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151 lines
7.1 KiB
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<head><title>2.3.1.0 tune_qnn_adaptive</title>
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<meta name="src" content="mammult_doc.tex">
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<meta name="date" content="2015-10-19 17:14:00">
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>
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<!--l. 3--><div class="crosslinks"><p class="noindent">[<a
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<h5 class="subsubsectionHead"><a
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id="x61-600002.3.1"></a><span
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class="cmtt-10x-x-109">tune</span><span
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class="cmtt-10x-x-109">_qnn</span><span
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class="cmtt-10x-x-109">_adaptive</span></h5>
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<!--l. 3--><p class="noindent" ><span
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class="cmbx-10x-x-109">NAME</span>
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<!--l. 3--><p class="indent" > <span
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class="cmbx-10x-x-109">tune</span><span
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class="cmbx-10x-x-109">_qnn</span><span
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class="cmbx-10x-x-109">_adaptive </span>- Construct a multiplex with prescribed inter-layer
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correlations.
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<!--l. 3--><p class="noindent" ><span
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class="cmbx-10x-x-109">SYNOPSYS</span>
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<!--l. 3--><p class="indent" > <span
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class="cmbx-10x-x-109">tune</span><span
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class="cmbx-10x-x-109">_qnn</span><span
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class="cmbx-10x-x-109">_adaptive </span><span
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class="cmmi-10x-x-109"><</span><span
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class="cmitt-10x-x-109">degs1</span><span
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class="cmmi-10x-x-109">> <</span><span
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class="cmitt-10x-x-109">degs2</span><span
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class="cmmi-10x-x-109">> <</span><span
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class="cmitt-10x-x-109">mu</span><span
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class="cmmi-10x-x-109">> <</span><span
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class="cmitt-10x-x-109">eps</span><span
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class="cmmi-10x-x-109">> <</span><span
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class="cmitt-10x-x-109">beta</span><span
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class="cmmi-10x-x-109">></span>
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<span
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class="cmitt-10x-x-109">[RND|NAT|INV]</span>
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<!--l. 52--><p class="noindent" ><span
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class="cmbx-10x-x-109">DESCRIPTION</span>
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<!--l. 52--><p class="indent" > This programs tunes the inter-layer degree correlation exponent <span
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class="cmmi-10x-x-109">μ</span>. If
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we consider two layers of a multiplex, and we denote by <span
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class="cmmi-10x-x-109">k </span>the degree
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of a node on the first layer and by <span
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class="cmmi-10x-x-109">q </span>the degree of the same node on
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the second layers, the inter-layer degree correlation function is defined
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as:
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<table
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class="equation-star"><tr><td>
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<center class="math-display" >
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<img
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src="mammult_doc25x.png" alt="-- ∑ ′ ′
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q(k) = q P(q |k)
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q′
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" class="math-display" ></center></td></tr></table>
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<!--l. 52--><p class="nopar" >
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<!--l. 52--><p class="indent" > where <span class="overline"><span
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class="cmmi-10x-x-109">q</span></span>(<span
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class="cmmi-10x-x-109">k</span>) is the average degree on layer 2 of nodes having degree <span
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class="cmmi-10x-x-109">k </span>on layer
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1.
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<!--l. 52--><p class="indent" > The program assumes that we want to set the degree correlation function
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such that:
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<table
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class="equation-star"><tr><td>
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<center class="math-display" >
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<img
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src="mammult_doc26x.png" alt="q(k) = akμ
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" class="math-display" ></center></td></tr></table>
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<!--l. 52--><p class="nopar" >
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<!--l. 52--><p class="indent" > where the exponent of the power-law function is given by the user
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(it is indeed the parameter <span
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class="cmti-10x-x-109">mu</span>), and successively adjusts the pairing
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between nodes at the two layers in order to obtain a correlation function as
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close as possible to the desired one. The files <span
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class="cmti-10x-x-109">degs1 </span>and <span
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class="cmti-10x-x-109">degs2 </span>contain,
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respectively, the degrees of the nodes on the first layer and on the second
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layer.
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<!--l. 52--><p class="indent" > The parameter <span
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class="cmti-10x-x-109">eps </span>is the accuracy of <span
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class="cmti-10x-x-109">mu</span>. For instance, if <span
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class="cmti-10x-x-109">mu </span>is set equal to
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-0.25 and <span
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class="cmti-10x-x-109">eps </span>is equal to 0.0001, the program stops when the configuration of
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node pairing corresponds to a value of the exponent <span
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class="cmmi-10x-x-109">μ </span>which differs from -0.25 by
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less than 0.0001.
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<!--l. 52--><p class="indent" > The parameter <span
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class="cmti-10x-x-109">beta </span>is the typical inverse temperature of simulated
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annealing.
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<!--l. 52--><p class="indent" > If no other parameter is specified, or if the last parameter is <span
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class="cmtt-10x-x-109">RND</span>, the program
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starts from a random pairing of nodes. If the last parameter is <span
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class="cmtt-10x-x-109">NAT </span>then the
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program assumes that the initial pairing is the natural one, where the nodes have
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the same ID on both layers. Finally, if <span
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class="cmtt-10x-x-109">INV </span>is specified, the initial pairing is the
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inverse pairing, i.e. the one where node 0 on layer 1 is paired with node N-1 on
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layer 2, and so on.
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<!--l. 62--><p class="noindent" ><span
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class="cmbx-10x-x-109">OUTPUT</span>
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<!--l. 62--><p class="indent" > The program prints on <span
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class="cmtt-10x-x-109">stdout </span>a pairing, i.e. a list of lines in the
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format:
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<!--l. 62--><p class="indent" >   <span
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class="cmti-10x-x-109">IDL1 IDL2</span>
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<!--l. 62--><p class="indent" > where <span
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class="cmti-10x-x-109">IDL1 </span>is the ID of the node on layer 1 and <span
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class="cmti-10x-x-109">IDL2 </span>is the corresponding
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ID of the same node on layer 2.
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<!--l. 64--><p class="noindent" ><span
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class="cmbx-10x-x-109">REFERENCE</span>
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<!--l. 64--><p class="indent" > V. Nicosia, V. Latora, “Measuring and modeling correlations in multiplex
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networks”, <span
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class="cmti-10x-x-109">Phys. Rev. E </span><span
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class="cmbx-10x-x-109">92</span>, 032805 (2015).
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<!--l. 64--><p class="indent" > Link to paper: <a
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href="http://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.032805" class="url" ><span
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class="cmtt-10x-x-109">http://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.032805</span></a>
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<!--l. 261--><div class="crosslinks"><p class="noindent">[<a
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href="mammult_docch3.html" >next</a>] [<a
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href="mammult_docsu51.html#tailmammult_docsu51.html" >prev-tail</a>] [<a
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href="mammult_docsu52.html" >front</a>] [<a
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href="mammult_docsu50.html#mammult_docsu52.html" >up</a>] </p></div>
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