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diff --git a/doc/html/mammult_docsu52.html b/doc/html/mammult_docsu52.html new file mode 100644 index 0000000..b0e0444 --- /dev/null +++ b/doc/html/mammult_docsu52.html @@ -0,0 +1,148 @@ +<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" + "http://www.w3.org/TR/html4/loose.dtd"> +<html > +<head><title>2.3.1.0 tune_qnn_adaptive</title> +<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1"> +<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<!-- html,index=2,3,4,5,next --> +<meta name="src" content="mammult_doc.tex"> +<meta name="date" content="2015-10-19 16:26:00"> +<link rel="stylesheet" type="text/css" href="mammult_doc.css"> +</head><body +> + <!--l. 3--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docch3.html" >next</a>] [<a +href="mammult_docsu51.html" >prev</a>] [<a +href="mammult_docsu51.html#tailmammult_docsu51.html" >prev-tail</a>] [<a +href="#tailmammult_docsu52.html">tail</a>] [<a +href="mammult_docsu50.html#mammult_docsu52.html" >up</a>] </p></div> + <h5 class="subsubsectionHead"><a + id="x60-590002.3.1"></a><span +class="cmtt-10x-x-109">tune</span><span +class="cmtt-10x-x-109">_qnn</span><span +class="cmtt-10x-x-109">_adaptive</span></h5> +<!--l. 3--><p class="noindent" ><span +class="cmbx-10x-x-109">NAME</span> +<!--l. 3--><p class="indent" > <span +class="cmbx-10x-x-109">tune</span><span +class="cmbx-10x-x-109">_qnn</span><span +class="cmbx-10x-x-109">_adaptive </span>- Construct a multiplex with prescribed inter-layer +correlations. +<!--l. 3--><p class="noindent" ><span +class="cmbx-10x-x-109">SYNOPSYS</span> +<!--l. 3--><p class="indent" > <span +class="cmbx-10x-x-109">tune</span><span +class="cmbx-10x-x-109">_qnn</span><span +class="cmbx-10x-x-109">_adaptive </span><span +class="cmmi-10x-x-109"><</span><span +class="cmitt-10x-x-109">degs1</span><span +class="cmmi-10x-x-109">> <</span><span +class="cmitt-10x-x-109">degs2</span><span +class="cmmi-10x-x-109">> <</span><span +class="cmitt-10x-x-109">mu</span><span +class="cmmi-10x-x-109">> <</span><span +class="cmitt-10x-x-109">eps</span><span +class="cmmi-10x-x-109">> <</span><span +class="cmitt-10x-x-109">beta</span><span +class="cmmi-10x-x-109">></span> +<span +class="cmitt-10x-x-109">[RND|NAT|INV]</span> +<!--l. 52--><p class="noindent" ><span +class="cmbx-10x-x-109">DESCRIPTION</span> +<!--l. 52--><p class="indent" > This programs tunes the inter-layer degree correlation exponent <span +class="cmmi-10x-x-109">μ</span>. If +we consider two layers of a multiplex, and we denote by <span +class="cmmi-10x-x-109">k </span>the degree +of a node on the first layer and by <span +class="cmmi-10x-x-109">q </span>the degree of the same node on +the second layers, the inter-layer degree correlation function is defined +as: + <table +class="equation-star"><tr><td> + <center class="math-display" > +<img +src="mammult_doc25x.png" alt="-- ∑ ′ ′ +q(k) = q P(q |k) + q′ +" class="math-display" ></center></td></tr></table> +<!--l. 52--><p class="nopar" > +<!--l. 52--><p class="indent" > where <span class="overline"><span +class="cmmi-10x-x-109">q</span></span>(<span +class="cmmi-10x-x-109">k</span>) is the average degree on layer 2 of nodes having degree <span +class="cmmi-10x-x-109">k </span>on layer +1. +<!--l. 52--><p class="indent" > The program assumes that we want to set the degree correlation function +such that: + <table +class="equation-star"><tr><td> + + + + <center class="math-display" > +<img +src="mammult_doc26x.png" alt="q(k) = akμ +" class="math-display" ></center></td></tr></table> +<!--l. 52--><p class="nopar" > +<!--l. 52--><p class="indent" > where the exponent of the power-law function is given by the user +(it is indeed the parameter <span +class="cmti-10x-x-109">mu</span>), and successively adjusts the pairing +between nodes at the two layers in order to obtain a correlation function as +close as possible to the desired one. The files <span +class="cmti-10x-x-109">degs1 </span>and <span +class="cmti-10x-x-109">degs2 </span>contain, +respectively, the degrees of the nodes on the first layer and on the second +layer. +<!--l. 52--><p class="indent" > The parameter <span +class="cmti-10x-x-109">eps </span>is the accuracy of <span +class="cmti-10x-x-109">mu</span>. For instance, if <span +class="cmti-10x-x-109">mu </span>is set equal to +-0.25 and <span +class="cmti-10x-x-109">eps </span>is equal to 0.0001, the program stops when the configuration of +node pairing corresponds to a value of the exponent <span +class="cmmi-10x-x-109">μ </span>which differs from -0.25 by +less than 0.0001. +<!--l. 52--><p class="indent" > The parameter <span +class="cmti-10x-x-109">beta </span>is the typical inverse temperature of simulated +annealing. +<!--l. 52--><p class="indent" > If no other parameter is specified, or if the last parameter is <span +class="cmtt-10x-x-109">RND</span>, the program +starts from a random pairing of nodes. If the last parameter is <span +class="cmtt-10x-x-109">NAT </span>then the +program assumes that the initial pairing is the natural one, where the nodes have +the same ID on both layers. Finally, if <span +class="cmtt-10x-x-109">INV </span>is specified, the initial pairing is the +inverse pairing, i.e. the one where node 0 on layer 1 is paired with node N-1 on +layer 2, and so on. +<!--l. 62--><p class="noindent" ><span +class="cmbx-10x-x-109">OUTPUT</span> +<!--l. 62--><p class="indent" > The program prints on <span +class="cmtt-10x-x-109">stdout </span>a pairing, i.e. a list of lines in the +format: +<!--l. 62--><p class="indent" >   <span +class="cmti-10x-x-109">IDL1 IDL2</span> +<!--l. 62--><p class="indent" > where <span +class="cmti-10x-x-109">IDL1 </span>is the ID of the node on layer 1 and <span +class="cmti-10x-x-109">IDL2 </span>is the corresponding +ID of the same node on layer 2. +<!--l. 64--><p class="noindent" ><span +class="cmbx-10x-x-109">REFERENCE</span> +<!--l. 64--><p class="indent" > V. Nicosia, V. Latora, “Measuring and modeling correlations in multiplex +networks”, <span +class="cmti-10x-x-109">Phys. Rev. E </span><span +class="cmbx-10x-x-109">92</span>, 032805 (2015). +<!--l. 64--><p class="indent" > Link to paper: <a +href="http://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.032805" class="url" ><span +class="cmtt-10x-x-109">http://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.032805</span></a> + + + + <!--l. 247--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docch3.html" >next</a>] [<a +href="mammult_docsu51.html" >prev</a>] [<a +href="mammult_docsu51.html#tailmammult_docsu51.html" >prev-tail</a>] [<a +href="mammult_docsu52.html" >front</a>] [<a +href="mammult_docsu50.html#mammult_docsu52.html" >up</a>] </p></div> +<!--l. 247--><p class="indent" > <a + id="tailmammult_docsu52.html"></a> +</body></html> |