri=2963"},{"id":607,"name":"Emergency Medicine","url":"https://www.academia.edu/Documents/in/Emergency_Medicine?f_ri=2963"},{"id":620,"name":"Internal Medicine (General Medicine)","url":"https://www.academia.edu/Documents/in/Internal_Medicine_General_Medicine_?f_ri=2963"},{"id":642,"name":"Respiratory Medicine","url":"https://www.academia.edu/Documents/in/Respiratory_Medicine?f_ri=2963"},{"id":646,"name":"Sports Medicine","url":"https://www.academia.edu/Documents/in/Sports_Medicine?f_ri=2963"},{"id":657,"name":"Veterinary Medicine","url":"https://www.academia.edu/Documents/in/Veterinary_Medicine?f_ri=2963"},{"id":823,"name":"Philosophy of Biology","url":"https://www.academia.edu/Documents/in/Philosophy_of_Biology?f_ri=2963"},{"id":1083,"name":"Developmental Biology","url":"https://www.academia.edu/Documents/in/Developmental_Biology?f_ri=2963"},{"id":1906,"name":"Veterinary Pathology","url":"https://www.academia.edu/Documents/in/Veterinary_Pathology?f_ri=2963"},{"id":2075,"name":"Speech Pathology","url":"https://www.academia.edu/Documents/in/Speech_Pathology?f_ri=2963"},{"id":2183,"name":"Cellular Biology","url":"https://www.academia.edu/Documents/in/Cellular_Biology?f_ri=2963"},{"id":2230,"name":"Bone Biology","url":"https://www.academia.edu/Documents/in/Bone_Biology?f_ri=2963"},{"id":2273,"name":"History of Medicine","url":"https://www.academia.edu/Documents/in/History_of_Medicine?f_ri=2963"},{"id":2361,"name":"Skeletal Biology","url":"https://www.academia.edu/Documents/in/Skeletal_Biology?f_ri=2963"},{"id":2447,"name":"Speech-Language Pathology/ Communication Disorders","url":"https://www.academia.edu/Documents/in/Speech-Language_Pathology_Communication_Disorders?f_ri=2963"},{"id":2467,"name":"Conservation Biology","url":"https://www.academia.edu/Documents/in/Conservation_Biology?f_ri=2963"},{"id":2513,"name":"Molecular Biology","url":"https://www.academia.edu/Documents/in/Molecular_Biology?f_ri=2963"},{"id":2541,"name":"Structural Biology","url":"https://www.academia.edu/Documents/in/Structural_Biology?f_ri=2963"},{"id":2894,"name":"Evolution of cooperation (Evolutionary Biology)","url":"https://www.academia.edu/Documents/in/Evolution_of_cooperation_Evolutionary_Biology_?f_ri=2963"},{"id":2963,"name":"Mathematical Biology","url":"https://www.academia.edu/Documents/in/Mathematical_Biology?f_ri=2963"},{"id":3313,"name":"Cultural Transmission (Evolutionary Biology)","url":"https://www.academia.edu/Documents/in/Cultural_Transmission_Evolutionary_Biology_?f_ri=2963"},{"id":3363,"name":"Systematic Biology","url":"https://www.academia.edu/Documents/in/Systematic_Biology?f_ri=2963"},{"id":3629,"name":"Synthetic Biology","url":"https://www.academia.edu/Documents/in/Synthetic_Biology?f_ri=2963"},{"id":3645,"name":"Evidence Based Medicine","url":"https://www.academia.edu/Documents/in/Evidence_Based_Medicine?f_ri=2963"},{"id":3699,"name":"Stem cell and Regenerative medicine","url":"https://www.academia.edu/Documents/in/Stem_cell_and_Regenerative_medicine?f_ri=2963"},{"id":3939,"name":"History and Philosophy of Biology","url":"https://www.academia.edu/Documents/in/History_and_Philosophy_of_Biology?f_ri=2963"},{"id":3940,"name":"Evolutionary Developmental Biology","url":"https://www.academia.edu/Documents/in/Evolutionary_Developmental_Biology?f_ri=2963"},{"id":4083,"name":"Complementary and Alternative Medicine","url":"https://www.academia.edu/Documents/in/Complementary_and_Alternative_Medicine?f_ri=2963"},{"id":4086,"name":"Traditional Medicine","url":"https://www.academia.edu/Documents/in/Traditional_Medicine?f_ri=2963"},{"id":4228,"name":"Skeletal muscle biology","url":"https://www.academia.edu/Documents/in/Skeletal_muscle_biology?f_ri=2963"},{"id":4233,"name":"Computational Biology","url":"https://www.academia.edu/Documents/in/Computational_Biology?f_ri=2963"},{"id":4258,"name":"Embryology","url":"https://www.academia.edu/Documents/in/Embryology?f_ri=2963"},{"id":4266,"name":"Wildlife Biology","url":"https://www.academia.edu/Documents/in/Wildlife_Biology?f_ri=2963"},{"id":4376,"name":"Family Medicine","url":"https://www.academia.edu/Documents/in/Family_Medicine?f_ri=2963"},{"id":4438,"name":"Functional Morphology","url":"https://www.academia.edu/Documents/in/Functional_Morphology?f_ri=2963"},{"id":4440,"name":"Philosophy of Medicine","url":"https://www.academia.edu/Documents/in/Philosophy_of_Medicine?f_ri=2963"},{"id":4558,"name":"Invertebrate Biology","url":"https://www.academia.edu/Documents/in/Invertebrate_Biology?f_ri=2963"},{"id":4926,"name":"Functional Anatomy","url":"https://www.academia.edu/Documents/in/Functional_Anatomy?f_ri=2963"},{"id":5072,"name":"Molecular Medicine","url":"https://www.academia.edu/Documents/in/Molecular_Medicine?f_ri=2963"},{"id":5400,"name":"Systems Biology","url":"https://www.academia.edu/Documents/in/Systems_Biology?f_ri=2963"},{"id":5541,"name":"Plant Biology","url":"https://www.academia.edu/Documents/in/Plant_Biology?f_ri=2963"},{"id":5971,"name":"Human Anatomy (Biological Anthropology)","url":"https://www.academia.edu/Documents/in/Human_Anatomy_Biological_Anthropology_?f_ri=2963"},{"id":7080,"name":"Freshwater Biology","url":"https://www.academia.edu/Documents/in/Freshwater_Biology?f_ri=2963"},{"id":7436,"name":"Population Biology","url":"https://www.academia.edu/Documents/in/Population_Biology?f_ri=2963"},{"id":7628,"name":"Urban Morphology","url":"https://www.academia.edu/Documents/in/Urban_Morphology?f_ri=2963"},{"id":7701,"name":"Membrane Biology","url":"https://www.academia.edu/Documents/in/Membrane_Biology?f_ri=2963"},{"id":7710,"name":"Biology","url":"https://www.academia.edu/Documents/in/Biology?f_ri=2963"},{"id":7987,"name":"Radiation Biology","url":"https://www.academia.edu/Documents/in/Radiation_Biology?f_ri=2963"},{"id":8241,"name":"Tropical Medicine","url":"https://www.academia.edu/Documents/in/Tropical_Medicine?f_ri=2963"},{"id":10024,"name":"Population genetics (Biology)","url":"https://www.academia.edu/Documents/in/Population_genetics_Biology_?f_ri=2963"},{"id":10035,"name":"Nuclear medicine","url":"https://www.academia.edu/Documents/in/Nuclear_medicine?f_ri=2963"},{"id":10154,"name":"Environmental Microbiology (Biology)","url":"https://www.academia.edu/Documents/in/Environmental_Microbiology_Biology_?f_ri=2963"},{"id":10866,"name":"Morphology","url":"https://www.academia.edu/Documents/in/Morphology?f_ri=2963"},{"id":11228,"name":"Mycology and Plant pathology","url":"https://www.academia.edu/Documents/in/Mycology_and_Plant_pathology?f_ri=2963"},{"id":11267,"name":"Wood Anatomy","url":"https://www.academia.edu/Documents/in/Wood_Anatomy?f_ri=2963"},{"id":11873,"name":"Fish Biology","url":"https://www.academia.edu/Documents/in/Fish_Biology?f_ri=2963"},{"id":12069,"name":"Histology","url":"https://www.academia.edu/Documents/in/Histology?f_ri=2963"},{"id":12808,"name":"Climate change biology","url":"https://www.academia.edu/Documents/in/Climate_change_biology?f_ri=2963"},{"id":13075,"name":"History of Biology","url":"https://www.academia.edu/Documents/in/History_of_Biology?f_ri=2963"},{"id":13397,"name":"Forensic Medicine","url":"https://www.academia.edu/Documents/in/Forensic_Medicine?f_ri=2963"},{"id":13827,"name":"Cell Biology","url":"https://www.academia.edu/Documents/in/Cell_Biology?f_ri=2963"},{"id":13828,"name":"Cancer Cell Biology","url":"https://www.academia.edu/Documents/in/Cancer_Cell_Biology?f_ri=2963"},{"id":14195,"name":"Cancer Biology","url":"https://www.academia.edu/Documents/in/Cancer_Biology?f_ri=2963"},{"id":14490,"name":"Fisheries Biology","url":"https://www.academia.edu/Documents/in/Fisheries_Biology?f_ri=2963"},{"id":14927,"name":"Agriculture (Biology)","url":"https://www.academia.edu/Documents/in/Agriculture_Biology_?f_ri=2963"},{"id":16580,"name":"Plant Physiology (Biology)","url":"https://www.academia.edu/Documents/in/Plant_Physiology_Biology_?f_ri=2963"},{"id":17605,"name":"Malacology (Biology)","url":"https://www.academia.edu/Documents/in/Malacology_Biology_?f_ri=2963"},{"id":17706,"name":"Molluscan Biology","url":"https://www.academia.edu/Documents/in/Molluscan_Biology?f_ri=2963"},{"id":17843,"name":"Landscape ecology (Biology)","url":"https://www.academia.edu/Documents/in/Landscape_ecology_Biology_?f_ri=2963"},{"id":18014,"name":"History of Anatomy","url":"https://www.academia.edu/Documents/in/History_of_Anatomy?f_ri=2963"},{"id":18147,"name":"Bioenergy (Biology)","url":"https://www.academia.edu/Documents/in/Bioenergy_Biology_?f_ri=2963"},{"id":19674,"name":"Behavioral Medicine","url":"https://www.academia.edu/Documents/in/Behavioral_Medicine?f_ri=2963"},{"id":20151,"name":"Ancient Medicine","url":"https://www.academia.edu/Documents/in/Ancient_Medicine?f_ri=2963"},{"id":21180,"name":"Chemical Biology","url":"https://www.academia.edu/Documents/in/Chemical_Biology?f_ri=2963"},{"id":21717,"name":"Forensic Pathology","url":"https://www.academia.edu/Documents/in/Forensic_Pathology?f_ri=2963"},{"id":22308,"name":"Marine Larval Biology \u0026 Ecology","url":"https://www.academia.edu/Documents/in/Marine_Larval_Biology_and_Ecology?f_ri=2963"},{"id":22844,"name":"Insect Molecular Biology","url":"https://www.academia.edu/Documents/in/Insect_Molecular_Biology?f_ri=2963"},{"id":23773,"name":"Avian Biology","url":"https://www.academia.edu/Documents/in/Avian_Biology?f_ri=2963"},{"id":23779,"name":"Population Ecology (Biology)","url":"https://www.academia.edu/Documents/in/Population_Ecology_Biology_?f_ri=2963"},{"id":25175,"name":"Social History of Medicine","url":"https://www.academia.edu/Documents/in/Social_History_of_Medicine?f_ri=2963"},{"id":25657,"name":"Plant Molecular Biology","url":"https://www.academia.edu/Documents/in/Plant_Molecular_Biology?f_ri=2963"},{"id":25872,"name":"Oral pathology","url":"https://www.academia.edu/Documents/in/Oral_pathology?f_ri=2963"},{"id":26282,"name":"Vascular biology","url":"https://www.academia.edu/Documents/in/Vascular_biology?f_ri=2963"},{"id":26327,"name":"Medicine","url":"https://www.academia.edu/Documents/in/Medicine?f_ri=2963"},{"id":26977,"name":"Theoretical biology","url":"https://www.academia.edu/Documents/in/Theoretical_biology?f_ri=2963"},{"id":27552,"name":"Reproductive Biology","url":"https://www.academia.edu/Documents/in/Reproductive_Biology?f_ri=2963"},{"id":29508,"name":"History of Medicine and the Body","url":"https://www.academia.edu/Documents/in/History_of_Medicine_and_the_Body?f_ri=2963"},{"id":30296,"name":"Cladistics (Systematic Biology)","url":"https://www.academia.edu/Documents/in/Cladistics_Systematic_Biology_?f_ri=2963"},{"id":31963,"name":"Morphology (Languages And Linguistics)","url":"https://www.academia.edu/Documents/in/Morphology_Languages_And_Linguistics_?f_ri=2963"},{"id":32511,"name":"Evo-Devo (Developmental Biology)","url":"https://www.academia.edu/Documents/in/Evo-Devo_Developmental_Biology_?f_ri=2963"},{"id":34875,"name":"Morphology and Syntax","url":"https://www.academia.edu/Documents/in/Morphology_and_Syntax?f_ri=2963"},{"id":35581,"name":"Clinical Pathology","url":"https://www.academia.edu/Documents/in/Clinical_Pathology?f_ri=2963"},{"id":36276,"name":"Mathematical Morphology","url":"https://www.academia.edu/Documents/in/Mathematical_Morphology?f_ri=2963"},{"id":37270,"name":"Biology Education","url":"https://www.academia.edu/Documents/in/Biology_Education?f_ri=2963"},{"id":37870,"name":"Organismal Biology","url":"https://www.academia.edu/Documents/in/Organismal_Biology?f_ri=2963"},{"id":37871,"name":"Integrative Biology","url":"https://www.academia.edu/Documents/in/Integrative_Biology?f_ri=2963"},{"id":38408,"name":"Phycology (Biology)","url":"https://www.academia.edu/Documents/in/Phycology_Biology_?f_ri=2963"},{"id":44297,"name":"Herbal Medicine","url":"https://www.academia.edu/Documents/in/Herbal_Medicine?f_ri=2963"},{"id":45223,"name":"Crustacean Biology","url":"https://www.academia.edu/Documents/in/Crustacean_Biology?f_ri=2963"},{"id":45614,"name":"Plant Morphology","url":"https://www.academia.edu/Documents/in/Plant_Morphology?f_ri=2963"},{"id":45615,"name":"Plant Anatomy","url":"https://www.academia.edu/Documents/in/Plant_Anatomy?f_ri=2963"},{"id":46578,"name":"Cell and Molecular Biology","url":"https://www.academia.edu/Documents/in/Cell_and_Molecular_Biology?f_ri=2963"},{"id":46901,"name":"Human Biology","url":"https://www.academia.edu/Documents/in/Human_Biology?f_ri=2963"},{"id":46992,"name":"Molecular Biology Cancer","url":"https://www.academia.edu/Documents/in/Molecular_Biology_Cancer?f_ri=2963"},{"id":50531,"name":"Clinical Anatomy","url":"https://www.academia.edu/Documents/in/Clinical_Anatomy?f_ri=2963"},{"id":51384,"name":"Distributed Morphology","url":"https://www.academia.edu/Documents/in/Distributed_Morphology?f_ri=2963"},{"id":52738,"name":"Sociology of Medicine","url":"https://www.academia.edu/Documents/in/Sociology_of_Medicine?f_ri=2963"},{"id":54381,"name":"Molecular Biology and genetics","url":"https://www.academia.edu/Documents/in/Molecular_Biology_and_genetics?f_ri=2963"},{"id":54589,"name":"Anatomy","url":"https://www.academia.edu/Documents/in/Anatomy?f_ri=2963"},{"id":60107,"name":"Traditional Chinese Medicine","url":"https://www.academia.edu/Documents/in/Traditional_Chinese_Medicine?f_ri=2963"},{"id":63067,"name":"Molecular and cellular biology","url":"https://www.academia.edu/Documents/in/Molecular_and_cellular_biology?f_ri=2963"},{"id":64801,"name":"Text-book of Biology","url":"https://www.academia.edu/Documents/in/Text-book_of_Biology?f_ri=2963"},{"id":65390,"name":"Internal Medicine","url":"https://www.academia.edu/Documents/in/Internal_Medicine?f_ri=2963"},{"id":68927,"name":"Anatomy and Physiology","url":"https://www.academia.edu/Documents/in/Anatomy_and_Physiology?f_ri=2963"},{"id":71058,"name":"Oral Medicine","url":"https://www.academia.edu/Documents/in/Oral_Medicine?f_ri=2963"},{"id":71260,"name":"Molecular plant pathology","url":"https://www.academia.edu/Documents/in/Molecular_plant_pathology?f_ri=2963"},{"id":75371,"name":"Human skeletal anatomy","url":"https://www.academia.edu/Documents/in/Human_skeletal_anatomy?f_ri=2963"},{"id":76054,"name":"Histology and Cell Biology","url":"https://www.academia.edu/Documents/in/Histology_and_Cell_Biology?f_ri=2963"},{"id":87472,"name":"Medicine and Surgery","url":"https://www.academia.edu/Documents/in/Medicine_and_Surgery?f_ri=2963"},{"id":95842,"name":"Ecology and Evolutionary Biology","url":"https://www.academia.edu/Documents/in/Ecology_and_Evolutionary_Biology-1?f_ri=2963"},{"id":96853,"name":"Human Anatomy","url":"https://www.academia.edu/Documents/in/Human_Anatomy?f_ri=2963"},{"id":97056,"name":"Clinical Medicine","url":"https://www.academia.edu/Documents/in/Clinical_Medicine?f_ri=2963"},{"id":97142,"name":"Environmental Biology","url":"https://www.academia.edu/Documents/in/Environmental_Biology?f_ri=2963"},{"id":101834,"name":"Cave Biology","url":"https://www.academia.edu/Documents/in/Cave_Biology?f_ri=2963"},{"id":103011,"name":"Plant Biotechnology and Molecular Biology","url":"https://www.academia.edu/Documents/in/Plant_Biotechnology_and_Molecular_Biology?f_ri=2963"},{"id":108995,"name":"To Know the Comparative Analysis of Filipino Language and English Language Morphology","url":"https://www.academia.edu/Documents/in/To_Know_the_Comparative_Analysis_of_Filipino_Language_and_English_Language_Morphology?f_ri=2963"},{"id":132282,"name":"Biochemistry and Molecular Biology of Lipids","url":"https://www.academia.edu/Documents/in/Biochemistry_and_Molecular_Biology_of_Lipids?f_ri=2963"},{"id":153663,"name":"Linguistics. Word-formation. Morphology. Lexicology. Semantics.","url":"https://www.academia.edu/Documents/in/Linguistics._Word-formation._Morphology._Lexicology._Semantics?f_ri=2963"},{"id":154188,"name":"History of Veterinary Medicine","url":"https://www.academia.edu/Documents/in/History_of_Veterinary_Medicine?f_ri=2963"},{"id":160097,"name":"Urban Morphology and Asian Cities","url":"https://www.academia.edu/Documents/in/Urban_Morphology_and_Asian_Cities?f_ri=2963"},{"id":172797,"name":"Plant morphology and anatomy","url":"https://www.academia.edu/Documents/in/Plant_morphology_and_anatomy?f_ri=2963"},{"id":179539,"name":"Derivational Morphology","url":"https://www.academia.edu/Documents/in/Derivational_Morphology?f_ri=2963"},{"id":194521,"name":"General medicine","url":"https://www.academia.edu/Documents/in/General_medicine?f_ri=2963"},{"id":198685,"name":"Geriatric medicine","url":"https://www.academia.edu/Documents/in/Geriatric_medicine?f_ri=2963"},{"id":205560,"name":"Molecular Cell Biology","url":"https://www.academia.edu/Documents/in/Molecular_Cell_Biology?f_ri=2963"},{"id":206504,"name":"General Biology","url":"https://www.academia.edu/Documents/in/General_Biology?f_ri=2963"},{"id":218599,"name":"Plant metabolomics and molecular biology","url":"https://www.academia.edu/Documents/in/Plant_metabolomics_and_molecular_biology?f_ri=2963"},{"id":254762,"name":"Marine Biology and Oceanography","url":"https://www.academia.edu/Documents/in/Marine_Biology_and_Oceanography?f_ri=2963"},{"id":254815,"name":"Freshwater Biology and Limnology","url":"https://www.academia.edu/Documents/in/Freshwater_Biology_and_Limnology?f_ri=2963"},{"id":285891,"name":"Animal Biology","url":"https://www.academia.edu/Documents/in/Animal_Biology?f_ri=2963"},{"id":290215,"name":"Molecular biology and/or Plant breeding and Genetics of Stress Tolerence","url":"https://www.academia.edu/Documents/in/Molecular_biology_and_or_Plant_breeding_and_Genetics_of_Stress_Tolerence?f_ri=2963"},{"id":362037,"name":"Veterinary Clinical Pathology","url":"https://www.academia.edu/Documents/in/Veterinary_Clinical_Pathology?f_ri=2963"},{"id":365106,"name":"Biology Teacher Education","url":"https://www.academia.edu/Documents/in/Biology_Teacher_Education?f_ri=2963"},{"id":382325,"name":"Internasional Journal of Biology Education","url":"https://www.academia.edu/Documents/in/Internasional_Journal_of_Biology_Education?f_ri=2963"},{"id":473228,"name":"Oral and Maxillofacial Pathology and Microbiology","url":"https://www.academia.edu/Documents/in/Oral_and_Maxillofacial_Pathology_and_Microbiology?f_ri=2963"},{"id":602219,"name":"Biochemistry and molecular biology","url":"https://www.academia.edu/Documents/in/Biochemistry_and_molecular_biology?f_ri=2963"},{"id":624980,"name":"Plant Pathology","url":"https://www.academia.edu/Documents/in/Plant_Pathology?f_ri=2963"},{"id":629618,"name":"Doctor of medicine","url":"https://www.academia.edu/Documents/in/Doctor_of_medicine?f_ri=2963"},{"id":643749,"name":"Human Anatomy and Physiology Teaching Methodologies","url":"https://www.academia.edu/Documents/in/Human_Anatomy_and_Physiology_Teaching_Methodologies?f_ri=2963"},{"id":662575,"name":"Family and Community Medicine","url":"https://www.academia.edu/Documents/in/Family_and_Community_Medicine?f_ri=2963"},{"id":685785,"name":"Science process skill in Biology at Secondary Education","url":"https://www.academia.edu/Documents/in/Science_process_skill_in_Biology_at_Secondary_Education?f_ri=2963"},{"id":741684,"name":"Biology and Educational Sciences","url":"https://www.academia.edu/Documents/in/Biology_and_Educational_Sciences?f_ri=2963"},{"id":882996,"name":"Medicine and Health Sciences","url":"https://www.academia.edu/Documents/in/Medicine_and_Health_Sciences?f_ri=2963"},{"id":902713,"name":"Speech Language Pathology and Audiology","url":"https://www.academia.edu/Documents/in/Speech_Language_Pathology_and_Audiology?f_ri=2963"},{"id":1112835,"name":"E.g. Biology","url":"https://www.academia.edu/Documents/in/E.g._Biology?f_ri=2963"},{"id":1115412,"name":"Vector Biology \u0026 Control","url":"https://www.academia.edu/Documents/in/Vector_Biology_and_Control-1?f_ri=2963"},{"id":1152892,"name":"Speech-language Pathology","url":"https://www.academia.edu/Documents/in/Speech-language_Pathology?f_ri=2963"},{"id":1161066,"name":"New England Journalof Medicine","url":"https://www.academia.edu/Documents/in/New_England_Journalof_Medicine?f_ri=2963"},{"id":1681026,"name":"Biochemistry and cell biology","url":"https://www.academia.edu/Documents/in/Biochemistry_and_cell_biology?f_ri=2963"}]}, }) } })();</script></ul></li></ul></div></div><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_35982140" data-work_id="35982140" itemscope="itemscope" itemtype="https://schema.org/ScholarlyArticle"><div class="header"><div class="title u-fontSerif u-fs22 u-lineHeight1_3"><a class="u-tcGrayDarkest js-work-link" href="https://www.academia.edu/35982140/15th_International_Congress_of_Histochemistry_and_Cytochemistry_From_Molecules_to_Diseases_">15th International Congress of Histochemistry and Cytochemistry “From Molecules to Diseases”</a></div></div><div class="u-pb4x u-mt3x"></div><ul class="InlineList u-ph0x u-fs13"><li class="InlineList-item logged_in_only"><div class="share_on_academia_work_button"><a class="academia_share Button Button--inverseBlue Button--sm js-bookmark-button" data-academia-share="Work/35982140" data-share-source="work_strip" data-spinner="small_white_hide_contents"><i class="fa fa-plus"></i><span class="work-strip-link-text u-ml1x" data-content="button_text">Bookmark</span></a></div></li><li class="InlineList-item"><div class="download"><a id="5f15da684507bb2ab3dbcf4ed4916363" rel="nofollow" data-download="{"attachment_id":55866578,"asset_id":35982140,"asset_type":"Work","always_allow_download":false,"track":null,"button_location":"work_strip","source":null,"hide_modal":null}" class="Button Button--sm Button--inverseGreen js-download-button prompt_button doc_download" href="https://www.academia.edu/attachments/55866578/download_file?st=MTczMjk4MzU1Miw4LjIyMi4yMDguMTQ2&s=work_strip"><i class="fa fa-arrow-circle-o-down fa-lg"></i><span class="u-textUppercase u-ml1x" data-content="button_text">Download</span></a></div></li><li class="InlineList-item"><ul class="InlineList InlineList--bordered u-ph0x"><li class="InlineList-item InlineList-item--bordered"><span class="InlineList-item-text">by <span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a class="u-tcGrayDark u-fw700" data-has-card-for-user="21972122" href="https://kau.academia.edu/HMustafa">Prof. Hesham N Mustafa</a><script data-card-contents-for-user="21972122" type="text/json">{"id":21972122,"first_name":"Prof. Hesham","last_name":"Mustafa","domain_name":"kau","page_name":"HMustafa","display_name":"Prof. Hesham N Mustafa","profile_url":"https://kau.academia.edu/HMustafa?f_ri=2963","photo":"https://0.academia-photos.com/21972122/6015802/7471085/s65_hesham.mustafa.jpg"}</script></span></span></li><li class="js-paper-rank-work_35982140 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="35982140"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 35982140, container: ".js-paper-rank-work_35982140", }); });</script></li><li class="js-percentile-work_35982140 InlineList-item InlineList-item--bordered hidden u-tcGrayDark"><span class="percentile-widget hidden"><span class="u-mr2x percentile-widget" style="display: none">•</span><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 35982140; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-percentile-work_35982140"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></li><li class="js-view-count-work_35982140 InlineList-item InlineList-item--bordered hidden"><div><span><span class="js-view-count view-count u-mr2x" data-work-id="35982140"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 35982140; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=35982140]").text(description); $(".js-view-count-work_35982140").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_35982140").removeClass('hidden') })</script></div></li><li class="InlineList-item u-positionRelative" style="max-width: 250px"><div class="u-positionAbsolute" data-has-card-for-ri-list="35982140"><i class="fa fa-tag InlineList-item-icon u-positionRelative"></i>  <a class="InlineList-item-text u-positionRelative">95</a>  </div><span class="InlineList-item-text u-textTruncate u-pl10x"><a class="InlineList-item-text" data-has-card-for-ri="144" href="https://www.academia.edu/Documents/in/Human_Anatomy_Biology_">Human Anatomy (Biology)</a>, <script data-card-contents-for-ri="144" type="text/json">{"id":144,"name":"Human Anatomy (Biology)","url":"https://www.academia.edu/Documents/in/Human_Anatomy_Biology_?f_ri=2963","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="155" href="https://www.academia.edu/Documents/in/Evolutionary_Biology">Evolutionary Biology</a>, <script data-card-contents-for-ri="155" type="text/json">{"id":155,"name":"Evolutionary Biology","url":"https://www.academia.edu/Documents/in/Evolutionary_Biology?f_ri=2963","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="158" href="https://www.academia.edu/Documents/in/Marine_Biology">Marine Biology</a>, <script data-card-contents-for-ri="158" type="text/json">{"id":158,"name":"Marine Biology","url":"https://www.academia.edu/Documents/in/Marine_Biology?f_ri=2963","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="768" href="https://www.academia.edu/Documents/in/Biological_Anthropology">Biological Anthropology</a><script data-card-contents-for-ri="768" type="text/json">{"id":768,"name":"Biological Anthropology","url":"https://www.academia.edu/Documents/in/Biological_Anthropology?f_ri=2963","nofollow":false}</script></span></li><script>(function(){ if (true) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=35982140]'), work: {"id":35982140,"title":"15th International Congress of Histochemistry and Cytochemistry “From Molecules to Diseases”","created_at":"2018-02-21T15:03:54.291-08:00","url":"https://www.academia.edu/35982140/15th_International_Congress_of_Histochemistry_and_Cytochemistry_From_Molecules_to_Diseases_?f_ri=2963","dom_id":"work_35982140","summary":null,"downloadable_attachments":[{"id":55866578,"asset_id":35982140,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":21972122,"first_name":"Prof. Hesham","last_name":"Mustafa","domain_name":"kau","page_name":"HMustafa","display_name":"Prof. Hesham N Mustafa","profile_url":"https://kau.academia.edu/HMustafa?f_ri=2963","photo":"https://0.academia-photos.com/21972122/6015802/7471085/s65_hesham.mustafa.jpg"}],"research_interests":[{"id":144,"name":"Human Anatomy (Biology)","url":"https://www.academia.edu/Documents/in/Human_Anatomy_Biology_?f_ri=2963","nofollow":false},{"id":155,"name":"Evolutionary Biology","url":"https://www.academia.edu/Documents/in/Evolutionary_Biology?f_ri=2963","nofollow":false},{"id":158,"name":"Marine Biology","url":"https://www.academia.edu/Documents/in/Marine_Biology?f_ri=2963","nofollow":false},{"id":768,"name":"Biological Anthropology","url":"https://www.academia.edu/Documents/in/Biological_Anthropology?f_ri=2963","nofollow":false},{"id":823,"name":"Philosophy of Biology","url":"https://www.academia.edu/Documents/in/Philosophy_of_Biology?f_ri=2963"},{"id":1083,"name":"Developmental Biology","url":"https://www.academia.edu/Documents/in/Developmental_Biology?f_ri=2963"},{"id":2183,"name":"Cellular Biology","url":"https://www.academia.edu/Documents/in/Cellular_Biology?f_ri=2963"},{"id":2230,"name":"Bone Biology","url":"https://www.academia.edu/Documents/in/Bone_Biology?f_ri=2963"},{"id":2361,"name":"Skeletal Biology","url":"https://www.academia.edu/Documents/in/Skeletal_Biology?f_ri=2963"},{"id":2467,"name":"Conservation Biology","url":"https://www.academia.edu/Documents/in/Conservation_Biology?f_ri=2963"},{"id":2513,"name":"Molecular Biology","url":"https://www.academia.edu/Documents/in/Molecular_Biology?f_ri=2963"},{"id":2541,"name":"Structural Biology","url":"https://www.academia.edu/Documents/in/Structural_Biology?f_ri=2963"},{"id":2894,"name":"Evolution of cooperation (Evolutionary Biology)","url":"https://www.academia.edu/Documents/in/Evolution_of_cooperation_Evolutionary_Biology_?f_ri=2963"},{"id":2963,"name":"Mathematical Biology","url":"https://www.academia.edu/Documents/in/Mathematical_Biology?f_ri=2963"},{"id":3313,"name":"Cultural Transmission (Evolutionary Biology)","url":"https://www.academia.edu/Documents/in/Cultural_Transmission_Evolutionary_Biology_?f_ri=2963"},{"id":3363,"name":"Systematic Biology","url":"https://www.academia.edu/Documents/in/Systematic_Biology?f_ri=2963"},{"id":3629,"name":"Synthetic Biology","url":"https://www.academia.edu/Documents/in/Synthetic_Biology?f_ri=2963"},{"id":3939,"name":"History and Philosophy of Biology","url":"https://www.academia.edu/Documents/in/History_and_Philosophy_of_Biology?f_ri=2963"},{"id":3940,"name":"Evolutionary Developmental Biology","url":"https://www.academia.edu/Documents/in/Evolutionary_Developmental_Biology?f_ri=2963"},{"id":4228,"name":"Skeletal muscle biology","url":"https://www.academia.edu/Documents/in/Skeletal_muscle_biology?f_ri=2963"},{"id":4233,"name":"Computational Biology","url":"https://www.academia.edu/Documents/in/Computational_Biology?f_ri=2963"},{"id":4266,"name":"Wildlife Biology","url":"https://www.academia.edu/Documents/in/Wildlife_Biology?f_ri=2963"},{"id":4558,"name":"Invertebrate Biology","url":"https://www.academia.edu/Documents/in/Invertebrate_Biology?f_ri=2963"},{"id":5400,"name":"Systems Biology","url":"https://www.academia.edu/Documents/in/Systems_Biology?f_ri=2963"},{"id":5541,"name":"Plant Biology","url":"https://www.academia.edu/Documents/in/Plant_Biology?f_ri=2963"},{"id":7080,"name":"Freshwater Biology","url":"https://www.academia.edu/Documents/in/Freshwater_Biology?f_ri=2963"},{"id":7436,"name":"Population Biology","url":"https://www.academia.edu/Documents/in/Population_Biology?f_ri=2963"},{"id":7701,"name":"Membrane Biology","url":"https://www.academia.edu/Documents/in/Membrane_Biology?f_ri=2963"},{"id":7710,"name":"Biology","url":"https://www.academia.edu/Documents/in/Biology?f_ri=2963"},{"id":7987,"name":"Radiation Biology","url":"https://www.academia.edu/Documents/in/Radiation_Biology?f_ri=2963"},{"id":10024,"name":"Population genetics (Biology)","url":"https://www.academia.edu/Documents/in/Population_genetics_Biology_?f_ri=2963"},{"id":10154,"name":"Environmental Microbiology (Biology)","url":"https://www.academia.edu/Documents/in/Environmental_Microbiology_Biology_?f_ri=2963"},{"id":11873,"name":"Fish Biology","url":"https://www.academia.edu/Documents/in/Fish_Biology?f_ri=2963"},{"id":12808,"name":"Climate change biology","url":"https://www.academia.edu/Documents/in/Climate_change_biology?f_ri=2963"},{"id":13075,"name":"History of Biology","url":"https://www.academia.edu/Documents/in/History_of_Biology?f_ri=2963"},{"id":13827,"name":"Cell Biology","url":"https://www.academia.edu/Documents/in/Cell_Biology?f_ri=2963"},{"id":13828,"name":"Cancer Cell Biology","url":"https://www.academia.edu/Documents/in/Cancer_Cell_Biology?f_ri=2963"},{"id":14195,"name":"Cancer Biology","url":"https://www.academia.edu/Documents/in/Cancer_Biology?f_ri=2963"},{"id":14490,"name":"Fisheries Biology","url":"https://www.academia.edu/Documents/in/Fisheries_Biology?f_ri=2963"},{"id":14927,"name":"Agriculture (Biology)","url":"https://www.academia.edu/Documents/in/Agriculture_Biology_?f_ri=2963"},{"id":16580,"name":"Plant Physiology (Biology)","url":"https://www.academia.edu/Documents/in/Plant_Physiology_Biology_?f_ri=2963"},{"id":17605,"name":"Malacology (Biology)","url":"https://www.academia.edu/Documents/in/Malacology_Biology_?f_ri=2963"},{"id":17706,"name":"Molluscan Biology","url":"https://www.academia.edu/Documents/in/Molluscan_Biology?f_ri=2963"},{"id":17843,"name":"Landscape ecology (Biology)","url":"https://www.academia.edu/Documents/in/Landscape_ecology_Biology_?f_ri=2963"},{"id":18147,"name":"Bioenergy (Biology)","url":"https://www.academia.edu/Documents/in/Bioenergy_Biology_?f_ri=2963"},{"id":21180,"name":"Chemical Biology","url":"https://www.academia.edu/Documents/in/Chemical_Biology?f_ri=2963"},{"id":22308,"name":"Marine Larval Biology \u0026 Ecology","url":"https://www.academia.edu/Documents/in/Marine_Larval_Biology_and_Ecology?f_ri=2963"},{"id":22844,"name":"Insect Molecular Biology","url":"https://www.academia.edu/Documents/in/Insect_Molecular_Biology?f_ri=2963"},{"id":23773,"name":"Avian Biology","url":"https://www.academia.edu/Documents/in/Avian_Biology?f_ri=2963"},{"id":23779,"name":"Population Ecology (Biology)","url":"https://www.academia.edu/Documents/in/Population_Ecology_Biology_?f_ri=2963"},{"id":25657,"name":"Plant Molecular Biology","url":"https://www.academia.edu/Documents/in/Plant_Molecular_Biology?f_ri=2963"},{"id":26282,"name":"Vascular biology","url":"https://www.academia.edu/Documents/in/Vascular_biology?f_ri=2963"},{"id":26977,"name":"Theoretical biology","url":"https://www.academia.edu/Documents/in/Theoretical_biology?f_ri=2963"},{"id":27552,"name":"Reproductive Biology","url":"https://www.academia.edu/Documents/in/Reproductive_Biology?f_ri=2963"},{"id":30296,"name":"Cladistics (Systematic Biology)","url":"https://www.academia.edu/Documents/in/Cladistics_Systematic_Biology_?f_ri=2963"},{"id":32511,"name":"Evo-Devo (Developmental Biology)","url":"https://www.academia.edu/Documents/in/Evo-Devo_Developmental_Biology_?f_ri=2963"},{"id":37270,"name":"Biology Education","url":"https://www.academia.edu/Documents/in/Biology_Education?f_ri=2963"},{"id":37870,"name":"Organismal Biology","url":"https://www.academia.edu/Documents/in/Organismal_Biology?f_ri=2963"},{"id":37871,"name":"Integrative Biology","url":"https://www.academia.edu/Documents/in/Integrative_Biology?f_ri=2963"},{"id":38408,"name":"Phycology (Biology)","url":"https://www.academia.edu/Documents/in/Phycology_Biology_?f_ri=2963"},{"id":45223,"name":"Crustacean Biology","url":"https://www.academia.edu/Documents/in/Crustacean_Biology?f_ri=2963"},{"id":46578,"name":"Cell and Molecular Biology","url":"https://www.academia.edu/Documents/in/Cell_and_Molecular_Biology?f_ri=2963"},{"id":46901,"name":"Human Biology","url":"https://www.academia.edu/Documents/in/Human_Biology?f_ri=2963"},{"id":46992,"name":"Molecular Biology Cancer","url":"https://www.academia.edu/Documents/in/Molecular_Biology_Cancer?f_ri=2963"},{"id":47884,"name":"Biological Sciences","url":"https://www.academia.edu/Documents/in/Biological_Sciences?f_ri=2963"},{"id":54381,"name":"Molecular Biology and genetics","url":"https://www.academia.edu/Documents/in/Molecular_Biology_and_genetics?f_ri=2963"},{"id":63067,"name":"Molecular and cellular biology","url":"https://www.academia.edu/Documents/in/Molecular_and_cellular_biology?f_ri=2963"},{"id":64801,"name":"Text-book of Biology","url":"https://www.academia.edu/Documents/in/Text-book_of_Biology?f_ri=2963"},{"id":76054,"name":"Histology and Cell Biology","url":"https://www.academia.edu/Documents/in/Histology_and_Cell_Biology?f_ri=2963"},{"id":83925,"name":"Biologia","url":"https://www.academia.edu/Documents/in/Biologia?f_ri=2963"},{"id":95842,"name":"Ecology and Evolutionary Biology","url":"https://www.academia.edu/Documents/in/Ecology_and_Evolutionary_Biology-1?f_ri=2963"},{"id":97142,"name":"Environmental Biology","url":"https://www.academia.edu/Documents/in/Environmental_Biology?f_ri=2963"},{"id":101834,"name":"Cave Biology","url":"https://www.academia.edu/Documents/in/Cave_Biology?f_ri=2963"},{"id":103011,"name":"Plant Biotechnology and Molecular Biology","url":"https://www.academia.edu/Documents/in/Plant_Biotechnology_and_Molecular_Biology?f_ri=2963"},{"id":103194,"name":"Biologie","url":"https://www.academia.edu/Documents/in/Biologie?f_ri=2963"},{"id":109250,"name":"Biología","url":"https://www.academia.edu/Documents/in/Biolog%C3%ADa?f_ri=2963"},{"id":132282,"name":"Biochemistry and Molecular Biology of Lipids","url":"https://www.academia.edu/Documents/in/Biochemistry_and_Molecular_Biology_of_Lipids?f_ri=2963"},{"id":147873,"name":"Biologia Molecular","url":"https://www.academia.edu/Documents/in/Biologia_Molecular?f_ri=2963"},{"id":205560,"name":"Molecular Cell Biology","url":"https://www.academia.edu/Documents/in/Molecular_Cell_Biology?f_ri=2963"},{"id":206504,"name":"General Biology","url":"https://www.academia.edu/Documents/in/General_Biology?f_ri=2963"},{"id":218599,"name":"Plant metabolomics and molecular biology","url":"https://www.academia.edu/Documents/in/Plant_metabolomics_and_molecular_biology?f_ri=2963"},{"id":254762,"name":"Marine Biology and Oceanography","url":"https://www.academia.edu/Documents/in/Marine_Biology_and_Oceanography?f_ri=2963"},{"id":254815,"name":"Freshwater Biology and Limnology","url":"https://www.academia.edu/Documents/in/Freshwater_Biology_and_Limnology?f_ri=2963"},{"id":265960,"name":"Biologi","url":"https://www.academia.edu/Documents/in/Biologi?f_ri=2963"},{"id":285891,"name":"Animal Biology","url":"https://www.academia.edu/Documents/in/Animal_Biology?f_ri=2963"},{"id":290215,"name":"Molecular biology and/or Plant breeding and Genetics of Stress Tolerence","url":"https://www.academia.edu/Documents/in/Molecular_biology_and_or_Plant_breeding_and_Genetics_of_Stress_Tolerence?f_ri=2963"},{"id":365106,"name":"Biology Teacher Education","url":"https://www.academia.edu/Documents/in/Biology_Teacher_Education?f_ri=2963"},{"id":382325,"name":"Internasional Journal of Biology Education","url":"https://www.academia.edu/Documents/in/Internasional_Journal_of_Biology_Education?f_ri=2963"},{"id":432167,"name":"Pendidikan Biologi","url":"https://www.academia.edu/Documents/in/Pendidikan_Biologi?f_ri=2963"},{"id":602219,"name":"Biochemistry and molecular biology","url":"https://www.academia.edu/Documents/in/Biochemistry_and_molecular_biology?f_ri=2963"},{"id":685785,"name":"Science process skill in Biology at Secondary Education","url":"https://www.academia.edu/Documents/in/Science_process_skill_in_Biology_at_Secondary_Education?f_ri=2963"},{"id":741684,"name":"Biology and Educational Sciences","url":"https://www.academia.edu/Documents/in/Biology_and_Educational_Sciences?f_ri=2963"},{"id":1112835,"name":"E.g. Biology","url":"https://www.academia.edu/Documents/in/E.g._Biology?f_ri=2963"},{"id":1115412,"name":"Vector Biology \u0026 Control","url":"https://www.academia.edu/Documents/in/Vector_Biology_and_Control-1?f_ri=2963"},{"id":1681026,"name":"Biochemistry and cell biology","url":"https://www.academia.edu/Documents/in/Biochemistry_and_cell_biology?f_ri=2963"}]}, }) } })();</script></ul></li></ul></div></div><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_15014293" data-work_id="15014293" itemscope="itemscope" itemtype="https://schema.org/ScholarlyArticle"><div class="header"><div class="title u-fontSerif u-fs22 u-lineHeight1_3"><a class="u-tcGrayDarkest js-work-link" href="https://www.academia.edu/15014293/Lyapunov_functionals_for_global_stability_of_Lotka_Volterra_cooperative_systems_with_discrete_delays">Lyapunov functionals for global stability of Lotka-Volterra cooperative systems with discrete delays</a></div></div><div class="u-pb4x u-mt3x"><div class="summary u-fs14 u-fw300 u-lineHeight1_5 u-tcGrayDarkest"><div class="summarized">This paper addresses the global stability of a two-species Lotka-Volterra cooperative system with four discrete delays via the method of Lyapunov functionals. We apply our Lyapunov functional techniques to prove stability of... <a class="more_link u-tcGrayDark u-linkUnstyled" data-container=".work_15014293" data-show=".complete" data-hide=".summarized" data-more-link-behavior="true" href="#">more</a></div><div class="complete hidden">This paper addresses the global stability of a two-species Lotka-Volterra cooperative system with four discrete delays via the method of Lyapunov functionals. We apply our Lyapunov functional techniques to prove stability of Lotka-Volterra models of mutualism with two delays or without delays. We note that, if all the delayed feedbacks are positive then the stability properties are independent of the values of the delays. We compare our results with known results. <br /> <br />Keywords: Lotka-Volterra cooperative system, discrete delays, delayed positive feedback, Lyapunov functional, global stability.</div></div></div><ul class="InlineList u-ph0x u-fs13"><li class="InlineList-item logged_in_only"><div class="share_on_academia_work_button"><a class="academia_share Button Button--inverseBlue Button--sm js-bookmark-button" data-academia-share="Work/15014293" data-share-source="work_strip" data-spinner="small_white_hide_contents"><i class="fa fa-plus"></i><span class="work-strip-link-text u-ml1x" data-content="button_text">Bookmark</span></a></div></li><li class="InlineList-item"><div class="download"><a id="59de8f319706b5e4fd0e93f5402be8f1" rel="nofollow" data-download="{"attachment_id":38507010,"asset_id":15014293,"asset_type":"Work","always_allow_download":false,"track":null,"button_location":"work_strip","source":null,"hide_modal":null}" class="Button Button--sm Button--inverseGreen js-download-button prompt_button doc_download" href="https://www.academia.edu/attachments/38507010/download_file?st=MTczMjk4MzU1Miw4LjIyMi4yMDguMTQ2&s=work_strip"><i class="fa fa-arrow-circle-o-down fa-lg"></i><span class="u-textUppercase u-ml1x" data-content="button_text">Download</span></a></div></li><li class="InlineList-item"><ul class="InlineList InlineList--bordered u-ph0x"><li class="InlineList-item InlineList-item--bordered"><span class="InlineList-item-text">by <span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a class="u-tcGrayDark u-fw700" data-has-card-for-user="2121744" href="https://independent.academia.edu/leoncruz82">Cruz Vargas-De-León</a><script data-card-contents-for-user="2121744" type="text/json">{"id":2121744,"first_name":"Cruz","last_name":"Vargas-De-León","domain_name":"independent","page_name":"leoncruz82","display_name":"Cruz Vargas-De-León","profile_url":"https://independent.academia.edu/leoncruz82?f_ri=2963","photo":"https://0.academia-photos.com/2121744/688983/19867024/s65_cruz.vargas-de-le_n.png"}</script></span></span></li><li class="js-paper-rank-work_15014293 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="15014293"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 15014293, container: ".js-paper-rank-work_15014293", }); });</script></li><li class="js-percentile-work_15014293 InlineList-item InlineList-item--bordered hidden u-tcGrayDark"><span class="percentile-widget hidden"><span class="u-mr2x percentile-widget" style="display: none">•</span><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 15014293; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-percentile-work_15014293"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></li><li class="js-view-count-work_15014293 InlineList-item InlineList-item--bordered hidden"><div><span><span class="js-view-count view-count u-mr2x" data-work-id="15014293"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 15014293; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=15014293]").text(description); $(".js-view-count-work_15014293").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_15014293").removeClass('hidden') })</script></div></li><li class="InlineList-item u-positionRelative" style="max-width: 250px"><div class="u-positionAbsolute" data-has-card-for-ri-list="15014293"><i class="fa fa-tag InlineList-item-icon u-positionRelative"></i>  <a class="InlineList-item-text u-positionRelative">12</a>  </div><span class="InlineList-item-text u-textTruncate u-pl10x"><a class="InlineList-item-text" data-has-card-for-ri="2963" href="https://www.academia.edu/Documents/in/Mathematical_Biology">Mathematical Biology</a>, <script data-card-contents-for-ri="2963" type="text/json">{"id":2963,"name":"Mathematical Biology","url":"https://www.academia.edu/Documents/in/Mathematical_Biology?f_ri=2963","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="15396" href="https://www.academia.edu/Documents/in/Mathematical_Ecology">Mathematical Ecology</a>, <script data-card-contents-for-ri="15396" type="text/json">{"id":15396,"name":"Mathematical Ecology","url":"https://www.academia.edu/Documents/in/Mathematical_Ecology?f_ri=2963","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="16521" href="https://www.academia.edu/Documents/in/Mathematical_biology_Mathematics_">Mathematical biology (Mathematics)</a>, <script data-card-contents-for-ri="16521" type="text/json">{"id":16521,"name":"Mathematical biology (Mathematics)","url":"https://www.academia.edu/Documents/in/Mathematical_biology_Mathematics_?f_ri=2963","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="51901" href="https://www.academia.edu/Documents/in/Time-Delay_Systems">Time-Delay Systems</a><script data-card-contents-for-ri="51901" type="text/json">{"id":51901,"name":"Time-Delay Systems","url":"https://www.academia.edu/Documents/in/Time-Delay_Systems?f_ri=2963","nofollow":false}</script></span></li><script>(function(){ if (true) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=15014293]'), work: {"id":15014293,"title":"Lyapunov functionals for global stability of Lotka-Volterra cooperative systems with discrete delays","created_at":"2015-08-18T10:33:43.112-07:00","url":"https://www.academia.edu/15014293/Lyapunov_functionals_for_global_stability_of_Lotka_Volterra_cooperative_systems_with_discrete_delays?f_ri=2963","dom_id":"work_15014293","summary":"This paper addresses the global stability of a two-species Lotka-Volterra cooperative system with four discrete delays via the method of Lyapunov functionals. We apply our Lyapunov functional techniques to prove stability of Lotka-Volterra models of mutualism with two delays or without delays. We note that, if all the delayed feedbacks are positive then the stability properties are independent of the values of the delays. We compare our results with known results. \r\n\r\nKeywords: Lotka-Volterra cooperative system, discrete delays, delayed positive feedback, Lyapunov functional, global stability.","downloadable_attachments":[{"id":38507010,"asset_id":15014293,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":2121744,"first_name":"Cruz","last_name":"Vargas-De-León","domain_name":"independent","page_name":"leoncruz82","display_name":"Cruz Vargas-De-León","profile_url":"https://independent.academia.edu/leoncruz82?f_ri=2963","photo":"https://0.academia-photos.com/2121744/688983/19867024/s65_cruz.vargas-de-le_n.png"}],"research_interests":[{"id":2963,"name":"Mathematical Biology","url":"https://www.academia.edu/Documents/in/Mathematical_Biology?f_ri=2963","nofollow":false},{"id":15396,"name":"Mathematical Ecology","url":"https://www.academia.edu/Documents/in/Mathematical_Ecology?f_ri=2963","nofollow":false},{"id":16521,"name":"Mathematical biology (Mathematics)","url":"https://www.academia.edu/Documents/in/Mathematical_biology_Mathematics_?f_ri=2963","nofollow":false},{"id":51901,"name":"Time-Delay Systems","url":"https://www.academia.edu/Documents/in/Time-Delay_Systems?f_ri=2963","nofollow":false},{"id":67038,"name":"Lyapunov Stability Theory","url":"https://www.academia.edu/Documents/in/Lyapunov_Stability_Theory?f_ri=2963"},{"id":84487,"name":"Delay Differential Equation","url":"https://www.academia.edu/Documents/in/Delay_Differential_Equation?f_ri=2963"},{"id":136174,"name":"Delay Differential Equations","url":"https://www.academia.edu/Documents/in/Delay_Differential_Equations?f_ri=2963"},{"id":420906,"name":"Lyapunov functions","url":"https://www.academia.edu/Documents/in/Lyapunov_functions?f_ri=2963"},{"id":543165,"name":"direct Lyapunov method","url":"https://www.academia.edu/Documents/in/direct_Lyapunov_method?f_ri=2963"},{"id":543171,"name":"Lyapunov function","url":"https://www.academia.edu/Documents/in/Lyapunov_function?f_ri=2963"},{"id":543197,"name":"Second Method of Lyapunov","url":"https://www.academia.edu/Documents/in/Second_Method_of_Lyapunov?f_ri=2963"},{"id":544875,"name":"Lyapunov techniques","url":"https://www.academia.edu/Documents/in/Lyapunov_techniques?f_ri=2963"}]}, }) } })();</script></ul></li></ul></div></div><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_7001978" data-work_id="7001978" itemscope="itemscope" itemtype="https://schema.org/ScholarlyArticle"><div class="header"><div class="title u-fontSerif u-fs22 u-lineHeight1_3"><a class="u-tcGrayDarkest js-work-link" href="https://www.academia.edu/7001978/The_Navier_Stokes_Equations_And_Turbulence">The Navier-Stokes Equations And Turbulence</a></div></div><div class="u-pb4x u-mt3x"><div class="summary u-fs14 u-fw300 u-lineHeight1_5 u-tcGrayDarkest"><div class="summarized">The Navier-Stokes differential equations describe the motion of fluids which are incompressible. The three-dimensional Navier-Stokes equations misbehave very badly although they are relatively simple-looking. The solutions could wind up... <a class="more_link u-tcGrayDark u-linkUnstyled" data-container=".work_7001978" data-show=".complete" data-hide=".summarized" data-more-link-behavior="true" href="#">more</a></div><div class="complete hidden">The Navier-Stokes differential equations describe the motion of fluids which are incompressible. The three-dimensional Navier-Stokes equations misbehave very badly although they are relatively simple-looking. The solutions could wind up being extremely unstable even with nice, smooth, reasonably harmless initial conditions. A mathematical understanding of the outrageous behaviour of these equations would dramatically alter the <br />field of fluid mechanics. This paper describes why the three-dimensional Navier-Stokes equations are not solvable, i.e., the equations cannot be used to model turbulence, which is <br />a three-dimensional phenomenon.</div></div></div><ul class="InlineList u-ph0x u-fs13"><li class="InlineList-item logged_in_only"><div class="share_on_academia_work_button"><a class="academia_share Button Button--inverseBlue Button--sm js-bookmark-button" data-academia-share="Work/7001978" data-share-source="work_strip" data-spinner="small_white_hide_contents"><i class="fa fa-plus"></i><span class="work-strip-link-text u-ml1x" data-content="button_text">Bookmark</span></a></div></li><li class="InlineList-item"><div class="download"><a id="171cd89ee1e8ff2786e296416df8c2c6" rel="nofollow" data-download="{"attachment_id":33905173,"asset_id":7001978,"asset_type":"Work","always_allow_download":false,"track":null,"button_location":"work_strip","source":null,"hide_modal":null}" class="Button Button--sm Button--inverseGreen js-download-button prompt_button doc_download" href="https://www.academia.edu/attachments/33905173/download_file?st=MTczMjk4MzU1Miw4LjIyMi4yMDguMTQ2&s=work_strip"><i class="fa fa-arrow-circle-o-down fa-lg"></i><span class="u-textUppercase u-ml1x" data-content="button_text">Download</span></a></div></li><li class="InlineList-item"><ul class="InlineList InlineList--bordered u-ph0x"><li class="InlineList-item InlineList-item--bordered"><span class="InlineList-item-text">by <span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a class="u-tcGrayDark u-fw700" data-has-card-for-user="11414130" href="https://independent.academia.edu/WongBertrand">Bertrand Wong</a><script data-card-contents-for-user="11414130" type="text/json">{"id":11414130,"first_name":"Bertrand","last_name":"Wong","domain_name":"independent","page_name":"WongBertrand","display_name":"Bertrand Wong","profile_url":"https://independent.academia.edu/WongBertrand?f_ri=2963","photo":"https://0.academia-photos.com/11414130/3329015/3917133/s65_bertrand.wong.jpg"}</script></span></span></li><li class="js-paper-rank-work_7001978 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="7001978"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 7001978, container: ".js-paper-rank-work_7001978", }); });</script></li><li class="js-percentile-work_7001978 InlineList-item InlineList-item--bordered hidden u-tcGrayDark"><span class="percentile-widget hidden"><span class="u-mr2x percentile-widget" style="display: none">•</span><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 7001978; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-percentile-work_7001978"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></li><li class="js-view-count-work_7001978 InlineList-item InlineList-item--bordered hidden"><div><span><span class="js-view-count view-count u-mr2x" data-work-id="7001978"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 7001978; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=7001978]").text(description); $(".js-view-count-work_7001978").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_7001978").removeClass('hidden') })</script></div></li><li class="InlineList-item u-positionRelative" style="max-width: 250px"><div class="u-positionAbsolute" data-has-card-for-ri-list="7001978"><i class="fa fa-tag InlineList-item-icon u-positionRelative"></i>  <a class="InlineList-item-text u-positionRelative">48</a>  </div><span class="InlineList-item-text u-textTruncate u-pl10x"><a class="InlineList-item-text" data-has-card-for-ri="300" href="https://www.academia.edu/Documents/in/Mathematics">Mathematics</a>, <script data-card-contents-for-ri="300" type="text/json">{"id":300,"name":"Mathematics","url":"https://www.academia.edu/Documents/in/Mathematics?f_ri=2963","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="305" href="https://www.academia.edu/Documents/in/Applied_Mathematics">Applied Mathematics</a>, <script data-card-contents-for-ri="305" type="text/json">{"id":305,"name":"Applied Mathematics","url":"https://www.academia.edu/Documents/in/Applied_Mathematics?f_ri=2963","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="307" href="https://www.academia.edu/Documents/in/Mathematical_Statistics">Mathematical Statistics</a>, <script data-card-contents-for-ri="307" type="text/json">{"id":307,"name":"Mathematical Statistics","url":"https://www.academia.edu/Documents/in/Mathematical_Statistics?f_ri=2963","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="892" href="https://www.academia.edu/Documents/in/Statistics">Statistics</a><script data-card-contents-for-ri="892" type="text/json">{"id":892,"name":"Statistics","url":"https://www.academia.edu/Documents/in/Statistics?f_ri=2963","nofollow":false}</script></span></li><script>(function(){ if (true) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=7001978]'), work: {"id":7001978,"title":"The Navier-Stokes Equations And Turbulence","created_at":"2014-05-09T19:28:30.858-07:00","url":"https://www.academia.edu/7001978/The_Navier_Stokes_Equations_And_Turbulence?f_ri=2963","dom_id":"work_7001978","summary":"The Navier-Stokes differential equations describe the motion of fluids which are incompressible. The three-dimensional Navier-Stokes equations misbehave very badly although they are relatively simple-looking. The solutions could wind up being extremely unstable even with nice, smooth, reasonably harmless initial conditions. A mathematical understanding of the outrageous behaviour of these equations would dramatically alter the\r\nfield of fluid mechanics. This paper describes why the three-dimensional Navier-Stokes equations are not solvable, i.e., the equations cannot be used to model turbulence, which is\r\na three-dimensional phenomenon.","downloadable_attachments":[{"id":33905173,"asset_id":7001978,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":11414130,"first_name":"Bertrand","last_name":"Wong","domain_name":"independent","page_name":"WongBertrand","display_name":"Bertrand Wong","profile_url":"https://independent.academia.edu/WongBertrand?f_ri=2963","photo":"https://0.academia-photos.com/11414130/3329015/3917133/s65_bertrand.wong.jpg"}],"research_interests":[{"id":300,"name":"Mathematics","url":"https://www.academia.edu/Documents/in/Mathematics?f_ri=2963","nofollow":false},{"id":305,"name":"Applied Mathematics","url":"https://www.academia.edu/Documents/in/Applied_Mathematics?f_ri=2963","nofollow":false},{"id":307,"name":"Mathematical Statistics","url":"https://www.academia.edu/Documents/in/Mathematical_Statistics?f_ri=2963","nofollow":false},{"id":892,"name":"Statistics","url":"https://www.academia.edu/Documents/in/Statistics?f_ri=2963","nofollow":false},{"id":1352,"name":"Multivariate Statistics","url":"https://www.academia.edu/Documents/in/Multivariate_Statistics?f_ri=2963"},{"id":2298,"name":"Computational Fluid Dynamics","url":"https://www.academia.edu/Documents/in/Computational_Fluid_Dynamics?f_ri=2963"},{"id":2435,"name":"Fluid Mechanics","url":"https://www.academia.edu/Documents/in/Fluid_Mechanics?f_ri=2963"},{"id":2802,"name":"Turbulence","url":"https://www.academia.edu/Documents/in/Turbulence?f_ri=2963"},{"id":2963,"name":"Mathematical Biology","url":"https://www.academia.edu/Documents/in/Mathematical_Biology?f_ri=2963"},{"id":3984,"name":"Turbulence Modelling","url":"https://www.academia.edu/Documents/in/Turbulence_Modelling?f_ri=2963"},{"id":4060,"name":"Applied Statistics","url":"https://www.academia.edu/Documents/in/Applied_Statistics?f_ri=2963"},{"id":4373,"name":"Computational Fluid Mechanics","url":"https://www.academia.edu/Documents/in/Computational_Fluid_Mechanics?f_ri=2963"},{"id":4388,"name":"Computational Statistics","url":"https://www.academia.edu/Documents/in/Computational_Statistics?f_ri=2963"},{"id":5495,"name":"Wave turbulence","url":"https://www.academia.edu/Documents/in/Wave_turbulence?f_ri=2963"},{"id":9138,"name":"Applied Physics","url":"https://www.academia.edu/Documents/in/Applied_Physics?f_ri=2963"},{"id":9434,"name":"Chaos Theory","url":"https://www.academia.edu/Documents/in/Chaos_Theory?f_ri=2963"},{"id":9648,"name":"Fluid structure interaction","url":"https://www.academia.edu/Documents/in/Fluid_structure_interaction?f_ri=2963"},{"id":16496,"name":"Fluid Dynamics","url":"https://www.academia.edu/Documents/in/Fluid_Dynamics?f_ri=2963"},{"id":16682,"name":"Mathematical Modelling","url":"https://www.academia.edu/Documents/in/Mathematical_Modelling?f_ri=2963"},{"id":18038,"name":"MHD (Fluid Dynamics)","url":"https://www.academia.edu/Documents/in/MHD_Fluid_Dynamics_?f_ri=2963"},{"id":22579,"name":"Chaos (Physics)","url":"https://www.academia.edu/Documents/in/Chaos_Physics_?f_ri=2963"},{"id":22613,"name":"Probability and statistics","url":"https://www.academia.edu/Documents/in/Probability_and_statistics?f_ri=2963"},{"id":23922,"name":"Dynamical systems and Chaos","url":"https://www.academia.edu/Documents/in/Dynamical_systems_and_Chaos?f_ri=2963"},{"id":24769,"name":"Chaos/Complexity Theory","url":"https://www.academia.edu/Documents/in/Chaos_Complexity_Theory?f_ri=2963"},{"id":48328,"name":"Environmental Fluid Mechanics","url":"https://www.academia.edu/Documents/in/Environmental_Fluid_Mechanics?f_ri=2963"},{"id":48543,"name":"Fluids","url":"https://www.academia.edu/Documents/in/Fluids?f_ri=2963"},{"id":49654,"name":"Experimental Fluid Dynamics","url":"https://www.academia.edu/Documents/in/Experimental_Fluid_Dynamics?f_ri=2963"},{"id":54172,"name":"Chaos","url":"https://www.academia.edu/Documents/in/Chaos?f_ri=2963"},{"id":57086,"name":"Turbulence modeling","url":"https://www.academia.edu/Documents/in/Turbulence_modeling?f_ri=2963"},{"id":61709,"name":"Computational Fluid Dynamics (CFD) modelling and simulation","url":"https://www.academia.edu/Documents/in/Computational_Fluid_Dynamics_CFD_modelling_and_simulation?f_ri=2963"},{"id":65139,"name":"Patterns","url":"https://www.academia.edu/Documents/in/Patterns?f_ri=2963"},{"id":96281,"name":"Applied mathematics and Modelling","url":"https://www.academia.edu/Documents/in/Applied_mathematics_and_Modelling?f_ri=2963"},{"id":125863,"name":"Applied Mathematics and Computational Science","url":"https://www.academia.edu/Documents/in/Applied_Mathematics_and_Computational_Science?f_ri=2963"},{"id":129220,"name":"Applied Mathematics, Applied Physics, Applied Statistics","url":"https://www.academia.edu/Documents/in/Applied_Mathematics_Applied_Physics_Applied_Statistics?f_ri=2963"},{"id":183079,"name":"Turbulence modelling using CFD","url":"https://www.academia.edu/Documents/in/Turbulence_modelling_using_CFD?f_ri=2963"},{"id":188735,"name":"Laminar to Turbulence Transitions","url":"https://www.academia.edu/Documents/in/Laminar_to_Turbulence_Transitions?f_ri=2963"},{"id":265402,"name":"Applied Mathematics and Statistics","url":"https://www.academia.edu/Documents/in/Applied_Mathematics_and_Statistics?f_ri=2963"},{"id":388873,"name":"Mathematics and Statistics","url":"https://www.academia.edu/Documents/in/Mathematics_and_Statistics?f_ri=2963"},{"id":579838,"name":"Experimental Statistics: Statistical Analysis of Experiments","url":"https://www.academia.edu/Documents/in/Experimental_Statistics_Statistical_Analysis_of_Experiments?f_ri=2963"},{"id":584704,"name":"Applied and Computational Mathematics","url":"https://www.academia.edu/Documents/in/Applied_and_Computational_Mathematics?f_ri=2963"},{"id":717029,"name":"Stability and Chaos","url":"https://www.academia.edu/Documents/in/Stability_and_Chaos?f_ri=2963"},{"id":730238,"name":"Fractals and Chaos","url":"https://www.academia.edu/Documents/in/Fractals_and_Chaos?f_ri=2963"},{"id":818655,"name":"Applied Mathematics and Physics","url":"https://www.academia.edu/Documents/in/Applied_Mathematics_and_Physics?f_ri=2963"},{"id":891586,"name":"Turbulence Models","url":"https://www.academia.edu/Documents/in/Turbulence_Models?f_ri=2963"},{"id":964276,"name":"Mathematical Aspects of Navier Stoke's Equations","url":"https://www.academia.edu/Documents/in/Mathematical_Aspects_of_Navier_Stokes_Equations?f_ri=2963"},{"id":1223725,"name":"Numerical and Experimental Methods in Fluid Dynamics","url":"https://www.academia.edu/Documents/in/Numerical_and_Experimental_Methods_in_Fluid_Dynamics?f_ri=2963"},{"id":2829181,"name":"Non Linear Dynamics \u0026 Chaos","url":"https://www.academia.edu/Documents/in/Non_Linear_Dynamics_and_Chaos?f_ri=2963"},{"id":2829182,"name":"Waves in Ecology","url":"https://www.academia.edu/Documents/in/Waves_in_Ecology?f_ri=2963"}]}, }) } })();</script></ul></li></ul></div></div><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_5996411" data-work_id="5996411" itemscope="itemscope" itemtype="https://schema.org/ScholarlyArticle"><div class="header"><div class="title u-fontSerif u-fs22 u-lineHeight1_3"><a class="u-tcGrayDarkest js-work-link" href="https://www.academia.edu/5996411/THE_ELECTRICAL_ACTIVITY_OF_THE_HEART_AND_THE_VAN_DER_POL_EQUATION_AS_ITS_MATHEMATICAL_MODEL_INTRODUCTION">THE ELECTRICAL ACTIVITY OF THE HEART AND THE VAN DER POL EQUATION AS ITS MATHEMATICAL MODEL INTRODUCTION</a></div></div><div class="u-pb4x u-mt3x"></div><ul class="InlineList u-ph0x u-fs13"><li class="InlineList-item logged_in_only"><div class="share_on_academia_work_button"><a class="academia_share Button Button--inverseBlue Button--sm js-bookmark-button" data-academia-share="Work/5996411" data-share-source="work_strip" data-spinner="small_white_hide_contents"><i class="fa fa-plus"></i><span class="work-strip-link-text u-ml1x" data-content="button_text">Bookmark</span></a></div></li><li class="InlineList-item"><div class="download"><a id="5b890d0a2cbb37b9937cdeadb31879d1" rel="nofollow" data-download="{"attachment_id":32947235,"asset_id":5996411,"asset_type":"Work","always_allow_download":false,"track":null,"button_location":"work_strip","source":null,"hide_modal":null}" class="Button Button--sm Button--inverseGreen js-download-button prompt_button doc_download" href="https://www.academia.edu/attachments/32947235/download_file?st=MTczMjk4MzU1Miw4LjIyMi4yMDguMTQ2&s=work_strip"><i class="fa fa-arrow-circle-o-down fa-lg"></i><span class="u-textUppercase u-ml1x" data-content="button_text">Download</span></a></div></li><li class="InlineList-item"><ul class="InlineList InlineList--bordered u-ph0x"><li class="InlineList-item InlineList-item--bordered"><span class="InlineList-item-text">by <span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a class="u-tcGrayDark u-fw700" data-has-card-for-user="4136272" href="https://ubuea.academia.edu/NsomConradTehsam">Nsom Conrad Tehsam</a><script data-card-contents-for-user="4136272" type="text/json">{"id":4136272,"first_name":"Nsom","last_name":"Conrad Tehsam","domain_name":"ubuea","page_name":"NsomConradTehsam","display_name":"Nsom Conrad Tehsam","profile_url":"https://ubuea.academia.edu/NsomConradTehsam?f_ri=2963","photo":"https://0.academia-photos.com/4136272/1606275/3424837/s65_nsom.conrad_tehsam.jpg"}</script></span></span></li><li class="js-paper-rank-work_5996411 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="5996411"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 5996411, container: ".js-paper-rank-work_5996411", }); });</script></li><li class="js-percentile-work_5996411 InlineList-item InlineList-item--bordered hidden u-tcGrayDark"><span class="percentile-widget hidden"><span class="u-mr2x percentile-widget" style="display: none">•</span><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 5996411; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-percentile-work_5996411"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></li><li class="js-view-count-work_5996411 InlineList-item InlineList-item--bordered hidden"><div><span><span class="js-view-count view-count u-mr2x" data-work-id="5996411"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 5996411; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=5996411]").text(description); $(".js-view-count-work_5996411").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_5996411").removeClass('hidden') })</script></div></li><li class="InlineList-item u-positionRelative" style="max-width: 250px"><div class="u-positionAbsolute" data-has-card-for-ri-list="5996411"><i class="fa fa-tag InlineList-item-icon u-positionRelative"></i>  <a class="InlineList-item-text u-positionRelative">6</a>  </div><span class="InlineList-item-text u-textTruncate u-pl9x"><a class="InlineList-item-text" data-has-card-for-ri="1131" href="https://www.academia.edu/Documents/in/Biomedical_Engineering">Biomedical Engineering</a>, <script data-card-contents-for-ri="1131" type="text/json">{"id":1131,"name":"Biomedical Engineering","url":"https://www.academia.edu/Documents/in/Biomedical_Engineering?f_ri=2963","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="2963" href="https://www.academia.edu/Documents/in/Mathematical_Biology">Mathematical Biology</a>, <script data-card-contents-for-ri="2963" type="text/json">{"id":2963,"name":"Mathematical Biology","url":"https://www.academia.edu/Documents/in/Mathematical_Biology?f_ri=2963","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="16682" href="https://www.academia.edu/Documents/in/Mathematical_Modelling">Mathematical Modelling</a>, <script data-card-contents-for-ri="16682" type="text/json">{"id":16682,"name":"Mathematical Modelling","url":"https://www.academia.edu/Documents/in/Mathematical_Modelling?f_ri=2963","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="65139" href="https://www.academia.edu/Documents/in/Patterns">Patterns</a><script data-card-contents-for-ri="65139" type="text/json">{"id":65139,"name":"Patterns","url":"https://www.academia.edu/Documents/in/Patterns?f_ri=2963","nofollow":false}</script></span></li><script>(function(){ if (true) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=5996411]'), work: {"id":5996411,"title":"THE ELECTRICAL ACTIVITY OF THE HEART AND THE VAN DER POL EQUATION AS ITS MATHEMATICAL MODEL INTRODUCTION","created_at":"2014-02-08T04:06:18.540-08:00","url":"https://www.academia.edu/5996411/THE_ELECTRICAL_ACTIVITY_OF_THE_HEART_AND_THE_VAN_DER_POL_EQUATION_AS_ITS_MATHEMATICAL_MODEL_INTRODUCTION?f_ri=2963","dom_id":"work_5996411","summary":null,"downloadable_attachments":[{"id":32947235,"asset_id":5996411,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":4136272,"first_name":"Nsom","last_name":"Conrad Tehsam","domain_name":"ubuea","page_name":"NsomConradTehsam","display_name":"Nsom Conrad Tehsam","profile_url":"https://ubuea.academia.edu/NsomConradTehsam?f_ri=2963","photo":"https://0.academia-photos.com/4136272/1606275/3424837/s65_nsom.conrad_tehsam.jpg"}],"research_interests":[{"id":1131,"name":"Biomedical Engineering","url":"https://www.academia.edu/Documents/in/Biomedical_Engineering?f_ri=2963","nofollow":false},{"id":2963,"name":"Mathematical Biology","url":"https://www.academia.edu/Documents/in/Mathematical_Biology?f_ri=2963","nofollow":false},{"id":16682,"name":"Mathematical Modelling","url":"https://www.academia.edu/Documents/in/Mathematical_Modelling?f_ri=2963","nofollow":false},{"id":65139,"name":"Patterns","url":"https://www.academia.edu/Documents/in/Patterns?f_ri=2963","nofollow":false},{"id":2829181,"name":"Non Linear Dynamics \u0026 Chaos","url":"https://www.academia.edu/Documents/in/Non_Linear_Dynamics_and_Chaos?f_ri=2963"},{"id":2829182,"name":"Waves in Ecology","url":"https://www.academia.edu/Documents/in/Waves_in_Ecology?f_ri=2963"}]}, }) } })();</script></ul></li></ul></div></div><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_9815512" data-work_id="9815512" itemscope="itemscope" itemtype="https://schema.org/ScholarlyArticle"><div class="header"><div class="title u-fontSerif u-fs22 u-lineHeight1_3"><a class="u-tcGrayDarkest js-work-link" href="https://www.academia.edu/9815512/Fourier_Solutions_to_the_Cable_Equation">Fourier Solutions to the Cable Equation</a></div></div><div class="u-pb4x u-mt3x"><div class="summary u-fs14 u-fw300 u-lineHeight1_5 u-tcGrayDarkest">Not original research</div></div><ul class="InlineList u-ph0x u-fs13"><li class="InlineList-item logged_in_only"><div class="share_on_academia_work_button"><a class="academia_share Button Button--inverseBlue Button--sm js-bookmark-button" data-academia-share="Work/9815512" data-share-source="work_strip" data-spinner="small_white_hide_contents"><i class="fa fa-plus"></i><span class="work-strip-link-text u-ml1x" data-content="button_text">Bookmark</span></a></div></li><li class="InlineList-item"><div class="download"><a id="6fc447ba81586b004ac0f8d926b1fc2b" rel="nofollow" data-download="{"attachment_id":35985445,"asset_id":9815512,"asset_type":"Work","always_allow_download":false,"track":null,"button_location":"work_strip","source":null,"hide_modal":null}" class="Button Button--sm Button--inverseGreen js-download-button prompt_button doc_download" href="https://www.academia.edu/attachments/35985445/download_file?st=MTczMjk4MzU1Miw4LjIyMi4yMDguMTQ2&s=work_strip"><i class="fa fa-arrow-circle-o-down fa-lg"></i><span class="u-textUppercase u-ml1x" data-content="button_text">Download</span></a></div></li><li class="InlineList-item"><ul class="InlineList InlineList--bordered u-ph0x"><li class="InlineList-item InlineList-item--bordered"><span class="InlineList-item-text">by <span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a class="u-tcGrayDark u-fw700" data-has-card-for-user="1203765" href="https://independent.academia.edu/NChung">Nelson Chung</a><script data-card-contents-for-user="1203765" type="text/json">{"id":1203765,"first_name":"Nelson","last_name":"Chung","domain_name":"independent","page_name":"NChung","display_name":"Nelson Chung","profile_url":"https://independent.academia.edu/NChung?f_ri=2963","photo":"https://0.academia-photos.com/1203765/432590/535662/s65_nelson.chung.jpg"}</script></span></span></li><li class="js-paper-rank-work_9815512 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="9815512"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 9815512, container: ".js-paper-rank-work_9815512", }); });</script></li><li class="js-percentile-work_9815512 InlineList-item InlineList-item--bordered hidden u-tcGrayDark"><span class="percentile-widget hidden"><span class="u-mr2x percentile-widget" style="display: none">•</span><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 9815512; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-percentile-work_9815512"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></li><li class="js-view-count-work_9815512 InlineList-item InlineList-item--bordered hidden"><div><span><span class="js-view-count view-count u-mr2x" data-work-id="9815512"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 9815512; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=9815512]").text(description); $(".js-view-count-work_9815512").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_9815512").removeClass('hidden') })</script></div></li><li class="InlineList-item u-positionRelative" style="max-width: 250px"><div class="u-positionAbsolute" data-has-card-for-ri-list="9815512"><i class="fa fa-tag InlineList-item-icon u-positionRelative"></i>  <a class="InlineList-item-text u-positionRelative">4</a>  </div><span class="InlineList-item-text u-textTruncate u-pl9x"><a class="InlineList-item-text" data-has-card-for-ri="161" href="https://www.academia.edu/Documents/in/Neuroscience">Neuroscience</a>, <script data-card-contents-for-ri="161" type="text/json">{"id":161,"name":"Neuroscience","url":"https://www.academia.edu/Documents/in/Neuroscience?f_ri=2963","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="377" href="https://www.academia.edu/Documents/in/Partial_Differential_Equations">Partial Differential Equations</a>, <script data-card-contents-for-ri="377" type="text/json">{"id":377,"name":"Partial Differential Equations","url":"https://www.academia.edu/Documents/in/Partial_Differential_Equations?f_ri=2963","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="2963" href="https://www.academia.edu/Documents/in/Mathematical_Biology">Mathematical Biology</a>, <script data-card-contents-for-ri="2963" type="text/json">{"id":2963,"name":"Mathematical Biology","url":"https://www.academia.edu/Documents/in/Mathematical_Biology?f_ri=2963","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="49731" href="https://www.academia.edu/Documents/in/Mathematical_Neuroscience">Mathematical Neuroscience</a><script data-card-contents-for-ri="49731" type="text/json">{"id":49731,"name":"Mathematical Neuroscience","url":"https://www.academia.edu/Documents/in/Mathematical_Neuroscience?f_ri=2963","nofollow":false}</script></span></li><script>(function(){ if (true) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=9815512]'), work: {"id":9815512,"title":"Fourier Solutions to the Cable Equation","created_at":"2014-12-17T11:56:16.255-08:00","url":"https://www.academia.edu/9815512/Fourier_Solutions_to_the_Cable_Equation?f_ri=2963","dom_id":"work_9815512","summary":"Not original research","downloadable_attachments":[{"id":35985445,"asset_id":9815512,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":1203765,"first_name":"Nelson","last_name":"Chung","domain_name":"independent","page_name":"NChung","display_name":"Nelson Chung","profile_url":"https://independent.academia.edu/NChung?f_ri=2963","photo":"https://0.academia-photos.com/1203765/432590/535662/s65_nelson.chung.jpg"}],"research_interests":[{"id":161,"name":"Neuroscience","url":"https://www.academia.edu/Documents/in/Neuroscience?f_ri=2963","nofollow":false},{"id":377,"name":"Partial Differential Equations","url":"https://www.academia.edu/Documents/in/Partial_Differential_Equations?f_ri=2963","nofollow":false},{"id":2963,"name":"Mathematical Biology","url":"https://www.academia.edu/Documents/in/Mathematical_Biology?f_ri=2963","nofollow":false},{"id":49731,"name":"Mathematical Neuroscience","url":"https://www.academia.edu/Documents/in/Mathematical_Neuroscience?f_ri=2963","nofollow":false}]}, }) } })();</script></ul></li></ul></div></div><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_33486032" data-work_id="33486032" itemscope="itemscope" itemtype="https://schema.org/ScholarlyArticle"><div class="header"><div class="title u-fontSerif u-fs22 u-lineHeight1_3"><a class="u-tcGrayDarkest js-work-link" href="https://www.academia.edu/33486032/Local_and_global_stability_analysis_of_a_two_prey_one_predator_model_with_help">Local and global stability analysis of a two prey one predator model with help</a></div></div><div class="u-pb4x u-mt3x"></div><ul class="InlineList u-ph0x u-fs13"><li class="InlineList-item logged_in_only"><div class="share_on_academia_work_button"><a class="academia_share Button Button--inverseBlue Button--sm js-bookmark-button" data-academia-share="Work/33486032" data-share-source="work_strip" data-spinner="small_white_hide_contents"><i class="fa fa-plus"></i><span class="work-strip-link-text u-ml1x" data-content="button_text">Bookmark</span></a></div></li><li class="InlineList-item"><div class="download"><a id="f60f45789237a8e641ad127ae670be48" rel="nofollow" data-download="{"attachment_id":53527137,"asset_id":33486032,"asset_type":"Work","always_allow_download":false,"track":null,"button_location":"work_strip","source":null,"hide_modal":null}" class="Button Button--sm Button--inverseGreen js-download-button prompt_button doc_download" href="https://www.academia.edu/attachments/53527137/download_file?st=MTczMjk4MzU1Miw4LjIyMi4yMDguMTQ2&s=work_strip"><i class="fa fa-arrow-circle-o-down fa-lg"></i><span class="u-textUppercase u-ml1x" data-content="button_text">Download</span></a></div></li><li class="InlineList-item"><ul class="InlineList InlineList--bordered u-ph0x"><li class="InlineList-item InlineList-item--bordered"><span class="InlineList-item-text">by <span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a class="u-tcGrayDark u-fw700" data-has-card-for-user="244809" href="https://iitmandi.academia.edu/SyedAbbas">Syed Abbas</a><script data-card-contents-for-user="244809" type="text/json">{"id":244809,"first_name":"Syed","last_name":"Abbas","domain_name":"iitmandi","page_name":"SyedAbbas","display_name":"Syed Abbas","profile_url":"https://iitmandi.academia.edu/SyedAbbas?f_ri=2963","photo":"https://0.academia-photos.com/244809/53075/48892/s65_syed.abbas.jpg"}</script></span></span></li><li class="js-paper-rank-work_33486032 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="33486032"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 33486032, container: ".js-paper-rank-work_33486032", }); });</script></li><li class="js-percentile-work_33486032 InlineList-item InlineList-item--bordered hidden u-tcGrayDark"><span class="percentile-widget hidden"><span class="u-mr2x percentile-widget" style="display: none">•</span><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 33486032; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-percentile-work_33486032"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></li><li class="js-view-count-work_33486032 InlineList-item InlineList-item--bordered hidden"><div><span><span class="js-view-count view-count u-mr2x" data-work-id="33486032"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 33486032; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=33486032]").text(description); $(".js-view-count-work_33486032").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_33486032").removeClass('hidden') })</script></div></li><li class="InlineList-item u-positionRelative" style="max-width: 250px"><div class="u-positionAbsolute" data-has-card-for-ri-list="33486032"><i class="fa fa-tag InlineList-item-icon u-positionRelative"></i>  <a class="InlineList-item-text u-positionRelative">7</a>  </div><span class="InlineList-item-text u-textTruncate u-pl9x"><a class="InlineList-item-text" data-has-card-for-ri="305" href="https://www.academia.edu/Documents/in/Applied_Mathematics">Applied Mathematics</a>, <script data-card-contents-for-ri="305" type="text/json">{"id":305,"name":"Applied Mathematics","url":"https://www.academia.edu/Documents/in/Applied_Mathematics?f_ri=2963","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="2963" href="https://www.academia.edu/Documents/in/Mathematical_Biology">Mathematical Biology</a>, <script data-card-contents-for-ri="2963" type="text/json">{"id":2963,"name":"Mathematical Biology","url":"https://www.academia.edu/Documents/in/Mathematical_Biology?f_ri=2963","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="16475" href="https://www.academia.edu/Documents/in/Competition">Competition</a>, <script data-card-contents-for-ri="16475" type="text/json">{"id":16475,"name":"Competition","url":"https://www.academia.edu/Documents/in/Competition?f_ri=2963","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="16605" href="https://www.academia.edu/Documents/in/Persistence">Persistence</a><script data-card-contents-for-ri="16605" type="text/json">{"id":16605,"name":"Persistence","url":"https://www.academia.edu/Documents/in/Persistence?f_ri=2963","nofollow":false}</script></span></li><script>(function(){ if (true) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=33486032]'), work: {"id":33486032,"title":"Local and global stability analysis of a two prey one predator model with help","created_at":"2017-06-15T10:24:48.772-07:00","url":"https://www.academia.edu/33486032/Local_and_global_stability_analysis_of_a_two_prey_one_predator_model_with_help?f_ri=2963","dom_id":"work_33486032","summary":null,"downloadable_attachments":[{"id":53527137,"asset_id":33486032,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":244809,"first_name":"Syed","last_name":"Abbas","domain_name":"iitmandi","page_name":"SyedAbbas","display_name":"Syed Abbas","profile_url":"https://iitmandi.academia.edu/SyedAbbas?f_ri=2963","photo":"https://0.academia-photos.com/244809/53075/48892/s65_syed.abbas.jpg"}],"research_interests":[{"id":305,"name":"Applied Mathematics","url":"https://www.academia.edu/Documents/in/Applied_Mathematics?f_ri=2963","nofollow":false},{"id":2963,"name":"Mathematical Biology","url":"https://www.academia.edu/Documents/in/Mathematical_Biology?f_ri=2963","nofollow":false},{"id":16475,"name":"Competition","url":"https://www.academia.edu/Documents/in/Competition?f_ri=2963","nofollow":false},{"id":16605,"name":"Persistence","url":"https://www.academia.edu/Documents/in/Persistence?f_ri=2963","nofollow":false},{"id":25600,"name":"Stability","url":"https://www.academia.edu/Documents/in/Stability?f_ri=2963"},{"id":556845,"name":"Numerical Analysis and Computational Mathematics","url":"https://www.academia.edu/Documents/in/Numerical_Analysis_and_Computational_Mathematics?f_ri=2963"},{"id":767089,"name":"Permanence","url":"https://www.academia.edu/Documents/in/Permanence?f_ri=2963"}]}, }) } })();</script></ul></li></ul></div></div><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_60659030" data-work_id="60659030" itemscope="itemscope" itemtype="https://schema.org/ScholarlyArticle"><div class="header"><div class="title u-fontSerif u-fs22 u-lineHeight1_3"><a class="u-tcGrayDarkest js-work-link" href="https://www.academia.edu/60659030/A_four_state_cross_bridge_model_for_muscle_contraction_Mathematical_study_and_validation">A four-state cross bridge model for muscle contraction. Mathematical study and validation</a></div></div><div class="u-pb4x u-mt3x"></div><ul class="InlineList u-ph0x u-fs13"><li class="InlineList-item logged_in_only"><div class="share_on_academia_work_button"><a class="academia_share Button Button--inverseBlue Button--sm js-bookmark-button" data-academia-share="Work/60659030" data-share-source="work_strip" data-spinner="small_white_hide_contents"><i class="fa fa-plus"></i><span class="work-strip-link-text u-ml1x" data-content="button_text">Bookmark</span></a></div></li><li class="InlineList-item"><div class="download"><a id="a938711b04c99f040e14345f3bffcc5b" rel="nofollow" data-download="{"attachment_id":74003038,"asset_id":60659030,"asset_type":"Work","always_allow_download":false,"track":null,"button_location":"work_strip","source":null,"hide_modal":null}" class="Button Button--sm Button--inverseGreen js-download-button prompt_button doc_download" href="https://www.academia.edu/attachments/74003038/download_file?st=MTczMjk4MzU1Miw4LjIyMi4yMDguMTQ2&s=work_strip"><i class="fa fa-arrow-circle-o-down fa-lg"></i><span class="u-textUppercase u-ml1x" data-content="button_text">Download</span></a></div></li><li class="InlineList-item"><ul class="InlineList InlineList--bordered u-ph0x"><li class="InlineList-item InlineList-item--bordered"><span class="InlineList-item-text">by <span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a class="u-tcGrayDark u-fw700" data-has-card-for-user="28655741" href="https://unipd.academia.edu/CReggiani">C. Reggiani</a><script data-card-contents-for-user="28655741" type="text/json">{"id":28655741,"first_name":"C.","last_name":"Reggiani","domain_name":"unipd","page_name":"CReggiani","display_name":"C. Reggiani","profile_url":"https://unipd.academia.edu/CReggiani?f_ri=2963","photo":"/images/s65_no_pic.png"}</script></span></span></li><li class="js-paper-rank-work_60659030 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="60659030"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 60659030, container: ".js-paper-rank-work_60659030", }); });</script></li><li class="js-percentile-work_60659030 InlineList-item InlineList-item--bordered hidden u-tcGrayDark"><span class="percentile-widget hidden"><span class="u-mr2x percentile-widget" style="display: none">•</span><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 60659030; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-percentile-work_60659030"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></li><li class="js-view-count-work_60659030 InlineList-item InlineList-item--bordered hidden"><div><span><span class="js-view-count view-count u-mr2x" data-work-id="60659030"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 60659030; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=60659030]").text(description); $(".js-view-count-work_60659030").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_60659030").removeClass('hidden') })</script></div></li><li class="InlineList-item u-positionRelative" style="max-width: 250px"><div class="u-positionAbsolute" data-has-card-for-ri-list="60659030"><i class="fa fa-tag InlineList-item-icon u-positionRelative"></i>  <a class="InlineList-item-text u-positionRelative">7</a>  </div><span class="InlineList-item-text u-textTruncate u-pl9x"><a class="InlineList-item-text" data-has-card-for-ri="300" href="https://www.academia.edu/Documents/in/Mathematics">Mathematics</a>, <script data-card-contents-for-ri="300" type="text/json">{"id":300,"name":"Mathematics","url":"https://www.academia.edu/Documents/in/Mathematics?f_ri=2963","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="2963" href="https://www.academia.edu/Documents/in/Mathematical_Biology">Mathematical Biology</a>, <script data-card-contents-for-ri="2963" type="text/json">{"id":2963,"name":"Mathematical Biology","url":"https://www.academia.edu/Documents/in/Mathematical_Biology?f_ri=2963","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="47884" href="https://www.academia.edu/Documents/in/Biological_Sciences">Biological Sciences</a>, <script data-card-contents-for-ri="47884" type="text/json">{"id":47884,"name":"Biological Sciences","url":"https://www.academia.edu/Documents/in/Biological_Sciences?f_ri=2963","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="80414" href="https://www.academia.edu/Documents/in/Mathematical_Sciences">Mathematical Sciences</a><script data-card-contents-for-ri="80414" type="text/json">{"id":80414,"name":"Mathematical Sciences","url":"https://www.academia.edu/Documents/in/Mathematical_Sciences?f_ri=2963","nofollow":false}</script></span></li><script>(function(){ if (true) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=60659030]'), work: {"id":60659030,"title":"A four-state cross bridge model for muscle contraction. Mathematical study and validation","created_at":"2021-11-01T01:27:44.023-07:00","url":"https://www.academia.edu/60659030/A_four_state_cross_bridge_model_for_muscle_contraction_Mathematical_study_and_validation?f_ri=2963","dom_id":"work_60659030","summary":null,"downloadable_attachments":[{"id":74003038,"asset_id":60659030,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":28655741,"first_name":"C.","last_name":"Reggiani","domain_name":"unipd","page_name":"CReggiani","display_name":"C. Reggiani","profile_url":"https://unipd.academia.edu/CReggiani?f_ri=2963","photo":"/images/s65_no_pic.png"}],"research_interests":[{"id":300,"name":"Mathematics","url":"https://www.academia.edu/Documents/in/Mathematics?f_ri=2963","nofollow":false},{"id":2963,"name":"Mathematical Biology","url":"https://www.academia.edu/Documents/in/Mathematical_Biology?f_ri=2963","nofollow":false},{"id":47884,"name":"Biological Sciences","url":"https://www.academia.edu/Documents/in/Biological_Sciences?f_ri=2963","nofollow":false},{"id":80414,"name":"Mathematical Sciences","url":"https://www.academia.edu/Documents/in/Mathematical_Sciences?f_ri=2963","nofollow":false},{"id":134095,"name":"Muscles","url":"https://www.academia.edu/Documents/in/Muscles?f_ri=2963"},{"id":556021,"name":"Muscle contraction","url":"https://www.academia.edu/Documents/in/Muscle_contraction?f_ri=2963"},{"id":1831948,"name":"Adenosine Diphosphate","url":"https://www.academia.edu/Documents/in/Adenosine_Diphosphate?f_ri=2963"}]}, }) } })();</script></ul></li></ul></div></div><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_53821590" data-work_id="53821590" itemscope="itemscope" itemtype="https://schema.org/ScholarlyArticle"><div class="header"><div class="title u-fontSerif u-fs22 u-lineHeight1_3"><a class="u-tcGrayDarkest js-work-link" href="https://www.academia.edu/53821590/Fitted_numerical_methods_for_delay_differential_equations_arising_in_biology">Fitted numerical methods for delay differential equations arising in biology</a></div></div><div class="u-pb4x u-mt3x"></div><ul class="InlineList u-ph0x u-fs13"><li class="InlineList-item logged_in_only"><div class="share_on_academia_work_button"><a class="academia_share Button Button--inverseBlue Button--sm js-bookmark-button" data-academia-share="Work/53821590" data-share-source="work_strip" data-spinner="small_white_hide_contents"><i class="fa fa-plus"></i><span class="work-strip-link-text u-ml1x" data-content="button_text">Bookmark</span></a></div></li><li class="InlineList-item"><div class="download"><a id="d0b69852067433889350d2b57d61285d" rel="nofollow" data-download="{"attachment_id":70483259,"asset_id":53821590,"asset_type":"Work","always_allow_download":false,"track":null,"button_location":"work_strip","source":null,"hide_modal":null}" class="Button Button--sm Button--inverseGreen js-download-button prompt_button doc_download" href="https://www.academia.edu/attachments/70483259/download_file?st=MTczMjk4MzU1Miw4LjIyMi4yMDguMTQ2&s=work_strip"><i class="fa fa-arrow-circle-o-down fa-lg"></i><span class="u-textUppercase u-ml1x" data-content="button_text">Download</span></a></div></li><li class="InlineList-item"><ul class="InlineList InlineList--bordered u-ph0x"><li class="InlineList-item InlineList-item--bordered"><span class="InlineList-item-text">by <span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a class="u-tcGrayDark u-fw700" data-has-card-for-user="678135" href="https://uofk.academia.edu/EihabBashier">Eihab Bashier</a><script data-card-contents-for-user="678135" type="text/json">{"id":678135,"first_name":"Eihab","last_name":"Bashier","domain_name":"uofk","page_name":"EihabBashier","display_name":"Eihab Bashier","profile_url":"https://uofk.academia.edu/EihabBashier?f_ri=2963","photo":"https://0.academia-photos.com/678135/12975072/14336716/s65_eihab.bashier.jpg"}</script></span></span></li><li class="js-paper-rank-work_53821590 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="53821590"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 53821590, container: ".js-paper-rank-work_53821590", }); });</script></li><li class="js-percentile-work_53821590 InlineList-item InlineList-item--bordered hidden u-tcGrayDark"><span class="percentile-widget hidden"><span class="u-mr2x percentile-widget" style="display: none">•</span><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 53821590; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-percentile-work_53821590"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></li><li class="js-view-count-work_53821590 InlineList-item InlineList-item--bordered hidden"><div><span><span class="js-view-count view-count u-mr2x" data-work-id="53821590"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 53821590; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=53821590]").text(description); $(".js-view-count-work_53821590").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_53821590").removeClass('hidden') })</script></div></li><li class="InlineList-item u-positionRelative" style="max-width: 250px"><div class="u-positionAbsolute" data-has-card-for-ri-list="53821590"><i class="fa fa-tag InlineList-item-icon u-positionRelative"></i>  <a class="InlineList-item-text u-positionRelative">2</a>  </div><span class="InlineList-item-text u-textTruncate u-pl9x"><a class="InlineList-item-text" data-has-card-for-ri="2963" href="https://www.academia.edu/Documents/in/Mathematical_Biology">Mathematical Biology</a>, <script data-card-contents-for-ri="2963" type="text/json">{"id":2963,"name":"Mathematical Biology","url":"https://www.academia.edu/Documents/in/Mathematical_Biology?f_ri=2963","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="6965" href="https://www.academia.edu/Documents/in/Singular_Perturbations">Singular Perturbations</a><script data-card-contents-for-ri="6965" type="text/json">{"id":6965,"name":"Singular Perturbations","url":"https://www.academia.edu/Documents/in/Singular_Perturbations?f_ri=2963","nofollow":false}</script></span></li><script>(function(){ if (true) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=53821590]'), work: {"id":53821590,"title":"Fitted numerical methods for delay differential equations arising in biology","created_at":"2021-09-28T18:36:39.246-07:00","url":"https://www.academia.edu/53821590/Fitted_numerical_methods_for_delay_differential_equations_arising_in_biology?f_ri=2963","dom_id":"work_53821590","summary":null,"downloadable_attachments":[{"id":70483259,"asset_id":53821590,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":678135,"first_name":"Eihab","last_name":"Bashier","domain_name":"uofk","page_name":"EihabBashier","display_name":"Eihab Bashier","profile_url":"https://uofk.academia.edu/EihabBashier?f_ri=2963","photo":"https://0.academia-photos.com/678135/12975072/14336716/s65_eihab.bashier.jpg"}],"research_interests":[{"id":2963,"name":"Mathematical Biology","url":"https://www.academia.edu/Documents/in/Mathematical_Biology?f_ri=2963","nofollow":false},{"id":6965,"name":"Singular Perturbations","url":"https://www.academia.edu/Documents/in/Singular_Perturbations?f_ri=2963","nofollow":false}]}, }) } })();</script></ul></li></ul></div></div><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_33039191" data-work_id="33039191" itemscope="itemscope" itemtype="https://schema.org/ScholarlyArticle"><div class="header"><div class="title u-fontSerif u-fs22 u-lineHeight1_3"><a class="u-tcGrayDarkest js-work-link" href="https://www.academia.edu/33039191/%D0%94%D0%B8%D0%BD%D0%B0%D0%BC%D0%B8%D1%87%D0%B5%D1%81%D0%BA%D0%BE%D0%B5_%D0%BC%D0%BE%D0%B4%D0%B5%D0%BB%D0%B8%D1%80%D0%BE%D0%B2%D0%B0%D0%BD%D0%B8%D0%B5_%D1%80%D0%BE%D1%81%D1%82%D0%B0_%D0%B4%D0%B5%D1%80%D0%B5%D0%B2%D1%8C%D0%B5%D0%B2_Dynamic_Modelling_of_Tree_Growth">Динамическое моделирование роста деревьев – Dynamic Modelling of Tree Growth</a></div></div><div class="u-pb4x u-mt3x"><div class="summary u-fs14 u-fw300 u-lineHeight1_5 u-tcGrayDarkest"><div class="summarized">The aim of this book is to give a contemporary review of tree growth modelling and represent our own results in this field. We demonstrate that the growth inhibition can be a result of a systemic level effect, which can be seen in a... <a class="more_link u-tcGrayDark u-linkUnstyled" data-container=".work_33039191" data-show=".complete" data-hide=".summarized" data-more-link-behavior="true" href="#">more</a></div><div class="complete hidden">The aim of this book is to give a contemporary review of tree growth modelling and represent our own results in this field. We demonstrate that the growth inhibition can be a result of a systemic level effect, which can be seen in a whole-tree physiological model which includes submodels for the processes of photosynthesis, mineral nutrition, respiration, phloem and xylem transport, and growth of roots, stems, and leaves.  <br /><br />The parts 1, 2 and 3 represent the review and analysis of existing models, beginning with simple growth formulas and then concentrating in contemporary dynamic (ecophysiological) models which contain many state variables and tens of parameters. The analysis of these models is given by the main components of growth process.<br /><br />Part 4 deals with the most important problem of causal tree growth analysis – the reason of growth cessation (self-inhibition) of too big tree. The arguments are given, showing the inadequacy of explanations which are based on Pütter-Bertalanffy equation. In the fig. 4.5 the numerical scheme of carbon balance for whole tree is represented, based on the experimental results of Estonian researchers.<br /><br />In part 5 the description of our model PUU-1 is given. It contains 9 state variables (see List of symbols), 6 driving variables (table 6.1) and 43 parameters (table 6.3). The model enables to analyze both seasonal and ontogenetic dynamics of evergreen tree growth. The summary of all equations of the model is represented in ch. 5.9.<br /><br />Part 6 deals with identification of the model: getting initial values of state variables and values of parameters and driving variables. More than half of them are based on the measurements made by Estonian researchers in Picea abies, others are taken from literature.<br /><br />Part 7 gives the results of numerical experiments with our model – analysis of sensitivity of model variables and parameters, examples of growth dynamics, including numerical experiments with fertilization. The model fits satisfactorily with measured data. The comparison of calculated tree ring dynamics with dendrochronological data shows great perspectives in applying dynamical growth models of whole tree in dendrochronology, as well as in growth analysis and prediction, including situations<br />and problems which arise in agroforestry.<br /><br />The most important theoretical result of our modelling is connected with self-inhibition of growth in tree ontogeny. It is shown, that self-inhibition of growth is taking place even without any aging factor, only because of size effects, which are mostly connected with changes in tree water exchange and trans port of assimilates (supplying of roots with assimilates becoming worse according to monotonous growth of cambium area). In the last chapter (7.6) the perspectives of tree growth modelling are discussed.</div></div></div><ul class="InlineList u-ph0x u-fs13"><li class="InlineList-item logged_in_only"><div class="share_on_academia_work_button"><a class="academia_share Button Button--inverseBlue Button--sm js-bookmark-button" data-academia-share="Work/33039191" data-share-source="work_strip" data-spinner="small_white_hide_contents"><i class="fa fa-plus"></i><span class="work-strip-link-text u-ml1x" data-content="button_text">Bookmark</span></a></div></li><li class="InlineList-item"><div class="download"><a id="e86718cbd4694a597bf3e8f889236786" rel="nofollow" data-download="{"attachment_id":53148195,"asset_id":33039191,"asset_type":"Work","always_allow_download":false,"track":null,"button_location":"work_strip","source":null,"hide_modal":null}" class="Button Button--sm Button--inverseGreen js-download-button prompt_button doc_download" href="https://www.academia.edu/attachments/53148195/download_file?st=MTczMjk4MzU1Miw4LjIyMi4yMDguMTQ2&s=work_strip"><i class="fa fa-arrow-circle-o-down fa-lg"></i><span class="u-textUppercase u-ml1x" data-content="button_text">Download</span></a></div></li><li class="InlineList-item"><ul class="InlineList InlineList--bordered u-ph0x"><li class="InlineList-item InlineList-item--bordered"><span class="InlineList-item-text">by <span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a class="u-tcGrayDark u-fw700" data-has-card-for-user="141980" href="https://ut-ee.academia.edu/KaleviKull">Kalevi Kull</a><script data-card-contents-for-user="141980" type="text/json">{"id":141980,"first_name":"Kalevi","last_name":"Kull","domain_name":"ut-ee","page_name":"KaleviKull","display_name":"Kalevi Kull","profile_url":"https://ut-ee.academia.edu/KaleviKull?f_ri=2963","photo":"https://0.academia-photos.com/141980/37665/34574905/s65_kalevi.kull.jpeg"}</script></span></span></li><li class="js-paper-rank-work_33039191 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="33039191"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 33039191, container: ".js-paper-rank-work_33039191", }); });</script></li><li class="js-percentile-work_33039191 InlineList-item InlineList-item--bordered hidden u-tcGrayDark"><span class="percentile-widget hidden"><span class="u-mr2x percentile-widget" style="display: none">•</span><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 33039191; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-percentile-work_33039191"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></li><li class="js-view-count-work_33039191 InlineList-item InlineList-item--bordered hidden"><div><span><span class="js-view-count view-count u-mr2x" data-work-id="33039191"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 33039191; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=33039191]").text(description); $(".js-view-count-work_33039191").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_33039191").removeClass('hidden') })</script></div></li><li class="InlineList-item u-positionRelative" style="max-width: 250px"><div class="u-positionAbsolute" data-has-card-for-ri-list="33039191"><i class="fa fa-tag InlineList-item-icon u-positionRelative"></i>  <a class="InlineList-item-text u-positionRelative">5</a>  </div><span class="InlineList-item-text u-textTruncate u-pl9x"><a class="InlineList-item-text" data-has-card-for-ri="2963" href="https://www.academia.edu/Documents/in/Mathematical_Biology">Mathematical Biology</a>, <script data-card-contents-for-ri="2963" type="text/json">{"id":2963,"name":"Mathematical Biology","url":"https://www.academia.edu/Documents/in/Mathematical_Biology?f_ri=2963","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="9708" href="https://www.academia.edu/Documents/in/System_Dynamics_Modeling">System Dynamics Modeling</a>, <script data-card-contents-for-ri="9708" type="text/json">{"id":9708,"name":"System Dynamics Modeling","url":"https://www.academia.edu/Documents/in/System_Dynamics_Modeling?f_ri=2963","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="37870" href="https://www.academia.edu/Documents/in/Organismal_Biology">Organismal Biology</a>, <script data-card-contents-for-ri="37870" type="text/json">{"id":37870,"name":"Organismal Biology","url":"https://www.academia.edu/Documents/in/Organismal_Biology?f_ri=2963","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="72643" href="https://www.academia.edu/Documents/in/Tree_Physiology">Tree Physiology</a><script data-card-contents-for-ri="72643" type="text/json">{"id":72643,"name":"Tree Physiology","url":"https://www.academia.edu/Documents/in/Tree_Physiology?f_ri=2963","nofollow":false}</script></span></li><script>(function(){ if (true) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=33039191]'), work: {"id":33039191,"title":"Динамическое моделирование роста деревьев – Dynamic Modelling of Tree Growth","created_at":"2017-05-16T07:17:13.715-07:00","url":"https://www.academia.edu/33039191/%D0%94%D0%B8%D0%BD%D0%B0%D0%BC%D0%B8%D1%87%D0%B5%D1%81%D0%BA%D0%BE%D0%B5_%D0%BC%D0%BE%D0%B4%D0%B5%D0%BB%D0%B8%D1%80%D0%BE%D0%B2%D0%B0%D0%BD%D0%B8%D0%B5_%D1%80%D0%BE%D1%81%D1%82%D0%B0_%D0%B4%D0%B5%D1%80%D0%B5%D0%B2%D1%8C%D0%B5%D0%B2_Dynamic_Modelling_of_Tree_Growth?f_ri=2963","dom_id":"work_33039191","summary":"The aim of this book is to give a contemporary review of tree growth modelling and represent our own results in this field. We demonstrate that the growth inhibition can be a result of a systemic level effect, which can be seen in a whole-tree physiological model which includes submodels for the processes of photosynthesis, mineral nutrition, respiration, phloem and xylem transport, and growth of roots, stems, and leaves. \n\nThe parts 1, 2 and 3 represent the review and analysis of existing models, beginning with simple growth formulas and then concentrating in contemporary dynamic (ecophysiological) models which contain many state variables and tens of parameters. The analysis of these models is given by the main components of growth process.\n\nPart 4 deals with the most important problem of causal tree growth analysis – the reason of growth cessation (self-inhibition) of too big tree. The arguments are given, showing the inadequacy of explanations which are based on Pütter-Bertalanffy equation. In the fig. 4.5 the numerical scheme of carbon balance for whole tree is represented, based on the experimental results of Estonian researchers.\n\nIn part 5 the description of our model PUU-1 is given. It contains 9 state variables (see List of symbols), 6 driving variables (table 6.1) and 43 parameters (table 6.3). The model enables to analyze both seasonal and ontogenetic dynamics of evergreen tree growth. The summary of all equations of the model is represented in ch. 5.9.\n\nPart 6 deals with identification of the model: getting initial values of state variables and values of parameters and driving variables. More than half of them are based on the measurements made by Estonian researchers in Picea abies, others are taken from literature.\n\nPart 7 gives the results of numerical experiments with our model – analysis of sensitivity of model variables and parameters, examples of growth dynamics, including numerical experiments with fertilization. The model fits satisfactorily with measured data. The comparison of calculated tree ring dynamics with dendrochronological data shows great perspectives in applying dynamical growth models of whole tree in dendrochronology, as well as in growth analysis and prediction, including situations\nand problems which arise in agroforestry.\n\nThe most important theoretical result of our modelling is connected with self-inhibition of growth in tree ontogeny. It is shown, that self-inhibition of growth is taking place even without any aging factor, only because of size effects, which are mostly connected with changes in tree water exchange and trans port of assimilates (supplying of roots with assimilates becoming worse according to monotonous growth of cambium area). In the last chapter (7.6) the perspectives of tree growth modelling are discussed.","downloadable_attachments":[{"id":53148195,"asset_id":33039191,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":141980,"first_name":"Kalevi","last_name":"Kull","domain_name":"ut-ee","page_name":"KaleviKull","display_name":"Kalevi Kull","profile_url":"https://ut-ee.academia.edu/KaleviKull?f_ri=2963","photo":"https://0.academia-photos.com/141980/37665/34574905/s65_kalevi.kull.jpeg"}],"research_interests":[{"id":2963,"name":"Mathematical Biology","url":"https://www.academia.edu/Documents/in/Mathematical_Biology?f_ri=2963","nofollow":false},{"id":9708,"name":"System Dynamics Modeling","url":"https://www.academia.edu/Documents/in/System_Dynamics_Modeling?f_ri=2963","nofollow":false},{"id":37870,"name":"Organismal Biology","url":"https://www.academia.edu/Documents/in/Organismal_Biology?f_ri=2963","nofollow":false},{"id":72643,"name":"Tree Physiology","url":"https://www.academia.edu/Documents/in/Tree_Physiology?f_ri=2963","nofollow":false},{"id":112160,"name":"Forest Growth Modelling","url":"https://www.academia.edu/Documents/in/Forest_Growth_Modelling?f_ri=2963"}]}, }) } })();</script></ul></li></ul></div></div><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_7435756" data-work_id="7435756" itemscope="itemscope" itemtype="https://schema.org/ScholarlyArticle"><div class="header"><div class="title u-fontSerif u-fs22 u-lineHeight1_3"><a class="u-tcGrayDarkest js-work-link" href="https://www.academia.edu/7435756/Modeling_Plant_Growth_With_Mathematical_Models">Modeling Plant Growth With Mathematical Models</a></div></div><div class="u-pb4x u-mt3x"></div><ul class="InlineList u-ph0x u-fs13"><li class="InlineList-item logged_in_only"><div class="share_on_academia_work_button"><a class="academia_share Button Button--inverseBlue Button--sm js-bookmark-button" data-academia-share="Work/7435756" data-share-source="work_strip" data-spinner="small_white_hide_contents"><i class="fa fa-plus"></i><span class="work-strip-link-text u-ml1x" data-content="button_text">Bookmark</span></a></div></li><li class="InlineList-item"><div class="download"><a id="5eb79d7310a0676823e40f120c6a3161" rel="nofollow" data-download="{"attachment_id":34018879,"asset_id":7435756,"asset_type":"Work","always_allow_download":false,"track":null,"button_location":"work_strip","source":null,"hide_modal":null}" class="Button Button--sm Button--inverseGreen js-download-button prompt_button doc_download" href="https://www.academia.edu/attachments/34018879/download_file?st=MTczMjk4MzU1Miw4LjIyMi4yMDguMTQ2&s=work_strip"><i class="fa fa-arrow-circle-o-down fa-lg"></i><span class="u-textUppercase u-ml1x" data-content="button_text">Download</span></a></div></li><li class="InlineList-item"><ul class="InlineList InlineList--bordered u-ph0x"><li class="InlineList-item InlineList-item--bordered"><span class="InlineList-item-text">by <span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a class="u-tcGrayDark u-fw700" data-has-card-for-user="6818463" href="https://mit.academia.edu/ShantanuJakhete">Shantanu Jakhete</a><script data-card-contents-for-user="6818463" type="text/json">{"id":6818463,"first_name":"Shantanu","last_name":"Jakhete","domain_name":"mit","page_name":"ShantanuJakhete","display_name":"Shantanu Jakhete","profile_url":"https://mit.academia.edu/ShantanuJakhete?f_ri=2963","photo":"https://0.academia-photos.com/6818463/3716865/4355200/s65_shantanu.jakhete.jpg"}</script></span></span></li><li class="js-paper-rank-work_7435756 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="7435756"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 7435756, container: ".js-paper-rank-work_7435756", }); });</script></li><li class="js-percentile-work_7435756 InlineList-item InlineList-item--bordered hidden u-tcGrayDark"><span class="percentile-widget hidden"><span class="u-mr2x percentile-widget" style="display: none">•</span><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 7435756; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-percentile-work_7435756"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></li><li class="js-view-count-work_7435756 InlineList-item InlineList-item--bordered hidden"><div><span><span class="js-view-count view-count u-mr2x" data-work-id="7435756"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 7435756; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=7435756]").text(description); $(".js-view-count-work_7435756").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_7435756").removeClass('hidden') })</script></div></li><li class="InlineList-item u-positionRelative" style="max-width: 250px"><div class="u-positionAbsolute" data-has-card-for-ri-list="7435756"><i class="fa fa-tag InlineList-item-icon u-positionRelative"></i>  <a class="InlineList-item-text u-positionRelative">3</a>  </div><span class="InlineList-item-text u-textTruncate u-pl9x"><a class="InlineList-item-text" data-has-card-for-ri="2963" href="https://www.academia.edu/Documents/in/Mathematical_Biology">Mathematical Biology</a>, <script data-card-contents-for-ri="2963" type="text/json">{"id":2963,"name":"Mathematical Biology","url":"https://www.academia.edu/Documents/in/Mathematical_Biology?f_ri=2963","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="16682" href="https://www.academia.edu/Documents/in/Mathematical_Modelling">Mathematical Modelling</a>, <script data-card-contents-for-ri="16682" type="text/json">{"id":16682,"name":"Mathematical Modelling","url":"https://www.academia.edu/Documents/in/Mathematical_Modelling?f_ri=2963","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="33408" href="https://www.academia.edu/Documents/in/Algebraic_Statistics">Algebraic Statistics</a><script data-card-contents-for-ri="33408" type="text/json">{"id":33408,"name":"Algebraic Statistics","url":"https://www.academia.edu/Documents/in/Algebraic_Statistics?f_ri=2963","nofollow":false}</script></span></li><script>(function(){ if (true) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=7435756]'), work: {"id":7435756,"title":"Modeling Plant Growth With Mathematical Models","created_at":"2014-06-23T09:37:07.367-07:00","url":"https://www.academia.edu/7435756/Modeling_Plant_Growth_With_Mathematical_Models?f_ri=2963","dom_id":"work_7435756","summary":null,"downloadable_attachments":[{"id":34018879,"asset_id":7435756,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":6818463,"first_name":"Shantanu","last_name":"Jakhete","domain_name":"mit","page_name":"ShantanuJakhete","display_name":"Shantanu Jakhete","profile_url":"https://mit.academia.edu/ShantanuJakhete?f_ri=2963","photo":"https://0.academia-photos.com/6818463/3716865/4355200/s65_shantanu.jakhete.jpg"}],"research_interests":[{"id":2963,"name":"Mathematical Biology","url":"https://www.academia.edu/Documents/in/Mathematical_Biology?f_ri=2963","nofollow":false},{"id":16682,"name":"Mathematical Modelling","url":"https://www.academia.edu/Documents/in/Mathematical_Modelling?f_ri=2963","nofollow":false},{"id":33408,"name":"Algebraic Statistics","url":"https://www.academia.edu/Documents/in/Algebraic_Statistics?f_ri=2963","nofollow":false}]}, }) } })();</script></ul></li></ul></div></div><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_9067342" data-work_id="9067342" itemscope="itemscope" itemtype="https://schema.org/ScholarlyArticle"><div class="header"><div class="title u-fontSerif u-fs22 u-lineHeight1_3"><a class="u-tcGrayDarkest js-work-link" href="https://www.academia.edu/9067342/Study_of_Van_Der_Pol_Oscillator">Study of Van Der Pol Oscillator</a></div></div><div class="u-pb4x u-mt3x"><div class="summary u-fs14 u-fw300 u-lineHeight1_5 u-tcGrayDarkest"><div class="summarized">We try to study the general properties of the Van der Pol oscillator like the occurrence of Hopf bifurcation and limit cycles. Thereafter we try to see the behavior of the oscillator near the limit cycle under periodic forcing and and... <a class="more_link u-tcGrayDark u-linkUnstyled" data-container=".work_9067342" data-show=".complete" data-hide=".summarized" data-more-link-behavior="true" href="#">more</a></div><div class="complete hidden">We try to study the general properties of the Van der Pol oscillator like the occurrence of Hopf bifurcation and limit cycles. Thereafter we try to see the behavior of the oscillator near the limit cycle under periodic forcing and and then under Gaussian white noise.</div></div></div><ul class="InlineList u-ph0x u-fs13"><li class="InlineList-item logged_in_only"><div class="share_on_academia_work_button"><a class="academia_share Button Button--inverseBlue Button--sm js-bookmark-button" data-academia-share="Work/9067342" data-share-source="work_strip" data-spinner="small_white_hide_contents"><i class="fa fa-plus"></i><span class="work-strip-link-text u-ml1x" data-content="button_text">Bookmark</span></a></div></li><li class="InlineList-item"><div class="download"><a id="549c02141c7e9bd98a791d67ab52af4b" rel="nofollow" data-download="{"attachment_id":35368375,"asset_id":9067342,"asset_type":"Work","always_allow_download":false,"track":null,"button_location":"work_strip","source":null,"hide_modal":null}" class="Button Button--sm Button--inverseGreen js-download-button prompt_button doc_download" href="https://www.academia.edu/attachments/35368375/download_file?st=MTczMjk4MzU1Miw4LjIyMi4yMDguMTQ2&s=work_strip"><i class="fa fa-arrow-circle-o-down fa-lg"></i><span class="u-textUppercase u-ml1x" data-content="button_text">Download</span></a></div></li><li class="InlineList-item"><ul class="InlineList InlineList--bordered u-ph0x"><li class="InlineList-item InlineList-item--bordered"><span class="InlineList-item-text">by <span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a class="u-tcGrayDark u-fw700" data-has-card-for-user="1248043" href="https://case.academia.edu/ShamreenIram">Shamreen Iram</a><script data-card-contents-for-user="1248043" type="text/json">{"id":1248043,"first_name":"Shamreen","last_name":"Iram","domain_name":"case","page_name":"ShamreenIram","display_name":"Shamreen Iram","profile_url":"https://case.academia.edu/ShamreenIram?f_ri=2963","photo":"/images/s65_no_pic.png"}</script></span></span></li><li class="js-paper-rank-work_9067342 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="9067342"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 9067342, container: ".js-paper-rank-work_9067342", }); });</script></li><li class="js-percentile-work_9067342 InlineList-item InlineList-item--bordered hidden u-tcGrayDark"><span class="percentile-widget hidden"><span class="u-mr2x percentile-widget" style="display: none">•</span><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 9067342; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-percentile-work_9067342"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></li><li class="js-view-count-work_9067342 InlineList-item InlineList-item--bordered hidden"><div><span><span class="js-view-count view-count u-mr2x" data-work-id="9067342"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 9067342; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=9067342]").text(description); $(".js-view-count-work_9067342").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_9067342").removeClass('hidden') })</script></div></li><li class="InlineList-item u-positionRelative" style="max-width: 250px"><div class="u-positionAbsolute" data-has-card-for-ri-list="9067342"><i class="fa fa-tag InlineList-item-icon u-positionRelative"></i>  <a class="InlineList-item-text u-positionRelative">7</a>  </div><span class="InlineList-item-text u-textTruncate u-pl9x"><a class="InlineList-item-text" data-has-card-for-ri="2963" href="https://www.academia.edu/Documents/in/Mathematical_Biology">Mathematical Biology</a>, <script data-card-contents-for-ri="2963" type="text/json">{"id":2963,"name":"Mathematical Biology","url":"https://www.academia.edu/Documents/in/Mathematical_Biology?f_ri=2963","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="5493" href="https://www.academia.edu/Documents/in/Nonlinear_dynamics">Nonlinear dynamics</a>, <script data-card-contents-for-ri="5493" type="text/json">{"id":5493,"name":"Nonlinear dynamics","url":"https://www.academia.edu/Documents/in/Nonlinear_dynamics?f_ri=2963","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="16682" href="https://www.academia.edu/Documents/in/Mathematical_Modelling">Mathematical Modelling</a>, <script data-card-contents-for-ri="16682" type="text/json">{"id":16682,"name":"Mathematical Modelling","url":"https://www.academia.edu/Documents/in/Mathematical_Modelling?f_ri=2963","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="65139" href="https://www.academia.edu/Documents/in/Patterns">Patterns</a><script data-card-contents-for-ri="65139" type="text/json">{"id":65139,"name":"Patterns","url":"https://www.academia.edu/Documents/in/Patterns?f_ri=2963","nofollow":false}</script></span></li><script>(function(){ if (true) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=9067342]'), work: {"id":9067342,"title":"Study of Van Der Pol Oscillator","created_at":"2014-11-01T16:23:01.767-07:00","url":"https://www.academia.edu/9067342/Study_of_Van_Der_Pol_Oscillator?f_ri=2963","dom_id":"work_9067342","summary":"We try to study the general properties of the Van der Pol oscillator like the occurrence of Hopf bifurcation and limit cycles. Thereafter we try to see the behavior of the oscillator near the limit cycle under periodic forcing and and then under Gaussian white noise. ","downloadable_attachments":[{"id":35368375,"asset_id":9067342,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":1248043,"first_name":"Shamreen","last_name":"Iram","domain_name":"case","page_name":"ShamreenIram","display_name":"Shamreen Iram","profile_url":"https://case.academia.edu/ShamreenIram?f_ri=2963","photo":"/images/s65_no_pic.png"}],"research_interests":[{"id":2963,"name":"Mathematical Biology","url":"https://www.academia.edu/Documents/in/Mathematical_Biology?f_ri=2963","nofollow":false},{"id":5493,"name":"Nonlinear dynamics","url":"https://www.academia.edu/Documents/in/Nonlinear_dynamics?f_ri=2963","nofollow":false},{"id":16682,"name":"Mathematical Modelling","url":"https://www.academia.edu/Documents/in/Mathematical_Modelling?f_ri=2963","nofollow":false},{"id":65139,"name":"Patterns","url":"https://www.academia.edu/Documents/in/Patterns?f_ri=2963","nofollow":false},{"id":222950,"name":"Oscillators","url":"https://www.academia.edu/Documents/in/Oscillators?f_ri=2963"},{"id":2829181,"name":"Non Linear Dynamics \u0026 Chaos","url":"https://www.academia.edu/Documents/in/Non_Linear_Dynamics_and_Chaos?f_ri=2963"},{"id":2829182,"name":"Waves in Ecology","url":"https://www.academia.edu/Documents/in/Waves_in_Ecology?f_ri=2963"}]}, }) } })();</script></ul></li></ul></div></div><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_21775677" data-work_id="21775677" itemscope="itemscope" itemtype="https://schema.org/ScholarlyArticle"><div class="header"><div class="title u-fontSerif u-fs22 u-lineHeight1_3"><a class="u-tcGrayDarkest js-work-link" href="https://www.academia.edu/21775677/DISCOVERIES_BOOKS_OF_SUNIRMAL_ROY">DISCOVERIES, BOOKS OF SUNIRMAL ROY</a></div></div><div class="u-pb4x u-mt3x"></div><ul class="InlineList u-ph0x u-fs13"><li class="InlineList-item logged_in_only"><div class="share_on_academia_work_button"><a class="academia_share Button Button--inverseBlue Button--sm js-bookmark-button" data-academia-share="Work/21775677" data-share-source="work_strip" data-spinner="small_white_hide_contents"><i class="fa fa-plus"></i><span class="work-strip-link-text u-ml1x" data-content="button_text">Bookmark</span></a></div></li><li class="InlineList-item"><div class="download"><a id="31f4bdbeaccb8df7f2d36e9983f9bd8e" rel="nofollow" data-download="{"attachment_id":42542791,"asset_id":21775677,"asset_type":"Work","always_allow_download":false,"track":null,"button_location":"work_strip","source":null,"hide_modal":null}" class="Button Button--sm Button--inverseGreen js-download-button prompt_button doc_download" href="https://www.academia.edu/attachments/42542791/download_file?st=MTczMjk4MzU1Miw4LjIyMi4yMDguMTQ2&s=work_strip"><i class="fa fa-arrow-circle-o-down fa-lg"></i><span class="u-textUppercase u-ml1x" data-content="button_text">Download</span></a></div></li><li class="InlineList-item"><ul class="InlineList InlineList--bordered u-ph0x"><li class="InlineList-item InlineList-item--bordered"><span class="InlineList-item-text">by <span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a class="u-tcGrayDark u-fw700" data-has-card-for-user="31576378" href="https://independent.academia.edu/SunirmalRoy">Sunirmal Roy</a><script data-card-contents-for-user="31576378" type="text/json">{"id":31576378,"first_name":"Sunirmal","last_name":"Roy","domain_name":"independent","page_name":"SunirmalRoy","display_name":"Sunirmal Roy","profile_url":"https://independent.academia.edu/SunirmalRoy?f_ri=2963","photo":"https://0.academia-photos.com/31576378/11491509/12817073/s65_sunirmal.roy.jpg"}</script></span></span></li><li class="js-paper-rank-work_21775677 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="21775677"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 21775677, container: ".js-paper-rank-work_21775677", }); });</script></li><li class="js-percentile-work_21775677 InlineList-item InlineList-item--bordered hidden u-tcGrayDark"><span class="percentile-widget hidden"><span class="u-mr2x percentile-widget" style="display: none">•</span><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 21775677; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-percentile-work_21775677"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></li><li class="js-view-count-work_21775677 InlineList-item InlineList-item--bordered hidden"><div><span><span class="js-view-count view-count u-mr2x" data-work-id="21775677"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 21775677; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=21775677]").text(description); $(".js-view-count-work_21775677").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_21775677").removeClass('hidden') })</script></div></li><li class="InlineList-item u-positionRelative" style="max-width: 250px"><div class="u-positionAbsolute" data-has-card-for-ri-list="21775677"><i class="fa fa-tag InlineList-item-icon u-positionRelative"></i></div><span class="InlineList-item-text u-textTruncate u-pl6x"><a class="InlineList-item-text" data-has-card-for-ri="2963" href="https://www.academia.edu/Documents/in/Mathematical_Biology">Mathematical Biology</a><script data-card-contents-for-ri="2963" type="text/json">{"id":2963,"name":"Mathematical Biology","url":"https://www.academia.edu/Documents/in/Mathematical_Biology?f_ri=2963","nofollow":false}</script></span></li><script>(function(){ if (false) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=21775677]'), work: {"id":21775677,"title":"DISCOVERIES, BOOKS OF SUNIRMAL ROY","created_at":"2016-02-10T07:20:07.322-08:00","url":"https://www.academia.edu/21775677/DISCOVERIES_BOOKS_OF_SUNIRMAL_ROY?f_ri=2963","dom_id":"work_21775677","summary":null,"downloadable_attachments":[{"id":42542791,"asset_id":21775677,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":31576378,"first_name":"Sunirmal","last_name":"Roy","domain_name":"independent","page_name":"SunirmalRoy","display_name":"Sunirmal Roy","profile_url":"https://independent.academia.edu/SunirmalRoy?f_ri=2963","photo":"https://0.academia-photos.com/31576378/11491509/12817073/s65_sunirmal.roy.jpg"}],"research_interests":[{"id":2963,"name":"Mathematical Biology","url":"https://www.academia.edu/Documents/in/Mathematical_Biology?f_ri=2963","nofollow":false}]}, }) } })();</script></ul></li></ul></div></div><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_11902260" data-work_id="11902260" itemscope="itemscope" itemtype="https://schema.org/ScholarlyArticle"><div class="header"><div class="title u-fontSerif u-fs22 u-lineHeight1_3"><a class="u-tcGrayDarkest js-work-link" href="https://www.academia.edu/11902260/PROOF_OF_GOLDBACHS_CONJECTURE">PROOF OF GOLDBACH'S CONJECTURE</a></div></div><div class="u-pb4x u-mt3x"><div class="summary u-fs14 u-fw300 u-lineHeight1_5 u-tcGrayDarkest">Every even integer > 2 is the sum of  two prime numbers  <br />                                      & equivalent <br />Each odd integer > 5 is the sum of three prime numbers <br />USING THE SIEVE OF ERATOSTHENES</div></div><ul class="InlineList u-ph0x u-fs13"><li class="InlineList-item logged_in_only"><div class="share_on_academia_work_button"><a class="academia_share Button Button--inverseBlue Button--sm js-bookmark-button" data-academia-share="Work/11902260" data-share-source="work_strip" data-spinner="small_white_hide_contents"><i class="fa fa-plus"></i><span class="work-strip-link-text u-ml1x" data-content="button_text">Bookmark</span></a></div></li><li class="InlineList-item"><div class="download"><a id="fb3c7efa4cd45d3aa648f714068f3479" rel="nofollow" data-download="{"attachment_id":79145408,"asset_id":11902260,"asset_type":"Work","always_allow_download":false,"track":null,"button_location":"work_strip","source":null,"hide_modal":null}" class="Button Button--sm Button--inverseGreen js-download-button prompt_button doc_download" href="https://www.academia.edu/attachments/79145408/download_file?st=MTczMjk4MzU1Miw4LjIyMi4yMDguMTQ2&s=work_strip"><i class="fa fa-arrow-circle-o-down fa-lg"></i><span class="u-textUppercase u-ml1x" data-content="button_text">Download</span></a></div></li><li class="InlineList-item"><ul class="InlineList InlineList--bordered u-ph0x"><li class="InlineList-item InlineList-item--bordered"><span class="InlineList-item-text">by <span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a class="u-tcGrayDark u-fw700" data-has-card-for-user="9406133" href="https://uoa.academia.edu/NikosMantzakourasUniversityofAthens">Nikos Mantzakouras</a><script data-card-contents-for-user="9406133" type="text/json">{"id":9406133,"first_name":"Nikos","last_name":"Mantzakouras","domain_name":"uoa","page_name":"NikosMantzakourasUniversityofAthens","display_name":"Nikos Mantzakouras","profile_url":"https://uoa.academia.edu/NikosMantzakourasUniversityofAthens?f_ri=2963","photo":"https://0.academia-photos.com/9406133/4334045/14414440/s65_nikos.mantzakouras.jpg"}</script></span></span></li><li class="js-paper-rank-work_11902260 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="11902260"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 11902260, container: ".js-paper-rank-work_11902260", }); });</script></li><li class="js-percentile-work_11902260 InlineList-item InlineList-item--bordered hidden u-tcGrayDark"><span class="percentile-widget hidden"><span class="u-mr2x percentile-widget" style="display: none">•</span><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 11902260; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-percentile-work_11902260"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></li><li class="js-view-count-work_11902260 InlineList-item InlineList-item--bordered hidden"><div><span><span class="js-view-count view-count u-mr2x" data-work-id="11902260"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 11902260; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=11902260]").text(description); $(".js-view-count-work_11902260").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_11902260").removeClass('hidden') })</script></div></li><li class="InlineList-item u-positionRelative" style="max-width: 250px"><div class="u-positionAbsolute" data-has-card-for-ri-list="11902260"><i class="fa fa-tag InlineList-item-icon u-positionRelative"></i>  <a class="InlineList-item-text u-positionRelative">52</a>  </div><span class="InlineList-item-text u-textTruncate u-pl10x"><a class="InlineList-item-text" data-has-card-for-ri="94" href="https://www.academia.edu/Documents/in/Discourse_Analysis">Discourse Analysis</a>, <script data-card-contents-for-ri="94" type="text/json">{"id":94,"name":"Discourse Analysis","url":"https://www.academia.edu/Documents/in/Discourse_Analysis?f_ri=2963","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="300" href="https://www.academia.edu/Documents/in/Mathematics">Mathematics</a>, <script data-card-contents-for-ri="300" type="text/json">{"id":300,"name":"Mathematics","url":"https://www.academia.edu/Documents/in/Mathematics?f_ri=2963","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="301" href="https://www.academia.edu/Documents/in/Number_Theory">Number Theory</a>, <script data-card-contents-for-ri="301" type="text/json">{"id":301,"name":"Number Theory","url":"https://www.academia.edu/Documents/in/Number_Theory?f_ri=2963","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="302" href="https://www.academia.edu/Documents/in/Analytic_Number_Theory">Analytic Number Theory</a><script data-card-contents-for-ri="302" type="text/json">{"id":302,"name":"Analytic Number Theory","url":"https://www.academia.edu/Documents/in/Analytic_Number_Theory?f_ri=2963","nofollow":false}</script></span></li><script>(function(){ if (true) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=11902260]'), work: {"id":11902260,"title":"PROOF OF GOLDBACH'S CONJECTURE","created_at":"2015-04-11T13:42:19.059-07:00","url":"https://www.academia.edu/11902260/PROOF_OF_GOLDBACHS_CONJECTURE?f_ri=2963","dom_id":"work_11902260","summary":"Every even integer \u003e 2 is the sum of two prime numbers \r\n \u0026 equivalent \r\nEach odd integer \u003e 5 is the sum of three prime numbers \r\nUSING THE SIEVE OF ERATOSTHENES ","downloadable_attachments":[{"id":79145408,"asset_id":11902260,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":9406133,"first_name":"Nikos","last_name":"Mantzakouras","domain_name":"uoa","page_name":"NikosMantzakourasUniversityofAthens","display_name":"Nikos Mantzakouras","profile_url":"https://uoa.academia.edu/NikosMantzakourasUniversityofAthens?f_ri=2963","photo":"https://0.academia-photos.com/9406133/4334045/14414440/s65_nikos.mantzakouras.jpg"}],"research_interests":[{"id":94,"name":"Discourse Analysis","url":"https://www.academia.edu/Documents/in/Discourse_Analysis?f_ri=2963","nofollow":false},{"id":300,"name":"Mathematics","url":"https://www.academia.edu/Documents/in/Mathematics?f_ri=2963","nofollow":false},{"id":301,"name":"Number Theory","url":"https://www.academia.edu/Documents/in/Number_Theory?f_ri=2963","nofollow":false},{"id":302,"name":"Analytic Number Theory","url":"https://www.academia.edu/Documents/in/Analytic_Number_Theory?f_ri=2963","nofollow":false},{"id":303,"name":"Algebraic Number Theory","url":"https://www.academia.edu/Documents/in/Algebraic_Number_Theory?f_ri=2963"},{"id":305,"name":"Applied Mathematics","url":"https://www.academia.edu/Documents/in/Applied_Mathematics?f_ri=2963"},{"id":318,"name":"Mathematical Physics","url":"https://www.academia.edu/Documents/in/Mathematical_Physics?f_ri=2963"},{"id":360,"name":"Logic And Foundations Of Mathematics","url":"https://www.academia.edu/Documents/in/Logic_And_Foundations_Of_Mathematics?f_ri=2963"},{"id":511,"name":"Materials Science","url":"https://www.academia.edu/Documents/in/Materials_Science?f_ri=2963"},{"id":757,"name":"Game Theory","url":"https://www.academia.edu/Documents/in/Game_Theory?f_ri=2963"},{"id":2084,"name":"History of Mathematics","url":"https://www.academia.edu/Documents/in/History_of_Mathematics?f_ri=2963"},{"id":2509,"name":"Philosophy Of Mathematics","url":"https://www.academia.edu/Documents/in/Philosophy_Of_Mathematics?f_ri=2963"},{"id":2620,"name":"Composite Materials and Structures","url":"https://www.academia.edu/Documents/in/Composite_Materials_and_Structures?f_ri=2963"},{"id":2731,"name":"Mathematics Education","url":"https://www.academia.edu/Documents/in/Mathematics_Education?f_ri=2963"},{"id":2963,"name":"Mathematical Biology","url":"https://www.academia.edu/Documents/in/Mathematical_Biology?f_ri=2963"},{"id":3853,"name":"Optimization (Mathematics)","url":"https://www.academia.edu/Documents/in/Optimization_Mathematics_?f_ri=2963"},{"id":4205,"name":"Data Analysis","url":"https://www.academia.edu/Documents/in/Data_Analysis?f_ri=2963"},{"id":10389,"name":"Philosophy of Mathematics Education","url":"https://www.academia.edu/Documents/in/Philosophy_of_Mathematics_Education?f_ri=2963"},{"id":10633,"name":"Critical Discourse Analysis","url":"https://www.academia.edu/Documents/in/Critical_Discourse_Analysis?f_ri=2963"},{"id":12022,"name":"Numerical Analysis","url":"https://www.academia.edu/Documents/in/Numerical_Analysis?f_ri=2963"},{"id":16221,"name":"Mathematical Modeling","url":"https://www.academia.edu/Documents/in/Mathematical_Modeling?f_ri=2963"},{"id":16682,"name":"Mathematical Modelling","url":"https://www.academia.edu/Documents/in/Mathematical_Modelling?f_ri=2963"},{"id":17442,"name":"Mathematical Logic","url":"https://www.academia.edu/Documents/in/Mathematical_Logic?f_ri=2963"},{"id":19997,"name":"Pure Mathematics","url":"https://www.academia.edu/Documents/in/Pure_Mathematics?f_ri=2963"},{"id":20254,"name":"Elementary Number Theory","url":"https://www.academia.edu/Documents/in/Elementary_Number_Theory?f_ri=2963"},{"id":20418,"name":"Mathematics Education Pedagogy","url":"https://www.academia.edu/Documents/in/Mathematics_Education_Pedagogy?f_ri=2963"},{"id":21093,"name":"Education (Mathematics)","url":"https://www.academia.edu/Documents/in/Education_Mathematics_?f_ri=2963"},{"id":27305,"name":"Computational Mathematics","url":"https://www.academia.edu/Documents/in/Computational_Mathematics?f_ri=2963"},{"id":27801,"name":"Mathematics Teacher Education","url":"https://www.academia.edu/Documents/in/Mathematics_Teacher_Education?f_ri=2963"},{"id":37345,"name":"Discrete Mathematics","url":"https://www.academia.edu/Documents/in/Discrete_Mathematics?f_ri=2963"},{"id":41130,"name":"Didactics of Mathematics","url":"https://www.academia.edu/Documents/in/Didactics_of_Mathematics?f_ri=2963"},{"id":50272,"name":"Maths","url":"https://www.academia.edu/Documents/in/Maths?f_ri=2963"},{"id":51604,"name":"Mathematic","url":"https://www.academia.edu/Documents/in/Mathematic?f_ri=2963"},{"id":56287,"name":"Matematica","url":"https://www.academia.edu/Documents/in/Matematica?f_ri=2963"},{"id":57698,"name":"Realistic Mathematics Education","url":"https://www.academia.edu/Documents/in/Realistic_Mathematics_Education?f_ri=2963"},{"id":72443,"name":"Prime Numbers","url":"https://www.academia.edu/Documents/in/Prime_Numbers?f_ri=2963"},{"id":77317,"name":"Mathmatics","url":"https://www.academia.edu/Documents/in/Mathmatics?f_ri=2963"},{"id":80414,"name":"Mathematical Sciences","url":"https://www.academia.edu/Documents/in/Mathematical_Sciences?f_ri=2963"},{"id":89676,"name":"Science and Mathematics Education","url":"https://www.academia.edu/Documents/in/Science_and_Mathematics_Education?f_ri=2963"},{"id":94827,"name":"Matemáticas","url":"https://www.academia.edu/Documents/in/Matem%C3%A1ticas?f_ri=2963"},{"id":102669,"name":"Mathematics for Primary and Secondary School","url":"https://www.academia.edu/Documents/in/Mathematics_for_Primary_and_Secondary_School?f_ri=2963"},{"id":126353,"name":"EDUCACION MATEMÁTICA","url":"https://www.academia.edu/Documents/in/EDUCACION_MATEMATICA?f_ri=2963"},{"id":153546,"name":"Primes","url":"https://www.academia.edu/Documents/in/Primes?f_ri=2963"},{"id":200014,"name":"Goldbach's Conjecture","url":"https://www.academia.edu/Documents/in/Goldbachs_Conjecture?f_ri=2963"},{"id":256975,"name":"Mathematics and Computer Science","url":"https://www.academia.edu/Documents/in/Mathematics_and_Computer_Science?f_ri=2963"},{"id":262138,"name":"Matematika","url":"https://www.academia.edu/Documents/in/Matematika?f_ri=2963"},{"id":265402,"name":"Applied Mathematics and Statistics","url":"https://www.academia.edu/Documents/in/Applied_Mathematics_and_Statistics?f_ri=2963"},{"id":388873,"name":"Mathematics and Statistics","url":"https://www.academia.edu/Documents/in/Mathematics_and_Statistics?f_ri=2963"},{"id":473227,"name":"Mathematic Education","url":"https://www.academia.edu/Documents/in/Mathematic_Education?f_ri=2963"},{"id":536161,"name":"Mesopotamian mathematics","url":"https://www.academia.edu/Documents/in/Mesopotamian_mathematics?f_ri=2963"},{"id":773824,"name":"Problem Posing in Mathematics","url":"https://www.academia.edu/Documents/in/Problem_Posing_in_Mathematics?f_ri=2963"},{"id":904819,"name":"Using Digital Technology for Teaching Mathematics","url":"https://www.academia.edu/Documents/in/Using_Digital_Technology_for_Teaching_Mathematics?f_ri=2963"}]}, }) } })();</script></ul></li></ul></div></div><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_7628110" data-work_id="7628110" itemscope="itemscope" itemtype="https://schema.org/ScholarlyArticle"><div class="header"><div class="title u-fontSerif u-fs22 u-lineHeight1_3"><a class="u-tcGrayDarkest js-work-link" href="https://www.academia.edu/7628110/mathematical_modelling_in_nature">mathematical modelling in nature</a></div></div><div class="u-pb4x u-mt3x"></div><ul class="InlineList u-ph0x u-fs13"><li class="InlineList-item logged_in_only"><div class="share_on_academia_work_button"><a class="academia_share Button Button--inverseBlue Button--sm js-bookmark-button" data-academia-share="Work/7628110" data-share-source="work_strip" data-spinner="small_white_hide_contents"><i class="fa fa-plus"></i><span class="work-strip-link-text u-ml1x" data-content="button_text">Bookmark</span></a></div></li><li class="InlineList-item"><div class="download"><a id="a38a6c2df628dd3e730798e8f5f6f658" rel="nofollow" data-download="{"attachment_id":34172147,"asset_id":7628110,"asset_type":"Work","always_allow_download":false,"track":null,"button_location":"work_strip","source":null,"hide_modal":null}" class="Button Button--sm Button--inverseGreen js-download-button prompt_button doc_download" href="https://www.academia.edu/attachments/34172147/download_file?st=MTczMjk4MzU1Miw4LjIyMi4yMDguMTQ2&s=work_strip"><i class="fa fa-arrow-circle-o-down fa-lg"></i><span class="u-textUppercase u-ml1x" data-content="button_text">Download</span></a></div></li><li class="InlineList-item"><ul class="InlineList InlineList--bordered u-ph0x"><li class="InlineList-item InlineList-item--bordered"><span class="InlineList-item-text">by <span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a class="u-tcGrayDark u-fw700" data-has-card-for-user="13791731" href="https://iiserb.academia.edu/merina">Merin Abraham</a><script data-card-contents-for-user="13791731" type="text/json">{"id":13791731,"first_name":"Merin","last_name":"Abraham","domain_name":"iiserb","page_name":"merina","display_name":"Merin Abraham","profile_url":"https://iiserb.academia.edu/merina?f_ri=2963","photo":"/images/s65_no_pic.png"}</script></span></span></li><li class="js-paper-rank-work_7628110 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="7628110"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 7628110, container: ".js-paper-rank-work_7628110", }); });</script></li><li class="js-percentile-work_7628110 InlineList-item InlineList-item--bordered hidden u-tcGrayDark"><span class="percentile-widget hidden"><span class="u-mr2x percentile-widget" style="display: none">•</span><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 7628110; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-percentile-work_7628110"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></li><li class="js-view-count-work_7628110 InlineList-item InlineList-item--bordered hidden"><div><span><span class="js-view-count view-count u-mr2x" data-work-id="7628110"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 7628110; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=7628110]").text(description); $(".js-view-count-work_7628110").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_7628110").removeClass('hidden') })</script></div></li><li class="InlineList-item u-positionRelative" style="max-width: 250px"><div class="u-positionAbsolute" data-has-card-for-ri-list="7628110"><i class="fa fa-tag InlineList-item-icon u-positionRelative"></i>  <a class="InlineList-item-text u-positionRelative">5</a>  </div><span class="InlineList-item-text u-textTruncate u-pl9x"><a class="InlineList-item-text" data-has-card-for-ri="300" href="https://www.academia.edu/Documents/in/Mathematics">Mathematics</a>, <script data-card-contents-for-ri="300" type="text/json">{"id":300,"name":"Mathematics","url":"https://www.academia.edu/Documents/in/Mathematics?f_ri=2963","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="2963" href="https://www.academia.edu/Documents/in/Mathematical_Biology">Mathematical Biology</a>, <script data-card-contents-for-ri="2963" type="text/json">{"id":2963,"name":"Mathematical Biology","url":"https://www.academia.edu/Documents/in/Mathematical_Biology?f_ri=2963","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="16221" href="https://www.academia.edu/Documents/in/Mathematical_Modeling">Mathematical Modeling</a>, <script data-card-contents-for-ri="16221" type="text/json">{"id":16221,"name":"Mathematical Modeling","url":"https://www.academia.edu/Documents/in/Mathematical_Modeling?f_ri=2963","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="16521" href="https://www.academia.edu/Documents/in/Mathematical_biology_Mathematics_">Mathematical biology (Mathematics)</a><script data-card-contents-for-ri="16521" type="text/json">{"id":16521,"name":"Mathematical biology (Mathematics)","url":"https://www.academia.edu/Documents/in/Mathematical_biology_Mathematics_?f_ri=2963","nofollow":false}</script></span></li><script>(function(){ if (true) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=7628110]'), work: {"id":7628110,"title":"mathematical modelling in nature","created_at":"2014-07-10T21:45:21.016-07:00","url":"https://www.academia.edu/7628110/mathematical_modelling_in_nature?f_ri=2963","dom_id":"work_7628110","summary":null,"downloadable_attachments":[{"id":34172147,"asset_id":7628110,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":13791731,"first_name":"Merin","last_name":"Abraham","domain_name":"iiserb","page_name":"merina","display_name":"Merin Abraham","profile_url":"https://iiserb.academia.edu/merina?f_ri=2963","photo":"/images/s65_no_pic.png"}],"research_interests":[{"id":300,"name":"Mathematics","url":"https://www.academia.edu/Documents/in/Mathematics?f_ri=2963","nofollow":false},{"id":2963,"name":"Mathematical Biology","url":"https://www.academia.edu/Documents/in/Mathematical_Biology?f_ri=2963","nofollow":false},{"id":16221,"name":"Mathematical Modeling","url":"https://www.academia.edu/Documents/in/Mathematical_Modeling?f_ri=2963","nofollow":false},{"id":16521,"name":"Mathematical biology (Mathematics)","url":"https://www.academia.edu/Documents/in/Mathematical_biology_Mathematics_?f_ri=2963","nofollow":false},{"id":16682,"name":"Mathematical Modelling","url":"https://www.academia.edu/Documents/in/Mathematical_Modelling?f_ri=2963"}]}, }) } })();</script></ul></li></ul></div></div><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_33861231" data-work_id="33861231" itemscope="itemscope" itemtype="https://schema.org/ScholarlyArticle"><div class="header"><div class="title u-fontSerif u-fs22 u-lineHeight1_3"><a class="u-tcGrayDarkest js-work-link" href="https://www.academia.edu/33861231/Symmetry_Breaking_Dynamics_in_Development">Symmetry-Breaking Dynamics in Development</a></div></div><div class="u-pb4x u-mt3x"><div class="summary u-fs14 u-fw300 u-lineHeight1_5 u-tcGrayDarkest"><div class="summarized">This article surveys and synthesizes dynamic systems models of development from biology, neuroscience, and psychology in order to propose an integrated account of growth, learning, and behavior. Key to this account is the concept of... <a class="more_link u-tcGrayDark u-linkUnstyled" data-container=".work_33861231" data-show=".complete" data-hide=".summarized" data-more-link-behavior="true" href="#">more</a></div><div class="complete hidden">This article surveys and synthesizes dynamic systems models of development from biology, neuroscience, and psychology in order to propose an integrated account of growth, learning, and behavior. Key to this account is the concept of self-differentiation or symmetry-breaking. I argue that development can be understood as a cascade of symmetry-breaking events brought about by the ongoing interactions of multiple, nested, nonlinear dynamic systems whose self-organizing behaviors gradually alter their own anatomical conditions.</div></div></div><ul class="InlineList u-ph0x u-fs13"><li class="InlineList-item logged_in_only"><div class="share_on_academia_work_button"><a class="academia_share Button Button--inverseBlue Button--sm js-bookmark-button" data-academia-share="Work/33861231" data-share-source="work_strip" data-spinner="small_white_hide_contents"><i class="fa fa-plus"></i><span class="work-strip-link-text u-ml1x" data-content="button_text">Bookmark</span></a></div></li><li class="InlineList-item"><div class="download"><a id="59c2ddd29d1c0c2993bac8daa8f55e48" rel="nofollow" data-download="{"attachment_id":54404601,"asset_id":33861231,"asset_type":"Work","always_allow_download":false,"track":null,"button_location":"work_strip","source":null,"hide_modal":null}" class="Button Button--sm Button--inverseGreen js-download-button prompt_button doc_download" href="https://www.academia.edu/attachments/54404601/download_file?st=MTczMjk4MzU1Miw4LjIyMi4yMDguMTQ2&s=work_strip"><i class="fa fa-arrow-circle-o-down fa-lg"></i><span class="u-textUppercase u-ml1x" data-content="button_text">Download</span></a></div></li><li class="InlineList-item"><ul class="InlineList InlineList--bordered u-ph0x"><li class="InlineList-item InlineList-item--bordered"><span class="InlineList-item-text">by <span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a class="u-tcGrayDark u-fw700" data-has-card-for-user="141511" href="https://dawsoncollege.academia.edu/NoahMossBrender">Noah Moss Brender</a><script data-card-contents-for-user="141511" type="text/json">{"id":141511,"first_name":"Noah","last_name":"Moss Brender","domain_name":"dawsoncollege","page_name":"NoahMossBrender","display_name":"Noah Moss Brender","profile_url":"https://dawsoncollege.academia.edu/NoahMossBrender?f_ri=2963","photo":"https://0.academia-photos.com/141511/37536/467829/s65_noah.moss_brender.jpg"}</script></span></span></li><li class="js-paper-rank-work_33861231 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="33861231"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 33861231, container: ".js-paper-rank-work_33861231", }); });</script></li><li class="js-percentile-work_33861231 InlineList-item InlineList-item--bordered hidden u-tcGrayDark"><span class="percentile-widget hidden"><span class="u-mr2x percentile-widget" style="display: none">•</span><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 33861231; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-percentile-work_33861231"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></li><li class="js-view-count-work_33861231 InlineList-item InlineList-item--bordered hidden"><div><span><span class="js-view-count view-count u-mr2x" data-work-id="33861231"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 33861231; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=33861231]").text(description); $(".js-view-count-work_33861231").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_33861231").removeClass('hidden') })</script></div></li><li class="InlineList-item u-positionRelative" style="max-width: 250px"><div class="u-positionAbsolute" data-has-card-for-ri-list="33861231"><i class="fa fa-tag InlineList-item-icon u-positionRelative"></i>  <a class="InlineList-item-text u-positionRelative">58</a>  </div><span class="InlineList-item-text u-textTruncate u-pl10x"><a class="InlineList-item-text" data-has-card-for-ri="156" href="https://www.academia.edu/Documents/in/Genetics">Genetics</a>, <script data-card-contents-for-ri="156" type="text/json">{"id":156,"name":"Genetics","url":"https://www.academia.edu/Documents/in/Genetics?f_ri=2963","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="161" href="https://www.academia.edu/Documents/in/Neuroscience">Neuroscience</a>, <script data-card-contents-for-ri="161" type="text/json">{"id":161,"name":"Neuroscience","url":"https://www.academia.edu/Documents/in/Neuroscience?f_ri=2963","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="221" href="https://www.academia.edu/Documents/in/Psychology">Psychology</a>, <script data-card-contents-for-ri="221" type="text/json">{"id":221,"name":"Psychology","url":"https://www.academia.edu/Documents/in/Psychology?f_ri=2963","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="237" href="https://www.academia.edu/Documents/in/Cognitive_Science">Cognitive Science</a><script data-card-contents-for-ri="237" type="text/json">{"id":237,"name":"Cognitive Science","url":"https://www.academia.edu/Documents/in/Cognitive_Science?f_ri=2963","nofollow":false}</script></span></li><script>(function(){ if (true) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=33861231]'), work: {"id":33861231,"title":"Symmetry-Breaking Dynamics in Development","created_at":"2017-07-12T12:47:10.553-07:00","url":"https://www.academia.edu/33861231/Symmetry_Breaking_Dynamics_in_Development?f_ri=2963","dom_id":"work_33861231","summary":"This article surveys and synthesizes dynamic systems models of development from biology, neuroscience, and psychology in order to propose an integrated account of growth, learning, and behavior. Key to this account is the concept of self-differentiation or symmetry-breaking. I argue that development can be understood as a cascade of symmetry-breaking events brought about by the ongoing interactions of multiple, nested, nonlinear dynamic systems whose self-organizing behaviors gradually alter their own anatomical conditions.","downloadable_attachments":[{"id":54404601,"asset_id":33861231,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":141511,"first_name":"Noah","last_name":"Moss Brender","domain_name":"dawsoncollege","page_name":"NoahMossBrender","display_name":"Noah Moss Brender","profile_url":"https://dawsoncollege.academia.edu/NoahMossBrender?f_ri=2963","photo":"https://0.academia-photos.com/141511/37536/467829/s65_noah.moss_brender.jpg"}],"research_interests":[{"id":156,"name":"Genetics","url":"https://www.academia.edu/Documents/in/Genetics?f_ri=2963","nofollow":false},{"id":161,"name":"Neuroscience","url":"https://www.academia.edu/Documents/in/Neuroscience?f_ri=2963","nofollow":false},{"id":221,"name":"Psychology","url":"https://www.academia.edu/Documents/in/Psychology?f_ri=2963","nofollow":false},{"id":237,"name":"Cognitive Science","url":"https://www.academia.edu/Documents/in/Cognitive_Science?f_ri=2963","nofollow":false},{"id":251,"name":"Neuropsychology","url":"https://www.academia.edu/Documents/in/Neuropsychology?f_ri=2963"},{"id":252,"name":"Developmental Psychology","url":"https://www.academia.edu/Documents/in/Developmental_Psychology?f_ri=2963"},{"id":977,"name":"Development Studies","url":"https://www.academia.edu/Documents/in/Development_Studies?f_ri=2963"},{"id":1047,"name":"Behavioral Sciences","url":"https://www.academia.edu/Documents/in/Behavioral_Sciences?f_ri=2963"},{"id":1080,"name":"Dynamical Systems","url":"https://www.academia.edu/Documents/in/Dynamical_Systems?f_ri=2963"},{"id":1083,"name":"Developmental Biology","url":"https://www.academia.edu/Documents/in/Developmental_Biology?f_ri=2963"},{"id":2380,"name":"Plasticity","url":"https://www.academia.edu/Documents/in/Plasticity?f_ri=2963"},{"id":2749,"name":"Animal Behavior","url":"https://www.academia.edu/Documents/in/Animal_Behavior?f_ri=2963"},{"id":2963,"name":"Mathematical Biology","url":"https://www.academia.edu/Documents/in/Mathematical_Biology?f_ri=2963"},{"id":3155,"name":"Complexity Theory","url":"https://www.academia.edu/Documents/in/Complexity_Theory?f_ri=2963"},{"id":3375,"name":"Self-Organization","url":"https://www.academia.edu/Documents/in/Self-Organization?f_ri=2963"},{"id":4117,"name":"Motor Development","url":"https://www.academia.edu/Documents/in/Motor_Development?f_ri=2963"},{"id":4258,"name":"Embryology","url":"https://www.academia.edu/Documents/in/Embryology?f_ri=2963"},{"id":5178,"name":"Phenomenology","url":"https://www.academia.edu/Documents/in/Phenomenology?f_ri=2963"},{"id":5493,"name":"Nonlinear dynamics","url":"https://www.academia.edu/Documents/in/Nonlinear_dynamics?f_ri=2963"},{"id":5960,"name":"Continental Philosophy","url":"https://www.academia.edu/Documents/in/Continental_Philosophy?f_ri=2963"},{"id":7150,"name":"Complex Systems","url":"https://www.academia.edu/Documents/in/Complex_Systems?f_ri=2963"},{"id":7466,"name":"Human Development","url":"https://www.academia.edu/Documents/in/Human_Development?f_ri=2963"},{"id":8418,"name":"Maurice Merleau-Ponty","url":"https://www.academia.edu/Documents/in/Maurice_Merleau-Ponty?f_ri=2963"},{"id":10500,"name":"Intentionality","url":"https://www.academia.edu/Documents/in/Intentionality?f_ri=2963"},{"id":16577,"name":"Biological Physics","url":"https://www.academia.edu/Documents/in/Biological_Physics?f_ri=2963"},{"id":21071,"name":"Phenotypic Plasticity","url":"https://www.academia.edu/Documents/in/Phenotypic_Plasticity?f_ri=2963"},{"id":23922,"name":"Dynamical systems and Chaos","url":"https://www.academia.edu/Documents/in/Dynamical_systems_and_Chaos?f_ri=2963"},{"id":24769,"name":"Chaos/Complexity Theory","url":"https://www.academia.edu/Documents/in/Chaos_Complexity_Theory?f_ri=2963"},{"id":27784,"name":"Gene expression","url":"https://www.academia.edu/Documents/in/Gene_expression?f_ri=2963"},{"id":27785,"name":"Enactivism","url":"https://www.academia.edu/Documents/in/Enactivism?f_ri=2963"},{"id":30545,"name":"Dynamical Systems Approach to Cognition","url":"https://www.academia.edu/Documents/in/Dynamical_Systems_Approach_to_Cognition?f_ri=2963"},{"id":31091,"name":"Complex Adaptive Systems","url":"https://www.academia.edu/Documents/in/Complex_Adaptive_Systems?f_ri=2963"},{"id":39002,"name":"Sensorimotor Neuroscience","url":"https://www.academia.edu/Documents/in/Sensorimotor_Neuroscience?f_ri=2963"},{"id":39495,"name":"Human Growth and Development","url":"https://www.academia.edu/Documents/in/Human_Growth_and_Development?f_ri=2963"},{"id":42276,"name":"Neuroplasticity","url":"https://www.academia.edu/Documents/in/Neuroplasticity?f_ri=2963"},{"id":50680,"name":"Sensemaking","url":"https://www.academia.edu/Documents/in/Sensemaking?f_ri=2963"},{"id":53205,"name":"Sense-Making","url":"https://www.academia.edu/Documents/in/Sense-Making?f_ri=2963"},{"id":54589,"name":"Anatomy","url":"https://www.academia.edu/Documents/in/Anatomy?f_ri=2963"},{"id":54659,"name":"Subjectivity","url":"https://www.academia.edu/Documents/in/Subjectivity?f_ri=2963"},{"id":66092,"name":"Sensorimotor integration","url":"https://www.academia.edu/Documents/in/Sensorimotor_integration?f_ri=2963"},{"id":91722,"name":"Philosophy of the Subject","url":"https://www.academia.edu/Documents/in/Philosophy_of_the_Subject?f_ri=2963"},{"id":100966,"name":"Brain Plasticity","url":"https://www.academia.edu/Documents/in/Brain_Plasticity?f_ri=2963"},{"id":122266,"name":"Nonlinear and complex dynamical systems","url":"https://www.academia.edu/Documents/in/Nonlinear_and_complex_dynamical_systems?f_ri=2963"},{"id":126829,"name":"Symmetry","url":"https://www.academia.edu/Documents/in/Symmetry?f_ri=2963"},{"id":154228,"name":"Bifurcation","url":"https://www.academia.edu/Documents/in/Bifurcation?f_ri=2963"},{"id":156403,"name":"Enactive cognition","url":"https://www.academia.edu/Documents/in/Enactive_cognition?f_ri=2963"},{"id":162351,"name":"Self-Organized Criticality","url":"https://www.academia.edu/Documents/in/Self-Organized_Criticality?f_ri=2963"},{"id":279495,"name":"Robustness","url":"https://www.academia.edu/Documents/in/Robustness?f_ri=2963"},{"id":310813,"name":"Criticality","url":"https://www.academia.edu/Documents/in/Criticality?f_ri=2963"},{"id":312135,"name":"Sensorimotor learning","url":"https://www.academia.edu/Documents/in/Sensorimotor_learning?f_ri=2963"},{"id":362853,"name":"Embodied and Enactive Cognition","url":"https://www.academia.edu/Documents/in/Embodied_and_Enactive_Cognition?f_ri=2963"},{"id":679741,"name":"Sensorimotor Control","url":"https://www.academia.edu/Documents/in/Sensorimotor_Control?f_ri=2963"},{"id":717029,"name":"Stability and Chaos","url":"https://www.academia.edu/Documents/in/Stability_and_Chaos?f_ri=2963"},{"id":822720,"name":"Sensorimotor contingencies","url":"https://www.academia.edu/Documents/in/Sensorimotor_contingencies?f_ri=2963"},{"id":899203,"name":"Sensorimotor Approach","url":"https://www.academia.edu/Documents/in/Sensorimotor_Approach?f_ri=2963"},{"id":931948,"name":"Gene expression and regulation","url":"https://www.academia.edu/Documents/in/Gene_expression_and_regulation?f_ri=2963"},{"id":1009869,"name":"Self Organized Criticality","url":"https://www.academia.edu/Documents/in/Self_Organized_Criticality?f_ri=2963"},{"id":1239755,"name":"Neurosciences","url":"https://www.academia.edu/Documents/in/Neurosciences?f_ri=2963"}]}, }) } })();</script></ul></li></ul></div></div><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_38973209" data-work_id="38973209" itemscope="itemscope" itemtype="https://schema.org/ScholarlyArticle"><div class="header"><div class="title u-fontSerif u-fs22 u-lineHeight1_3"><a class="u-tcGrayDarkest js-work-link" href="https://www.academia.edu/38973209/On_Theoretical_Biology_Life_Science_between_Mathematics_and_Semiotics_Teoreetilisest_bioloogiast_Eluteadus_matemaatika_ja_semiootika_vahel_2019">On Theoretical Biology: Life Science between Mathematics and Semiotics (Teoreetilisest bioloogiast: Eluteadus matemaatika ja semiootika vahel) 2019.</a></div></div><div class="u-pb4x u-mt3x"><div class="summary u-fs14 u-fw300 u-lineHeight1_5 u-tcGrayDarkest">Includes a description of history of theoretical biology and the author's contributions to the Estonian Spring Schools in Theoretical Biology (1975–2019) – altogether over 50 essays. University of Tartu Press, 495 pp.</div></div><ul class="InlineList u-ph0x u-fs13"><li class="InlineList-item logged_in_only"><div class="share_on_academia_work_button"><a class="academia_share Button Button--inverseBlue Button--sm js-bookmark-button" data-academia-share="Work/38973209" data-share-source="work_strip" data-spinner="small_white_hide_contents"><i class="fa fa-plus"></i><span class="work-strip-link-text u-ml1x" data-content="button_text">Bookmark</span></a></div></li><li class="InlineList-item"><div class="download"><a id="ee6c001739169096db12dba457072aaa" rel="nofollow" data-download="{"attachment_id":65404253,"asset_id":38973209,"asset_type":"Work","always_allow_download":false,"track":null,"button_location":"work_strip","source":null,"hide_modal":null}" class="Button Button--sm Button--inverseGreen js-download-button prompt_button doc_download" href="https://www.academia.edu/attachments/65404253/download_file?st=MTczMjk4MzU1Miw4LjIyMi4yMDguMTQ2&s=work_strip"><i class="fa fa-arrow-circle-o-down fa-lg"></i><span class="u-textUppercase u-ml1x" data-content="button_text">Download</span></a></div></li><li class="InlineList-item"><ul class="InlineList InlineList--bordered u-ph0x"><li class="InlineList-item InlineList-item--bordered"><span class="InlineList-item-text">by <span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a class="u-tcGrayDark u-fw700" data-has-card-for-user="141980" href="https://ut-ee.academia.edu/KaleviKull">Kalevi Kull</a><script data-card-contents-for-user="141980" type="text/json">{"id":141980,"first_name":"Kalevi","last_name":"Kull","domain_name":"ut-ee","page_name":"KaleviKull","display_name":"Kalevi Kull","profile_url":"https://ut-ee.academia.edu/KaleviKull?f_ri=2963","photo":"https://0.academia-photos.com/141980/37665/34574905/s65_kalevi.kull.jpeg"}</script></span></span></li><li class="js-paper-rank-work_38973209 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="38973209"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 38973209, container: ".js-paper-rank-work_38973209", }); });</script></li><li class="js-percentile-work_38973209 InlineList-item InlineList-item--bordered hidden u-tcGrayDark"><span class="percentile-widget hidden"><span class="u-mr2x percentile-widget" style="display: none">•</span><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 38973209; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-percentile-work_38973209"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></li><li class="js-view-count-work_38973209 InlineList-item InlineList-item--bordered hidden"><div><span><span class="js-view-count view-count u-mr2x" data-work-id="38973209"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 38973209; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=38973209]").text(description); $(".js-view-count-work_38973209").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_38973209").removeClass('hidden') })</script></div></li><li class="InlineList-item u-positionRelative" style="max-width: 250px"><div class="u-positionAbsolute" data-has-card-for-ri-list="38973209"><i class="fa fa-tag InlineList-item-icon u-positionRelative"></i>  <a class="InlineList-item-text u-positionRelative">11</a>  </div><span class="InlineList-item-text u-textTruncate u-pl10x"><a class="InlineList-item-text" data-has-card-for-ri="823" href="https://www.academia.edu/Documents/in/Philosophy_of_Biology">Philosophy of Biology</a>, <script data-card-contents-for-ri="823" type="text/json">{"id":823,"name":"Philosophy of Biology","url":"https://www.academia.edu/Documents/in/Philosophy_of_Biology?f_ri=2963","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="2963" href="https://www.academia.edu/Documents/in/Mathematical_Biology">Mathematical Biology</a>, <script data-card-contents-for-ri="2963" type="text/json">{"id":2963,"name":"Mathematical Biology","url":"https://www.academia.edu/Documents/in/Mathematical_Biology?f_ri=2963","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="3939" href="https://www.academia.edu/Documents/in/History_and_Philosophy_of_Biology">History and Philosophy of Biology</a>, <script data-card-contents-for-ri="3939" type="text/json">{"id":3939,"name":"History and Philosophy of Biology","url":"https://www.academia.edu/Documents/in/History_and_Philosophy_of_Biology?f_ri=2963","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="5590" href="https://www.academia.edu/Documents/in/Biomathematics">Biomathematics</a><script data-card-contents-for-ri="5590" type="text/json">{"id":5590,"name":"Biomathematics","url":"https://www.academia.edu/Documents/in/Biomathematics?f_ri=2963","nofollow":false}</script></span></li><script>(function(){ if (true) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=38973209]'), work: {"id":38973209,"title":"On Theoretical Biology: Life Science between Mathematics and Semiotics (Teoreetilisest bioloogiast: Eluteadus matemaatika ja semiootika vahel) 2019.","created_at":"2019-04-29T12:06:42.325-07:00","url":"https://www.academia.edu/38973209/On_Theoretical_Biology_Life_Science_between_Mathematics_and_Semiotics_Teoreetilisest_bioloogiast_Eluteadus_matemaatika_ja_semiootika_vahel_2019?f_ri=2963","dom_id":"work_38973209","summary":"Includes a description of history of theoretical biology and the author's contributions to the Estonian Spring Schools in Theoretical Biology (1975–2019) – altogether over 50 essays. University of Tartu Press, 495 pp. ","downloadable_attachments":[{"id":65404253,"asset_id":38973209,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":141980,"first_name":"Kalevi","last_name":"Kull","domain_name":"ut-ee","page_name":"KaleviKull","display_name":"Kalevi Kull","profile_url":"https://ut-ee.academia.edu/KaleviKull?f_ri=2963","photo":"https://0.academia-photos.com/141980/37665/34574905/s65_kalevi.kull.jpeg"}],"research_interests":[{"id":823,"name":"Philosophy of Biology","url":"https://www.academia.edu/Documents/in/Philosophy_of_Biology?f_ri=2963","nofollow":false},{"id":2963,"name":"Mathematical Biology","url":"https://www.academia.edu/Documents/in/Mathematical_Biology?f_ri=2963","nofollow":false},{"id":3939,"name":"History and Philosophy of Biology","url":"https://www.academia.edu/Documents/in/History_and_Philosophy_of_Biology?f_ri=2963","nofollow":false},{"id":5590,"name":"Biomathematics","url":"https://www.academia.edu/Documents/in/Biomathematics?f_ri=2963","nofollow":false},{"id":7710,"name":"Biology","url":"https://www.academia.edu/Documents/in/Biology?f_ri=2963"},{"id":9231,"name":"Biosemiotics","url":"https://www.academia.edu/Documents/in/Biosemiotics?f_ri=2963"},{"id":13075,"name":"History of Biology","url":"https://www.academia.edu/Documents/in/History_of_Biology?f_ri=2963"},{"id":16682,"name":"Mathematical Modelling","url":"https://www.academia.edu/Documents/in/Mathematical_Modelling?f_ri=2963"},{"id":26977,"name":"Theoretical biology","url":"https://www.academia.edu/Documents/in/Theoretical_biology?f_ri=2963"},{"id":206504,"name":"General Biology","url":"https://www.academia.edu/Documents/in/General_Biology?f_ri=2963"},{"id":1943105,"name":"Integral Biomathics","url":"https://www.academia.edu/Documents/in/Integral_Biomathics?f_ri=2963"}]}, }) } })();</script></ul></li></ul></div></div><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_37424427 coauthored" data-work_id="37424427" itemscope="itemscope" itemtype="https://schema.org/ScholarlyArticle"><div class="header"><div class="title u-fontSerif u-fs22 u-lineHeight1_3"><a class="u-tcGrayDarkest js-work-link" href="https://www.academia.edu/37424427/Golden_ratio_and_Klein_bottle_Logophysics_the_Keys_of_the_Codes_of_Life_and_Cognition_Reply_to_Liu_et_al_Is_the_golden_ratio_a_universal_constant_for_self_replication_">Golden ratio and Klein bottle Logophysics: the Keys of the Codes of Life and Cognition (Reply to Liu et al, " Is the golden ratio a universal constant for self-replication? "</a></div></div><div class="u-pb4x u-mt3x"><div class="summary u-fs14 u-fw300 u-lineHeight1_5 u-tcGrayDarkest"><div class="summarized">We present 1) a novel unified conception of science, cognition and phenomenology in terms of the Klein Bottle logophysics, 2) as a supradual creative agency based on self and hetero-reference and multistate logic associated to the... <a class="more_link u-tcGrayDark u-linkUnstyled" data-container=".work_37424427" data-show=".complete" data-hide=".summarized" data-more-link-behavior="true" href="#">more</a></div><div class="complete hidden">We present 1) a novel unified conception of science, cognition and phenomenology in terms of the Klein Bottle logophysics, 2) as a supradual creative agency based on self and hetero-reference and multistate logic associated to the non-orientable topologies of the Moebius strip and Klein Bottle surfaces, 3) the Golden ratio in several areas of biology (particularly genomics), cognition, perception, physics and music, and the multiple biochemical codes of life ; 4) semiosis and topological folding in the génesis of life ; 5) the torsion geometries and non-orientable topologies, and apply them to 6) human-bodyplan, neurosciences, music cognition, structure and processes of thinking, particularly Quantum Mechanics, creativity and the logics of the psyche; 7) a universal principle of self-organization and the genesis of life, the π-related visual cortex and holography; 8) as an harmonic principle in the brain's pattern formation, pattern recognition and morphogenesis, and the topological paradigm to neuroscience; 9) higher-order cybernetics, ontopoiesis and autopoiesis in Systems Biology,the psyche's bi-logic; 10) a rebuttal of Dr. Liu et all's PLOS article claiming the appearance of Phi in genomes as accidental, in terms of the supradual ontopoiesis hereby presented and by reviewing several codes of life discovered by Pérez, which elicit their unity already starting at the level of the periodic table of elements and Life compounds atomic mass; and 11) the Golden mean in the rituals of whales.</div></div></div><ul class="InlineList u-ph0x u-fs13"><li class="InlineList-item logged_in_only"><div class="share_on_academia_work_button"><a class="academia_share Button Button--inverseBlue Button--sm js-bookmark-button" data-academia-share="Work/37424427" data-share-source="work_strip" data-spinner="small_white_hide_contents"><i class="fa fa-plus"></i><span class="work-strip-link-text u-ml1x" data-content="button_text">Bookmark</span></a></div></li><li class="InlineList-item"><div class="download"><a id="af0d8ab1c78be6a9bb67a47de9238d86" rel="nofollow" data-download="{"attachment_id":57389549,"asset_id":37424427,"asset_type":"Work","always_allow_download":false,"track":null,"button_location":"work_strip","source":null,"hide_modal":null}" class="Button Button--sm Button--inverseGreen js-download-button prompt_button doc_download" href="https://www.academia.edu/attachments/57389549/download_file?st=MTczMjk4MzU1Miw4LjIyMi4yMDguMTQ2&s=work_strip"><i class="fa fa-arrow-circle-o-down fa-lg"></i><span class="u-textUppercase u-ml1x" data-content="button_text">Download</span></a></div></li><li class="InlineList-item"><ul class="InlineList InlineList--bordered u-ph0x"><li class="InlineList-item InlineList-item--bordered"><span class="InlineList-item-text">by <span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a class="u-tcGrayDark u-fw700" data-has-card-for-user="1799161" href="https://unq.academia.edu/DiegoRapoport">Diego Lucio Rapoport (Campodonico)</a><script data-card-contents-for-user="1799161" type="text/json">{"id":1799161,"first_name":"Diego Lucio","last_name":"Rapoport (Campodonico)","domain_name":"unq","page_name":"DiegoRapoport","display_name":"Diego Lucio Rapoport (Campodonico)","profile_url":"https://unq.academia.edu/DiegoRapoport?f_ri=2963","photo":"https://0.academia-photos.com/1799161/615050/763655/s65_diego.rapoport.jpg"}</script></span></span><span class="u-displayInlineBlock InlineList-item-text"> and <span class="u-textDecorationUnderline u-clickable InlineList-item-text js-work-more-authors-37424427">+1</span><div class="hidden js-additional-users-37424427"><div><span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a href="https://independent.academia.edu/JeanclaudePerez">Jean-claude Perez</a></span></div></div></span><script>(function(){ var popoverSettings = { el: $('.js-work-more-authors-37424427'), placement: 'bottom', hide_delay: 200, html: true, content: function(){ return $('.js-additional-users-37424427').html(); } } new HoverPopover(popoverSettings); })();</script></li><li class="js-paper-rank-work_37424427 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="37424427"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 37424427, container: ".js-paper-rank-work_37424427", }); });</script></li><li class="js-percentile-work_37424427 InlineList-item InlineList-item--bordered hidden u-tcGrayDark"><span class="percentile-widget hidden"><span class="u-mr2x percentile-widget" style="display: none">•</span><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 37424427; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-percentile-work_37424427"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></li><li class="js-view-count-work_37424427 InlineList-item InlineList-item--bordered hidden"><div><span><span class="js-view-count view-count u-mr2x" data-work-id="37424427"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 37424427; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=37424427]").text(description); $(".js-view-count-work_37424427").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_37424427").removeClass('hidden') })</script></div></li><li class="InlineList-item u-positionRelative" style="max-width: 250px"><div class="u-positionAbsolute" data-has-card-for-ri-list="37424427"><i class="fa fa-tag InlineList-item-icon u-positionRelative"></i>  <a class="InlineList-item-text u-positionRelative">17</a>  </div><span class="InlineList-item-text u-textTruncate u-pl10x"><a class="InlineList-item-text" data-has-card-for-ri="98" href="https://www.academia.edu/Documents/in/Semiotics">Semiotics</a>, <script data-card-contents-for-ri="98" type="text/json">{"id":98,"name":"Semiotics","url":"https://www.academia.edu/Documents/in/Semiotics?f_ri=2963","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="146" href="https://www.academia.edu/Documents/in/Bioinformatics">Bioinformatics</a>, <script data-card-contents-for-ri="146" type="text/json">{"id":146,"name":"Bioinformatics","url":"https://www.academia.edu/Documents/in/Bioinformatics?f_ri=2963","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="155" href="https://www.academia.edu/Documents/in/Evolutionary_Biology">Evolutionary Biology</a>, <script data-card-contents-for-ri="155" type="text/json">{"id":155,"name":"Evolutionary Biology","url":"https://www.academia.edu/Documents/in/Evolutionary_Biology?f_ri=2963","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="161" href="https://www.academia.edu/Documents/in/Neuroscience">Neuroscience</a><script data-card-contents-for-ri="161" type="text/json">{"id":161,"name":"Neuroscience","url":"https://www.academia.edu/Documents/in/Neuroscience?f_ri=2963","nofollow":false}</script></span></li><script>(function(){ if (true) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=37424427]'), work: {"id":37424427,"title":"Golden ratio and Klein bottle Logophysics: the Keys of the Codes of Life and Cognition (Reply to Liu et al, \" Is the golden ratio a universal constant for self-replication? \"","created_at":"2018-09-16T05:26:10.911-07:00","url":"https://www.academia.edu/37424427/Golden_ratio_and_Klein_bottle_Logophysics_the_Keys_of_the_Codes_of_Life_and_Cognition_Reply_to_Liu_et_al_Is_the_golden_ratio_a_universal_constant_for_self_replication_?f_ri=2963","dom_id":"work_37424427","summary":"We present 1) a novel unified conception of science, cognition and phenomenology in terms of the Klein Bottle logophysics, 2) as a supradual creative agency based on self and hetero-reference and multistate logic associated to the non-orientable topologies of the Moebius strip and Klein Bottle surfaces, 3) the Golden ratio in several areas of biology (particularly genomics), cognition, perception, physics and music, and the multiple biochemical codes of life ; 4) semiosis and topological folding in the génesis of life ; 5) the torsion geometries and non-orientable topologies, and apply them to 6) human-bodyplan, neurosciences, music cognition, structure and processes of thinking, particularly Quantum Mechanics, creativity and the logics of the psyche; 7) a universal principle of self-organization and the genesis of life, the π-related visual cortex and holography; 8) as an harmonic principle in the brain's pattern formation, pattern recognition and morphogenesis, and the topological paradigm to neuroscience; 9) higher-order cybernetics, ontopoiesis and autopoiesis in Systems Biology,the psyche's bi-logic; 10) a rebuttal of Dr. Liu et all's PLOS article claiming the appearance of Phi in genomes as accidental, in terms of the supradual ontopoiesis hereby presented and by reviewing several codes of life discovered by Pérez, which elicit their unity already starting at the level of the periodic table of elements and Life compounds atomic mass; and 11) the Golden mean in the rituals of whales.","downloadable_attachments":[{"id":57389549,"asset_id":37424427,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":1799161,"first_name":"Diego Lucio","last_name":"Rapoport (Campodonico)","domain_name":"unq","page_name":"DiegoRapoport","display_name":"Diego Lucio Rapoport (Campodonico)","profile_url":"https://unq.academia.edu/DiegoRapoport?f_ri=2963","photo":"https://0.academia-photos.com/1799161/615050/763655/s65_diego.rapoport.jpg"},{"id":4902080,"first_name":"Jean-claude","last_name":"Perez","domain_name":"independent","page_name":"JeanclaudePerez","display_name":"Jean-claude Perez","profile_url":"https://independent.academia.edu/JeanclaudePerez?f_ri=2963","photo":"https://0.academia-photos.com/4902080/2110319/2479751/s65_jean-claude.perez.jpg"}],"research_interests":[{"id":98,"name":"Semiotics","url":"https://www.academia.edu/Documents/in/Semiotics?f_ri=2963","nofollow":false},{"id":146,"name":"Bioinformatics","url":"https://www.academia.edu/Documents/in/Bioinformatics?f_ri=2963","nofollow":false},{"id":155,"name":"Evolutionary Biology","url":"https://www.academia.edu/Documents/in/Evolutionary_Biology?f_ri=2963","nofollow":false},{"id":161,"name":"Neuroscience","url":"https://www.academia.edu/Documents/in/Neuroscience?f_ri=2963","nofollow":false},{"id":167,"name":"Physiology","url":"https://www.academia.edu/Documents/in/Physiology?f_ri=2963"},{"id":237,"name":"Cognitive Science","url":"https://www.academia.edu/Documents/in/Cognitive_Science?f_ri=2963"},{"id":360,"name":"Logic And Foundations Of Mathematics","url":"https://www.academia.edu/Documents/in/Logic_And_Foundations_Of_Mathematics?f_ri=2963"},{"id":518,"name":"Quantum Physics","url":"https://www.academia.edu/Documents/in/Quantum_Physics?f_ri=2963"},{"id":805,"name":"Ontology","url":"https://www.academia.edu/Documents/in/Ontology?f_ri=2963"},{"id":2963,"name":"Mathematical Biology","url":"https://www.academia.edu/Documents/in/Mathematical_Biology?f_ri=2963"},{"id":3216,"name":"Genomics","url":"https://www.academia.edu/Documents/in/Genomics?f_ri=2963"},{"id":5178,"name":"Phenomenology","url":"https://www.academia.edu/Documents/in/Phenomenology?f_ri=2963"},{"id":5400,"name":"Systems Biology","url":"https://www.academia.edu/Documents/in/Systems_Biology?f_ri=2963"},{"id":13279,"name":"Philosophy of Logic","url":"https://www.academia.edu/Documents/in/Philosophy_of_Logic?f_ri=2963"},{"id":37360,"name":"Second-Order Cybernetics","url":"https://www.academia.edu/Documents/in/Second-Order_Cybernetics?f_ri=2963"},{"id":41023,"name":"Social Cognitive Affective Neuroscience","url":"https://www.academia.edu/Documents/in/Social_Cognitive_Affective_Neuroscience?f_ri=2963"},{"id":85695,"name":"Music Perception and Cognition","url":"https://www.academia.edu/Documents/in/Music_Perception_and_Cognition?f_ri=2963"}]}, }) } })();</script></ul></li></ul></div></div></div><div class="u-taCenter Pagination"><ul class="pagination"><li class="next_page"><a href="/Documents/in/Mathematical_Biology?after=50%2C37424427" rel="next">Next</a></li><li class="last next"><a href="/Documents/in/Mathematical_Biology?page=last">Last »</a></li></ul></div></div><div class="hidden-xs hidden-sm"><div class="u-pl6x"><div style="width: 300px;"><div class="panel panel-flat u-mt7x"><div class="panel-heading u-p5x"><div class="u-tcGrayDark u-taCenter u-fw700 u-textUppercase">Related Topics</div></div><ul class="list-group"><li class="list-group-item media_v2 u-mt0x u-p3x"><div class="media-body"><div class="u-tcGrayDarker u-fw700"><a class="u-tcGrayDarker" href="https://www.academia.edu/Documents/in/Mathematical_Modelling">Mathematical Modelling</a></div></div><div class="media-right media-middle"><a class="u-tcGreen u-textDecorationNone u-linkUnstyled u-fw500 hidden" data-follow-ri-id="16682">Follow</a><a class="u-tcGray u-textDecorationNone u-linkUnstyled u-fw500 hidden" data-unfollow-ri-id="16682">Following</a></div></li><li class="list-group-item media_v2 u-mt0x u-p3x"><div class="media-body"><div class="u-tcGrayDarker u-fw700"><a class="u-tcGrayDarker" href="https://www.academia.edu/Documents/in/Waves_in_Ecology">Waves in Ecology</a></div></div><div class="media-right media-middle"><a class="u-tcGreen u-textDecorationNone u-linkUnstyled u-fw500 hidden" data-follow-ri-id="2829182">Follow</a><a class="u-tcGray u-textDecorationNone u-linkUnstyled u-fw500 hidden" data-unfollow-ri-id="2829182">Following</a></div></li><li class="list-group-item media_v2 u-mt0x u-p3x"><div class="media-body"><div class="u-tcGrayDarker u-fw700"><a class="u-tcGrayDarker" href="https://www.academia.edu/Documents/in/Non_Linear_Dynamics_and_Chaos">Non Linear Dynamics & Chaos</a></div></div><div class="media-right media-middle"><a class="u-tcGreen u-textDecorationNone u-linkUnstyled u-fw500 hidden" data-follow-ri-id="2829181">Follow</a><a class="u-tcGray u-textDecorationNone u-linkUnstyled u-fw500 hidden" data-unfollow-ri-id="2829181">Following</a></div></li><li class="list-group-item media_v2 u-mt0x u-p3x"><div class="media-body"><div class="u-tcGrayDarker u-fw700"><a class="u-tcGrayDarker" href="https://www.academia.edu/Documents/in/Mathematical_Epidemiology">Mathematical Epidemiology</a></div></div><div class="media-right media-middle"><a class="u-tcGreen u-textDecorationNone u-linkUnstyled u-fw500 hidden" data-follow-ri-id="13398">Follow</a><a class="u-tcGray u-textDecorationNone u-linkUnstyled u-fw500 hidden" data-unfollow-ri-id="13398">Following</a></div></li><li class="list-group-item media_v2 u-mt0x u-p3x"><div class="media-body"><div class="u-tcGrayDarker u-fw700"><a class="u-tcGrayDarker" href="https://www.academia.edu/Documents/in/Patterns">Patterns</a></div></div><div class="media-right media-middle"><a class="u-tcGreen u-textDecorationNone u-linkUnstyled u-fw500 hidden" data-follow-ri-id="65139">Follow</a><a class="u-tcGray u-textDecorationNone u-linkUnstyled u-fw500 hidden" data-unfollow-ri-id="65139">Following</a></div></li><li class="list-group-item media_v2 u-mt0x u-p3x"><div class="media-body"><div class="u-tcGrayDarker u-fw700"><a class="u-tcGrayDarker" href="https://www.academia.edu/Documents/in/Mathematical_Ecology">Mathematical Ecology</a></div></div><div class="media-right media-middle"><a class="u-tcGreen u-textDecorationNone u-linkUnstyled u-fw500 hidden" data-follow-ri-id="15396">Follow</a><a class="u-tcGray u-textDecorationNone u-linkUnstyled u-fw500 hidden" data-unfollow-ri-id="15396">Following</a></div></li><li class="list-group-item media_v2 u-mt0x u-p3x"><div class="media-body"><div class="u-tcGrayDarker u-fw700"><a class="u-tcGrayDarker" href="https://www.academia.edu/Documents/in/Dynamical_Systems">Dynamical Systems</a></div></div><div class="media-right media-middle"><a class="u-tcGreen u-textDecorationNone u-linkUnstyled u-fw500 hidden" data-follow-ri-id="1080">Follow</a><a class="u-tcGray u-textDecorationNone u-linkUnstyled u-fw500 hidden" data-unfollow-ri-id="1080">Following</a></div></li><li class="list-group-item media_v2 u-mt0x u-p3x"><div class="media-body"><div class="u-tcGrayDarker u-fw700"><a class="u-tcGrayDarker" href="https://www.academia.edu/Documents/in/Biomathematics">Biomathematics</a></div></div><div class="media-right media-middle"><a class="u-tcGreen u-textDecorationNone u-linkUnstyled u-fw500 hidden" data-follow-ri-id="5590">Follow</a><a class="u-tcGray u-textDecorationNone u-linkUnstyled u-fw500 hidden" data-unfollow-ri-id="5590">Following</a></div></li><li class="list-group-item media_v2 u-mt0x u-p3x"><div class="media-body"><div class="u-tcGrayDarker u-fw700"><a class="u-tcGrayDarker" href="https://www.academia.edu/Documents/in/Systems_Biology">Systems Biology</a></div></div><div class="media-right media-middle"><a class="u-tcGreen u-textDecorationNone u-linkUnstyled u-fw500 hidden" data-follow-ri-id="5400">Follow</a><a class="u-tcGray u-textDecorationNone u-linkUnstyled u-fw500 hidden" data-unfollow-ri-id="5400">Following</a></div></li><li class="list-group-item media_v2 u-mt0x u-p3x"><div class="media-body"><div class="u-tcGrayDarker u-fw700"><a class="u-tcGrayDarker" href="https://www.academia.edu/Documents/in/Mathematics">Mathematics</a></div></div><div class="media-right media-middle"><a class="u-tcGreen u-textDecorationNone u-linkUnstyled u-fw500 hidden" data-follow-ri-id="300">Follow</a><a class="u-tcGray u-textDecorationNone u-linkUnstyled u-fw500 hidden" data-unfollow-ri-id="300">Following</a></div></li></ul></div></div></div></div></div></div><script>// MIT License // Copyright © 2011 Sebastian Tschan, https://blueimp.net // Permission is hereby granted, free of charge, to any person obtaining a copy of // this software and associated documentation files (the "Software"), to deal in // the Software without restriction, including without limitation the rights to // use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of // the Software, and to permit persons to whom the Software is furnished to do so, // subject to the following conditions: // The above copyright notice and this permission notice shall be included in all // copies or substantial portions of the Software. // THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR // IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS // FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR // COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER // IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN // CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. !function(n){"use strict";function d(n,t){var r=(65535&n)+(65535&t);return(n>>16)+(t>>16)+(r>>16)<<16|65535&r}function f(n,t,r,e,o,u){return d((c=d(d(t,n),d(e,u)))<<(f=o)|c>>>32-f,r);var c,f}function l(n,t,r,e,o,u,c){return f(t&r|~t&e,n,t,o,u,c)}function v(n,t,r,e,o,u,c){return f(t&e|r&~e,n,t,o,u,c)}function g(n,t,r,e,o,u,c){return f(t^r^e,n,t,o,u,c)}function m(n,t,r,e,o,u,c){return f(r^(t|~e),n,t,o,u,c)}function i(n,t){var r,e,o,u;n[t>>5]|=128<<t%32,n[14+(t+64>>>9<<4)]=t;for(var c=1732584193,f=-271733879,i=-1732584194,a=271733878,h=0;h<n.length;h+=16)c=l(r=c,e=f,o=i,u=a,n[h],7,-680876936),a=l(a,c,f,i,n[h+1],12,-389564586),i=l(i,a,c,f,n[h+2],17,606105819),f=l(f,i,a,c,n[h+3],22,-1044525330),c=l(c,f,i,a,n[h+4],7,-176418897),a=l(a,c,f,i,n[h+5],12,1200080426),i=l(i,a,c,f,n[h+6],17,-1473231341),f=l(f,i,a,c,n[h+7],22,-45705983),c=l(c,f,i,a,n[h+8],7,1770035416),a=l(a,c,f,i,n[h+9],12,-1958414417),i=l(i,a,c,f,n[h+10],17,-42063),f=l(f,i,a,c,n[h+11],22,-1990404162),c=l(c,f,i,a,n[h+12],7,1804603682),a=l(a,c,f,i,n[h+13],12,-40341101),i=l(i,a,c,f,n[h+14],17,-1502002290),c=v(c,f=l(f,i,a,c,n[h+15],22,1236535329),i,a,n[h+1],5,-165796510),a=v(a,c,f,i,n[h+6],9,-1069501632),i=v(i,a,c,f,n[h+11],14,643717713),f=v(f,i,a,c,n[h],20,-373897302),c=v(c,f,i,a,n[h+5],5,-701558691),a=v(a,c,f,i,n[h+10],9,38016083),i=v(i,a,c,f,n[h+15],14,-660478335),f=v(f,i,a,c,n[h+4],20,-405537848),c=v(c,f,i,a,n[h+9],5,568446438),a=v(a,c,f,i,n[h+14],9,-1019803690),i=v(i,a,c,f,n[h+3],14,-187363961),f=v(f,i,a,c,n[h+8],20,1163531501),c=v(c,f,i,a,n[h+13],5,-1444681467),a=v(a,c,f,i,n[h+2],9,-51403784),i=v(i,a,c,f,n[h+7],14,1735328473),c=g(c,f=v(f,i,a,c,n[h+12],20,-1926607734),i,a,n[h+5],4,-378558),a=g(a,c,f,i,n[h+8],11,-2022574463),i=g(i,a,c,f,n[h+11],16,1839030562),f=g(f,i,a,c,n[h+14],23,-35309556),c=g(c,f,i,a,n[h+1],4,-1530992060),a=g(a,c,f,i,n[h+4],11,1272893353),i=g(i,a,c,f,n[h+7],16,-155497632),f=g(f,i,a,c,n[h+10],23,-1094730640),c=g(c,f,i,a,n[h+13],4,681279174),a=g(a,c,f,i,n[h],11,-358537222),i=g(i,a,c,f,n[h+3],16,-722521979),f=g(f,i,a,c,n[h+6],23,76029189),c=g(c,f,i,a,n[h+9],4,-640364487),a=g(a,c,f,i,n[h+12],11,-421815835),i=g(i,a,c,f,n[h+15],16,530742520),c=m(c,f=g(f,i,a,c,n[h+2],23,-995338651),i,a,n[h],6,-198630844),a=m(a,c,f,i,n[h+7],10,1126891415),i=m(i,a,c,f,n[h+14],15,-1416354905),f=m(f,i,a,c,n[h+5],21,-57434055),c=m(c,f,i,a,n[h+12],6,1700485571),a=m(a,c,f,i,n[h+3],10,-1894986606),i=m(i,a,c,f,n[h+10],15,-1051523),f=m(f,i,a,c,n[h+1],21,-2054922799),c=m(c,f,i,a,n[h+8],6,1873313359),a=m(a,c,f,i,n[h+15],10,-30611744),i=m(i,a,c,f,n[h+6],15,-1560198380),f=m(f,i,a,c,n[h+13],21,1309151649),c=m(c,f,i,a,n[h+4],6,-145523070),a=m(a,c,f,i,n[h+11],10,-1120210379),i=m(i,a,c,f,n[h+2],15,718787259),f=m(f,i,a,c,n[h+9],21,-343485551),c=d(c,r),f=d(f,e),i=d(i,o),a=d(a,u);return[c,f,i,a]}function a(n){for(var t="",r=32*n.length,e=0;e<r;e+=8)t+=String.fromCharCode(n[e>>5]>>>e%32&255);return t}function h(n){var t=[];for(t[(n.length>>2)-1]=void 0,e=0;e<t.length;e+=1)t[e]=0;for(var r=8*n.length,e=0;e<r;e+=8)t[e>>5]|=(255&n.charCodeAt(e/8))<<e%32;return t}function e(n){for(var t,r="0123456789abcdef",e="",o=0;o<n.length;o+=1)t=n.charCodeAt(o),e+=r.charAt(t>>>4&15)+r.charAt(15&t);return e}function r(n){return unescape(encodeURIComponent(n))}function o(n){return a(i(h(t=r(n)),8*t.length));var t}function u(n,t){return function(n,t){var r,e,o=h(n),u=[],c=[];for(u[15]=c[15]=void 0,16<o.length&&(o=i(o,8*n.length)),r=0;r<16;r+=1)u[r]=909522486^o[r],c[r]=1549556828^o[r];return e=i(u.concat(h(t)),512+8*t.length),a(i(c.concat(e),640))}(r(n),r(t))}function t(n,t,r){return t?r?u(t,n):e(u(t,n)):r?o(n):e(o(n))}"function"==typeof define&&define.amd?define(function(){return t}):"object"==typeof module&&module.exports?module.exports=t:n.md5=t}(this);</script><script>window.AbTest = (function() { return { 'ab_test': (uniqueId, test_name, buckets) => { let override = new URLSearchParams(window.location.search).get(`ab_test[${test_name}]`); if ( override ) { return override; } const bucketNames = buckets.map((bucket) => { return typeof bucket === 'string' ? bucket : Object.keys(bucket)[0]; }); const weights = buckets.map((bucket) => { return typeof bucket === 'string' ? 1 : Object.values(bucket)[0]; }); const total = weights.reduce((sum, weight) => sum + weight); const hash = md5(`${uniqueId}${test_name}`); const hashNum = parseInt(hash.slice(-12), 16); let bucketPoint = total * (hashNum % 100000) / 100000; const bucket = bucketNames.find((_, i) => { if (weights[i] > bucketPoint) { return true; } bucketPoint -= weights[i]; return false; }); return bucket; } }; })();</script><div data-auto_select="false" data-client_id="331998490334-rsn3chp12mbkiqhl6e7lu2q0mlbu0f1b" data-landing_url="https://www.academia.edu/Documents/in/Mathematical_Biology" data-login_uri="https://www.academia.edu/registrations/google_one_tap" data-moment_callback="onGoogleOneTapEvent" id="g_id_onload"></div><script>function onGoogleOneTapEvent(event) { var momentType = event.getMomentType(); var momentReason = null; if (event.isNotDisplayed()) { momentReason = event.getNotDisplayedReason(); } else if (event.isSkippedMoment()) { momentReason = event.getSkippedReason(); } else if (event.isDismissedMoment()) { momentReason = event.getDismissedReason(); } Aedu.arbitraryEvents.write('GoogleOneTapEvent', { moment_type: momentType, moment_reason: momentReason, }); }</script><script>(function() { var auvid = unescape( document.cookie .split(/; ?/) .find((s) => s.startsWith('auvid')) .substring(6)); var bucket = AbTest.ab_test(auvid, 'lo_ri_one_tap_google_sign_on', ['control', 'one_tap_google_sign_on']); if (bucket === 'control') return; var oneTapTag = document.createElement('script') oneTapTag.async = true oneTapTag.defer = true oneTapTag.src = 'https://accounts.google.com/gsi/client' document.body.appendChild(oneTapTag) })();</script></div></div></div> </div> <div class="bootstrap login"><div class="modal fade login-modal" id="login-modal"><div class="login-modal-dialog modal-dialog"><div class="modal-content"><div class="modal-header"><button class="close close" data-dismiss="modal" type="button"><span aria-hidden="true">×</span><span class="sr-only">Close</span></button><h4 class="modal-title text-center"><strong>Log In</strong></h4></div><div class="modal-body"><div class="row"><div class="col-xs-10 col-xs-offset-1"><button class="btn btn-fb btn-lg btn-block btn-v-center-content" id="login-facebook-oauth-button"><svg style="float: left; width: 19px; line-height: 1em; margin-right: .3em;" aria-hidden="true" focusable="false" data-prefix="fab" data-icon="facebook-square" class="svg-inline--fa fa-facebook-square fa-w-14" role="img" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 448 512"><path fill="currentColor" d="M400 32H48A48 48 0 0 0 0 80v352a48 48 0 0 0 48 48h137.25V327.69h-63V256h63v-54.64c0-62.15 37-96.48 93.67-96.48 27.14 0 55.52 4.84 55.52 4.84v61h-31.27c-30.81 0-40.42 19.12-40.42 38.73V256h68.78l-11 71.69h-57.78V480H400a48 48 0 0 0 48-48V80a48 48 0 0 0-48-48z"></path></svg><small><strong>Log in</strong> with <strong>Facebook</strong></small></button><br /><button class="btn btn-google btn-lg btn-block btn-v-center-content" id="login-google-oauth-button"><svg style="float: left; width: 22px; line-height: 1em; margin-right: .3em;" aria-hidden="true" focusable="false" data-prefix="fab" data-icon="google-plus" class="svg-inline--fa fa-google-plus fa-w-16" role="img" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512"><path fill="currentColor" d="M256,8C119.1,8,8,119.1,8,256S119.1,504,256,504,504,392.9,504,256,392.9,8,256,8ZM185.3,380a124,124,0,0,1,0-248c31.3,0,60.1,11,83,32.3l-33.6,32.6c-13.2-12.9-31.3-19.1-49.4-19.1-42.9,0-77.2,35.5-77.2,78.1S142.3,334,185.3,334c32.6,0,64.9-19.1,70.1-53.3H185.3V238.1H302.2a109.2,109.2,0,0,1,1.9,20.7c0,70.8-47.5,121.2-118.8,121.2ZM415.5,273.8v35.5H380V273.8H344.5V238.3H380V202.8h35.5v35.5h35.2v35.5Z"></path></svg><small><strong>Log in</strong> with <strong>Google</strong></small></button><br /><style type="text/css">.sign-in-with-apple-button { width: 100%; height: 52px; border-radius: 3px; border: 1px solid black; cursor: pointer; }</style><script src="https://appleid.cdn-apple.com/appleauth/static/jsapi/appleid/1/en_US/appleid.auth.js" type="text/javascript"></script><div class="sign-in-with-apple-button" data-border="false" data-color="white" id="appleid-signin"><span   ="Sign Up with Apple" class="u-fs11"></span></div><script>AppleID.auth.init({ clientId: 'edu.academia.applesignon', scope: 'name email', redirectURI: 'https://www.academia.edu/sessions', state: "b4951f2b26866a83ceede61bb96eec3eae4737e2aa6681028c2d5b97c29ed827", });</script><script>// Hacky way of checking if on fast loswp if (window.loswp == null) { (function() { const Google = window?.Aedu?.Auth?.OauthButton?.Login?.Google; const Facebook = window?.Aedu?.Auth?.OauthButton?.Login?.Facebook; if (Google) { new Google({ el: '#login-google-oauth-button', rememberMeCheckboxId: 'remember_me', track: null }); } if (Facebook) { new Facebook({ el: '#login-facebook-oauth-button', rememberMeCheckboxId: 'remember_me', track: null }); } })(); }</script></div></div></div><div class="modal-body"><div class="row"><div class="col-xs-10 col-xs-offset-1"><div class="hr-heading login-hr-heading"><span class="hr-heading-text">or</span></div></div></div></div><div class="modal-body"><div class="row"><div class="col-xs-10 col-xs-offset-1"><form class="js-login-form" action="https://www.academia.edu/sessions" accept-charset="UTF-8" method="post"><input name="utf8" type="hidden" value="✓" autocomplete="off" /><input type="hidden" name="authenticity_token" value="kh0YMq3139N09jeW5AkUv1Sqn+pLL3GndfeCC7bmdenofzRzOnxmBc0mxkxQIekLTQeifbq/9DVIBzJLIkm3mw==" autocomplete="off" /><div class="form-group"><label class="control-label" for="login-modal-email-input" style="font-size: 14px;">Email</label><input class="form-control" id="login-modal-email-input" name="login" type="email" /></div><div class="form-group"><label class="control-label" for="login-modal-password-input" style="font-size: 14px;">Password</label><input class="form-control" id="login-modal-password-input" name="password" type="password" /></div><input type="hidden" name="post_login_redirect_url" id="post_login_redirect_url" value="https://www.academia.edu/Documents/in/Mathematical_Biology" autocomplete="off" /><div class="checkbox"><label><input type="checkbox" name="remember_me" id="remember_me" value="1" checked="checked" /><small style="font-size: 12px; margin-top: 2px; display: inline-block;">Remember me on this computer</small></label></div><br><input type="submit" name="commit" value="Log In" class="btn btn-primary btn-block btn-lg js-login-submit" data-disable-with="Log In" /></br></form><script>typeof window?.Aedu?.recaptchaManagedForm === 'function' && window.Aedu.recaptchaManagedForm( document.querySelector('.js-login-form'), document.querySelector('.js-login-submit') );</script><small style="font-size: 12px;"><br />or <a data-target="#login-modal-reset-password-container" data-toggle="collapse" href="javascript:void(0)">reset password</a></small><div class="collapse" id="login-modal-reset-password-container"><br /><div class="well margin-0x"><form class="js-password-reset-form" action="https://www.academia.edu/reset_password" accept-charset="UTF-8" method="post"><input name="utf8" type="hidden" value="✓" autocomplete="off" /><input type="hidden" name="authenticity_token" value="HTN73brbHsNtW4OKhKPSe1qfmGhQLzbISxIR3wzPUDhnUVecLVKnFdSLclAwiy/PQzKl/6G/s1p24qGfmGCSSg==" autocomplete="off" /><p>Enter the email address you signed up with and we'll email you a reset link.</p><div class="form-group"><input class="form-control" name="email" type="email" /></div><script src="https://recaptcha.net/recaptcha/api.js" async defer></script> <script> var invisibleRecaptchaSubmit = function () { var closestForm = function (ele) { var curEle = ele.parentNode; while (curEle.nodeName !== 'FORM' && curEle.nodeName !== 'BODY'){ curEle = curEle.parentNode; } return curEle.nodeName === 'FORM' ? curEle : null }; var eles = document.getElementsByClassName('g-recaptcha'); if (eles.length > 0) { var form = closestForm(eles[0]); if (form) { form.submit(); } } }; </script> <input type="submit" data-sitekey="6Lf3KHUUAAAAACggoMpmGJdQDtiyrjVlvGJ6BbAj" data-callback="invisibleRecaptchaSubmit" class="g-recaptcha btn btn-primary btn-block" value="Email me a link" value=""/> </form></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/collapse-45805421cf446ca5adf7aaa1935b08a3a8d1d9a6cc5d91a62a2a3a00b20b3e6a.js"], function() { // from javascript_helper.rb $("#login-modal-reset-password-container").on("shown.bs.collapse", function() { $(this).find("input[type=email]").focus(); }); }); </script> </div></div></div><div class="modal-footer"><div class="text-center"><small style="font-size: 12px;">Need an account? <a rel="nofollow" href="https://www.academia.edu/signup">Click here to sign up</a></small></div></div></div></div></div></div><script>// If we are on subdomain or non-bootstrapped page, redirect to login page instead of showing modal (function(){ if (typeof $ === 'undefined') return; var host = window.location.hostname; if ((host === $domain || host === "www."+$domain) && (typeof $().modal === 'function')) { $("#nav_log_in").click(function(e) { // Don't follow the link and open the modal e.preventDefault(); $("#login-modal").on('shown.bs.modal', function() { $(this).find("#login-modal-email-input").focus() }).modal('show'); }); } })()</script> <div class="bootstrap" id="footer"><div class="footer-content clearfix text-center padding-top-7x" style="width:100%;"><ul class="footer-links-secondary footer-links-wide list-inline margin-bottom-1x"><li><a href="https://www.academia.edu/about">About</a></li><li><a href="https://www.academia.edu/press">Press</a></li><li><a rel="nofollow" href="https://medium.com/academia">Blog</a></li><li><a href="https://www.academia.edu/documents">Papers</a></li><li><a href="https://www.academia.edu/topics">Topics</a></li><li><a href="https://www.academia.edu/journals">Academia.edu Journals</a></li><li><a rel="nofollow" href="https://www.academia.edu/hiring"><svg style="width: 13px; height: 13px;" aria-hidden="true" focusable="false" data-prefix="fas" data-icon="briefcase" class="svg-inline--fa fa-briefcase fa-w-16" role="img" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512"><path fill="currentColor" d="M320 336c0 8.84-7.16 16-16 16h-96c-8.84 0-16-7.16-16-16v-48H0v144c0 25.6 22.4 48 48 48h416c25.6 0 48-22.4 48-48V288H320v48zm144-208h-80V80c0-25.6-22.4-48-48-48H176c-25.6 0-48 22.4-48 48v48H48c-25.6 0-48 22.4-48 48v80h512v-80c0-25.6-22.4-48-48-48zm-144 0H192V96h128v32z"></path></svg> <strong>We're Hiring!</strong></a></li><li><a rel="nofollow" href="https://support.academia.edu/"><svg style="width: 12px; height: 12px;" aria-hidden="true" focusable="false" data-prefix="fas" data-icon="question-circle" class="svg-inline--fa fa-question-circle fa-w-16" role="img" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512"><path fill="currentColor" d="M504 256c0 136.997-111.043 248-248 248S8 392.997 8 256C8 119.083 119.043 8 256 8s248 111.083 248 248zM262.655 90c-54.497 0-89.255 22.957-116.549 63.758-3.536 5.286-2.353 12.415 2.715 16.258l34.699 26.31c5.205 3.947 12.621 3.008 16.665-2.122 17.864-22.658 30.113-35.797 57.303-35.797 20.429 0 45.698 13.148 45.698 32.958 0 14.976-12.363 22.667-32.534 33.976C247.128 238.528 216 254.941 216 296v4c0 6.627 5.373 12 12 12h56c6.627 0 12-5.373 12-12v-1.333c0-28.462 83.186-29.647 83.186-106.667 0-58.002-60.165-102-116.531-102zM256 338c-25.365 0-46 20.635-46 46 0 25.364 20.635 46 46 46s46-20.636 46-46c0-25.365-20.635-46-46-46z"></path></svg> <strong>Help Center</strong></a></li></ul><ul class="footer-links-tertiary list-inline margin-bottom-1x"><li class="small">Find new research papers in:</li><li class="small"><a href="https://www.academia.edu/Documents/in/Physics">Physics</a></li><li class="small"><a href="https://www.academia.edu/Documents/in/Chemistry">Chemistry</a></li><li class="small"><a href="https://www.academia.edu/Documents/in/Biology">Biology</a></li><li class="small"><a href="https://www.academia.edu/Documents/in/Health_Sciences">Health Sciences</a></li><li class="small"><a href="https://www.academia.edu/Documents/in/Ecology">Ecology</a></li><li class="small"><a href="https://www.academia.edu/Documents/in/Earth_Sciences">Earth Sciences</a></li><li class="small"><a href="https://www.academia.edu/Documents/in/Cognitive_Science">Cognitive Science</a></li><li class="small"><a href="https://www.academia.edu/Documents/in/Mathematics">Mathematics</a></li><li class="small"><a href="https://www.academia.edu/Documents/in/Computer_Science">Computer Science</a></li></ul></div></div><div class="DesignSystem" id="credit" style="width:100%;"><ul class="u-pl0x footer-links-legal list-inline"><li><a rel="nofollow" href="https://www.academia.edu/terms">Terms</a></li><li><a rel="nofollow" href="https://www.academia.edu/privacy">Privacy</a></li><li><a rel="nofollow" href="https://www.academia.edu/copyright">Copyright</a></li><li>Academia ©2024</li></ul></div><script> //<![CDATA[ window.detect_gmtoffset = true; window.Academia && window.Academia.set_gmtoffset && Academia.set_gmtoffset('/gmtoffset'); //]]> </script> <div id='overlay_background'></div> <div id='bootstrap-modal-container' class='bootstrap'></div> <div id='ds-modal-container' class='bootstrap DesignSystem'></div> <div id='full-screen-modal'></div> </div> </body> </html>