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6.5 KiB
141 lines
6.5 KiB
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<head><title>2.1.1.0 model_layer_growth.py</title>
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<meta name="date" content="2015-10-19 17:14:00">
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<h5 class="subsubsectionHead"><a
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id="x47-460002.1.1"></a><span
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class="cmtt-10x-x-109">model</span><span
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class="cmtt-10x-x-109">_layer</span><span
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class="cmtt-10x-x-109">_growth.py</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">model</span><span
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class="cmbx-10x-x-109">_layer</span><span
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class="cmbx-10x-x-109">_growth.py </span>- Layer growth with preferential activation
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model.
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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">model</span><span
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class="cmbx-10x-x-109">_layer</span><span
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class="cmbx-10x-x-109">_growth.py </span><span
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class="cmmi-10x-x-109"><</span><span
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class="cmitt-10x-x-109">layer</span><span
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class="cmitt-10x-x-109">_N</span><span
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class="cmitt-10x-x-109">_file</span><span
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class="cmmi-10x-x-109">> <</span><span
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class="cmitt-10x-x-109">N</span><span
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class="cmmi-10x-x-109">> <</span><span
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class="cmitt-10x-x-109">M0</span><span
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class="cmmi-10x-x-109">> <</span><span
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class="cmitt-10x-x-109">A</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]</span>
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<!--l. 29--><p class="noindent" ><span
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class="cmbx-10x-x-109">DESCRIPTION</span>
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<!--l. 29--><p class="indent" > This is the model of layer growth with preferential node activation. In this
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model an entire new layer arrives at time <span
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class="cmmi-10x-x-109">t </span>and a number of nodes <span
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class="cmmi-10x-x-109">N</span><sub><span
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class="cmmi-8">t</span></sub> is
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activated (<span
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class="cmmi-10x-x-109">N</span>_<span
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class="cmmi-10x-x-109">t </span>is equal to the number of nodes active on that layer in the
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reference multiplex). Then, each node <span
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class="cmmi-10x-x-109">i </span>of the new layer is activated with a
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probability:
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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_doc12x.png" alt="Pi(t) ∝ A + Bi (t)
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" class="math-display" ></center></td></tr></table>
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<!--l. 29--><p class="nopar" >
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<!--l. 29--><p class="indent" > where <span
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class="cmmi-10x-x-109">B</span><sub><span
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class="cmmi-8">i</span></sub>(<span
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class="cmmi-10x-x-109">t</span>) is the activity of node <span
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class="cmmi-10x-x-109">i </span>at time <span
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class="cmmi-10x-x-109">t </span>(i.e., the number of
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layers in which node <span
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class="cmmi-10x-x-109">i </span>is active at time <span
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class="cmmi-10x-x-109">t</span>) while <span
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class="cmmi-10x-x-109">A > </span>0 is an intrinsic
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attractiveness.
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<!--l. 29--><p class="indent" > The file <span
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class="cmti-10x-x-109">layer</span><span
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class="cmti-10x-x-109">_N</span><span
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class="cmti-10x-x-109">_file </span>reports on the n-th line the number of active nodes on
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the n-th layer.
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<!--l. 29--><p class="indent" > The parameter <span
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class="cmti-10x-x-109">N </span>is the number of nodes in the multiplex, <span
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class="cmti-10x-x-109">M0 </span>is the number
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of layers in the initial network, <span
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class="cmti-10x-x-109">A </span>is the value of node attractiveness.
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<!--l. 29--><p class="indent" > If the user specifies <span
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class="cmtt-10x-x-109">RND </span>as the last parameter, the sequence of layers
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is
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<!--l. 44--><p class="noindent" ><span
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class="cmbx-10x-x-109">OUTPUT</span>
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<!--l. 44--><p class="indent" > The program prints on <span
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class="cmtt-10x-x-109">stdout </span>a node-layer list of lines in the format:
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<!--l. 44--><p class="indent" >   <span
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class="cmti-10x-x-109">node</span><span
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class="cmti-10x-x-109">_i layer</span><span
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class="cmti-10x-x-109">_i</span>
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<!--l. 44--><p class="indent" > where <span
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class="cmti-10x-x-109">node</span><span
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class="cmti-10x-x-109">_i </span>is the ID of a node and <span
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class="cmti-10x-x-109">layre</span><span
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class="cmti-10x-x-109">_i </span>is the ID of a layer. This
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list indicates which nodes are active in which layer. For instance, the
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line:
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<!--l. 44--><p class="indent" >   <span
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class="cmti-10x-x-109">24 3</span>
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<!--l. 44--><p class="indent" > indicates that the node with ID <span
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class="cmti-10x-x-109">24 </span>is active on layer <span
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class="cmti-10x-x-109">3</span>.
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<!--l. 46--><p class="noindent" ><span
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class="cmbx-10x-x-109">REFERENCE</span>
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<!--l. 46--><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. 46--><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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