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While in this position my research interests spanned medical phenomena, crucial event time series and rehabilitation of illness and injury using the fractal-paradigm along with the fractional calculus.<br /><div class="js-profile-less-about u-linkUnstyled u-tcGrayDarker u-textDecorationUnderline u-displayNone">less</div></div></div><div class="ri-section"><div class="ri-section-header"><span>Interests</span></div><div class="ri-tags-container"><a data-click-track="profile-user-info-expand-research-interests" data-has-card-for-ri-list="66220250" href="https://www.academia.edu/Documents/in/Material_Physics"><div id="js-react-on-rails-context" style="display:none" data-rails-context="{"inMailer":false,"i18nLocale":"en","i18nDefaultLocale":"en","href":"https://independent.academia.edu/BruceWest3","location":"/BruceWest3","scheme":"https","host":"independent.academia.edu","port":null,"pathname":"/BruceWest3","search":null,"httpAcceptLanguage":null,"serverSide":false}"></div> <div 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backbone-social-profile-documents" style="width: 100%;"><div class="u-taCenter"></div><div class="profile--tab_content_container js-tab-pane tab-pane active" id="all"><div class="profile--tab_heading_container js-section-heading" data-section="Papers" id="Papers"><h3 class="profile--tab_heading_container">Papers by Bruce West</h3></div><div class="js-work-strip profile--work_container" data-work-id="91648566"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/91648566/Fractal_fluctuations_in_transcranial_Doppler_signals"><img alt="Research paper thumbnail of Fractal fluctuations in transcranial Doppler signals" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/91648566/Fractal_fluctuations_in_transcranial_Doppler_signals">Fractal fluctuations in transcranial Doppler signals</a></div><div class="wp-workCard_item"><span>Physical Review E</span><span>, 1999</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">... BJ West,1 R. Zhang,2 AW Sanders,1 S. Miniyar,2 JH Zuckerman,2 and BD Levine2 1Center for Nonl...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">... BJ West,1 R. Zhang,2 AW Sanders,1 S. Miniyar,2 JH Zuckerman,2 and BD Levine2 1Center for Nonlinear Science, University of North Texas, Denton, Texas 76203 2Institute for Exercise and Environmental Medicine, Presbyterian Hospital at Dallas, University of Texas ...</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="91648566"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="91648566"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 91648566; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=91648566]").text(description); $(".js-view-count[data-work-id=91648566]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 91648566; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='91648566']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 91648566, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (false){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "-1" } } $('.js-work-strip[data-work-id=91648566]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":91648566,"title":"Fractal fluctuations in transcranial Doppler signals","translated_title":"","metadata":{"abstract":"... 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="81284004"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/81284004/Relating_size_and_functionality_in_human_social_networks_through_complexity"><img alt="Research paper thumbnail of Relating size and functionality in human social networks through complexity" class="work-thumbnail" src="https://attachments.academia-assets.com/87382304/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/81284004/Relating_size_and_functionality_in_human_social_networks_through_complexity">Relating size and functionality in human social networks through complexity</a></div><div class="wp-workCard_item wp-workCard--coauthors"><span>by </span><span><a class="" data-click-track="profile-work-strip-authors" href="https://oxford.academia.edu/rdunbar">robin dunbar</a> and <a class="" data-click-track="profile-work-strip-authors" href="https://independent.academia.edu/BruceWest3">Bruce West</a></span></div><div class="wp-workCard_item"><span>PNAS </span><span>, 2020</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Extensive empirical evidence suggests that there is a maximal number of people with whom an indiv...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Extensive empirical evidence suggests that there is a maximal<br />number of people with whom an individual can maintain stable<br />social relationships (the Dunbar number). We argue that this arises<br />as a consequence of a natural phase transition in the dynamic selforganization<br />among N individuals within a social system. We present<br />the calculated size dependence of the scaling properties of<br />complex social network models to argue that this collective behavior<br />is an enhanced form of collective intelligence. Direct calculation<br />establishes that the complexity of social networks as measured by<br />their scaling behavior is nonmonotonic, peaking around 150,<br />thereby providing a theoretical basis for the value of the Dunbar<br />number. Thus, we establish a theory-based bridge spanning the<br />gap between sociology and psychology.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="1bd2e1487f6e05c556eb17758c6b8e6d" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":87382304,"asset_id":81284004,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/87382304/download_file?st=MTczMjc2NTkzMCw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="81284004"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="81284004"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 81284004; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=81284004]").text(description); $(".js-view-count[data-work-id=81284004]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 81284004; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='81284004']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 81284004, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "1bd2e1487f6e05c556eb17758c6b8e6d" } } $('.js-work-strip[data-work-id=81284004]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":81284004,"title":"Relating size and functionality in human social networks through complexity","translated_title":"","metadata":{"abstract":"Extensive empirical evidence suggests that there is a maximal\nnumber of people with whom an individual can maintain stable\nsocial relationships (the Dunbar number). 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The generator of the deterministic evolution is a nonlinear map belonging to a class of maps recently tailored to mimic the processes of weak chaos responsible for the birth of anomalous diffusion. It is assumed that the deterministic process corresponds to unknown biological rules that determine the DNA path, whereas the noise mimics the inQuence of an infinite-dimensional environment on the biological process under study. We prove that the resulting diffusion process, if the effect of the random process is neglected, is an o.-stable Levy process with 1 (o. (2. We also show that, if the diffusion process is determined by the joint action of the deterministic and the random process, the correlation effects of the \"deterministic dynamics\" are canceled on the shortrange scale, but show up in the long-range one. We denote our prescription to generate statistical sequences as the copying mistake map (CMM). We carry out our analysis of several DNA sequences and their CMM realizations with a variety of techniques and we especially focus on a method of regression to equilibrium, which we call the Onsager analysis. With these techniques we establish the statistical equivalence of the real DNA sequences with their CMM realizations. We show that long-range correlations are present in exons as well as in introns, but are diKcult to detect, since the exon \"dynamics\" is shown to be determined by the entanglement of three distinct and independent CMM's.","publication_date":{"day":null,"month":null,"year":1995,"errors":{}},"grobid_abstract_attachment_id":77071437},"translated_abstract":null,"internal_url":"https://www.academia.edu/65504375/Dynamical_model_for_DNA_sequences","translated_internal_url":"","created_at":"2021-12-22T06:44:31.379-08:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":66220250,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[{"id":77071437,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/77071437/thumbnails/1.jpg","file_name":"87f7147bcf4ac885986905e3f61936337b88.pdf","download_url":"https://www.academia.edu/attachments/77071437/download_file?st=MTczMjc2NTkzMCw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Dynamical_model_for_DNA_sequences.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/77071437/87f7147bcf4ac885986905e3f61936337b88-libre.pdf?1640295593=\u0026response-content-disposition=attachment%3B+filename%3DDynamical_model_for_DNA_sequences.pdf\u0026Expires=1732769530\u0026Signature=KLJcB1nTbJ8RLs7q-1Ava1D9K-hmrrB32qOC5u5qoutlmLvpQDUHMBI29fHDaVUWDlsS78~gr7AHh3vTN7s-d-Dsygg4qHM1pYHe2dZ7hoRPW666quDj2Z1JA8TBh326Er6pryxakpWdmSdNlO3VFOADBQrIwbqBQKWAgaIeUUaXu5f1ZO9~vy1tdWK8AkwKAIu-pOaa49w2Jg-lcNoWrLh5sAWwtHiTL3wSun4ko3V756ChDMaYe80lQDjZPCCqVb00DY88x50augiVj8GGaLboC3p77D9hKD6O~d21h8eKiupOX1E8TLKrJ6sdpDiQDjf9~Ou24ZOqngKqASIrpA__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"Dynamical_model_for_DNA_sequences","translated_slug":"","page_count":16,"language":"en","content_type":"Work","owner":{"id":66220250,"first_name":"Bruce","middle_initials":null,"last_name":"West","page_name":"BruceWest3","domain_name":"independent","created_at":"2017-07-07T14:39:25.483-07:00","display_name":"Bruce West","url":"https://independent.academia.edu/BruceWest3"},"attachments":[{"id":77071437,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/77071437/thumbnails/1.jpg","file_name":"87f7147bcf4ac885986905e3f61936337b88.pdf","download_url":"https://www.academia.edu/attachments/77071437/download_file?st=MTczMjc2NTkzMCw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Dynamical_model_for_DNA_sequences.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/77071437/87f7147bcf4ac885986905e3f61936337b88-libre.pdf?1640295593=\u0026response-content-disposition=attachment%3B+filename%3DDynamical_model_for_DNA_sequences.pdf\u0026Expires=1732769530\u0026Signature=KLJcB1nTbJ8RLs7q-1Ava1D9K-hmrrB32qOC5u5qoutlmLvpQDUHMBI29fHDaVUWDlsS78~gr7AHh3vTN7s-d-Dsygg4qHM1pYHe2dZ7hoRPW666quDj2Z1JA8TBh326Er6pryxakpWdmSdNlO3VFOADBQrIwbqBQKWAgaIeUUaXu5f1ZO9~vy1tdWK8AkwKAIu-pOaa49w2Jg-lcNoWrLh5sAWwtHiTL3wSun4ko3V756ChDMaYe80lQDjZPCCqVb00DY88x50augiVj8GGaLboC3p77D9hKD6O~d21h8eKiupOX1E8TLKrJ6sdpDiQDjf9~Ou24ZOqngKqASIrpA__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[{"id":48,"name":"Engineering","url":"https://www.academia.edu/Documents/in/Engineering"},{"id":300,"name":"Mathematics","url":"https://www.academia.edu/Documents/in/Mathematics"},{"id":26327,"name":"Medicine","url":"https://www.academia.edu/Documents/in/Medicine"},{"id":50926,"name":"Joint Action","url":"https://www.academia.edu/Documents/in/Joint_Action"},{"id":80414,"name":"Mathematical Sciences","url":"https://www.academia.edu/Documents/in/Mathematical_Sciences"},{"id":118582,"name":"Physical sciences","url":"https://www.academia.edu/Documents/in/Physical_sciences"},{"id":148995,"name":"Long Range","url":"https://www.academia.edu/Documents/in/Long_Range"},{"id":428833,"name":"Statistical Properties","url":"https://www.academia.edu/Documents/in/Statistical_Properties"},{"id":495625,"name":"Biological Process","url":"https://www.academia.edu/Documents/in/Biological_Process"},{"id":758675,"name":"Anomalous Diffusion","url":"https://www.academia.edu/Documents/in/Anomalous_Diffusion"},{"id":990491,"name":"Irreversible Thermodynamics","url":"https://www.academia.edu/Documents/in/Irreversible_Thermodynamics"},{"id":2274872,"name":"DNA sequence","url":"https://www.academia.edu/Documents/in/DNA_sequence"},{"id":2626792,"name":"dynamic model","url":"https://www.academia.edu/Documents/in/dynamic_model"}],"urls":[]}, dispatcherData: dispatcherData }); 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Repeating stnictural and design elements of the same size will define a particular scale. Most pleasing designs obey an inverse power-law distribution: the product of the relative multiplicity p of a substructure with an algebraic power of its size x is a constant, px' 1 = constant, which is derived here from basic principles. This means that the logarithmic plot of/? versus x has a slope of-//, where typically / ^ p ^ 2, and this is a widely observed relationship in both the natural and the social sciences. Departures from this rule apparently result in incoherent, alien structures. Three applications to urban systems arc proposed. It is argued that in living cities (I) the distribution of path lengths, (2) the allocation of project funding, and (3) the distribution of built elements all follow the derived multiplicity rule. By violating all three, modernist cities create inhuman urban environments.","publication_date":{"day":null,"month":null,"year":1999,"errors":{}},"publication_name":"Environment and Planning B","grobid_abstract_attachment_id":77071460},"translated_abstract":null,"internal_url":"https://www.academia.edu/65504372/A_Universal_Rule_for_the_Distribution_of_Sizes","translated_internal_url":"","created_at":"2021-12-22T06:44:31.251-08:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":66220250,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[{"id":77071460,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/77071460/thumbnails/1.jpg","file_name":"00a453686c6dd9cdff7d1b968e19a3c04a8b.pdf","download_url":"https://www.academia.edu/attachments/77071460/download_file?st=MTczMjc2NTkzMCw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"A_Universal_Rule_for_the_Distribution_of.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/77071460/00a453686c6dd9cdff7d1b968e19a3c04a8b-libre.pdf?1640295586=\u0026response-content-disposition=attachment%3B+filename%3DA_Universal_Rule_for_the_Distribution_of.pdf\u0026Expires=1732769530\u0026Signature=Esi8Gi1cZIDDLWhCDDSFciDKmJa76SgiWfQmk2C3cQ4MeXWyqWPyHvE3X7mPQH-pF~BzlBEE7uv730RvE0tabuxFNoS6~vlYtiRlIa6G6KAlVnTZxefRTropSXpqA7NN~87Zjrjs5vk9hDzkEKu~xSVIlQ0zbkA9e4JW5YXPbtF7cV6MX8W1WXqjlk9FlS9HifArR~ojTSgTJbEAZd7WlbibaZW7XTNA2PrFuHvQ2EiydiDYFPX~ZgALaU4QgVgWJupqfNE53HGFvCNKfsE~MFWQ6twUVm7KehjPCe7xwPvfiCmvT80zdfTa9aaXFZIWGSh46cbPn2TD30SgJmczQA__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"A_Universal_Rule_for_the_Distribution_of_Sizes","translated_slug":"","page_count":15,"language":"en","content_type":"Work","owner":{"id":66220250,"first_name":"Bruce","middle_initials":null,"last_name":"West","page_name":"BruceWest3","domain_name":"independent","created_at":"2017-07-07T14:39:25.483-07:00","display_name":"Bruce West","url":"https://independent.academia.edu/BruceWest3"},"attachments":[{"id":77071460,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/77071460/thumbnails/1.jpg","file_name":"00a453686c6dd9cdff7d1b968e19a3c04a8b.pdf","download_url":"https://www.academia.edu/attachments/77071460/download_file?st=MTczMjc2NTkzMCw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"A_Universal_Rule_for_the_Distribution_of.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/77071460/00a453686c6dd9cdff7d1b968e19a3c04a8b-libre.pdf?1640295586=\u0026response-content-disposition=attachment%3B+filename%3DA_Universal_Rule_for_the_Distribution_of.pdf\u0026Expires=1732769530\u0026Signature=Esi8Gi1cZIDDLWhCDDSFciDKmJa76SgiWfQmk2C3cQ4MeXWyqWPyHvE3X7mPQH-pF~BzlBEE7uv730RvE0tabuxFNoS6~vlYtiRlIa6G6KAlVnTZxefRTropSXpqA7NN~87Zjrjs5vk9hDzkEKu~xSVIlQ0zbkA9e4JW5YXPbtF7cV6MX8W1WXqjlk9FlS9HifArR~ojTSgTJbEAZd7WlbibaZW7XTNA2PrFuHvQ2EiydiDYFPX~ZgALaU4QgVgWJupqfNE53HGFvCNKfsE~MFWQ6twUVm7KehjPCe7xwPvfiCmvT80zdfTa9aaXFZIWGSh46cbPn2TD30SgJmczQA__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[{"id":300,"name":"Mathematics","url":"https://www.academia.edu/Documents/in/Mathematics"},{"id":422,"name":"Computer Science","url":"https://www.academia.edu/Documents/in/Computer_Science"},{"id":1372,"name":"Architecture","url":"https://www.academia.edu/Documents/in/Architecture"},{"id":20436,"name":"Urban And Regional Planning","url":"https://www.academia.edu/Documents/in/Urban_And_Regional_Planning"},{"id":183166,"name":"Urban Environment","url":"https://www.academia.edu/Documents/in/Urban_Environment"},{"id":603842,"name":"Urban System","url":"https://www.academia.edu/Documents/in/Urban_System"},{"id":1197942,"name":"Social Science","url":"https://www.academia.edu/Documents/in/Social_Science"},{"id":1482264,"name":"Power Law Distribution","url":"https://www.academia.edu/Documents/in/Power_Law_Distribution"}],"urls":[{"id":15533502,"url":"http://direct.bl.uk/research/54/48/RN069473611.html"}]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="65504158"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/65504158/Path_integral_formation_of_wave_propagation_in_the_ionosphere_4"><img alt="Research paper thumbnail of Path integral formation of wave propagation in the ionosphere, 4" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/65504158/Path_integral_formation_of_wave_propagation_in_the_ionosphere_4">Path integral formation of wave propagation in the ionosphere, 4</a></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">The validity of the application of weak scatter theory to ionospheric scattering data has been ex...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">The validity of the application of weak scatter theory to ionospheric scattering data has been examined. It is concluded that the weak scatter theory is not universally applicable. Born and Rytov weak scatter calculations are compared and the Rytov calculations is found superior. The Rytov calculations appear to explain the enhancement in the scintillation index (the ratio on the intensity variance to variance of phase) in the equatorial vis a vis the polar stations. This research effort will be completed under Contract Number 49620-82-C-0058.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="65504158"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="65504158"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 65504158; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=65504158]").text(description); $(".js-view-count[data-work-id=65504158]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 65504158; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='65504158']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 65504158, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (false){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "-1" } } $('.js-work-strip[data-work-id=65504158]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":65504158,"title":"Path integral formation of wave propagation in the ionosphere, 4","translated_title":"","metadata":{"abstract":"The validity of the application of weak scatter theory to ionospheric scattering data has been examined. It is concluded that the weak scatter theory is not universally applicable. Born and Rytov weak scatter calculations are compared and the Rytov calculations is found superior. The Rytov calculations appear to explain the enhancement in the scintillation index (the ratio on the intensity variance to variance of phase) in the equatorial vis a vis the polar stations. This research effort will be completed under Contract Number 49620-82-C-0058.","publication_date":{"day":null,"month":null,"year":1982,"errors":{}}},"translated_abstract":"The validity of the application of weak scatter theory to ionospheric scattering data has been examined. It is concluded that the weak scatter theory is not universally applicable. Born and Rytov weak scatter calculations are compared and the Rytov calculations is found superior. The Rytov calculations appear to explain the enhancement in the scintillation index (the ratio on the intensity variance to variance of phase) in the equatorial vis a vis the polar stations. 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Meanwhile, in the study of phase transitions and critical phenomena, it was found that the self–similarity of systems near critical points can be described using RG methods. Furthermore, since self–similarity is often a defining feature of a complex system, the RG method is also devoted to characterizing complexity. In addition, the RG approach has also proven to be a useful tool to analyze the asymptotic behavior of solutions in the singular perturbation theory. In this review paper, we discuss the origin, development, and application of the RG method in a variety of fields from the physical, social and life sciences, in singular perturbation theory, and reveal the need to connect the RG and the fractional calculus (FC). 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The FC is another basic mathematical approach for describin...","publisher":"Walter de Gruyter GmbH","publication_name":"Fractional Calculus and Applied Analysis"},"translated_abstract":"The concept of the renormalization group (RG) emerged from the renormalization of quantum field variables, which is typically used to deal with the issue of divergences to infinity in quantum field theory. Meanwhile, in the study of phase transitions and critical phenomena, it was found that the self–similarity of systems near critical points can be described using RG methods. Furthermore, since self–similarity is often a defining feature of a complex system, the RG method is also devoted to characterizing complexity. In addition, the RG approach has also proven to be a useful tool to analyze the asymptotic behavior of solutions in the singular perturbation theory. In this review paper, we discuss the origin, development, and application of the RG method in a variety of fields from the physical, social and life sciences, in singular perturbation theory, and reveal the need to connect the RG and the fractional calculus (FC). The FC is another basic mathematical approach for describin...","internal_url":"https://www.academia.edu/57641919/Renormalization_group_and_fractional_calculus_methods_in_a_complex_world_A_review","translated_internal_url":"","created_at":"2021-10-13T17:35:32.576-07:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":66220250,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[{"id":72443542,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/72443542/thumbnails/1.jpg","file_name":"pdf.pdf","download_url":"https://www.academia.edu/attachments/72443542/download_file?st=MTczMjc2NTkzMCw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Renormalization_group_and_fractional_cal.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/72443542/pdf-libre.pdf?1634272204=\u0026response-content-disposition=attachment%3B+filename%3DRenormalization_group_and_fractional_cal.pdf\u0026Expires=1732769530\u0026Signature=AVwtgFy~x8vqB2kez7704tSodbKt7W-Zlnp9JEM52hJ7GcJCfphhpX7hwj3j38h9ZLRsl0sgrB6SErOM9fryy9XrSvRSYduDNkOJSZjfcyW-1eI45z4u-9GPU1R8KSZUQy146bnsPNaQk4hARsPqBmSPGnpKhrdueFvq2uDErGeOZqH4ruKS3i7h2JGI2JbUN9djvp6kt0BE8ei2MtTkanO-eZPPc52dw9wu2fu9HS5p3O3j~g3ORW2N0iiNycAPbQVN08fi758H06RCKblm2yKleTUaV8NI4PdBtq9jlrNvQ9agEkcGU7ZQ8eiajmlVYU6cFN6KXmgDrI9i~bbSwQ__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"Renormalization_group_and_fractional_calculus_methods_in_a_complex_world_A_review","translated_slug":"","page_count":49,"language":"en","content_type":"Work","owner":{"id":66220250,"first_name":"Bruce","middle_initials":null,"last_name":"West","page_name":"BruceWest3","domain_name":"independent","created_at":"2017-07-07T14:39:25.483-07:00","display_name":"Bruce West","url":"https://independent.academia.edu/BruceWest3"},"attachments":[{"id":72443542,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/72443542/thumbnails/1.jpg","file_name":"pdf.pdf","download_url":"https://www.academia.edu/attachments/72443542/download_file?st=MTczMjc2NTkzMCw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Renormalization_group_and_fractional_cal.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/72443542/pdf-libre.pdf?1634272204=\u0026response-content-disposition=attachment%3B+filename%3DRenormalization_group_and_fractional_cal.pdf\u0026Expires=1732769530\u0026Signature=AVwtgFy~x8vqB2kez7704tSodbKt7W-Zlnp9JEM52hJ7GcJCfphhpX7hwj3j38h9ZLRsl0sgrB6SErOM9fryy9XrSvRSYduDNkOJSZjfcyW-1eI45z4u-9GPU1R8KSZUQy146bnsPNaQk4hARsPqBmSPGnpKhrdueFvq2uDErGeOZqH4ruKS3i7h2JGI2JbUN9djvp6kt0BE8ei2MtTkanO-eZPPc52dw9wu2fu9HS5p3O3j~g3ORW2N0iiNycAPbQVN08fi758H06RCKblm2yKleTUaV8NI4PdBtq9jlrNvQ9agEkcGU7ZQ8eiajmlVYU6cFN6KXmgDrI9i~bbSwQ__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[],"urls":[{"id":12936218,"url":"https://www.degruyter.com/document/doi/10.1515/fca-2021-0002/xml"}]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="57641918"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/57641918/Sir_Isaac_Newton_Stranger_in_a_Strange_Land"><img alt="Research paper thumbnail of Sir Isaac Newton Stranger in a Strange Land" class="work-thumbnail" src="https://attachments.academia-assets.com/72443441/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/57641918/Sir_Isaac_Newton_Stranger_in_a_Strange_Land">Sir Isaac Newton Stranger in a Strange Land</a></div><div class="wp-workCard_item"><span>Entropy</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">The theme of this essay is that the time of dominance of Newton’s world view in science is drawin...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">The theme of this essay is that the time of dominance of Newton’s world view in science is drawing to a close. The harbinger of its demise was the work of Poincaré on the three-body problem and its culmination into what is now called chaos theory. The signature of chaos is the sensitive dependence on initial conditions resulting in the unpredictability of single particle trajectories. Classical determinism has become increasingly rare with the advent of chaos, being replaced by erratic stochastic processes. However, even the probability calculus could not withstand the non-Newtonian assault from the social and life sciences. The ordinary partial differential equations that traditionally determined the evolution of probability density functions (PDFs) in phase space are replaced with their fractional counterparts. Allometry relation is proven to result from a system’s complexity using exact solutions for the PDF of the Fractional Kinetic Theory (FKT). Complexity theory is shown to be...</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="a6c64f9a762b736ee0d9e5aeeb8f5876" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":72443441,"asset_id":57641918,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/72443441/download_file?st=MTczMjc2NTkzMCw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="57641918"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="57641918"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 57641918; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=57641918]").text(description); $(".js-view-count[data-work-id=57641918]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 57641918; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='57641918']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 57641918, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "a6c64f9a762b736ee0d9e5aeeb8f5876" } } $('.js-work-strip[data-work-id=57641918]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":57641918,"title":"Sir Isaac Newton Stranger in a Strange Land","translated_title":"","metadata":{"abstract":"The theme of this essay is that the time of dominance of Newton’s world view in science is drawing to a close. The harbinger of its demise was the work of Poincaré on the three-body problem and its culmination into what is now called chaos theory. The signature of chaos is the sensitive dependence on initial conditions resulting in the unpredictability of single particle trajectories. Classical determinism has become increasingly rare with the advent of chaos, being replaced by erratic stochastic processes. However, even the probability calculus could not withstand the non-Newtonian assault from the social and life sciences. The ordinary partial differential equations that traditionally determined the evolution of probability density functions (PDFs) in phase space are replaced with their fractional counterparts. Allometry relation is proven to result from a system’s complexity using exact solutions for the PDF of the Fractional Kinetic Theory (FKT). Complexity theory is shown to be...","publisher":"MDPI AG","publication_name":"Entropy"},"translated_abstract":"The theme of this essay is that the time of dominance of Newton’s world view in science is drawing to a close. The harbinger of its demise was the work of Poincaré on the three-body problem and its culmination into what is now called chaos theory. The signature of chaos is the sensitive dependence on initial conditions resulting in the unpredictability of single particle trajectories. Classical determinism has become increasingly rare with the advent of chaos, being replaced by erratic stochastic processes. However, even the probability calculus could not withstand the non-Newtonian assault from the social and life sciences. The ordinary partial differential equations that traditionally determined the evolution of probability density functions (PDFs) in phase space are replaced with their fractional counterparts. Allometry relation is proven to result from a system’s complexity using exact solutions for the PDF of the Fractional Kinetic Theory (FKT). 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="57641917"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/57641917/Entropic_Approach_to_the_Detection_of_Crucial_Events"><img alt="Research paper thumbnail of Entropic Approach to the Detection of Crucial Events" class="work-thumbnail" src="https://attachments.academia-assets.com/72443435/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/57641917/Entropic_Approach_to_the_Detection_of_Crucial_Events">Entropic Approach to the Detection of Crucial Events</a></div><div class="wp-workCard_item"><span>Entropy</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">In this paper, we establish a clear distinction between two processes yielding anomalous diffusio...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">In this paper, we establish a clear distinction between two processes yielding anomalous diffusion and 1 / f noise. The first process is called Stationary Fractional Brownian Motion (SFBM) and is characterized by the use of stationary correlation functions. The second process rests on the action of crucial events generating ergodicity breakdown and aging effects. We refer to the latter as Aging Fractional Brownian Motion (AFBM). To settle the confusion between these different forms of Fractional Brownian Motion (FBM) we use an entropic approach properly updated to incorporate the recent advances of biology and psychology sciences on cognition. We show that although the joint action of crucial and non-crucial events may have the effect of making the crucial events virtually invisible, the entropic approach allows us to detect their action. The results of this paper lead us to the conclusion that the communication between the heart and the brain is accomplished by AFBM processes.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="db4590d52613c738335952f9bf97e884" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":72443435,"asset_id":57641917,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/72443435/download_file?st=MTczMjc2NTkzMCw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="57641917"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="57641917"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 57641917; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=57641917]").text(description); $(".js-view-count[data-work-id=57641917]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 57641917; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='57641917']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 57641917, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "db4590d52613c738335952f9bf97e884" } } $('.js-work-strip[data-work-id=57641917]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":57641917,"title":"Entropic Approach to the Detection of Crucial Events","translated_title":"","metadata":{"abstract":"In this paper, we establish a clear distinction between two processes yielding anomalous diffusion and 1 / f noise. The first process is called Stationary Fractional Brownian Motion (SFBM) and is characterized by the use of stationary correlation functions. The second process rests on the action of crucial events generating ergodicity breakdown and aging effects. We refer to the latter as Aging Fractional Brownian Motion (AFBM). To settle the confusion between these different forms of Fractional Brownian Motion (FBM) we use an entropic approach properly updated to incorporate the recent advances of biology and psychology sciences on cognition. We show that although the joint action of crucial and non-crucial events may have the effect of making the crucial events virtually invisible, the entropic approach allows us to detect their action. The results of this paper lead us to the conclusion that the communication between the heart and the brain is accomplished by AFBM processes.","publisher":"MDPI AG","publication_name":"Entropy"},"translated_abstract":"In this paper, we establish a clear distinction between two processes yielding anomalous diffusion and 1 / f noise. The first process is called Stationary Fractional Brownian Motion (SFBM) and is characterized by the use of stationary correlation functions. The second process rests on the action of crucial events generating ergodicity breakdown and aging effects. We refer to the latter as Aging Fractional Brownian Motion (AFBM). To settle the confusion between these different forms of Fractional Brownian Motion (FBM) we use an entropic approach properly updated to incorporate the recent advances of biology and psychology sciences on cognition. We show that although the joint action of crucial and non-crucial events may have the effect of making the crucial events virtually invisible, the entropic approach allows us to detect their action. The results of this paper lead us to the conclusion that the communication between the heart and the brain is accomplished by AFBM processes.","internal_url":"https://www.academia.edu/57641917/Entropic_Approach_to_the_Detection_of_Crucial_Events","translated_internal_url":"","created_at":"2021-10-13T17:35:31.704-07:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":66220250,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[{"id":72443435,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/72443435/thumbnails/1.jpg","file_name":"pdf.pdf","download_url":"https://www.academia.edu/attachments/72443435/download_file?st=MTczMjc2NTkzMCw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Entropic_Approach_to_the_Detection_of_Cr.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/72443435/pdf-libre.pdf?1634272208=\u0026response-content-disposition=attachment%3B+filename%3DEntropic_Approach_to_the_Detection_of_Cr.pdf\u0026Expires=1732769530\u0026Signature=W6fiYHKAqmajbIvh~NKVFrVpDdfWlk884aeKnKL96bhXtumyOalYErcmx9UyS7q19Lz0qVI5VEUF6HTun6HgWkcfl7Lh-N-ceWgqhKZTZ0pEwY8zyCYF6vHO5mzsxXupMXDMc0qw7seeVLRIBgjrdvGgoEAgD3W8bur6SzF2b~bTEHkvJF3uFhE5ZEQyRunMdLaWxmGKJoT4IiZkiuhha2EUnoGyoXhOb7ic6U9WvUIEy8xciNhzvbIC8v~FTAOjTLiksB4Ze0jIegjuooK61aWTa-vQCMxVuyZJNBI1~vnW4wqJpDRHwhICpZD9DV5Lj~wD0Ma6PsW5pvOtWAxhJw__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"Entropic_Approach_to_the_Detection_of_Crucial_Events","translated_slug":"","page_count":19,"language":"en","content_type":"Work","owner":{"id":66220250,"first_name":"Bruce","middle_initials":null,"last_name":"West","page_name":"BruceWest3","domain_name":"independent","created_at":"2017-07-07T14:39:25.483-07:00","display_name":"Bruce West","url":"https://independent.academia.edu/BruceWest3"},"attachments":[{"id":72443435,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/72443435/thumbnails/1.jpg","file_name":"pdf.pdf","download_url":"https://www.academia.edu/attachments/72443435/download_file?st=MTczMjc2NTkzMCw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Entropic_Approach_to_the_Detection_of_Cr.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/72443435/pdf-libre.pdf?1634272208=\u0026response-content-disposition=attachment%3B+filename%3DEntropic_Approach_to_the_Detection_of_Cr.pdf\u0026Expires=1732769530\u0026Signature=W6fiYHKAqmajbIvh~NKVFrVpDdfWlk884aeKnKL96bhXtumyOalYErcmx9UyS7q19Lz0qVI5VEUF6HTun6HgWkcfl7Lh-N-ceWgqhKZTZ0pEwY8zyCYF6vHO5mzsxXupMXDMc0qw7seeVLRIBgjrdvGgoEAgD3W8bur6SzF2b~bTEHkvJF3uFhE5ZEQyRunMdLaWxmGKJoT4IiZkiuhha2EUnoGyoXhOb7ic6U9WvUIEy8xciNhzvbIC8v~FTAOjTLiksB4Ze0jIegjuooK61aWTa-vQCMxVuyZJNBI1~vnW4wqJpDRHwhICpZD9DV5Lj~wD0Ma6PsW5pvOtWAxhJw__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[{"id":36265,"name":"Entropy","url":"https://www.academia.edu/Documents/in/Entropy"},{"id":80414,"name":"Mathematical Sciences","url":"https://www.academia.edu/Documents/in/Mathematical_Sciences"},{"id":118582,"name":"Physical sciences","url":"https://www.academia.edu/Documents/in/Physical_sciences"}],"urls":[{"id":12936216,"url":"http://www.mdpi.com/1099-4300/21/2/178/pdf"}]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="57641916"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/57641916/Crucial_events_randomness_and_multifractality_in_heartbeats"><img alt="Research paper thumbnail of Crucial events, randomness, and multifractality in heartbeats" class="work-thumbnail" src="https://attachments.academia-assets.com/72443540/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/57641916/Crucial_events_randomness_and_multifractality_in_heartbeats">Crucial events, randomness, and multifractality in heartbeats</a></div><div class="wp-workCard_item"><span>Physical review. E</span><span>, 2017</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">We study the connection between multifractality and crucial events. Multifractality is frequently...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">We study the connection between multifractality and crucial events. Multifractality is frequently used as a measure of physiological variability, where crucial events are known to play a fundamental role in the transport of information between complex networks. To establish the connection of interest we focus on the special case of heartbeat time series and on the search for a diagnostic prescription to distinguish healthy from pathologic subjects. Over the past 20 years two apparently different diagnostic techniques have been established: the first is based on the observation that the multifractal spectrum of healthy patients is broader than the multifractal spectrum of pathologic subjects; the second is based on the observation that heartbeat dynamics are a superposition of crucial and uncorrelated Poisson-like events, with pathologic patients hosting uncorrelated Poisson-like events with larger probability than the healthy patients. In this paper, we prove that increasing the per...</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="8b5e346a8cde5765c10dca2a32fb8b47" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":72443540,"asset_id":57641916,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/72443540/download_file?st=MTczMjc2NTkzMCw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="57641916"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="57641916"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 57641916; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=57641916]").text(description); $(".js-view-count[data-work-id=57641916]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 57641916; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='57641916']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 57641916, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "8b5e346a8cde5765c10dca2a32fb8b47" } } $('.js-work-strip[data-work-id=57641916]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":57641916,"title":"Crucial events, randomness, and multifractality in heartbeats","translated_title":"","metadata":{"abstract":"We study the connection between multifractality and crucial events. 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The resonant test field (RTF) is shown to obey a nonlinear generalized Langevin equation in general. In the Markov limit a Fokker-Planck equation is obtained and the exact steady-state solution is determined. An algebraic expression for the power spectral density is obtained in terms of the number of resonantly interacting waves (n) in the RTF, the interaction strength (Vk), and the dimensionality of the wave field (d). 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="57641910"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/57641910/The_complex_dynamics_of_diabetes_modeled_as_a_fractal_complex_adaptive_system_FCAS_"><img alt="Research paper thumbnail of The complex dynamics of diabetes modeled as a fractal complex-adaptive-system (FCAS)" class="work-thumbnail" src="https://attachments.academia-assets.com/72443423/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/57641910/The_complex_dynamics_of_diabetes_modeled_as_a_fractal_complex_adaptive_system_FCAS_">The complex dynamics of diabetes modeled as a fractal complex-adaptive-system (FCAS)</a></div><div class="wp-workCard_item"><span>Revista Brasileira de Epidemiologia</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">An approach is suggested in this paper that has successfully been applied in physics, ecology, an...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">An approach is suggested in this paper that has successfully been applied in physics, ecology, and the biomedical sciences. This is called fractal-complex-adaptive-system (FCAS) modeling. The objective of this type of analysis is to reconstruct the dynamics of the pathological process that has been leading to the disease. Diabetes, a complexdisease, has been used to test the methodology. Biometrical analyses were undertaken on subjects diagnosed with overt diabetes (hereafter called IDDM), chemical diabetes (NIDDM), and a group of normal subjects. The studied variables were plasma glucose, insulin concentration, and insulin sensitivity. FCAS modeling consists in fitting a power-law function to the bivariate lognormal distribution of the variables. The power-law exponent is estimated by principal component analysis (PCA). Analyses have shown that glucose disposal can be considered a fractal process, thereby implying a complex hierarchy of interacting scales and mechanisms in glucose ...</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="be91c52cd8bad1e9533e973e8d9623ea" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":72443423,"asset_id":57641910,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/72443423/download_file?st=MTczMjc2NTkzMCw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="57641910"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="57641910"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 57641910; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=57641910]").text(description); $(".js-view-count[data-work-id=57641910]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 57641910; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='57641910']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 57641910, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "be91c52cd8bad1e9533e973e8d9623ea" } } $('.js-work-strip[data-work-id=57641910]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":57641910,"title":"The complex dynamics of diabetes modeled as a fractal complex-adaptive-system (FCAS)","translated_title":"","metadata":{"abstract":"An approach is suggested in this paper that has successfully been applied in physics, ecology, and the biomedical sciences. This is called fractal-complex-adaptive-system (FCAS) modeling. The objective of this type of analysis is to reconstruct the dynamics of the pathological process that has been leading to the disease. Diabetes, a complexdisease, has been used to test the methodology. Biometrical analyses were undertaken on subjects diagnosed with overt diabetes (hereafter called IDDM), chemical diabetes (NIDDM), and a group of normal subjects. The studied variables were plasma glucose, insulin concentration, and insulin sensitivity. FCAS modeling consists in fitting a power-law function to the bivariate lognormal distribution of the variables. The power-law exponent is estimated by principal component analysis (PCA). Analyses have shown that glucose disposal can be considered a fractal process, thereby implying a complex hierarchy of interacting scales and mechanisms in glucose ...","publisher":"FapUNIFESP (SciELO)","publication_name":"Revista Brasileira de Epidemiologia"},"translated_abstract":"An approach is suggested in this paper that has successfully been applied in physics, ecology, and the biomedical sciences. This is called fractal-complex-adaptive-system (FCAS) modeling. The objective of this type of analysis is to reconstruct the dynamics of the pathological process that has been leading to the disease. Diabetes, a complexdisease, has been used to test the methodology. Biometrical analyses were undertaken on subjects diagnosed with overt diabetes (hereafter called IDDM), chemical diabetes (NIDDM), and a group of normal subjects. The studied variables were plasma glucose, insulin concentration, and insulin sensitivity. 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="81284004"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/81284004/Relating_size_and_functionality_in_human_social_networks_through_complexity"><img alt="Research paper thumbnail of Relating size and functionality in human social networks through complexity" class="work-thumbnail" src="https://attachments.academia-assets.com/87382304/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/81284004/Relating_size_and_functionality_in_human_social_networks_through_complexity">Relating size and functionality in human social networks through complexity</a></div><div class="wp-workCard_item wp-workCard--coauthors"><span>by </span><span><a class="" data-click-track="profile-work-strip-authors" href="https://oxford.academia.edu/rdunbar">robin dunbar</a> and <a class="" data-click-track="profile-work-strip-authors" href="https://independent.academia.edu/BruceWest3">Bruce West</a></span></div><div class="wp-workCard_item"><span>PNAS </span><span>, 2020</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Extensive empirical evidence suggests that there is a maximal number of people with whom an indiv...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Extensive empirical evidence suggests that there is a maximal<br />number of people with whom an individual can maintain stable<br />social relationships (the Dunbar number). We argue that this arises<br />as a consequence of a natural phase transition in the dynamic selforganization<br />among N individuals within a social system. We present<br />the calculated size dependence of the scaling properties of<br />complex social network models to argue that this collective behavior<br />is an enhanced form of collective intelligence. Direct calculation<br />establishes that the complexity of social networks as measured by<br />their scaling behavior is nonmonotonic, peaking around 150,<br />thereby providing a theoretical basis for the value of the Dunbar<br />number. Thus, we establish a theory-based bridge spanning the<br />gap between sociology and psychology.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="1bd2e1487f6e05c556eb17758c6b8e6d" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":87382304,"asset_id":81284004,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/87382304/download_file?st=MTczMjc2NTkzMCw4LjIyMi4yMDguMTQ2&st=MTczMjc2NTkzMCw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="81284004"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="81284004"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 81284004; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=81284004]").text(description); $(".js-view-count[data-work-id=81284004]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 81284004; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='81284004']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 81284004, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "1bd2e1487f6e05c556eb17758c6b8e6d" } } $('.js-work-strip[data-work-id=81284004]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":81284004,"title":"Relating size and functionality in human social networks through complexity","translated_title":"","metadata":{"abstract":"Extensive empirical evidence suggests that there is a maximal\nnumber of people with whom an individual can maintain stable\nsocial relationships (the Dunbar number). We argue that this arises\nas a consequence of a natural phase transition in the dynamic selforganization\namong N individuals within a social system. We present\nthe calculated size dependence of the scaling properties of\ncomplex social network models to argue that this collective behavior\nis an enhanced form of collective intelligence. Direct calculation\nestablishes that the complexity of social networks as measured by\ntheir scaling behavior is nonmonotonic, peaking around 150,\nthereby providing a theoretical basis for the value of the Dunbar\nnumber. Thus, we establish a theory-based bridge spanning the\ngap between sociology and psychology.","publication_date":{"day":null,"month":null,"year":2020,"errors":{}},"publication_name":"PNAS "},"translated_abstract":"Extensive empirical evidence suggests that there is a maximal\nnumber of people with whom an individual can maintain stable\nsocial relationships (the Dunbar number). 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The conditions under which the autocorrelation function of X shows any direct connection with criticality are discussed. We find that if the network is prepared in a state far from equilibrium, X(0) = 1, the autocorrelation function is characterized by evident signs of critical slowing down as well as by significant aging effects, while the preparation X(0) = 0 does not generate evident signs of criticality on X(t), in spite of the fact that the same initial state makes the fluctuating variable η(t) ≡ sgn(X(t)) yield significant aging effects. These latter effects arise because the dynamics of η(t) are directly dependent on crucial events, namely the re-crossings of the origin, which undergo a significant aging process with the preparation X(0) = 0. The time scale dominated by temporal complexity, aging and ergodicity breakdown of η(t) is properly evaluated by adopting the method of stochastic linearization which is used to explain the exponential-like behavior of the equilibrium autocorrelation function of X(t).","grobid_abstract_attachment_id":77071436},"translated_abstract":null,"internal_url":"https://www.academia.edu/65504376/Critical_slowing_down_in_networks_generating_temporal_complexity","translated_internal_url":"","created_at":"2021-12-22T06:44:31.464-08:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":66220250,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[{"id":77071436,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/77071436/thumbnails/1.jpg","file_name":"ce42fe2a61d9b564ac50aa054bfd13efc13a.pdf","download_url":"https://www.academia.edu/attachments/77071436/download_file?st=MTczMjc2NTkzMCw4LjIyMi4yMDguMTQ2&st=MTczMjc2NTkzMCw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Critical_slowing_down_in_networks_genera.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/77071436/ce42fe2a61d9b564ac50aa054bfd13efc13a-libre.pdf?1640295586=\u0026response-content-disposition=attachment%3B+filename%3DCritical_slowing_down_in_networks_genera.pdf\u0026Expires=1732769530\u0026Signature=AQ2KYVCAJgLEVC86tBhNnN~LxgqQRugO~8e~9Igfge2pWVRVdLWXHRFUUA8pqte-sCiZIhQ45G5hcqvJccaNeq-rzhvbAFRRIOI5V5QrK-LqWWIdfvlMW7piZ5jT7XzWp40BHKHwLRXjAdjkhkn42~Hw9eoc~VHO5GRq9kveNaRwrtDxdvxm0CNoeaH1LqOuFAHlByqv5DrAx49Jgh0gTH26AqgQi0K-8N9Fuhk9bfLG1wi2SPt~bhebEJaGEbHSPfzJlWNpDRj68PwRVj57KRGUoZTbI28Xcql3m3wnrxEPpemsQG9eU7JLG0LJTktt3qhuUKvvz5u6PSnqIqOEjg__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"Critical_slowing_down_in_networks_generating_temporal_complexity","translated_slug":"","page_count":9,"language":"en","content_type":"Work","owner":{"id":66220250,"first_name":"Bruce","middle_initials":null,"last_name":"West","page_name":"BruceWest3","domain_name":"independent","created_at":"2017-07-07T14:39:25.483-07:00","display_name":"Bruce West","url":"https://independent.academia.edu/BruceWest3"},"attachments":[{"id":77071436,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/77071436/thumbnails/1.jpg","file_name":"ce42fe2a61d9b564ac50aa054bfd13efc13a.pdf","download_url":"https://www.academia.edu/attachments/77071436/download_file?st=MTczMjc2NTkzMCw4LjIyMi4yMDguMTQ2&st=MTczMjc2NTkzMCw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Critical_slowing_down_in_networks_genera.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/77071436/ce42fe2a61d9b564ac50aa054bfd13efc13a-libre.pdf?1640295586=\u0026response-content-disposition=attachment%3B+filename%3DCritical_slowing_down_in_networks_genera.pdf\u0026Expires=1732769530\u0026Signature=AQ2KYVCAJgLEVC86tBhNnN~LxgqQRugO~8e~9Igfge2pWVRVdLWXHRFUUA8pqte-sCiZIhQ45G5hcqvJccaNeq-rzhvbAFRRIOI5V5QrK-LqWWIdfvlMW7piZ5jT7XzWp40BHKHwLRXjAdjkhkn42~Hw9eoc~VHO5GRq9kveNaRwrtDxdvxm0CNoeaH1LqOuFAHlByqv5DrAx49Jgh0gTH26AqgQi0K-8N9Fuhk9bfLG1wi2SPt~bhebEJaGEbHSPfzJlWNpDRj68PwRVj57KRGUoZTbI28Xcql3m3wnrxEPpemsQG9eU7JLG0LJTktt3qhuUKvvz5u6PSnqIqOEjg__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[{"id":48,"name":"Engineering","url":"https://www.academia.edu/Documents/in/Engineering"},{"id":498,"name":"Physics","url":"https://www.academia.edu/Documents/in/Physics"},{"id":26327,"name":"Medicine","url":"https://www.academia.edu/Documents/in/Medicine"},{"id":80414,"name":"Mathematical Sciences","url":"https://www.academia.edu/Documents/in/Mathematical_Sciences"},{"id":118582,"name":"Physical sciences","url":"https://www.academia.edu/Documents/in/Physical_sciences"}],"urls":[]}, dispatcherData: dispatcherData }); 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The generator of the deterministic evolution is a nonlinear map belonging to a class of maps recently tailored to mimic the processes of weak chaos responsible for the birth of anomalous diffusion. It is assumed that the deterministic process corresponds to unknown biological rules that determine the DNA path, whereas the noise mimics the inQuence of an infinite-dimensional environment on the biological process under study. We prove that the resulting diffusion process, if the effect of the random process is neglected, is an o.-stable Levy process with 1 (o. (2. We also show that, if the diffusion process is determined by the joint action of the deterministic and the random process, the correlation effects of the \"deterministic dynamics\" are canceled on the shortrange scale, but show up in the long-range one. We denote our prescription to generate statistical sequences as the copying mistake map (CMM). We carry out our analysis of several DNA sequences and their CMM realizations with a variety of techniques and we especially focus on a method of regression to equilibrium, which we call the Onsager analysis. With these techniques we establish the statistical equivalence of the real DNA sequences with their CMM realizations. We show that long-range correlations are present in exons as well as in introns, but are diKcult to detect, since the exon \"dynamics\" is shown to be determined by the entanglement of three distinct and independent CMM's.","publication_date":{"day":null,"month":null,"year":1995,"errors":{}},"grobid_abstract_attachment_id":77071437},"translated_abstract":null,"internal_url":"https://www.academia.edu/65504375/Dynamical_model_for_DNA_sequences","translated_internal_url":"","created_at":"2021-12-22T06:44:31.379-08:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":66220250,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[{"id":77071437,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/77071437/thumbnails/1.jpg","file_name":"87f7147bcf4ac885986905e3f61936337b88.pdf","download_url":"https://www.academia.edu/attachments/77071437/download_file?st=MTczMjc2NTkzMCw4LjIyMi4yMDguMTQ2&st=MTczMjc2NTkzMCw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Dynamical_model_for_DNA_sequences.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/77071437/87f7147bcf4ac885986905e3f61936337b88-libre.pdf?1640295593=\u0026response-content-disposition=attachment%3B+filename%3DDynamical_model_for_DNA_sequences.pdf\u0026Expires=1732769530\u0026Signature=KLJcB1nTbJ8RLs7q-1Ava1D9K-hmrrB32qOC5u5qoutlmLvpQDUHMBI29fHDaVUWDlsS78~gr7AHh3vTN7s-d-Dsygg4qHM1pYHe2dZ7hoRPW666quDj2Z1JA8TBh326Er6pryxakpWdmSdNlO3VFOADBQrIwbqBQKWAgaIeUUaXu5f1ZO9~vy1tdWK8AkwKAIu-pOaa49w2Jg-lcNoWrLh5sAWwtHiTL3wSun4ko3V756ChDMaYe80lQDjZPCCqVb00DY88x50augiVj8GGaLboC3p77D9hKD6O~d21h8eKiupOX1E8TLKrJ6sdpDiQDjf9~Ou24ZOqngKqASIrpA__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"Dynamical_model_for_DNA_sequences","translated_slug":"","page_count":16,"language":"en","content_type":"Work","owner":{"id":66220250,"first_name":"Bruce","middle_initials":null,"last_name":"West","page_name":"BruceWest3","domain_name":"independent","created_at":"2017-07-07T14:39:25.483-07:00","display_name":"Bruce West","url":"https://independent.academia.edu/BruceWest3"},"attachments":[{"id":77071437,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/77071437/thumbnails/1.jpg","file_name":"87f7147bcf4ac885986905e3f61936337b88.pdf","download_url":"https://www.academia.edu/attachments/77071437/download_file?st=MTczMjc2NTkzMCw4LjIyMi4yMDguMTQ2&st=MTczMjc2NTkzMCw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Dynamical_model_for_DNA_sequences.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/77071437/87f7147bcf4ac885986905e3f61936337b88-libre.pdf?1640295593=\u0026response-content-disposition=attachment%3B+filename%3DDynamical_model_for_DNA_sequences.pdf\u0026Expires=1732769530\u0026Signature=KLJcB1nTbJ8RLs7q-1Ava1D9K-hmrrB32qOC5u5qoutlmLvpQDUHMBI29fHDaVUWDlsS78~gr7AHh3vTN7s-d-Dsygg4qHM1pYHe2dZ7hoRPW666quDj2Z1JA8TBh326Er6pryxakpWdmSdNlO3VFOADBQrIwbqBQKWAgaIeUUaXu5f1ZO9~vy1tdWK8AkwKAIu-pOaa49w2Jg-lcNoWrLh5sAWwtHiTL3wSun4ko3V756ChDMaYe80lQDjZPCCqVb00DY88x50augiVj8GGaLboC3p77D9hKD6O~d21h8eKiupOX1E8TLKrJ6sdpDiQDjf9~Ou24ZOqngKqASIrpA__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[{"id":48,"name":"Engineering","url":"https://www.academia.edu/Documents/in/Engineering"},{"id":300,"name":"Mathematics","url":"https://www.academia.edu/Documents/in/Mathematics"},{"id":26327,"name":"Medicine","url":"https://www.academia.edu/Documents/in/Medicine"},{"id":50926,"name":"Joint Action","url":"https://www.academia.edu/Documents/in/Joint_Action"},{"id":80414,"name":"Mathematical Sciences","url":"https://www.academia.edu/Documents/in/Mathematical_Sciences"},{"id":118582,"name":"Physical sciences","url":"https://www.academia.edu/Documents/in/Physical_sciences"},{"id":148995,"name":"Long Range","url":"https://www.academia.edu/Documents/in/Long_Range"},{"id":428833,"name":"Statistical Properties","url":"https://www.academia.edu/Documents/in/Statistical_Properties"},{"id":495625,"name":"Biological Process","url":"https://www.academia.edu/Documents/in/Biological_Process"},{"id":758675,"name":"Anomalous Diffusion","url":"https://www.academia.edu/Documents/in/Anomalous_Diffusion"},{"id":990491,"name":"Irreversible Thermodynamics","url":"https://www.academia.edu/Documents/in/Irreversible_Thermodynamics"},{"id":2274872,"name":"DNA sequence","url":"https://www.academia.edu/Documents/in/DNA_sequence"},{"id":2626792,"name":"dynamic model","url":"https://www.academia.edu/Documents/in/dynamic_model"}],"urls":[]}, dispatcherData: dispatcherData }); 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="65504158"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/65504158/Path_integral_formation_of_wave_propagation_in_the_ionosphere_4"><img alt="Research paper thumbnail of Path integral formation of wave propagation in the ionosphere, 4" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/65504158/Path_integral_formation_of_wave_propagation_in_the_ionosphere_4">Path integral formation of wave propagation in the ionosphere, 4</a></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">The validity of the application of weak scatter theory to ionospheric scattering data has been ex...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">The validity of the application of weak scatter theory to ionospheric scattering data has been examined. It is concluded that the weak scatter theory is not universally applicable. Born and Rytov weak scatter calculations are compared and the Rytov calculations is found superior. The Rytov calculations appear to explain the enhancement in the scintillation index (the ratio on the intensity variance to variance of phase) in the equatorial vis a vis the polar stations. This research effort will be completed under Contract Number 49620-82-C-0058.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="65504158"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="65504158"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 65504158; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=65504158]").text(description); $(".js-view-count[data-work-id=65504158]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 65504158; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='65504158']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 65504158, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (false){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "-1" } } $('.js-work-strip[data-work-id=65504158]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":65504158,"title":"Path integral formation of wave propagation in the ionosphere, 4","translated_title":"","metadata":{"abstract":"The validity of the application of weak scatter theory to ionospheric scattering data has been examined. It is concluded that the weak scatter theory is not universally applicable. Born and Rytov weak scatter calculations are compared and the Rytov calculations is found superior. The Rytov calculations appear to explain the enhancement in the scintillation index (the ratio on the intensity variance to variance of phase) in the equatorial vis a vis the polar stations. This research effort will be completed under Contract Number 49620-82-C-0058.","publication_date":{"day":null,"month":null,"year":1982,"errors":{}}},"translated_abstract":"The validity of the application of weak scatter theory to ionospheric scattering data has been examined. It is concluded that the weak scatter theory is not universally applicable. Born and Rytov weak scatter calculations are compared and the Rytov calculations is found superior. The Rytov calculations appear to explain the enhancement in the scintillation index (the ratio on the intensity variance to variance of phase) in the equatorial vis a vis the polar stations. 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Meanwhile, in the study of phase transitions and critical phenomena, it was found that the self–similarity of systems near critical points can be described using RG methods. Furthermore, since self–similarity is often a defining feature of a complex system, the RG method is also devoted to characterizing complexity. In addition, the RG approach has also proven to be a useful tool to analyze the asymptotic behavior of solutions in the singular perturbation theory. In this review paper, we discuss the origin, development, and application of the RG method in a variety of fields from the physical, social and life sciences, in singular perturbation theory, and reveal the need to connect the RG and the fractional calculus (FC). 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The FC is another basic mathematical approach for describin...","publisher":"Walter de Gruyter GmbH","publication_name":"Fractional Calculus and Applied Analysis"},"translated_abstract":"The concept of the renormalization group (RG) emerged from the renormalization of quantum field variables, which is typically used to deal with the issue of divergences to infinity in quantum field theory. Meanwhile, in the study of phase transitions and critical phenomena, it was found that the self–similarity of systems near critical points can be described using RG methods. Furthermore, since self–similarity is often a defining feature of a complex system, the RG method is also devoted to characterizing complexity. In addition, the RG approach has also proven to be a useful tool to analyze the asymptotic behavior of solutions in the singular perturbation theory. In this review paper, we discuss the origin, development, and application of the RG method in a variety of fields from the physical, social and life sciences, in singular perturbation theory, and reveal the need to connect the RG and the fractional calculus (FC). The FC is another basic mathematical approach for describin...","internal_url":"https://www.academia.edu/57641919/Renormalization_group_and_fractional_calculus_methods_in_a_complex_world_A_review","translated_internal_url":"","created_at":"2021-10-13T17:35:32.576-07:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":66220250,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[{"id":72443542,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/72443542/thumbnails/1.jpg","file_name":"pdf.pdf","download_url":"https://www.academia.edu/attachments/72443542/download_file?st=MTczMjc2NTkzMCw4LjIyMi4yMDguMTQ2&st=MTczMjc2NTkzMCw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Renormalization_group_and_fractional_cal.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/72443542/pdf-libre.pdf?1634272204=\u0026response-content-disposition=attachment%3B+filename%3DRenormalization_group_and_fractional_cal.pdf\u0026Expires=1732769530\u0026Signature=AVwtgFy~x8vqB2kez7704tSodbKt7W-Zlnp9JEM52hJ7GcJCfphhpX7hwj3j38h9ZLRsl0sgrB6SErOM9fryy9XrSvRSYduDNkOJSZjfcyW-1eI45z4u-9GPU1R8KSZUQy146bnsPNaQk4hARsPqBmSPGnpKhrdueFvq2uDErGeOZqH4ruKS3i7h2JGI2JbUN9djvp6kt0BE8ei2MtTkanO-eZPPc52dw9wu2fu9HS5p3O3j~g3ORW2N0iiNycAPbQVN08fi758H06RCKblm2yKleTUaV8NI4PdBtq9jlrNvQ9agEkcGU7ZQ8eiajmlVYU6cFN6KXmgDrI9i~bbSwQ__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"Renormalization_group_and_fractional_calculus_methods_in_a_complex_world_A_review","translated_slug":"","page_count":49,"language":"en","content_type":"Work","owner":{"id":66220250,"first_name":"Bruce","middle_initials":null,"last_name":"West","page_name":"BruceWest3","domain_name":"independent","created_at":"2017-07-07T14:39:25.483-07:00","display_name":"Bruce West","url":"https://independent.academia.edu/BruceWest3"},"attachments":[{"id":72443542,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/72443542/thumbnails/1.jpg","file_name":"pdf.pdf","download_url":"https://www.academia.edu/attachments/72443542/download_file?st=MTczMjc2NTkzMCw4LjIyMi4yMDguMTQ2&st=MTczMjc2NTkzMCw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Renormalization_group_and_fractional_cal.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/72443542/pdf-libre.pdf?1634272204=\u0026response-content-disposition=attachment%3B+filename%3DRenormalization_group_and_fractional_cal.pdf\u0026Expires=1732769530\u0026Signature=AVwtgFy~x8vqB2kez7704tSodbKt7W-Zlnp9JEM52hJ7GcJCfphhpX7hwj3j38h9ZLRsl0sgrB6SErOM9fryy9XrSvRSYduDNkOJSZjfcyW-1eI45z4u-9GPU1R8KSZUQy146bnsPNaQk4hARsPqBmSPGnpKhrdueFvq2uDErGeOZqH4ruKS3i7h2JGI2JbUN9djvp6kt0BE8ei2MtTkanO-eZPPc52dw9wu2fu9HS5p3O3j~g3ORW2N0iiNycAPbQVN08fi758H06RCKblm2yKleTUaV8NI4PdBtq9jlrNvQ9agEkcGU7ZQ8eiajmlVYU6cFN6KXmgDrI9i~bbSwQ__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[],"urls":[{"id":12936218,"url":"https://www.degruyter.com/document/doi/10.1515/fca-2021-0002/xml"}]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="57641918"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/57641918/Sir_Isaac_Newton_Stranger_in_a_Strange_Land"><img alt="Research paper thumbnail of Sir Isaac Newton Stranger in a Strange Land" class="work-thumbnail" src="https://attachments.academia-assets.com/72443441/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/57641918/Sir_Isaac_Newton_Stranger_in_a_Strange_Land">Sir Isaac Newton Stranger in a Strange Land</a></div><div class="wp-workCard_item"><span>Entropy</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">The theme of this essay is that the time of dominance of Newton’s world view in science is drawin...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">The theme of this essay is that the time of dominance of Newton’s world view in science is drawing to a close. The harbinger of its demise was the work of Poincaré on the three-body problem and its culmination into what is now called chaos theory. The signature of chaos is the sensitive dependence on initial conditions resulting in the unpredictability of single particle trajectories. Classical determinism has become increasingly rare with the advent of chaos, being replaced by erratic stochastic processes. However, even the probability calculus could not withstand the non-Newtonian assault from the social and life sciences. The ordinary partial differential equations that traditionally determined the evolution of probability density functions (PDFs) in phase space are replaced with their fractional counterparts. Allometry relation is proven to result from a system’s complexity using exact solutions for the PDF of the Fractional Kinetic Theory (FKT). Complexity theory is shown to be...</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="a6c64f9a762b736ee0d9e5aeeb8f5876" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":72443441,"asset_id":57641918,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/72443441/download_file?st=MTczMjc2NTkzMCw4LjIyMi4yMDguMTQ2&st=MTczMjc2NTkzMCw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="57641918"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="57641918"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 57641918; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=57641918]").text(description); $(".js-view-count[data-work-id=57641918]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 57641918; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='57641918']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 57641918, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "a6c64f9a762b736ee0d9e5aeeb8f5876" } } $('.js-work-strip[data-work-id=57641918]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":57641918,"title":"Sir Isaac Newton Stranger in a Strange Land","translated_title":"","metadata":{"abstract":"The theme of this essay is that the time of dominance of Newton’s world view in science is drawing to a close. 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Complexity theory is shown to be...","publisher":"MDPI AG","publication_name":"Entropy"},"translated_abstract":"The theme of this essay is that the time of dominance of Newton’s world view in science is drawing to a close. The harbinger of its demise was the work of Poincaré on the three-body problem and its culmination into what is now called chaos theory. The signature of chaos is the sensitive dependence on initial conditions resulting in the unpredictability of single particle trajectories. Classical determinism has become increasingly rare with the advent of chaos, being replaced by erratic stochastic processes. However, even the probability calculus could not withstand the non-Newtonian assault from the social and life sciences. The ordinary partial differential equations that traditionally determined the evolution of probability density functions (PDFs) in phase space are replaced with their fractional counterparts. Allometry relation is proven to result from a system’s complexity using exact solutions for the PDF of the Fractional Kinetic Theory (FKT). 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="57641917"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/57641917/Entropic_Approach_to_the_Detection_of_Crucial_Events"><img alt="Research paper thumbnail of Entropic Approach to the Detection of Crucial Events" class="work-thumbnail" src="https://attachments.academia-assets.com/72443435/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/57641917/Entropic_Approach_to_the_Detection_of_Crucial_Events">Entropic Approach to the Detection of Crucial Events</a></div><div class="wp-workCard_item"><span>Entropy</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">In this paper, we establish a clear distinction between two processes yielding anomalous diffusio...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">In this paper, we establish a clear distinction between two processes yielding anomalous diffusion and 1 / f noise. The first process is called Stationary Fractional Brownian Motion (SFBM) and is characterized by the use of stationary correlation functions. The second process rests on the action of crucial events generating ergodicity breakdown and aging effects. We refer to the latter as Aging Fractional Brownian Motion (AFBM). To settle the confusion between these different forms of Fractional Brownian Motion (FBM) we use an entropic approach properly updated to incorporate the recent advances of biology and psychology sciences on cognition. We show that although the joint action of crucial and non-crucial events may have the effect of making the crucial events virtually invisible, the entropic approach allows us to detect their action. The results of this paper lead us to the conclusion that the communication between the heart and the brain is accomplished by AFBM processes.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="db4590d52613c738335952f9bf97e884" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":72443435,"asset_id":57641917,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/72443435/download_file?st=MTczMjc2NTkzMCw4LjIyMi4yMDguMTQ2&st=MTczMjc2NTkzMCw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="57641917"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="57641917"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 57641917; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=57641917]").text(description); $(".js-view-count[data-work-id=57641917]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 57641917; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='57641917']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 57641917, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "db4590d52613c738335952f9bf97e884" } } $('.js-work-strip[data-work-id=57641917]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":57641917,"title":"Entropic Approach to the Detection of Crucial Events","translated_title":"","metadata":{"abstract":"In this paper, we establish a clear distinction between two processes yielding anomalous diffusion and 1 / f noise. The first process is called Stationary Fractional Brownian Motion (SFBM) and is characterized by the use of stationary correlation functions. The second process rests on the action of crucial events generating ergodicity breakdown and aging effects. We refer to the latter as Aging Fractional Brownian Motion (AFBM). To settle the confusion between these different forms of Fractional Brownian Motion (FBM) we use an entropic approach properly updated to incorporate the recent advances of biology and psychology sciences on cognition. We show that although the joint action of crucial and non-crucial events may have the effect of making the crucial events virtually invisible, the entropic approach allows us to detect their action. The results of this paper lead us to the conclusion that the communication between the heart and the brain is accomplished by AFBM processes.","publisher":"MDPI AG","publication_name":"Entropy"},"translated_abstract":"In this paper, we establish a clear distinction between two processes yielding anomalous diffusion and 1 / f noise. The first process is called Stationary Fractional Brownian Motion (SFBM) and is characterized by the use of stationary correlation functions. The second process rests on the action of crucial events generating ergodicity breakdown and aging effects. We refer to the latter as Aging Fractional Brownian Motion (AFBM). To settle the confusion between these different forms of Fractional Brownian Motion (FBM) we use an entropic approach properly updated to incorporate the recent advances of biology and psychology sciences on cognition. We show that although the joint action of crucial and non-crucial events may have the effect of making the crucial events virtually invisible, the entropic approach allows us to detect their action. The results of this paper lead us to the conclusion that the communication between the heart and the brain is accomplished by AFBM processes.","internal_url":"https://www.academia.edu/57641917/Entropic_Approach_to_the_Detection_of_Crucial_Events","translated_internal_url":"","created_at":"2021-10-13T17:35:31.704-07:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":66220250,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[{"id":72443435,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/72443435/thumbnails/1.jpg","file_name":"pdf.pdf","download_url":"https://www.academia.edu/attachments/72443435/download_file?st=MTczMjc2NTkzMCw4LjIyMi4yMDguMTQ2&st=MTczMjc2NTkzMCw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Entropic_Approach_to_the_Detection_of_Cr.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/72443435/pdf-libre.pdf?1634272208=\u0026response-content-disposition=attachment%3B+filename%3DEntropic_Approach_to_the_Detection_of_Cr.pdf\u0026Expires=1732769530\u0026Signature=W6fiYHKAqmajbIvh~NKVFrVpDdfWlk884aeKnKL96bhXtumyOalYErcmx9UyS7q19Lz0qVI5VEUF6HTun6HgWkcfl7Lh-N-ceWgqhKZTZ0pEwY8zyCYF6vHO5mzsxXupMXDMc0qw7seeVLRIBgjrdvGgoEAgD3W8bur6SzF2b~bTEHkvJF3uFhE5ZEQyRunMdLaWxmGKJoT4IiZkiuhha2EUnoGyoXhOb7ic6U9WvUIEy8xciNhzvbIC8v~FTAOjTLiksB4Ze0jIegjuooK61aWTa-vQCMxVuyZJNBI1~vnW4wqJpDRHwhICpZD9DV5Lj~wD0Ma6PsW5pvOtWAxhJw__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"Entropic_Approach_to_the_Detection_of_Crucial_Events","translated_slug":"","page_count":19,"language":"en","content_type":"Work","owner":{"id":66220250,"first_name":"Bruce","middle_initials":null,"last_name":"West","page_name":"BruceWest3","domain_name":"independent","created_at":"2017-07-07T14:39:25.483-07:00","display_name":"Bruce West","url":"https://independent.academia.edu/BruceWest3"},"attachments":[{"id":72443435,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/72443435/thumbnails/1.jpg","file_name":"pdf.pdf","download_url":"https://www.academia.edu/attachments/72443435/download_file?st=MTczMjc2NTkzMCw4LjIyMi4yMDguMTQ2&st=MTczMjc2NTkzMCw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Entropic_Approach_to_the_Detection_of_Cr.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/72443435/pdf-libre.pdf?1634272208=\u0026response-content-disposition=attachment%3B+filename%3DEntropic_Approach_to_the_Detection_of_Cr.pdf\u0026Expires=1732769530\u0026Signature=W6fiYHKAqmajbIvh~NKVFrVpDdfWlk884aeKnKL96bhXtumyOalYErcmx9UyS7q19Lz0qVI5VEUF6HTun6HgWkcfl7Lh-N-ceWgqhKZTZ0pEwY8zyCYF6vHO5mzsxXupMXDMc0qw7seeVLRIBgjrdvGgoEAgD3W8bur6SzF2b~bTEHkvJF3uFhE5ZEQyRunMdLaWxmGKJoT4IiZkiuhha2EUnoGyoXhOb7ic6U9WvUIEy8xciNhzvbIC8v~FTAOjTLiksB4Ze0jIegjuooK61aWTa-vQCMxVuyZJNBI1~vnW4wqJpDRHwhICpZD9DV5Lj~wD0Ma6PsW5pvOtWAxhJw__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[{"id":36265,"name":"Entropy","url":"https://www.academia.edu/Documents/in/Entropy"},{"id":80414,"name":"Mathematical Sciences","url":"https://www.academia.edu/Documents/in/Mathematical_Sciences"},{"id":118582,"name":"Physical sciences","url":"https://www.academia.edu/Documents/in/Physical_sciences"}],"urls":[{"id":12936216,"url":"http://www.mdpi.com/1099-4300/21/2/178/pdf"}]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="57641916"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/57641916/Crucial_events_randomness_and_multifractality_in_heartbeats"><img alt="Research paper thumbnail of Crucial events, randomness, and multifractality in heartbeats" class="work-thumbnail" src="https://attachments.academia-assets.com/72443540/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/57641916/Crucial_events_randomness_and_multifractality_in_heartbeats">Crucial events, randomness, and multifractality in heartbeats</a></div><div class="wp-workCard_item"><span>Physical review. E</span><span>, 2017</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">We study the connection between multifractality and crucial events. Multifractality is frequently...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">We study the connection between multifractality and crucial events. Multifractality is frequently used as a measure of physiological variability, where crucial events are known to play a fundamental role in the transport of information between complex networks. To establish the connection of interest we focus on the special case of heartbeat time series and on the search for a diagnostic prescription to distinguish healthy from pathologic subjects. Over the past 20 years two apparently different diagnostic techniques have been established: the first is based on the observation that the multifractal spectrum of healthy patients is broader than the multifractal spectrum of pathologic subjects; the second is based on the observation that heartbeat dynamics are a superposition of crucial and uncorrelated Poisson-like events, with pathologic patients hosting uncorrelated Poisson-like events with larger probability than the healthy patients. In this paper, we prove that increasing the per...</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="8b5e346a8cde5765c10dca2a32fb8b47" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":72443540,"asset_id":57641916,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/72443540/download_file?st=MTczMjc2NTkzMCw4LjIyMi4yMDguMTQ2&st=MTczMjc2NTkzMCw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="57641916"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="57641916"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 57641916; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=57641916]").text(description); $(".js-view-count[data-work-id=57641916]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 57641916; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='57641916']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 57641916, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "8b5e346a8cde5765c10dca2a32fb8b47" } } $('.js-work-strip[data-work-id=57641916]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":57641916,"title":"Crucial events, randomness, and multifractality in heartbeats","translated_title":"","metadata":{"abstract":"We study the connection between multifractality and crucial events. 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In this paper, we prove that increasing the per...","publication_date":{"day":null,"month":null,"year":2017,"errors":{}},"publication_name":"Physical review. E"},"translated_abstract":"We study the connection between multifractality and crucial events. Multifractality is frequently used as a measure of physiological variability, where crucial events are known to play a fundamental role in the transport of information between complex networks. To establish the connection of interest we focus on the special case of heartbeat time series and on the search for a diagnostic prescription to distinguish healthy from pathologic subjects. 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="57641910"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/57641910/The_complex_dynamics_of_diabetes_modeled_as_a_fractal_complex_adaptive_system_FCAS_"><img alt="Research paper thumbnail of The complex dynamics of diabetes modeled as a fractal complex-adaptive-system (FCAS)" class="work-thumbnail" src="https://attachments.academia-assets.com/72443423/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/57641910/The_complex_dynamics_of_diabetes_modeled_as_a_fractal_complex_adaptive_system_FCAS_">The complex dynamics of diabetes modeled as a fractal complex-adaptive-system (FCAS)</a></div><div class="wp-workCard_item"><span>Revista Brasileira de Epidemiologia</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">An approach is suggested in this paper that has successfully been applied in physics, ecology, an...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">An approach is suggested in this paper that has successfully been applied in physics, ecology, and the biomedical sciences. This is called fractal-complex-adaptive-system (FCAS) modeling. The objective of this type of analysis is to reconstruct the dynamics of the pathological process that has been leading to the disease. Diabetes, a complexdisease, has been used to test the methodology. Biometrical analyses were undertaken on subjects diagnosed with overt diabetes (hereafter called IDDM), chemical diabetes (NIDDM), and a group of normal subjects. The studied variables were plasma glucose, insulin concentration, and insulin sensitivity. FCAS modeling consists in fitting a power-law function to the bivariate lognormal distribution of the variables. The power-law exponent is estimated by principal component analysis (PCA). Analyses have shown that glucose disposal can be considered a fractal process, thereby implying a complex hierarchy of interacting scales and mechanisms in glucose ...</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="be91c52cd8bad1e9533e973e8d9623ea" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":72443423,"asset_id":57641910,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/72443423/download_file?st=MTczMjc2NTkzMCw4LjIyMi4yMDguMTQ2&st=MTczMjc2NTkzMCw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="57641910"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="57641910"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 57641910; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=57641910]").text(description); $(".js-view-count[data-work-id=57641910]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 57641910; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='57641910']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 57641910, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "be91c52cd8bad1e9533e973e8d9623ea" } } $('.js-work-strip[data-work-id=57641910]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":57641910,"title":"The complex dynamics of diabetes modeled as a fractal complex-adaptive-system (FCAS)","translated_title":"","metadata":{"abstract":"An approach is suggested in this paper that has successfully been applied in physics, ecology, and the biomedical sciences. This is called fractal-complex-adaptive-system (FCAS) modeling. The objective of this type of analysis is to reconstruct the dynamics of the pathological process that has been leading to the disease. Diabetes, a complexdisease, has been used to test the methodology. Biometrical analyses were undertaken on subjects diagnosed with overt diabetes (hereafter called IDDM), chemical diabetes (NIDDM), and a group of normal subjects. The studied variables were plasma glucose, insulin concentration, and insulin sensitivity. FCAS modeling consists in fitting a power-law function to the bivariate lognormal distribution of the variables. The power-law exponent is estimated by principal component analysis (PCA). Analyses have shown that glucose disposal can be considered a fractal process, thereby implying a complex hierarchy of interacting scales and mechanisms in glucose ...","publisher":"FapUNIFESP (SciELO)","publication_name":"Revista Brasileira de Epidemiologia"},"translated_abstract":"An approach is suggested in this paper that has successfully been applied in physics, ecology, and the biomedical sciences. This is called fractal-complex-adaptive-system (FCAS) modeling. The objective of this type of analysis is to reconstruct the dynamics of the pathological process that has been leading to the disease. Diabetes, a complexdisease, has been used to test the methodology. Biometrical analyses were undertaken on subjects diagnosed with overt diabetes (hereafter called IDDM), chemical diabetes (NIDDM), and a group of normal subjects. The studied variables were plasma glucose, insulin concentration, and insulin sensitivity. FCAS modeling consists in fitting a power-law function to the bivariate lognormal distribution of the variables. The power-law exponent is estimated by principal component analysis (PCA). Analyses have shown that glucose disposal can be considered a fractal process, thereby implying a complex hierarchy of interacting scales and mechanisms in glucose ...","internal_url":"https://www.academia.edu/57641910/The_complex_dynamics_of_diabetes_modeled_as_a_fractal_complex_adaptive_system_FCAS_","translated_internal_url":"","created_at":"2021-10-13T17:35:29.142-07:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":66220250,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[{"id":72443423,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/72443423/thumbnails/1.jpg","file_name":"07.pdf","download_url":"https://www.academia.edu/attachments/72443423/download_file?st=MTczMjc2NTkzMCw4LjIyMi4yMDguMTQ2&st=MTczMjc2NTkzMCw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"The_complex_dynamics_of_diabetes_modeled.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/72443423/07-libre.pdf?1634272204=\u0026response-content-disposition=attachment%3B+filename%3DThe_complex_dynamics_of_diabetes_modeled.pdf\u0026Expires=1732769530\u0026Signature=J-9M-RBaYPfd6pgio6HvGBD---KDvvyXAqY10JL1Jx~0Q6HMBc-RhEXt3dPOfZT7IRh7WnXEDzlE9vOwVx6z0AOSUPPEp~zpRDuk48Giv9AXTxMQYJ0Cm9RxEn3Jw-eAaOV0rFKNyoh~yTZXJYbxxQCnD1-u1zvNOG-H4ACa5tuSUDj6zC7YQ-In81pGKZ0Xzvuk48RvzVj7oJKtkB5rdD~LwfEvO96fj0zw9voNrdaFwXguWMS72vqg8ICmiukgszL7IGZSh6lLPD6hpI0TpoFWm8SCmk2xhh7vzCtAxq2MrbHgBcte7CSeLFcCdrk6Jtag5iYTvzDJ4byHyLgGZA__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"The_complex_dynamics_of_diabetes_modeled_as_a_fractal_complex_adaptive_system_FCAS_","translated_slug":"","page_count":14,"language":"en","content_type":"Work","owner":{"id":66220250,"first_name":"Bruce","middle_initials":null,"last_name":"West","page_name":"BruceWest3","domain_name":"independent","created_at":"2017-07-07T14:39:25.483-07:00","display_name":"Bruce West","url":"https://independent.academia.edu/BruceWest3"},"attachments":[{"id":72443423,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/72443423/thumbnails/1.jpg","file_name":"07.pdf","download_url":"https://www.academia.edu/attachments/72443423/download_file?st=MTczMjc2NTkzMCw4LjIyMi4yMDguMTQ2&st=MTczMjc2NTkzMCw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"The_complex_dynamics_of_diabetes_modeled.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/72443423/07-libre.pdf?1634272204=\u0026response-content-disposition=attachment%3B+filename%3DThe_complex_dynamics_of_diabetes_modeled.pdf\u0026Expires=1732769530\u0026Signature=J-9M-RBaYPfd6pgio6HvGBD---KDvvyXAqY10JL1Jx~0Q6HMBc-RhEXt3dPOfZT7IRh7WnXEDzlE9vOwVx6z0AOSUPPEp~zpRDuk48Giv9AXTxMQYJ0Cm9RxEn3Jw-eAaOV0rFKNyoh~yTZXJYbxxQCnD1-u1zvNOG-H4ACa5tuSUDj6zC7YQ-In81pGKZ0Xzvuk48RvzVj7oJKtkB5rdD~LwfEvO96fj0zw9voNrdaFwXguWMS72vqg8ICmiukgszL7IGZSh6lLPD6hpI0TpoFWm8SCmk2xhh7vzCtAxq2MrbHgBcte7CSeLFcCdrk6Jtag5iYTvzDJ4byHyLgGZA__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"},{"id":72443424,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/72443424/thumbnails/1.jpg","file_name":"07.pdf","download_url":"https://www.academia.edu/attachments/72443424/download_file","bulk_download_file_name":"The_complex_dynamics_of_diabetes_modeled.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/72443424/07-libre.pdf?1634272204=\u0026response-content-disposition=attachment%3B+filename%3DThe_complex_dynamics_of_diabetes_modeled.pdf\u0026Expires=1732769530\u0026Signature=ZuGUBxmre4N6fwEir695aA5G9M-HCDtWAl1bIUUgVxY87WqSstqGdt23~XpPxgTpVafZfKwIHmkkiYb9ouxYNCvNiQPw6OVWzfn-0YMgobuRFjMTloeMtlWj6ECimJkBav5KtApisZ2TJ2Y2FmYiKyCIzZOopM9z0u6G9y7T5D4yg4uauVaqpLwuuI7YSsc48QWfHVSMIIrC3YbCcfPv4GE6ZWJfoBiGren7uTdLqSihOaEf7iKhrTXlASmKOuSJKvcZXo93VvW89FBQC9Rzp2smGItAz~9HkPwXIYxgZmtq4i0knXVl8Ny3OXC5PG7m3MVY3NlWjAkqrttH7pFmVQ__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[],"urls":[{"id":12936211,"url":"http://www.scielo.br/pdf/rbepid/v1n3/07.pdf"}]}, dispatcherData: dispatcherData }); 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