1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
|
<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"
"http://www.w3.org/TR/html4/loose.dtd">
<html >
<head><title>2.1.1.0 model_layer_growth.py</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 17:06:00">
<link rel="stylesheet" type="text/css" href="mammult_doc.css">
</head><body
>
<!--l. 3--><div class="crosslinks"><p class="noindent">[<a
href="mammult_docse4.html" >next</a>] [<a
href="mammult_docsu39.html" >prev</a>] [<a
href="mammult_docsu39.html#tailmammult_docsu39.html" >prev-tail</a>] [<a
href="#tailmammult_docsu40.html">tail</a>] [<a
href="mammult_docsu36.html#mammult_docsu40.html" >up</a>] </p></div>
<h5 class="subsubsectionHead"><a
id="x46-450002.1.1"></a><span
class="cmtt-10x-x-109">model</span><span
class="cmtt-10x-x-109">_layer</span><span
class="cmtt-10x-x-109">_growth.py</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">model</span><span
class="cmbx-10x-x-109">_layer</span><span
class="cmbx-10x-x-109">_growth.py </span>- Layer growth with preferential activation
model.
<!--l. 3--><p class="noindent" ><span
class="cmbx-10x-x-109">SYNOPSYS</span>
<!--l. 3--><p class="indent" > <span
class="cmbx-10x-x-109">model</span><span
class="cmbx-10x-x-109">_layer</span><span
class="cmbx-10x-x-109">_growth.py </span><span
class="cmmi-10x-x-109"><</span><span
class="cmitt-10x-x-109">layer</span><span
class="cmitt-10x-x-109">_N</span><span
class="cmitt-10x-x-109">_file</span><span
class="cmmi-10x-x-109">> <</span><span
class="cmitt-10x-x-109">N</span><span
class="cmmi-10x-x-109">> <</span><span
class="cmitt-10x-x-109">M0</span><span
class="cmmi-10x-x-109">> <</span><span
class="cmitt-10x-x-109">A</span><span
class="cmmi-10x-x-109">></span>
<span
class="cmitt-10x-x-109">[RND]</span>
<!--l. 29--><p class="noindent" ><span
class="cmbx-10x-x-109">DESCRIPTION</span>
<!--l. 29--><p class="indent" > This is the model of layer growth with preferential node activation. In this
model an entire new layer arrives at time <span
class="cmmi-10x-x-109">t </span>and a number of nodes <span
class="cmmi-10x-x-109">N</span><sub><span
class="cmmi-8">t</span></sub> is
activated (<span
class="cmmi-10x-x-109">N</span>_<span
class="cmmi-10x-x-109">t </span>is equal to the number of nodes active on that layer in the
reference multiplex). Then, each node <span
class="cmmi-10x-x-109">i </span>of the new layer is activated with a
probability:
<table
class="equation-star"><tr><td>
<center class="math-display" >
<img
src="mammult_doc12x.png" alt="Pi(t) ∝ A + Bi (t)
" class="math-display" ></center></td></tr></table>
<!--l. 29--><p class="nopar" >
<!--l. 29--><p class="indent" > where <span
class="cmmi-10x-x-109">B</span><sub><span
class="cmmi-8">i</span></sub>(<span
class="cmmi-10x-x-109">t</span>) is the activity of node <span
class="cmmi-10x-x-109">i </span>at time <span
class="cmmi-10x-x-109">t </span>(i.e., the number of
layers in which node <span
class="cmmi-10x-x-109">i </span>is active at time <span
class="cmmi-10x-x-109">t</span>) while <span
class="cmmi-10x-x-109">A > </span>0 is an intrinsic
attractiveness.
<!--l. 29--><p class="indent" > The file <span
class="cmti-10x-x-109">layer</span><span
class="cmti-10x-x-109">_N</span><span
class="cmti-10x-x-109">_file </span>reports on the n-th line the number of active nodes on
the n-th layer.
<!--l. 29--><p class="indent" > The parameter <span
class="cmti-10x-x-109">N </span>is the number of nodes in the multiplex, <span
class="cmti-10x-x-109">M0 </span>is the number
of layers in the initial network, <span
class="cmti-10x-x-109">A </span>is the value of node attractiveness.
<!--l. 29--><p class="indent" > If the user specifies <span
class="cmtt-10x-x-109">RND </span>as the last parameter, the sequence of layers
is
<!--l. 44--><p class="noindent" ><span
class="cmbx-10x-x-109">OUTPUT</span>
<!--l. 44--><p class="indent" > The program prints on <span
class="cmtt-10x-x-109">stdout </span>a node-layer list of lines in the format:
<!--l. 44--><p class="indent" >   <span
class="cmti-10x-x-109">node</span><span
class="cmti-10x-x-109">_i layer</span><span
class="cmti-10x-x-109">_i</span>
<!--l. 44--><p class="indent" > where <span
class="cmti-10x-x-109">node</span><span
class="cmti-10x-x-109">_i </span>is the ID of a node and <span
class="cmti-10x-x-109">layre</span><span
class="cmti-10x-x-109">_i </span>is the ID of a layer. This
list indicates which nodes are active in which layer. For instance, the
line:
<!--l. 44--><p class="indent" >   <span
class="cmti-10x-x-109">24 3</span>
<!--l. 44--><p class="indent" > indicates that the node with ID <span
class="cmti-10x-x-109">24 </span>is active on layer <span
class="cmti-10x-x-109">3</span>.
<!--l. 46--><p class="noindent" ><span
class="cmbx-10x-x-109">REFERENCE</span>
<!--l. 46--><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. 46--><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. 220--><div class="crosslinks"><p class="noindent">[<a
href="mammult_docse4.html" >next</a>] [<a
href="mammult_docsu39.html" >prev</a>] [<a
href="mammult_docsu39.html#tailmammult_docsu39.html" >prev-tail</a>] [<a
href="mammult_docsu40.html" >front</a>] [<a
href="mammult_docsu36.html#mammult_docsu40.html" >up</a>] </p></div>
<!--l. 220--><p class="indent" > <a
id="tailmammult_docsu40.html"></a>
</body></html>
|
