Document Zbl 07590594

<!doctype html> <html lang="en"> <head> <meta charset="utf-8"> <title>Document Zbl 07590594 - zbMATH Open</title> <meta name="viewport" content="width=device-width, minimum-scale=0.1, maximum-scale=5.0"> <meta name="robots" content="noarchive, noindex"> <meta name="referrer" content="origin-when-cross-origin"> <link href="https://static.zbmath.org/contrib/bootstrap/v3.3.7/css/bootstrap.min.css" rel="stylesheet" media="screen,print"> <link href="https://static.zbmath.org/contrib/bootstrap/v3.3.7/css/bootstrap-theme.min.css" rel="stylesheet" media="screen,print"> <link href="https://static.zbmath.org/contrib/bootstrap-lightbox/v0.7.0/bootstrap-lightbox.min.css" rel="stylesheet" media="screen,print"> <link rel="stylesheet" href="https://static.zbmath.org/contrib/bootstrap-select/v1.13.14/css/bootstrap-select.min.css"> <link href="/static/css/smoothness/jquery-ui-1.10.1.custom.min.css" rel="stylesheet" media="screen"> <link href="/static/styles.css?v=20241024" rel="stylesheet" media="screen,print"> <link href="https://static.zbmath.org/zbMathJax/v0.1.38/zbmathjax.css" rel="stylesheet" media="screen,print"> <link rel="shortcut icon" href="/static/zbmath.ico"> <script type="application/ld+json"> { "@context": "http://schema.org", "@type": "Organization", "url": "https://zbmath.org/", "logo": "https://zbmath.org/static/zbMATH.png" } </script> </head> <body> <div id="line"></div> <span id="clear" style="cursor: pointer;">×</span> <div id="page"> <div id="head"> <nav id="menu" class="navbar navbar-default"> <div class="container-fluid"> <div class="navbar-header"> <button type="button" class="navbar-toggle collapsed" data-toggle="collapse" data-target="#zbnav" aria-expanded="false"> <span class="sr-only">Toggle navigation</span> <span class="icon-bar"></span> <span class="icon-bar"></span> <span class="icon-bar"></span> </button> <a class="navbar-brand" href="#"> <img class="logo" src="/static/zbmath.gif" alt="zbMATH Open logo"> </a> </div> <div id="zbnav" class="collapse navbar-collapse"> <ul class="nav navbar-nav pages"> <li class="about"> <a href="/about/">About</a> </li> <li class="frequently-asked-questions"> <a href="/frequently-asked-questions/">FAQ</a> </li> <li class="general-help"> <a href="/general-help/">General Help</a> </li> <li class="reviewer-service"> <a href="https://zbmath.org/reviewer-service/" target="_self" >Reviewer Service</a> </li> <li> <a href="/tools-and-resources/">Tools & Resources</a> </li> <li class="contact"> <a href="/contact/">Contact</a> </li> </ul> <ul class="nav navbar-nav navbar-right prefs"> <li class="preferences dropdown"> <a data-toggle="dropdown" href="#">Preferences <i class="caret"></i></a> <ul class="dropdown-menu preferences"> <li> <form id="preferences" class="navbar-form" method="post" action="/preferences/" onsubmit="return confirm('This website uses cookies for the purposes of storing preference information on your device. Do you agree to this?\n\nPlease refer to our Privacy Policy to learn more about our use of cookies.')" > <input type="hidden" name="path" value="/07590594?"> <span class=""> <label class="title">Search Form</label> <div class="form-group"> <input id="search-multi-line" type="radio" name="search" value="multi-line" checked> <label for="search-multi-line" class="radio">Multi-Line Search (default)</label> </div> <div class="form-group"> <input id="search-one-line" type="radio" name="search" value="one-line"> <label for="search-one-line" class="radio">One-Line Search</label> </div> </span> <span class="count"> <label class="title">Hits per Page</label> <div class="form-group"> <input id="count-10" type="radio" name="count" value="10"> <label for="count-10" class="radio">10</label> </div> <div class="form-group"> <input id="count-20" type="radio" name="count" value="20"> <label for="count-20" class="radio">20</label> </div> <div class="form-group"> <input id="count-50" type="radio" name="count" value="50"> <label for="count-50" class="radio">50</label> </div> <div class="form-group"> <input id="count-100" type="radio" name="count" value="100" checked> <label for="count-100" class="radio">100 (default)</label> </div> <div class="form-group"> <input id="count-200" type="radio" name="count" value="200"> <label for="count-200" class="radio">200</label> </div> </span> <span class="format"> <label class="title">Display Format</label> <div class="form-group"> <input id="format-mathjax" type="radio" name="format" value="mathjax" checked> <label for="format-mathjax" class="radio">MathJax (default)</label> </div> <div class="form-group"> <input id="format-amstex" type="radio" name="format" value="latex"> <label for="format-amstex" class="radio">LaTeX</label> </div> </span> <span class="ranking"> <label class="title">Documents Sorting</label> <div class="form-group"> <input id="documents-ranking-default" type="radio" name="documents_ranking" value="date" checked> <label for="documents-ranking-default" class="radio">Newest first (default)</label> </div> <div class="form-group"> <input id="documents-ranking-references" type="radio" name="documents_ranking" value="references"> <label for="documents-ranking-references" class="radio">Citations</label> </div> <div class="form-group"> <input id="documents-ranking-relevance" type="radio" name="documents_ranking" value="relevance"> <label for="documents-ranking-relevance" class="radio">Relevance</label> </div> </span> <span class="ranking"> <label class="title">Authors Sorting</label> <div class="form-group"> <input id="authors-ranking-default" type="radio" name="authors_ranking" value="alpha" checked> <label for="authors-ranking-default" class="radio">Alphabetically (default)</label> </div> <div class="form-group"> <input id="authors-ranking-references" type="radio" name="authors_ranking" value="references"> <label for="authors-ranking-references" class="radio">Citations</label> </div> </span> <span class="ranking"> <label class="title">Serials Sorting</label> <div class="form-group"> <input id="serials-ranking-default" type="radio" name="serials_ranking" value="alpha" checked> <label for="serials-ranking-default" class="radio">Alphabetically (default)</label> </div> <div class="form-group"> <input id="serials-ranking-references" type="radio" name="serials_ranking" value="references"> <label for="serials-ranking-references" class="radio">Citations</label> </div> </span> <span class="ranking"> <label class="title">Software Sorting</label> <div class="form-group"> <input id="software-ranking-default" type="radio" name="software_ranking" value="references" checked> <label for="software-ranking-default" class="radio">Citations (default)</label> </div> <div class="form-group"> <input id="software-ranking-alpha" type="radio" name="software_ranking" value="alpha"> <label for="software-ranking-alpha" class="radio">Alphabetically</label> </div> </span> <button type="submit" class="btn btn-default">OK</button> <div class="clearfix"> </form> </li> </ul> </li> </ul> </div> </div> </nav> <div id="tabs"> <h1 class="logo"> <a class="logo" href="/"> <img class="logo" src="/static/zbmath.gif" alt="zbMATH Open — the first resource for mathematics" > </a> </h1> <nav> <ul class="nav nav-tabs"> <li class="tab-documents active"> <a href="/">Documents</a> </li> <li class="tab-authors"> <a href="/authors/">Authors</a> </li> <li class="tab-serials"> <a href="/serials/">Serials</a> </li> <li class="tab-software"> <a href="/software/">Software</a> </li> <li class="tab-classification"> <a href="/classification/">Classification</a> </li> <li class="tab-formulae"> <a href="/formulae/">Formulæ</a> </li> </ul> </nav> <div class="clearfix"></div> </div> <div class="content-fixed"> <div class="content-formular"> <div style="display: none;"> <div class="row ml-0"id="multi-line-new-line" style="display: none;"> <div class="col-xs-12 form-inline multi-line"> <select class="form-control multi-line-field multi-line-selectpicker" name="ml-0-f" aria-label="field"> <option data-type="input" value="any" selected>Anywhere</option> <option data-type="input" value="au">Authors</option> <option data-type="input" value="ti">Title</option> <option data-type="input" value="py">Year</option> <option data-type="range" value="pyr">Year Range</option> <option data-type="input" value="cc">MSC</option> <option data-type="input" value="cc1">MSC Primary</option> <option data-type="input" value="so">Source / Journal</option> <option data-type="input" value="pu">Publisher</option> <option data-type="input" value="la">Language</option> <option data-type="input" value="ab">Summary / Review</option> <option data-type="input" value="rv">Reviewer</option> <option data-type="input" value="an">zbMATH ID</option> <option data-type="input" value="en">External ID</option> <option data-type="input" value="ut">Keywords</option> <option data-type="input" value="sw">Software</option> <option data-type="input" value="br">Biographic Ref</option> <option data-type="input" value="rft">Reference Text</option> <option data-type="multiselect-db" value="db">Database</option> <option data-divider="true"></option> <option data-function="remove-line" data-content='<span class="glyphicon glyphicon-minus" aria-hidden="true"></span> remove line' value="any">remove line</option> </select><input name="ml-0-v" class="form-control multi-line-value multi-line-input" type="text" value="" aria-label="value"><select class="form-control multi-line-operators multi-line-selectpicker" name="ml-0-op" aria-label="operator"> <option value="and" selected>AND</option> <option value="andnot">AND NOT</option> <option value="or">OR</option> </select></div> </div> <input name="ml-0-v" class="form-control multi-line-value multi-line-input" type="text" value="" aria-label="value" id="multi-line-type-input"> <span class="multi-line-value" id="multi-line-type-range"><span style="padding-left: 5px;">from</span> <input name="ml-0-v1" class="form-control multi-line-input" type="text" value="" aria-label="value"> until <input name="ml-0-v2" class="form-control multi-line-input" type="text" value="" aria-label="value"></span> <input name="ml-0-v" class="form-control multi-line-value multi-line-input" type="text" value="" aria-label="value" id="multi-line-type-input-la" placeholder="use name or ISO code"> <input name="ml-0-v" class="form-control multi-line-value multi-line-input" type="text" value="" aria-label="value" id="multi-line-type-input-rv" placeholder="enter name or zbMATH reviewer number"> <input name="ml-0-v" class="form-control multi-line-value multi-line-input" type="text" value="" aria-label="value" id="multi-line-type-input-an" placeholder="Zbl, JFM or ERAM number"> <input name="ml-0-v" class="form-control multi-line-value multi-line-input" type="text" value="" aria-label="value" id="multi-line-type-input-en" placeholder="e.g. DOI, ISBN, arXiv ID"> <input name="ml-0-v" class="form-control multi-line-value multi-line-input" type="text" value="" aria-label="value" id="multi-line-type-input-sw" placeholder="use * to find all documents using software"> <input name="ml-0-v" class="form-control multi-line-value multi-line-input" type="text" value="" aria-label="value" id="multi-line-type-input-br" placeholder="find documents about the life or work of a person"> <span class="multi-line-value" id="multi-line-type-multiselect-db"> <select class="multi-line-selectpicker" data-width="100%" multiple> <option value="zbl">Zbl</option> <option value="arxiv">arXiv</option> <option value="jfm">JFM</option> <option value="eram">ERAM</option> </select> <input type="hidden" class="multi-line-input" name="ml-0-v" value=""> </span> </div> <form name="documents" method="GET" action="/" autocomplete="off"> <div class="documents multi-line" style="display: none;"> <div class="forms"> <ul class="nav forms"> <li class="one-line"> <span tabindex="0" class="glyphicon glyphicon-question-sign" title="One-Line Search allows for free logical combinations of search fields" aria-label="One-Line Search allows for free logical combinations of search fields" data-placement="bottom"></span> <a style="display: inline-block;" href="#">One-Line Search <span class="glyphicon glyphicon-search"></span></a> </li> </ul> </div> <div class="clearfix"></div> <div class="container-fluid"> <input type="hidden" id="multi-line-ml" name="ml" value="3"> <div id="multi-line-row-wrapper"> <div class="row ml-1"> <div class="col-xs-12 form-inline multi-line"> <select class="form-control multi-line-field multi-line-selectpicker" name="ml-1-f" aria-label="field"> <option data-type="input" value="any" selected>Anywhere</option> <option data-type="input" value="au">Authors</option> <option data-type="input" value="ti">Title</option> <option data-type="input" value="py">Year</option> <option data-type="range" value="pyr">Year Range</option> <option data-type="input" value="cc">MSC</option> <option data-type="input" value="cc1">MSC Primary</option> <option data-type="input" value="so">Source / Journal</option> <option data-type="input" value="pu">Publisher</option> <option data-type="input" value="la">Language</option> <option data-type="input" value="ab">Summary / Review</option> <option data-type="input" value="rv">Reviewer</option> <option data-type="input" value="an">zbMATH ID</option> <option data-type="input" value="en">External ID</option> <option data-type="input" value="ut">Keywords</option> <option data-type="input" value="sw">Software</option> <option data-type="input" value="br">Biographic Ref</option> <option data-type="input" value="rft">Reference Text</option> <option data-type="multiselect-db" value="db">Database</option> <option data-divider="true"></option> <option data-function="remove-line" data-content='<span class="glyphicon glyphicon-minus" aria-hidden="true"></span> remove line' value="any">remove line</option> </select><input name="ml-1-v" class="form-control multi-line-value multi-line-input" type="text" value="" aria-label="value"><select class="form-control multi-line-operators multi-line-selectpicker" name="ml-1-op" aria-label="operator"> <option value="and" selected>AND</option> <option value="andnot">AND NOT</option> <option value="or">OR</option> </select></div> </div> <div class="row ml-2"> <div class="col-xs-12 form-inline multi-line"> <select class="form-control multi-line-field multi-line-selectpicker" name="ml-2-f" aria-label="field"> <option data-type="input" value="any">Anywhere</option> <option data-type="input" value="au" selected>Authors</option> <option data-type="input" value="ti">Title</option> <option data-type="input" value="py">Year</option> <option data-type="range" value="pyr">Year Range</option> <option data-type="input" value="cc">MSC</option> <option data-type="input" value="cc1">MSC Primary</option> <option data-type="input" value="so">Source / Journal</option> <option data-type="input" value="pu">Publisher</option> <option data-type="input" value="la">Language</option> <option data-type="input" value="ab">Summary / Review</option> <option data-type="input" value="rv">Reviewer</option> <option data-type="input" value="an">zbMATH ID</option> <option data-type="input" value="en">External ID</option> <option data-type="input" value="ut">Keywords</option> <option data-type="input" value="sw">Software</option> <option data-type="input" value="br">Biographic Ref</option> <option data-type="input" value="rft">Reference Text</option> <option data-type="multiselect-db" value="db">Database</option> <option data-divider="true"></option> <option data-function="remove-line" data-content='<span class="glyphicon glyphicon-minus" aria-hidden="true"></span> remove line' value="any">remove line</option> </select><input name="ml-2-v" class="form-control multi-line-value multi-line-input" type="text" value="" aria-label="value"><select class="form-control multi-line-operators multi-line-selectpicker" name="ml-2-op" aria-label="operator"> <option value="and" selected>AND</option> <option value="andnot">AND NOT</option> <option value="or">OR</option> </select></div> </div> <div class="row ml-3"> <div class="col-xs-12 form-inline multi-line"> <select class="form-control multi-line-field multi-line-selectpicker" name="ml-3-f" aria-label="field"> <option data-type="input" value="any">Anywhere</option> <option data-type="input" value="au">Authors</option> <option data-type="input" value="ti" selected>Title</option> <option data-type="input" value="py">Year</option> <option data-type="range" value="pyr">Year Range</option> <option data-type="input" value="cc">MSC</option> <option data-type="input" value="cc1">MSC Primary</option> <option data-type="input" value="so">Source / Journal</option> <option data-type="input" value="pu">Publisher</option> <option data-type="input" value="la">Language</option> <option data-type="input" value="ab">Summary / Review</option> <option data-type="input" value="rv">Reviewer</option> <option data-type="input" value="an">zbMATH ID</option> <option data-type="input" value="en">External ID</option> <option data-type="input" value="ut">Keywords</option> <option data-type="input" value="sw">Software</option> <option data-type="input" value="br">Biographic Ref</option> <option data-type="input" value="rft">Reference Text</option> <option data-type="multiselect-db" value="db">Database</option> <option data-divider="true"></option> <option data-function="remove-line" data-content='<span class="glyphicon glyphicon-minus" aria-hidden="true"></span> remove line' value="any">remove line</option> </select><input name="ml-3-v" class="form-control multi-line-value multi-line-input" type="text" value="" aria-label="value"><div id="multi-line-plus"> <a href="#"><span class="glyphicon glyphicon-plus" aria-hidden="true"></span> add line</a> </div></div> </div> </div> <div class="row"> <div class="col-xs-12 form-inline"> <div class="form-group field checkboxes-wrapper" id="checkboxes-wrapper-test" style="visibility: hidden; position: fixed;"> <label>Document Type:</label> <div class="checkboxes"> <div class="slider"> <label title="search for Articles in Journals"> <input type="checkbox" class="form-control" value="j" checked> <span tabindex="0"><small></small></span> Journal Articles </label> </div> <div class="slider"> <label title="search for Articles in Conference Proceedings and Collected Volumes"> <input type="checkbox" class="form-control" value="a" checked> <span tabindex="0"><small></small></span> Collection Articles </label> </div> <div class="slider"> <label title="search for Monographs, Proceedings, Dissertations etc."> <input type="checkbox" class="form-control" value="b" checked> <span tabindex="0"><small></small></span> Books </label> </div> <div class="slider"> <label title="search for arXiv Preprints"> <input type="checkbox" class="form-control" value="p" checked> <span tabindex="0"><small></small></span> arXiv Preprints </label> </div> </div> </div> <div class="form-group field checkboxes-wrapper" id="checkboxes-wrapper-real"> <label>Document Type:</label> <div class="checkboxes"> <div class="slider"> <label for="dt-j" title="search for Articles in Journals"> <input type="checkbox" id="dt-j" name="dt" class="form-control" value="j" checked> <span tabindex="0"><small></small></span> Journal Articles </label> </div> <div class="slider"> <label for="dt-a" title="search for Articles in Conference Proceedings and Collected Volumes"> <input type="checkbox" id="dt-a" name="dt" class="form-control" value="a" checked> <span tabindex="0"><small></small></span> Collection Articles </label> </div> <div class="slider"> <label for="dt-b" title="search for Monographs, Proceedings, Dissertations etc."> <input type="checkbox" id="dt-b" name="dt" class="form-control" value="b" checked> <span tabindex="0"><small></small></span> Books </label> </div> <div class="slider"> <label for="dt-p" title="search for arXiv Preprints"> <input type="checkbox" id="dt-p" name="dt" class="form-control" value="p" checked> <span tabindex="0"><small></small></span> arXiv Preprints </label> </div> </div> </div> </div> </div> <div class="row"> <div class="col-xs-12 buttons"> <a tabindex="0" class="btn btn-default clear-all">Reset all <span class="glyphicon glyphicon-remove"></span></a> <div class="submit"> <button class="btn btn-default search" type="submit">Search <span class="glyphicon glyphicon-search"></span></button> </div> </div> </div> </div> </div> </form> <form class="form-inline" name="documents" method="GET" action="/"> <div class="documents one-line" style="display: block;"> <div class="forms"> <ul class="nav forms"> <li class="multi-line"><a href="#">New Multi-Line Search <span class="glyphicon glyphicon-list"></span></a></li> </ul> </div> <div id="search-row" class="input-group box"> <span> <div id="search-field"> <input class="query form-control" type="text" name="q" value="an:07590594" aria-label="Search for documents" placeholder="Search for documents" autocomplete="off"> </div> <div class="search-buttons input-group-btn"> <div class="btn-group"> <button class="btn btn-default search" type="submit"><span class="virtual">Search</span> <span class="glyphicon glyphicon-search" style="top: 2px;"></span></button> </div> </div> </span> <span> <div class="search-buttons input-group-btn"> <div class="btn-group"> <div class="btn-group fields"> <button class="btn btn-default dropdown-toggle" data-toggle="dropdown">Fields <i class="caret"></i></button> <ul id="fields" class="dropdown-menu pull-right"> <li><a href="#"><span class="token item">any:</span><span> </span>anywhere (default)</a></li> <li><a href="#"><span class="token item">ab:</span><span>  </span>review text</a></li> <li><a href="#"><span class="token item">an:</span><span>  </span>zbmath id</a></li> <li><a href="#"><span class="token item">any:</span><span>  </span>anywhere</a></li> <li><a href="#"><span class="token item">au:</span><span>  </span>contributor name</a></li> <li><a href="#"><span class="token item">br:</span><span>  </span>biographic reference name</a></li> <li><a href="#"><span class="token item">cc:</span><span>  </span>msc title</a></li> <li><a href="#"><span class="token item">dt:</span><span>  </span>document type</a></li> <li><a href="#"><span class="token item">doi:</span><span>  </span>doi</a></li> <li><a href="#"><span class="token item">en:</span><span>  </span>external id</a></li> <li><a href="#"><span class="token item">la:</span><span>  </span>language</a></li> <li><a href="#"><span class="token item">pu:</span><span>  </span>publisher</a></li> <li><a href="#"><span class="token item">py:</span><span>  </span>year</a></li> <li><a href="#"><span class="token item">rv:</span><span>  </span>reviewer name</a></li> <li><a href="#"><span class="token item">so:</span><span>  </span>source</a></li> <li><a href="#"><span class="token item">sw:</span><span>  </span>software name</a></li> <li><a href="#"><span class="token item">ti:</span><span>  </span>title</a></li> <li><a href="#"><span class="token item">ut:</span><span>  </span>keyword</a></li> </ul> </div> <div class="btn-group operators"> <button class="btn btn-default dropdown-toggle" data-toggle="dropdown">Operators <i class="caret"></i></button> <ul id="operators" class="dropdown-menu pull-right"> <li><a href="#"><span class="token">a <span class="item">&</span> b </span><span> </span>logical and (default)</a></li> <li><a href="#"><span class="token">a <span class="item">|</span> b </span><span> </span>logical or</a></li> <li><a href="#"><span class="token"><span class="item">!</span>ab   </span><span> </span>logical not</a></li> <li><a href="#"><span class="token">abc<span class="item">*</span>  </span><span> </span>right wildcard</a></li> <li><a href="#"><span class="token"><span class="item">"</span>ab c<span class="item">"</span></span><span> </span>phrase</a></li> <li><a href="#"><span class="token"><span class="item">(</span>ab c<span class="item">)</span></span><span> </span>parentheses</a></li> </ul> </div> </div> </div> <div class="special"> <ul class="nav help-button"> <li class="dropdown pull-right"> <a href="#">Help <i class="caret"></i></a> </li> </ul> </div> </span> </div> <div class="help"><h2>Examples</h2> <div id="help-terms" role="table"> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=Geometry">Geometry</a></span> <span class="search-explanation" role="cell" role="cell">Search for the term <em>Geometry</em> in <strong>any</strong> field. Queries are <strong>case-independent</strong>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=Funct%2A">Funct*</a></span> <span class="search-explanation" role="cell"><strong>Wildcard</strong> queries are specified by <strong><u>*</u></strong> (e.g. <em>functions</em>, <em>functorial</em>, etc.). Otherwise the search is <strong>exact</strong>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=%22Topological+group%22">"Topological group"</a></span> <span class="search-explanation" role="cell"><strong>Phrases</strong> (multi-words) should be set in <u>"</u>straight quotation marks<u>"</u>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=au%3A+Bourbaki+%26+ti%3A+Algebra">au: Bourbaki & ti: Algebra</a></span> <span class="search-explanation" role="cell">Search for <strong><u>au</u>thor</strong> and <strong><u>ti</u>tle</strong>. The <strong>and-operator &</strong> is default and can be omitted.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=Chebyshev+%7C+Tschebyscheff">Chebyshev | Tschebyscheff</a></span> <span class="search-explanation" role="cell">The <strong>or-operator |</strong> allows to search for <em>Chebyshev</em> or <em>Tschebyscheff</em>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=Quasi%2A+map%2A+py%3A+1989">Quasi* map* py: 1989</a></span> <span class="search-explanation" role="cell">The resulting documents have <strong><u>p</u>ublication <u>y</u>ear</strong> <em>1989</em>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=so%3A+Eur%2A+J%2A+Mat%2A+Soc%2A+cc%3A+14">so: Eur* J* Mat* Soc* cc: 14</a></span> <span class="search-explanation" role="cell">Search for publications in a particular <strong><u>so</u>urce</strong> with a <strong>Mathematics Subject <u>C</u>lassification <u>c</u>ode (<u>cc</u>)</strong> in <em>14</em>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=%22Partial+diff%2A+eq%2A%22+%21+elliptic">"Partial diff* eq*" ! elliptic</a></span> <span class="search-explanation" role="cell">The <strong>not</strong>-operator <strong>!</strong> eliminates all results containing the word <em>elliptic</em>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=dt%3A+b+%26+au%3A+Hilbert">dt: b & au: Hilbert</a></span> <span class="search-explanation" role="cell">The <strong><u>d</u>ocument <u>t</u>ype</strong> is set to books; alternatively: <u>j</u> for <strong>journal articles</strong>, <u>a</u> for <strong>book articles</strong>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=py%3A+2000-2015+cc%3A+%2894A+%7C+11T%29">py: 2000-2015 cc: (94A | 11T)</a></span> <span class="search-explanation" role="cell">Number <strong>ranges</strong> are accepted. Terms can be grouped within <strong><u>(</u>parentheses<u>)</u></strong>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=la%3A+chinese">la: chinese</a></span> <span class="search-explanation" role="cell">Find documents in a given <strong><u>la</u>nguage</strong>. <a href="http://en.wikipedia.org/wiki/ISO_639-1">ISO 639-1</a> language codes can also be used.</span> </div> </div> <div id="help-fields"> <h2>Fields</h2> <table> <tr> <td class="nowrap padding" role="rowheader"><strong>any</strong></td> <td class="padding">anywhere</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>an</strong></td> <td class="padding">internal document identifier</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>au</strong></td> <td class="padding">author, editor</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>ai</strong></td> <td class="padding">internal author identifier</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>ti</strong></td> <td class="padding">title</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>la</strong></td> <td class="padding">language</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>so</strong></td> <td class="padding">source</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>ab</strong></td> <td class="padding">review, abstract</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>py</strong></td> <td class="padding">publication year</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>rv</strong></td> <td class="padding">reviewer</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>cc</strong></td> <td class="padding">MSC code</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>ut</strong></td> <td class="padding">uncontrolled term</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>dt</strong></td> <td class="padding" colspan="4">document type (<strong>j</strong>: journal article; <strong>b</strong>: book; <strong>a</strong>: book article)</td> </tr> </table> </div> <div id="help-operators"> <h2>Operators</h2> <table> <tr> <td class="nowrap padding" role="rowheader">a <strong>&</strong> b</td> <td class="padding">logic and</td> </tr> <tr> <td class="nowrap padding" role="rowheader">a <strong>|</strong> b</td> <td class="padding">logic or</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>!</strong>ab</td> <td class="padding">logic not</td> </tr> <tr> <td class="nowrap padding" role="rowheader">abc<strong>*</strong></td> <td class="padding">right wildcard</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>"</strong>ab c<strong>"</strong></td> <td class="padding">phrase</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>(</strong>ab c<strong>)</strong></td> <td class="padding">parentheses</td> </tr> </table> </div> <p> See also our <a href="/general-help/">General Help</a>. </p></div> </div> </form> <div class="clearfix"></div> </div> <div class="content-shadow"></div> </div> </div> <div id="body"> <div id="main"> <div class="messages"> </div> <div id="documents"> <div class="content-main"> <div class="content-item"><div class="item"> <article> <div class="author"><a href="/authors/schweinberger.michael" title="Author Profile">Schweinberger, Michael</a>; <a href="/authors/bomiriya.rashmi-p" title="Author Profile">Bomiriya, Rashmi P.</a>; <a href="/authors/babkin.sergii" title="Author Profile">Babkin, Sergii</a></div> <h2 class="title"> <strong>A semiparametric Bayesian approach to epidemics, with application to the spread of the coronavirus MERS in South Korea in 2015.</strong> <i>(English)</i> <a class="label nowrap" href="/7590594">Zbl 07590594</a> </h2> <div class="source"> <a href="/serials/2233" title="Journal Profile">J. Nonparametric Stat.</a> <a href="/?q=in%3A487273" title="Articles in this Issue">34, No. 3, 628-662 (2022)</a>. </div> <div class="abstract">Summary: We consider incomplete observations of stochastic processes governing the spread of infectious diseases through finite populations by way of contact. We propose a flexible semiparametric modelling framework with at least three advantages. First, it enables researchers to study the structure of a population contact network and its impact on the spread of infectious diseases. Second, it can accommodate short- and long-tailed degree distributions and detect potential superspreaders, who represent an important public health concern. Third, it addresses the important issue of incomplete data. Starting from first principles, we show when the incomplete-data generating process is ignorable for the purpose of Bayesian inference for the parameters of the population model. We demonstrate the semiparametric modelling framework by simulations and an application to the partially observed MERS epidemic in South Korea in 2015. We conclude with an extended discussion of open questions and directions for future research.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7590594">Cited in <strong>2</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A62Gxx" title="MSC2020">62Gxx</a> </td> <td class="space"> Nonparametric inference </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A05C80" title="MSC2020">05C80</a> </td> <td class="space"> Random graphs (graph-theoretic aspects) </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A05C81" title="MSC2020">05C81</a> </td> <td class="space"> Random walks on graphs </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Acontact+networks">contact networks</a>; <a href="/?q=ut%3Anetwork+sampling">network sampling</a>; <a href="/?q=ut%3Alink-tracing">link-tracing</a>; <a href="/?q=ut%3Amissing+data">missing data</a></div> <div class="software"> <h3>Software:</h3><a href="/software/12588">BEAST</a>; <a href="/software/24733">epinet</a></div>  <div class="modal fade" id="metadataModal" tabindex="-1" role="dialog" aria-labelledby="myModalLabel"> <div class="modal-dialog" role="document"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">×</span></button> <h4 class="modal-title" id="myModalLabel">Cite</h4> </div> <div class="modal-body"> <div class="form-group"> <label for="select-output" class="control-label">Format</label> <select id="select-output" class="form-control" aria-label="Select Metadata format"></select> </div> <div class="form-group"> <label for="metadataText" class="control-label">Result</label> <textarea class="form-control" id="metadataText" rows="10" style="min-width: 100%;max-width: 100%"></textarea> </div> <div id="metadata-alert" class="alert alert-danger" role="alert" style="display: none;">  </div> </div> <div class="modal-footer"> <button type="button" class="btn btn-primary" onclick="copyMetadata()">Copy to clipboard</button> <button type="button" class="btn btn-default" data-dismiss="modal">Close</button> </div> </div> </div> </div> <div class="functions clearfix"> <div class="function">  <a type="button" class="btn btn-default btn-xs pdf" data-toggle="modal" data-target="#metadataModal" data-itemtype="Zbl" data-itemname="Zbl 07590594" data-ciurl="/ci/07590594" data-biburl="/bibtex/07590594.bib" data-amsurl="/amsrefs/07590594.bib" data-xmlurl="/xml/07590594.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07590594.pdf" title="Zbl 07590594 as PDF">Review PDF</a> </div> <div class="fulltexts"> <span class="fulltext">Full Text:</span> <a class="btn btn-default btn-xs" type="button" href="https://doi.org/10.1080/10485252.2021.1972294" aria-label="DOI for “A semiparametric Bayesian approach to epidemics, with application to the spread of the coronavirus MERS in South Korea in 2015”" title="10.1080/10485252.2021.1972294">DOI</a> <a class="btn btn-default btn-xs" type="button" href="https://arxiv.org/abs/2107.00375"title="Note: arXiv document may differ from published version">arXiv</a> <a class="btn btn-default btn-xs" type="button" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9512273" title="Full Text Link">Link</a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">Albert, R.; Barabàsi, A. L., Statistical Mechanics of Complex Networks, Review of Modern Physics, 74, 47-97 (2002) · <a href="/1205.82086" class="nowrap">Zbl 1205.82086</a></td> </tr><tr> <td>[2]</td> <td class="space">Amini, A. A.; Chen, A.; Bickel, P. J.; Levina, E., Pseudo-likelihood Methods for Community Detection in Large Sparse Networks, The Annals of Statistics, 41, 2097-2122 (2013) · <a href="/1277.62166" class="nowrap">Zbl 1277.62166</a></td> </tr><tr> <td>[3]</td> <td class="space">Andersson, H.; Britton, T., Stochastic Epidemic Models and Their Statistical Analysis (2000), New York: Springer-Verlag, New York · <a href="/0951.92021" class="nowrap">Zbl 0951.92021</a></td> </tr><tr> <td>[4]</td> <td class="space">Ball, F., Central Limit Theorems for SIR Epidemics and Percolation on Configuration Model Random Graphs, The Annals of Applied Probability, 1-71 (2021)</td> </tr><tr> <td>[5]</td> <td class="space">Barabàsi, A. L.; Albert, R., Emergence of Scaling in Random Networks, Science, 286, 509-512 (1999) · <a href="/1226.05223" class="nowrap">Zbl 1226.05223</a></td> </tr><tr> <td>[6]</td> <td class="space">Barbour, A. D.; Reinert, G., Approximating the Epidemic Curve, Electronic Journal of Probability, 18, 1-30 (2013) · <a href="/1301.92072" class="nowrap">Zbl 1301.92072</a></td> </tr><tr> <td>[7]</td> <td class="space">Bhamidi, S.; Bresler, G.; Sly, A., Mixing Time of Exponential Random Graphs, The Annals of Applied Probability, 21, 2146-2170 (2011) · <a href="/1238.60011" class="nowrap">Zbl 1238.60011</a></td> </tr><tr> <td>[8]</td> <td class="space">Bollobáś, B.; Riordan, O.; Spencer, J.; Tusnády, G., The Degree Sequence of a Scale-free Random Graph Process, Random Structures & Algorithms, 18, 279-290 (2001) · <a href="/0985.05047" class="nowrap">Zbl 0985.05047</a></td> </tr><tr> <td>[9]</td> <td class="space">Bouckaert, R.; Vaughan, T. G.; Barido-Sottani, J.; Duchne, S.; Fourment, M.; Gavryushkina, A.; Heled, J.; Jones, G.; Kuhnert, D.; De Maio, N.; Matschiner, M.; Mendes, F. K.; Moller, N. F.; Ogilvie, H. A.; Popinga, A.; Rambaut, A.; Rasmussen, D.; Siveroni, I.; Suchard, M. A.; Wu, C.-H.; Xie, D.; Zhang, C.; Stadler, T.; Drummond, A. J., BEAST 2.5: An Advanced Software Platform for Bayesian Evolutionary Analysis, PLOS Computational Biology, 15, 1-28 (2019)</td> </tr><tr> <td>[10]</td> <td class="space">Britton, T., Estimation in Multitype Epidemics, Journal of the Royal Statistical Society: Series B (Statistical Methodology), 60, 663-679 (1998) · <a href="/0909.62111" class="nowrap">Zbl 0909.62111</a></td> </tr><tr> <td>[11]</td> <td class="space">Britton, T., Epidemics in Heterogeneous Communities: Estimation of R0 and Secure Vaccination Coverage, Journal of the Royal Statistical Society: Series B (Statistical Methodology), 63, 705-715 (2001) · <a href="/0986.62089" class="nowrap">Zbl 0986.62089</a></td> </tr><tr> <td>[12]</td> <td class="space">Britton, T.; Lindholm, M.; Turova, T., A Dynamic Network in a Dynamic Population: Asymptotic Properties, Journal of Applied Probability, 48, 1163-1178 (2011) · <a href="/1231.92054" class="nowrap">Zbl 1231.92054</a></td> </tr><tr> <td>[13]</td> <td class="space">Britton, T.; O’Neill, P. D., Statistical Inference for Stochastic Epidemics in Populations with Network Structure, Scandinavian Journal of Statistics, 29, 375-390 (2002) · <a href="/1036.62017" class="nowrap">Zbl 1036.62017</a></td> </tr><tr> <td>[14]</td> <td class="space">Britton, T.; Pardoux, E., Stochastic Epidemic Models with Inference (2019), Springer · <a href="/1431.92007" class="nowrap">Zbl 1431.92007</a></td> </tr><tr> <td>[15]</td> <td class="space">Bu, F.; Aiello, A. E.; Xu, J.; Volfovsky, A., Likelihood-based Inference for Partially Observed Epidemics on Dynamic Networks, Journal of the American Statistical Association (2021)</td> </tr><tr> <td>[16]</td> <td class="space">Butts, C. T., A Relational Event Framework for Social Action, Sociological Methodology, 38, 155-200 (2008)</td> </tr><tr> <td>[17]</td> <td class="space">Butts, C. T., A Dynamic Process Interpretation of the Sparse ERGM Reference Model, Journal of Mathematical Sociology (2019) · <a href="/1485.91180" class="nowrap">Zbl 1485.91180</a></td> </tr><tr> <td>[18]</td> <td class="space">Chatterjee, S.; Diaconis, P., Estimating and Understanding Exponential Random Graph Models, The Annals of Statistics, 41, 2428-2461 (2013) · <a href="/1293.62046" class="nowrap">Zbl 1293.62046</a></td> </tr><tr> <td>[19]</td> <td class="space">Chatterjee, S.; Diaconis, P.; Sly, A., Random Graphs with a Given Degree Sequence, The Annals of Applied Probability, 21, 1400-1435 (2011) · <a href="/1234.05206" class="nowrap">Zbl 1234.05206</a></td> </tr><tr> <td>[20]</td> <td class="space">Chen, M.; Kato, K.; Leng, C., Analysis of Networks Via the Sparse β-model, Journal of the Royal Statistical Society, Series B (Statistical Methodology) (2021) · <a href="/07555285" class="nowrap">Zbl 07555285</a></td> </tr><tr> <td>[21]</td> <td class="space">Crane, H., Probabilistic Foundations of Statistical Network Analysis (2018), Chapman and Hall/CRC · <a href="/1490.62001" class="nowrap">Zbl 1490.62001</a></td> </tr><tr> <td>[22]</td> <td class="space">Danon, L.; Ford, A. P.; House, T.; Jewell, C. P.; Keeling, M. J.; Roberts, G. O.; Ross, J. V.; Vernon, M. C., Networks and the Epidemiology of Infectious Disease, Interdisciplinary Perspectives on Infectious Diseases, 2011, 1-28 (2011)</td> </tr><tr> <td>[23]</td> <td class="space">Dawid, A. P.; Dickey, J. M., Likelihood and Bayesian Inference From Selectively Reported Data, Journal of the American Statistical Association, 72, 845-850 (1977) · <a href="/0372.62025" class="nowrap">Zbl 0372.62025</a></td> </tr><tr> <td>[24]</td> <td class="space">Dempster, A. P.; Laird, N. M.; Rubin, R. B., Maximum Likelihood From Incomplete Data Via the EM-algorithm, Journal of the Royal Statistical Society, Series B, 39, 1-38 (1977) · <a href="/0364.62022" class="nowrap">Zbl 0364.62022</a></td> </tr><tr> <td>[25]</td> <td class="space">Dunbar, R. I.M., Neocortex Size As a Constraint on Group Size in Primates, Journal of Human Evolution, 22, 469-493 (1992)</td> </tr><tr> <td>[26]</td> <td class="space">Durante, D.; Dunson, D. B., Nonparametric Bayes Dynamic Modelling of Relational Data, Biometrika, 101, 125-138 (2014) · <a href="/1306.62075" class="nowrap">Zbl 1306.62075</a></td> </tr><tr> <td>[27]</td> <td class="space">Ferguson, T., A Bayesian Analysis of Some Nonparametric Problems, The Annals of Statistics, 1, 209-230 (1973) · <a href="/0255.62037" class="nowrap">Zbl 0255.62037</a></td> </tr><tr> <td>[28]</td> <td class="space">Fienberg, S. E.; Slavković, A. (2010)</td> </tr><tr> <td>[29]</td> <td class="space">Fosdick, B. K.; Hoff, P. D., Testing and Modeling Dependencies Between a Network and Nodal Attributes, Journal of the American Statistical Association, 110, 1047-1056 (2015) · <a href="/1373.62273" class="nowrap">Zbl 1373.62273</a></td> </tr><tr> <td>[30]</td> <td class="space">Frank, O., Random Sampling and Social Networks: A Survey of Various Approaches, Mathématiques, Informatique et Sciences Humaines, 26, 19-33 (1988) · <a href="/0682.62088" class="nowrap">Zbl 0682.62088</a></td> </tr><tr> <td>[31]</td> <td class="space">Frank, O.; Strauss, D., Markov Graphs, Journal of the American Statistical Association, 81, 832-842 (1986) · <a href="/0607.05057" class="nowrap">Zbl 0607.05057</a></td> </tr><tr> <td>[32]</td> <td class="space">Fu, W., Song, L., and Xing, E.P. (2009), ‘Dynamic Mixed Membership Blockmodel for Evolving Networks’, in Proceedings of the 26th Annual International Conference on Machine Learning.</td> </tr><tr> <td>[33]</td> <td class="space">Gile, K., Improved Inference for Respondent-driven Sampling Data with Application to HIV Prevalence Estimation, Journal of the American Statistical Association, 106, 135-146 (2011) · <a href="/1396.62009" class="nowrap">Zbl 1396.62009</a></td> </tr><tr> <td>[34]</td> <td class="space">Gile, K., and Handcock, M.S. (2006), ‘Model-based Assessment of the Impact of Missing Data on Inference for Networks’, Technical Report, Center for Statistics and the Social Sciences, University of Washington, Seattle, available at https://www.csss.washington.edu/Papers/wp66.pdf.</td> </tr><tr> <td>[35]</td> <td class="space">Gile, K.; Handcock, M. H., Respondent-driven Sampling: An Assessment of Current Methodology, Sociological Methodology, 40, 285-327 (2010)</td> </tr><tr> <td>[36]</td> <td class="space">Goodman, L. A., Snowball Sampling, Annals of Mathematical Statistics, 32, 148-170 (1961) · <a href="/0099.14203" class="nowrap">Zbl 0099.14203</a></td> </tr><tr> <td>[37]</td> <td class="space">Groendyke, C.; Welch, D., epinet: An R Package to Analyze Epidemics Spread Across Contact Networks, Journal of Statistical Software, 83, 1-22 (2018)</td> </tr><tr> <td>[38]</td> <td class="space">Groendyke, C.; Welch, D.; Hunter, D. R., Bayesian Inference for Contact Networks Given Epidemic Data, Scandinavian Journal of Statistics, 38, 600-616 (2011) · <a href="/1246.62207" class="nowrap">Zbl 1246.62207</a></td> </tr><tr> <td>[39]</td> <td class="space">Groendyke, C.; Welch, D.; Hunter, D. R., A Network-based Analysis of the 1861 Hagelloch Measles Data, Biometrics, 68, 755-765 (2012) · <a href="/1270.62136" class="nowrap">Zbl 1270.62136</a></td> </tr><tr> <td>[40]</td> <td class="space">Handcock, M. S.; Gile, K., Modeling Social Networks From Sampled Data, The Annals of Applied Statistics, 4, 5-25 (2010) · <a href="/1189.62187" class="nowrap">Zbl 1189.62187</a></td> </tr><tr> <td>[41]</td> <td class="space">Handcock, M. S.; Gile, K., Analysis of Networks with Missing Data with Application to the National Longitudinal Study of Adolescent Health, Journal of the Royal Statistical Society. Series C (Applied Statistics), 66, 501-519 (2017) · <a href="/07951443" class="nowrap">Zbl 07951443</a></td> </tr><tr> <td>[42]</td> <td class="space">Handcock, M. S.; Raftery, A. E.; Tantrum, J. M., Model-based Clustering for Social Networks, Journal of the Royal Statistical Society, Series A (with discussion), 170, 301-354 (2007)</td> </tr><tr> <td>[43]</td> <td class="space">Hanneke, S.; Fu, W.; Xing, E. P., Discrete Temporal Models of Social Networks, Electronic Journal of Statistics, 4, 585-605 (2010) · <a href="/1329.91113" class="nowrap">Zbl 1329.91113</a></td> </tr><tr> <td>[44]</td> <td class="space">Hartley, H.; Sielken Jr., R., A “super-population Viewpoint” for Finite Population Sampling, Biometrics, 31, 411-422 (1975) · <a href="/0334.62005" class="nowrap">Zbl 0334.62005</a></td> </tr><tr> <td>[45]</td> <td class="space">Heckathorn, D. D., Respondent-driven Sampling: A New Approach to the Study of Hidden Populations, Social Problems, 44, 174-199 (1997)</td> </tr><tr> <td>[46]</td> <td class="space">Hoff, P. D., Additive and Multiplicative Effects Network Models, Statistical Science, 36, 34-50 (2021) · <a href="/07368218" class="nowrap">Zbl 07368218</a></td> </tr><tr> <td>[47]</td> <td class="space">Hoff, P. D.; Raftery, A. E.; Handcock, M. S., Latent Space Approaches to Social Network Analysis, Journal of the American Statistical Association, 97, 1090-1098 (2002) · <a href="/1041.62098" class="nowrap">Zbl 1041.62098</a></td> </tr><tr> <td>[48]</td> <td class="space">Holland, P. W.; Leinhardt, S., An Exponential Family of Probability Distributions for Directed Graphs, Journal of the American Statistical Association, 76, 33-65 (1981) · <a href="/0457.62090" class="nowrap">Zbl 0457.62090</a></td> </tr><tr> <td>[49]</td> <td class="space">Ishwaran, H.; James, L. F., Gibbs Sampling Methods for Stick-breaking Priors, Journal of the American Statistical Association, 96, 161-173 (2001) · <a href="/1014.62006" class="nowrap">Zbl 1014.62006</a></td> </tr><tr> <td>[50]</td> <td class="space">Jones, J. H.; Handcock, M. S., An Assessment of Preferential Attachment As a Mechanism for Human Sexual Network Formation, Proceedings of the Royal Society Series B, 270, 1123-1128 (2003)</td> </tr><tr> <td>[51]</td> <td class="space">Jones, J. H.; Handcock, M. S., Social Networks: Sexual Contacts and Epidemic Thresholds, Nature, 423, 605-606 (2003)</td> </tr><tr> <td>[52]</td> <td class="space">Jones, J. H.H.; Handcock, M. S., Likelihood-Based Inference for Stochastic Models of Sexual Network Formation, Population Biology, 65, 413-422 (2004) · <a href="/1110.92040" class="nowrap">Zbl 1110.92040</a></td> </tr><tr> <td>[53]</td> <td class="space">Karwa, V., Petrović, S., and Bajić, D. (2016), ‘DERGMs: Degeneracy-Restricted Exponential Random Graph Models’, arXiv preprint arXiv:1612.03054.</td> </tr><tr> <td>[54]</td> <td class="space">Karwa, V.; Slavković, A. B., Inference Using Noisy Degrees: Differentially Private β-model and Synthetic Graphs, The Annals of Statistics, 44, 87-112 (2016) · <a href="/1331.62114" class="nowrap">Zbl 1331.62114</a></td> </tr><tr> <td>[55]</td> <td class="space">Katz, L.; Proctor, C. H., The Configuration of Interpersonal Relations in a Group As a Time-dependent Stochastic Process, Psychometrika, 24, 317-327 (1959)</td> </tr><tr> <td>[56]</td> <td class="space">Keeling, M. J.; Eames, K. T.D., Networks and Epidemic Models, Journal of the Royal Society Interface, 2, 295-307 (2005)</td> </tr><tr> <td>[57]</td> <td class="space">Ki, M., 2015 MERS Outbreak in Korea: Hospital-to-hospital Transmission, Epidemiology and Health, 37, 1-4 (2015)</td> </tr><tr> <td>[58]</td> <td class="space">Kolaczyk, E. D., Statistical Analysis of Network Data: Methods and Models (2009), New York: Springer-Verlag, New York · <a href="/1277.62021" class="nowrap">Zbl 1277.62021</a></td> </tr><tr> <td>[59]</td> <td class="space">Koskinen, J. H.; Robins, G. L.; Pattison, P. E., Analysing Exponential Random Graph (p-star) Models with Missing Data Using Bayesian Data Augmentation, Statistical Methodology, 7, 366-384 (2010) · <a href="/1233.62206" class="nowrap">Zbl 1233.62206</a></td> </tr><tr> <td>[60]</td> <td class="space">Krivitsky, P. N.; Handcock, M. S., A Separable Model for Dynamic Networks, Journal of the Royal Statistical Society B, 76, 29-46 (2014) · <a href="/1411.90079" class="nowrap">Zbl 1411.90079</a></td> </tr><tr> <td>[61]</td> <td class="space">Krivitsky, P. N.; Handcock, M. S.; Morris, M., Adjusting for Network Size and Composition Effects in Exponential-family Random Graph Models, Statistical Methodology, 8, 319-339 (2011) · <a href="/1215.91069" class="nowrap">Zbl 1215.91069</a></td> </tr><tr> <td>[62]</td> <td class="space">Krivitsky, P. N.; Handcock, M. S.; Raftery, A. E.; Hoff, P. D., Representing Degree Distributions, Clustering, and Homophily in Social Networks With Latent Cluster Random Effects Models, Social Networks, 31, 204-213 (2009)</td> </tr><tr> <td>[63]</td> <td class="space">Krivitsky, P. N.; Kolaczyk, E. D., On the Question of Effective Sample Size in Network Modeling: An Asymptotic Inquiry, Statistical Science, 30, 184-198 (2015) · <a href="/1332.62036" class="nowrap">Zbl 1332.62036</a></td> </tr><tr> <td>[64]</td> <td class="space">Krivitsky, P. N.; Morris, M., Inference for Social Network Models From Egocentrically-sampled Data, with Application to Understanding Persistent Racial Disparities in HIV Prevalence in the US, Annals of Applied Statistics, 11, 427-455 (2017) · <a href="/1366.62225" class="nowrap">Zbl 1366.62225</a></td> </tr><tr> <td>[65]</td> <td class="space">Kurant, M.; Markopoulou, A.; Thiran, P., Towards Unbiased BFS Sampling, IEEE Journal on Selected Areas in Communications, 29, 1799-1809 (2011)</td> </tr><tr> <td>[66]</td> <td class="space">Laumann, E.O., Gagnon, J.H., Michael, T., and Michaels, S. (1994), The Social Organization of Sexuality: Sexual Practices in the United States, Chicago: University of Chicago Press.</td> </tr><tr> <td>[67]</td> <td class="space">Liu, J. S., Monte Carlo Strategies in Scientific Computing (2008), New York: Springer-Verlag, New York · <a href="/1132.65003" class="nowrap">Zbl 1132.65003</a></td> </tr><tr> <td>[68]</td> <td class="space">Lovász, L., Large Networks and Graph Limits (2012), Providence: American Mathematical Society, Providence · <a href="/1292.05001" class="nowrap">Zbl 1292.05001</a></td> </tr><tr> <td>[69]</td> <td class="space">Lusher, D.; Koskinen, J.; Robins, G., Exponential Random Graph Models for Social Networks (2013), Cambridge, UK: Cambridge University Press, Cambridge, UK</td> </tr><tr> <td>[70]</td> <td class="space">Ouzienko, V.; Guo, Y.; Obradovic, Z., A Decoupled Exponential Random Graph Model for Prediction of Structure and Attributes in Temporal Social Networks, Statistical Analysis and Data Mining, 4, 470-486 (2011) · <a href="/07260297" class="nowrap">Zbl 07260297</a></td> </tr><tr> <td>[71]</td> <td class="space">Pang, G., and Pardoux, E. (2020), ‘Functional Limit Theorems for Non-Markovian Epidemic Models’, arXiv preprint arXiv:2003.03249, 1-45.</td> </tr><tr> <td>[72]</td> <td class="space">Raftery, A. E.; Niu, X.; Hoff, P. D.; Yeung, K. Y., Fast Inference for the Latent Space Network Model Using a Case-control Approximate Likelihood, Journal of Computational and Graphical Statistics, 21, 901-919 (2012)</td> </tr><tr> <td>[73]</td> <td class="space">Rastelli, R.; Friel, N.; Raftery, A. E., Properties of Latent Variable Network Models, Network Science, 4, 407-432 (2016)</td> </tr><tr> <td>[74]</td> <td class="space">Reinert, G., The Asymptotic Evolution of the General Stochastic Epidemic, The Annals of Applied Probability, 5, 1061-1086 (1995) · <a href="/0851.60093" class="nowrap">Zbl 0851.60093</a></td> </tr><tr> <td>[75]</td> <td class="space">Rinaldo, A.; Petrović, S.; Fienberg, S. E., Maximum Likelihood Estimation in the β-model, The Annals of Statistics, 41, 1085-1110 (2013) · <a href="/1292.62052" class="nowrap">Zbl 1292.62052</a></td> </tr><tr> <td>[76]</td> <td class="space">Robins, G.; Pattison, P., Random Graph Models for Temporal Processes in Social Networks, Journal of Mathematical Sociology, 25, 5-41 (2001) · <a href="/0986.91048" class="nowrap">Zbl 0986.91048</a></td> </tr><tr> <td>[77]</td> <td class="space">Rohe, K.; Chatterjee, S.; Yu, B., Spectral Clustering and the High-dimensional Stochastic Block Model, The Annals of Statistics, 39, 1878-1915 (2011) · <a href="/1227.62042" class="nowrap">Zbl 1227.62042</a></td> </tr><tr> <td>[78]</td> <td class="space">Rubin, D. B., Inference and Missing Data, Biometrika, 63, 581-592 (1976) · <a href="/0344.62034" class="nowrap">Zbl 0344.62034</a></td> </tr><tr> <td>[79]</td> <td class="space">Salganik, M. J.; Heckathorn, D. D., Sampling and Estimation in Hidden Populations Using Respondent-driven Sampling, Sociological Methodology, 34, 193-239 (2004)</td> </tr><tr> <td>[80]</td> <td class="space">Salter-Townshend, M.; Murphy, T. B., Variational Bayesian Inference for the Latent Position Cluster Model for Network Data, Computational Statistics and Data Analysis, 57, 661-671 (2013) · <a href="/1365.62246" class="nowrap">Zbl 1365.62246</a></td> </tr><tr> <td>[81]</td> <td class="space">Salter-Townshend, M.; White, A.; Gollini, I.; Murphy, T. B., Review of Statistical Network Analysis: Models, Algorithms, and Software, Statistical Analysis and Data Mining, 5, 243-264 (2012) · <a href="/07260329" class="nowrap">Zbl 07260329</a></td> </tr><tr> <td>[82]</td> <td class="space">Schweinberger, M.; Handcock, M. S., Local Dependence in Random Graph Models: Characterization, Properties and Statistical Inference, Journal of the Royal Statistical Society, Series B, 77, 647-676 (2015) · <a href="/1414.62096" class="nowrap">Zbl 1414.62096</a></td> </tr><tr> <td>[83]</td> <td class="space">Schweinberger, M.; Krivitsky, P. N.; Butts, C. T.; Stewart, J. R., Exponential-family Models of Random Graphs: Inference in Finite, Super, and Infinite Population Scenarios, Statistical Science, 35, 627-662 (2020) · <a href="/07307194" class="nowrap">Zbl 07307194</a></td> </tr><tr> <td>[84]</td> <td class="space">Schweinberger, M.; Luna, P., HERGM: Hierarchical Exponential-family Random Graph Models, Journal of Statistical Software, 85, 1-39 (2018)</td> </tr><tr> <td>[85]</td> <td class="space">Sethuraman, J., A Constructive Definition of Dirichlet Priors, Statistica Sinica, 4, 639-650 (1994) · <a href="/0823.62007" class="nowrap">Zbl 0823.62007</a></td> </tr><tr> <td>[86]</td> <td class="space">Sewell, D. K., Network Autocorrelation Models with Egocentric Data, Social Networks, 49, 113-123 (2017)</td> </tr><tr> <td>[87]</td> <td class="space">Sewell, D. K.; Chen, Y., Latent Space Models for Dynamic Networks, Journal of the American Statistical Association, 110, 1646-1657 (2015) · <a href="/1373.62580" class="nowrap">Zbl 1373.62580</a></td> </tr><tr> <td>[88]</td> <td class="space">Sewell, D. K.; Chen, Y., Latent Space Approaches to Community Detection in Dynamic Networks, Bayesian Analysis, 12, 351-377 (2016) · <a href="/1384.62203" class="nowrap">Zbl 1384.62203</a></td> </tr><tr> <td>[89]</td> <td class="space">Sewell, D. K.; Chen, Y.; Bernhard, W.; Sulkin, T., Model-based Longitudinal Clustering with Varying Cluster Assignments, Statistica Sinica, 26, 205-233 (2016) · <a href="/1419.62157" class="nowrap">Zbl 1419.62157</a></td> </tr><tr> <td>[90]</td> <td class="space">Smith, A. L.; Asta, D. M.; Calder, C. A., The Geometry of Continuous Latent Space Models for Network Data, Statistical Science, 34, 428-453 (2019) · <a href="/1429.62433" class="nowrap">Zbl 1429.62433</a></td> </tr><tr> <td>[91]</td> <td class="space">Snijders, T.A.B. (2001), ‘The Statistical Evaluation of Social Network Dynamics’, in Sociological Methodology, eds. M. Sobel and M. Becker, Boston and London: Basil Blackwell, pp. 361-395.</td> </tr><tr> <td>[92]</td> <td class="space">Snijders, T. A.B.; Pattison, P. E.; Robins, G. L.; Handcock, M. S., New Specifications for Exponential Random Graph Models, Sociological Methodology, 36, 99-153 (2006)</td> </tr><tr> <td>[93]</td> <td class="space">Stephens, M., Dealing with Label-switching in Mixture Models, Journal of the Royal Statistical Society, Series B, 62, 795-809 (2000) · <a href="/0957.62020" class="nowrap">Zbl 0957.62020</a></td> </tr><tr> <td>[94]</td> <td class="space">Sundberg, R., Statistical Modelling by Exponential Families (2019), Cambridge, UK: Cambridge University Press, Cambridge, UK · <a href="/1454.62003" class="nowrap">Zbl 1454.62003</a></td> </tr><tr> <td>[95]</td> <td class="space">Teh, Y.W. (2010), ‘Dirichlet Processes’, in Encyclopedia of Machine Learning, eds. C. Sammut and G. I. Webb, New York: Springer-Verlag.</td> </tr><tr> <td>[96]</td> <td class="space">Thiemichen, S.; Friel, N.; Caimo, A.; Kauermann, G., Bayesian Exponential Random Graph Models with Nodal Random Effects, Social Networks, 46, 11-28 (2016)</td> </tr><tr> <td>[97]</td> <td class="space">Thompson, S., Sampling (2012), John Wiley & Sons · <a href="/1267.62020" class="nowrap">Zbl 1267.62020</a></td> </tr><tr> <td>[98]</td> <td class="space">Thompson, S.; Frank, O., Model-based Estimation with Link-tracing Sampling Designs, Survey Methodology, 26, 87-98 (2000)</td> </tr><tr> <td>[99]</td> <td class="space">Tierney, L., Markov Chains for Exploring Posterior Distributions, The Annals of Statistics, 22, 1701-1728 (1994) · <a href="/0829.62080" class="nowrap">Zbl 0829.62080</a></td> </tr><tr> <td>[100]</td> <td class="space">Vu, D. Q.; Hunter, D. R.; Schweinberger, M., Model-based Clustering of Large Networks, The Annals of Applied Statistics, 7, 1010-1039 (2013) · <a href="/1288.62106" class="nowrap">Zbl 1288.62106</a></td> </tr><tr> <td>[101]</td> <td class="space">Wainwright, M. J., High-Dimensional Statistics. A Non-Asymptotic Viewpoint (2019), Cambridge, UK: Cambridge University Press, Cambridge, UK · <a href="/1457.62011" class="nowrap">Zbl 1457.62011</a></td> </tr><tr> <td>[102]</td> <td class="space">Wasserman, S.; Faust, K., Social Network Analysis: Methods and Applications (1994), Cambridge: Cambridge University Press, Cambridge</td> </tr><tr> <td>[103]</td> <td class="space">Welch, D., Is Network Clustering Detectable in Transmission Trees?, Viruses, 3, 659-676 (2011)</td> </tr><tr> <td>[104]</td> <td class="space">Welch, D.; Bansal, S.; Hunter, D. R., Statistical Inference to Advance Network Models in Epidemiology, Epidemics, 3, 38-45 (2011)</td> </tr><tr> <td>[105]</td> <td class="space">Willinger, W.; Alderson, D.; Doyle, J. C., Mathematics and the Internet: A Source of Enormous Confusion and Great Potential, Notices of the American Mathematical Society, 56, 586-599 (2009) · <a href="/1168.90004" class="nowrap">Zbl 1168.90004</a></td> </tr></table> <div class="reference_disclaimer"> This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching. </div> </div></article> </div></div> </div> </div> <div class="clearfix"></div> </div> </div> <div id="foot"><div class="copyright"> © 2025 <a target="fiz" href="https://www.fiz-karlsruhe.de/en">FIZ Karlsruhe GmbH</a> <a href="/privacy-policy/">Privacy Policy</a> <a href="/legal-notices/">Legal Notices</a> <a href="/terms-conditions/">Terms & Conditions</a> <div class="info"> <ul class="nav"> <li class="mastodon"> <a href="https://mathstodon.xyz/@zbMATH" target="_blank" class="no-new-tab-icon"> <img src="/static/mastodon.png" title="zbMATH at Mathstodon (opens in new tab)" alt="Mastodon logo"> </a> </li> </ul> </div> </div> <div class="clearfix" style="height: 0px;"></div> </div> </div> <script src="https://static.zbmath.org/contrib/jquery/1.9.1/jquery.min.js"></script> <script src="https://static.zbmath.org/contrib/jquery-caret/1.5.2/jquery.caret.min.js"></script> <script src="/static/js/jquery-ui-1.10.1.custom.min.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap/v3.3.7zb1/js/bootstrap.min.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap-lightbox/v0.7.0/bootstrap-lightbox.min.js"></script> <script src="https://static.zbmath.org/contrib/retina/unknown/retina.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap-select/v1.13.14/js/bootstrap-select.min.js"></script> <script> var SCRIPT_ROOT = ""; </script> <script src="/static/scripts.js?v=20240926"> </script> <script src="https://static.zbmath.org/contrib/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script> <script type="text/x-mathjax-config"> MathJax.Hub.Config({ "HTML-CSS": { preferredFont: "TeX", availableFonts: [ "STIX", "TeX" ], linebreaks: { automatic: true }, EqnChunk: (MathJax.Hub.Browser.isMobile ? 10 : 50) }, tex2jax: { processEscapes: true, ignoreClass: "tex2jax_ignore|dno" }, TeX: { Macros: { Aut: "\\operatorname{Aut}", Hom: "\\operatorname{Hom}" }, noUndefined: { attributes: { mathcolor: "#039", //"red", mathbackground: "white", //"#FFEEEE", mathsize: "90%" } } }, messageStyle: "none" }); </script> <script type="text/javascript"> $(document).ready(function() { $("#MathInput").stop(true, true).keyup(function() { $.ajax({ url: "/mwsq/", type: "POST", data: { query : $("#MathInput").val() }, dataType: "text" }) .done(function(xml) { $("#MathPreview").html(xml); $(window).resize(); }); }); var press = jQuery.Event("keyup"); press.ctrlKey = false; press.which = 40; $("#MathInput").trigger(press); }); </script> <div id="new_tab_icon" style="display: none"> <span class="glyphicon glyphicon-new-window" aria-hidden="true"></span><span class="sr-only">(opens in new tab)</span></div> </body> </html>

CINXE.COM

Document Zbl 07590594 - zbMATH Open