-
Notifications
You must be signed in to change notification settings - Fork 0
/
Copy pathdata_integration_and_mining_with_graphs-dynamic_graphs.html
216 lines (216 loc) · 297 KB
/
data_integration_and_mining_with_graphs-dynamic_graphs.html
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
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.1 plus MathML 2.0//EN" "http://www.w3.org/Math/DTD/mathml2/xhtml-math11-f.dtd">
<html xmlns="http://www.w3.org/1999/xhtml"><!--This file was converted to xhtml by LibreOffice - see http://cgit.freedesktop.org/libreoffice/core/tree/filter/source/xslt for the code.--><head profile="http://dublincore.org/documents/dcmi-terms/"><meta http-equiv="Content-Type" content="application/xhtml+xml; charset=utf-8"/><title xml:lang="en-US">- no title specified</title><meta name="DCTERMS.title" content="" xml:lang="en-US"/><meta name="DCTERMS.language" content="en-US" scheme="DCTERMS.RFC4646"/><meta name="DCTERMS.source" content="http://xml.openoffice.org/odf2xhtml"/><meta name="DCTERMS.creator" content="JeanKarim Heriche"/><meta name="DCTERMS.issued" content="2015-12-03T10:16:03.988869442" scheme="DCTERMS.W3CDTF"/><meta name="DCTERMS.modified" content="2015-12-17T20:34:38.193941000" scheme="DCTERMS.W3CDTF"/><meta name="DCTERMS.provenance" content="" xml:lang="en-US"/><meta name="DCTERMS.subject" content="," xml:lang="en-US"/><link rel="schema.DC" href="http://purl.org/dc/elements/1.1/" hreflang="en"/><link rel="schema.DCTERMS" href="http://purl.org/dc/terms/" hreflang="en"/><link rel="schema.DCTYPE" href="http://purl.org/dc/dcmitype/" hreflang="en"/><link rel="schema.DCAM" href="http://purl.org/dc/dcam/" hreflang="en"/><style type="text/css">
@page { }
table { border-collapse:collapse; border-spacing:0; empty-cells:show }
td, th { vertical-align:top; font-size:12pt;}
h1, h2, h3, h4, h5, h6 { clear:both }
ol, ul { margin:0; padding:0;}
li { list-style: none; margin:0; padding:0;}
<!-- "li span.odfLiEnd" - IE 7 issue-->
li span. { clear: both; line-height:0; width:0; height:0; margin:0; padding:0; }
span.footnodeNumber { padding-right:1em; }
span.annotation_style_by_filter { font-size:95%; font-family:Arial; background-color:#fff000; margin:0; border:0; padding:0; }
* { margin:0;}
.fr1 { border-style:none; font-size:12pt; margin-bottom:0in; margin-left:0in; margin-right:0in; margin-top:0in; padding:0in; font-family:Liberation Serif; text-align:center; vertical-align:top; writing-mode:lr-tb; }
.fr2 { font-size:12pt; font-family:Liberation Serif; text-align:center; vertical-align:top; writing-mode:lr-tb; }
.fr3 { font-size:12pt; font-family:Liberation Serif; text-align:center; vertical-align:top; writing-mode:lr-tb; margin-left:0in; margin-right:0in; margin-top:0in; margin-bottom:0in; padding:0in; border-style:none; }
.fr4 { font-size:12pt; font-family:Liberation Serif; text-align:center; vertical-align:top; writing-mode:lr-tb; }
.Caption { font-size:12pt; font-family:Liberation Serif; writing-mode:lr-tb; margin-top:0.0835in; margin-bottom:0.0835in; font-style:italic; }
.Footer { font-size:12pt; font-family:Liberation Serif; writing-mode:lr-tb; }
.P1 { font-size:12pt; font-family:Arial; writing-mode:lr-tb; text-align:left ! important; font-weight:normal; }
.P10 { font-size:12pt; font-family:Arial; writing-mode:lr-tb; line-height:150%; text-align:left ! important; text-decoration:none ! important; font-weight:normal; }
.P11 { font-size:12pt; font-family:Arial; writing-mode:lr-tb; line-height:150%; text-align:left ! important; text-decoration:none ! important; font-weight:normal; }
.P12 { font-size:12pt; font-family:Arial; writing-mode:lr-tb; line-height:150%; text-align:left ! important; text-decoration:none ! important; font-weight:normal; }
.P13 { font-size:12pt; font-family:Arial; writing-mode:lr-tb; line-height:150%; text-align:left ! important; text-decoration:none ! important; font-weight:normal; }
.P14 { font-size:12pt; font-family:Arial; writing-mode:lr-tb; line-height:150%; text-align:left ! important; text-decoration:none ! important; font-weight:normal; }
.P15 { font-size:12pt; font-family:Arial; writing-mode:lr-tb; line-height:150%; text-align:left ! important; text-decoration:none ! important; font-weight:normal; }
.P16 { font-size:12pt; font-family:Arial; writing-mode:lr-tb; line-height:150%; text-align:left ! important; text-decoration:none ! important; font-weight:normal; }
.P17 { font-size:12pt; font-family:Arial; writing-mode:lr-tb; line-height:150%; text-align:left ! important; text-decoration:none ! important; font-weight:normal; }
.P18 { font-size:12pt; font-family:Arial; writing-mode:lr-tb; line-height:150%; text-align:left ! important; text-decoration:none ! important; font-weight:normal; }
.P19 { font-size:14pt; font-family:Arial; writing-mode:lr-tb; text-align:left ! important; }
.P2 { font-size:12pt; font-family:Arial; writing-mode:lr-tb; line-height:150%; text-align:left ! important; font-weight:normal; }
.P20 { font-size:14pt; font-family:Arial; writing-mode:lr-tb; text-align:center ! important; }
.P21 { font-size:14pt; font-family:Arial; writing-mode:lr-tb; text-align:center ! important; }
.P22 { font-size:14pt; font-family:Arial; writing-mode:lr-tb; text-align:center ! important; }
.P23 { font-size:14pt; font-family:Arial; writing-mode:lr-tb; text-align:center ! important; }
.P24 { font-size:14pt; font-family:Arial; writing-mode:lr-tb; text-align:left ! important; font-weight:bold; }
.P25 { font-size:14pt; font-family:Arial; writing-mode:lr-tb; line-height:150%; text-align:left ! important; font-weight:bold; }
.P26 { font-size:14pt; font-family:Arial; writing-mode:lr-tb; line-height:150%; text-align:left ! important; text-decoration:none ! important; font-weight:bold; }
.P27 { font-size:14pt; font-family:Arial; writing-mode:lr-tb; line-height:150%; text-align:left ! important; text-decoration:none ! important; font-weight:bold; }
.P28 { font-size:14pt; font-family:Arial; writing-mode:lr-tb; line-height:150%; text-align:left ! important; text-decoration:none ! important; font-weight:bold; }
.P29 { font-size:14pt; font-family:Arial; writing-mode:lr-tb; line-height:150%; text-align:left ! important; text-decoration:none ! important; font-weight:bold; }
.P3 { font-size:12pt; font-family:Arial; writing-mode:lr-tb; line-height:150%; text-align:left ! important; font-weight:normal; }
.P30 { font-size:14pt; font-family:Arial; writing-mode:lr-tb; line-height:150%; text-align:left ! important; text-decoration:none ! important; font-weight:bold; }
.P31 { font-size:14pt; font-family:Arial; writing-mode:lr-tb; line-height:150%; text-align:left ! important; text-decoration:none ! important; font-weight:bold; }
.P32 { font-size:28pt; font-family:Arial; writing-mode:lr-tb; text-align:center ! important; }
.P33 { font-size:26pt; font-family:Arial; writing-mode:lr-tb; text-align:center ! important; }
.P34 { font-size:26pt; font-family:Arial; writing-mode:lr-tb; text-align:center ! important; }
.P35 { font-size:12pt; font-family:Arial; writing-mode:lr-tb; line-height:150%; text-align:left ! important; }
.P36 { font-size:12pt; font-family:Arial; writing-mode:lr-tb; line-height:150%; text-align:left ! important; }
.P37 { font-size:12pt; font-family:Arial; writing-mode:lr-tb; line-height:150%; text-align:left ! important; font-style:italic; }
.P38 { font-size:12pt; font-family:Liberation Serif; writing-mode:lr-tb; line-height:150%; text-align:left ! important; }
.P39 { font-size:12pt; font-family:Liberation Serif; writing-mode:lr-tb; line-height:150%; text-align:left ! important; }
.P4 { font-size:12pt; font-family:Arial; writing-mode:lr-tb; line-height:150%; text-align:left ! important; font-weight:normal; }
.P40 { font-size:12pt; font-family:Liberation Serif; writing-mode:lr-tb; line-height:150%; text-align:left ! important; }
.P41 { font-size:12pt; font-family:Liberation Serif; writing-mode:lr-tb; line-height:150%; text-align:left ! important; }
.P42 { font-size:12pt; font-family:Liberation Serif; writing-mode:lr-tb; line-height:150%; text-align:left ! important; }
.P43 { font-size:12pt; font-family:Liberation Serif; writing-mode:lr-tb; line-height:150%; text-align:left ! important; }
.P44 { font-size:12pt; font-family:Arial; writing-mode:lr-tb; line-height:150%; text-align:left ! important; font-weight:normal; }
.P45 { font-size:12pt; font-family:Arial; writing-mode:lr-tb; line-height:150%; text-align:left ! important; color:#000000; letter-spacing:normal; text-decoration:none ! important; font-weight:normal; }
.P46 { font-size:12pt; font-family:Arial; writing-mode:lr-tb; line-height:150%; text-align:left ! important; color:#000000; letter-spacing:normal; text-decoration:none ! important; font-weight:normal; }
.P47 { font-size:14pt; font-family:Arial; writing-mode:lr-tb; line-height:150%; text-align:left ! important; color:#000000; letter-spacing:normal; text-decoration:none ! important; font-weight:bold; }
.P48 { font-size:14pt; font-family:Arial; writing-mode:lr-tb; line-height:150%; text-align:left ! important; color:#000000; letter-spacing:normal; text-decoration:none ! important; font-weight:bold; }
.P49 { font-size:12pt; font-family:GillSans; writing-mode:lr-tb; color:#000000; letter-spacing:normal; text-decoration:none ! important; font-weight:normal; }
.P5 { font-size:12pt; font-family:Arial; writing-mode:lr-tb; line-height:150%; font-weight:normal; }
.P50 { font-size:14pt; font-family:Arial; writing-mode:lr-tb; line-height:150%; text-align:left ! important; font-weight:bold; }
.P51 { font-size:14pt; font-family:Arial; writing-mode:lr-tb; line-height:150%; text-align:left ! important; text-decoration:none ! important; font-weight:bold; }
.P52 { font-size:12pt; font-family:Arial; writing-mode:lr-tb; margin-left:0in; margin-right:0in; line-height:150%; text-align:left ! important; text-indent:0in; font-weight:normal; }
.P53 { font-size:12pt; font-family:Arial; writing-mode:lr-tb; margin-left:0in; margin-right:0in; line-height:150%; text-align:left ! important; text-indent:0in; text-decoration:none ! important; font-weight:normal; }
.P54 { font-size:12pt; font-family:Ubuntu Mono; writing-mode:lr-tb; margin-left:0in; margin-right:0in; line-height:150%; text-align:left ! important; text-indent:0in; background-color:#e6e6e6; color:#000000; letter-spacing:normal; text-decoration:none ! important; font-weight:normal; }
.P55 { font-size:12pt; font-family:Ubuntu Mono; writing-mode:lr-tb; margin-left:0in; margin-right:0in; line-height:150%; text-align:left ! important; text-indent:0in; background-color:#e6e6e6; color:#000000; font-weight:normal; }
.P56 { font-size:12pt; font-family:Ubuntu Mono; writing-mode:lr-tb; margin-left:0in; margin-right:0in; line-height:150%; text-align:left ! important; text-indent:0in; background-color:#e6e6e6; color:#000000; font-weight:normal; }
.P57 { font-size:12pt; font-family:Ubuntu Mono; writing-mode:lr-tb; margin-left:0in; margin-right:0in; line-height:150%; text-align:left ! important; text-indent:0in; background-color:#e6e6e6; color:#000000; font-weight:normal; }
.P58 { font-size:12pt; font-family:Ubuntu Mono; writing-mode:lr-tb; margin-left:0in; margin-right:0in; line-height:150%; text-align:left ! important; text-indent:0in; background-color:#e6e6e6; color:#000000; font-weight:normal; }
.P59 { font-size:12pt; font-family:Ubuntu Mono; writing-mode:lr-tb; margin-left:0in; margin-right:0in; line-height:150%; text-align:left ! important; text-indent:0in; background-color:#e6e6e6; color:#000000; font-weight:normal; }
.P6 { font-size:12pt; font-family:Arial; writing-mode:lr-tb; line-height:150%; text-align:left ! important; text-decoration:none ! important; font-weight:normal; }
.P60 { font-size:12pt; font-family:Arial; writing-mode:lr-tb; line-height:150%; text-align:left ! important; text-decoration:none ! important; font-weight:normal; }
.P61 { font-size:12pt; font-family:Arial; writing-mode:lr-tb; line-height:150%; text-align:left ! important; text-decoration:none ! important; font-weight:normal; }
.P62 { font-size:12pt; font-family:Arial; writing-mode:lr-tb; line-height:150%; text-align:left ! important; text-decoration:none ! important; font-weight:normal; }
.P63 { font-size:12pt; font-family:Arial; writing-mode:lr-tb; line-height:150%; text-align:left ! important; font-weight:normal; }
.P64 { font-size:12pt; font-family:Arial; writing-mode:lr-tb; line-height:150%; text-align:left ! important; font-weight:normal; }
.P65 { font-size:12pt; font-family:Arial; writing-mode:lr-tb; line-height:150%; text-align:left ! important; font-weight:normal; }
.P7 { font-size:12pt; font-family:Arial; writing-mode:lr-tb; line-height:150%; text-align:left ! important; text-decoration:none ! important; font-weight:normal; }
.P8 { font-size:12pt; font-family:Arial; writing-mode:lr-tb; line-height:150%; text-align:left ! important; text-decoration:none ! important; font-weight:normal; }
.P9 { font-size:12pt; font-family:Arial; writing-mode:lr-tb; line-height:150%; text-align:left ! important; text-decoration:none ! important; font-weight:normal; }
.Bullet_20_Symbols { font-family:OpenSymbol; }
.Emphasis { font-style:italic; }
.Internet_20_link { color:#000080; text-decoration:underline; }
.T10 { text-decoration:none ! important; }
.T100 { font-family:Arial; font-style:normal; }
.T101 { font-family:Arial; font-weight:bold; }
.T102 { font-family:Arial; font-weight:bold; }
.T104 { font-style:italic; }
.T105 { font-style:normal; }
.T106 { font-style:normal; }
.T107 { font-family:Arial; font-weight:bold; }
.T108 { font-family:Arial; font-weight:bold; }
.T11 { text-decoration:none ! important; }
.T115 { vertical-align:super; font-size:58%;font-family:Arial; font-size:12pt; text-decoration:none ! important; font-weight:normal; }
.T12 { text-decoration:none ! important; }
.T123 { color:#000000; font-family:Arial; font-size:12pt; letter-spacing:normal; text-decoration:none ! important; }
.T124 { color:#000000; font-family:Arial; font-size:12pt; letter-spacing:normal; font-style:normal; text-decoration:none ! important; }
.T125 { color:#000000; vertical-align:super; font-size:58%;font-size:14pt; letter-spacing:normal; text-decoration:none ! important; }
.T126 { color:#000000; letter-spacing:normal; text-decoration:none ! important; }
.T127 { color:#000000; letter-spacing:normal; text-decoration:underline; }
.T13 { text-decoration:none ! important; }
.T14 { text-decoration:none ! important; }
.T15 { text-decoration:none ! important; }
.T16 { text-decoration:none ! important; }
.T17 { text-decoration:none ! important; }
.T18 { text-decoration:none ! important; }
.T19 { text-decoration:none ! important; }
.T20 { text-decoration:none ! important; }
.T21 { text-decoration:none ! important; }
.T22 { text-decoration:none ! important; }
.T23 { text-decoration:none ! important; }
.T24 { text-decoration:none ! important; }
.T25 { text-decoration:none ! important; }
.T26 { text-decoration:none ! important; }
.T27 { text-decoration:none ! important; }
.T28 { text-decoration:none ! important; }
.T29 { text-decoration:none ! important; }
.T3 { text-decoration:none ! important; }
.T30 { text-decoration:none ! important; }
.T31 { text-decoration:none ! important; }
.T32 { text-decoration:none ! important; }
.T33 { text-decoration:none ! important; }
.T34 { text-decoration:none ! important; }
.T35 { text-decoration:none ! important; }
.T4 { text-decoration:none ! important; }
.T43 { font-size:11pt; text-decoration:none ! important; }
.T44 { text-decoration:underline; font-weight:bold; }
.T45 { text-decoration:underline; font-weight:bold; }
.T46 { text-decoration:underline; font-weight:bold; }
.T47 { text-decoration:underline; font-weight:bold; }
.T48 { font-weight:bold; }
.T49 { font-weight:bold; }
.T5 { text-decoration:none ! important; }
.T50 { font-weight:bold; }
.T51 { font-weight:bold; }
.T52 { vertical-align:sub; font-size:70%;}
.T53 { vertical-align:sub; font-size:70%;}
.T54 { vertical-align:sub; font-size:70%;font-weight:bold; }
.T55 { vertical-align:sub; font-size:70%;font-family:Arial; font-size:12pt; text-decoration:none ! important; font-weight:normal; }
.T56 { vertical-align:sub; font-size:70%;font-family:Arial; font-size:12pt; text-decoration:none ! important; font-weight:normal; }
.T6 { text-decoration:none ! important; }
.T63 { font-family:Arial; font-weight:normal; }
.T64 { font-family:Arial; font-weight:normal; }
.T65 { font-family:Arial; font-weight:normal; }
.T66 { font-family:Arial; font-weight:normal; }
.T67 { font-family:Arial; font-weight:bold; }
.T69 { font-family:Arial; }
.T7 { text-decoration:none ! important; }
.T70 { font-family:Arial; font-size:12pt; text-decoration:none ! important; font-weight:normal; }
.T71 { font-family:Arial; font-size:12pt; text-decoration:none ! important; font-weight:normal; }
.T72 { font-family:Arial; font-size:12pt; text-decoration:none ! important; font-weight:normal; }
.T73 { font-family:Arial; font-size:12pt; text-decoration:none ! important; font-weight:normal; }
.T74 { font-family:Arial; font-size:12pt; text-decoration:none ! important; font-weight:normal; }
.T75 { font-family:Arial; font-size:12pt; text-decoration:none ! important; font-weight:normal; }
.T76 { font-family:Arial; font-size:12pt; text-decoration:none ! important; font-weight:normal; }
.T77 { font-family:Arial; font-size:12pt; text-decoration:none ! important; font-weight:normal; }
.T78 { font-family:Arial; font-size:12pt; text-decoration:none ! important; font-weight:normal; }
.T79 { font-family:Arial; font-size:12pt; text-decoration:none ! important; font-weight:normal; }
.T8 { text-decoration:none ! important; }
.T80 { font-family:Arial; font-size:12pt; text-decoration:none ! important; font-weight:normal; }
.T81 { font-family:Arial; font-size:12pt; text-decoration:none ! important; font-weight:normal; }
.T82 { font-family:Arial; font-size:12pt; text-decoration:none ! important; font-weight:normal; }
.T83 { font-family:Arial; font-size:12pt; text-decoration:none ! important; font-weight:normal; }
.T84 { font-family:Arial; font-size:12pt; text-decoration:none ! important; font-weight:bold; }
.T85 { font-family:Arial; font-size:12pt; text-decoration:none ! important; font-weight:bold; }
.T86 { font-family:Arial; font-size:12pt; text-decoration:none ! important; font-weight:bold; }
.T87 { font-family:Arial; font-size:12pt; text-decoration:none ! important; font-weight:bold; }
.T88 { font-family:Arial; font-size:12pt; text-decoration:none ! important; font-weight:bold; }
.T89 { font-family:Arial; font-size:12pt; font-style:italic; text-decoration:none ! important; font-weight:normal; }
.T9 { text-decoration:none ! important; }
.T90 { font-family:Arial; font-size:12pt; font-style:italic; text-decoration:none ! important; font-weight:normal; }
.T91 { font-family:Arial; font-size:12pt; font-style:italic; text-decoration:none ! important; font-weight:normal; }
.T92 { font-family:Arial; font-size:12pt; font-style:normal; text-decoration:none ! important; font-weight:normal; }
.T93 { font-family:Arial; font-size:12pt; font-style:normal; text-decoration:none ! important; font-weight:normal; }
.T94 { font-family:Arial; font-size:12pt; font-style:normal; text-decoration:none ! important; font-weight:normal; }
.T95 { font-family:Arial; font-style:italic; }
.T96 { font-family:Arial; font-style:normal; }
.T97 { font-family:Arial; font-style:normal; }
.T98 { font-family:Arial; font-style:normal; }
.T99 { font-family:Arial; font-style:normal; }
<!-- ODF styles with no properties representable as CSS -->
.T1 .T103 .T109 .T110 .T111 .T112 .T113 .T114 .T116 .T117 .T118 .T119 .T120 .T121 .T122 .T128 .T129 .T130 .T131 .T132 .T133 .T134 .T135 .T136 .T2 .T36 .T37 .T38 .T39 .T40 .T41 .T42 .T57 .T58 .T59 .T60 .T61 .T62 .T68 { }
</style></head><body dir="ltr" style="max-width:8.2681in;margin-top:0.7874in; margin-bottom:0.7874in; margin-left:0.7874in; margin-right:0.7874in; writing-mode:lr-tb; "><p class="P19">EMBL Centre for Network Analysis <span class="T1">workshop 9-11 December 2015</span></p><p class="P32"> </p><p class="P32"> </p><p class="P33">Data integration and mining with graphs:</p><p class="P33"> </p><p class="P34"><span class="T109">Tensor factorizations for d</span>ynamic graphs</p><p class="P20"> </p><p class="P20"> </p><p class="P21">Jean-Karim Hériché</p><p class="P22">Ellenberg lab</p><p class="P21">Cell Biology and Biophysics unit</p><p class="P20"> </p><p class="P23"> </p><p class="P20"> </p><p class="P20"> </p><p class="P20"> </p><p class="P20"> </p><p class="P20"> </p><p class="P24">Summary</p><p class="P1"> </p><p class="P1"><span> <span class="T36">As gene networks become available for multiple time points and experimental conditions, there's a need for principled ways of detecting patterns and their evolution in such dynamic graphs. We will introduce a tensor representation of dynamic graphs and tensor factorization methods as ways of investigating patterns in these graphs.</span></span></p><p class="P1"> </p><p class="P1"> </p><p class="P50">Motivation</p><p class="P4"><span> <span class="T2">Many biological processes are driven by systems that evolve over time. New technologies make the dynamics of such systems more accessible with increasingly higher time resolution. In particular, data on gene networks can be acquired for multiple time points and experimental conditions. </span><span class="T4">Detecting patterns and how they evolve over time </span><span class="T7">and/or across experimental conditions</span><span class="T4"> </span><span class="T5">in </span><span class="T6">such </span><span class="T5">multidimensional data is becoming a common task.</span><span class="T8"> For example, one may have performed AP-MS experiments of several proteins at different cell cycle or developmental stages </span><span class="T9">and be interested in identifying protein complexes and how they change between time points. </span></span></p><p class="P6"> </p><p class="P25"><span class="T9">D</span><span class="T3">ynamic graphs</span></p><p class="P11"><span> - What is a dynamic graph ?</span></p><p class="P3"><span class="T3"> </span><span class="T10">A dynamic graph </span><span class="T11">can be seen as multiple instances of </span><span class="T10">a graph whose edges change between two instances. This definition includes time-varying graphs whose edges change as a function of time </span><span class="T11">but also multigraphs </span><span class="T12">(graphs in</span><span class="T11"> which nodes </span><span class="T12">are</span><span class="T11"> connected with edges of different types</span><span class="T12">)</span><span class="T11"> if you segregate each edge type into </span><span class="T13">a separate</span><span class="T11"> </span><span class="T13">instance of the </span><span class="T11">graph. </span><span class="T14">Examples of </span><span class="T15">dynamic</span><span class="T14"> graphs are protein interaction networks </span><span class="T15">and</span><span class="T14"> gene co-expression networks </span><span class="T15">obtained </span><span class="T14">at different cell cycle or developmental stages</span><span class="T15"> or under different experimental conditions (e.g. control vs treatment vs disease). </span><span class="T16">With this definition, a dynamic graph can therefore be represented as a series of adjacency matrices.</span></p><p class="P11"> </p><p class="P11"><span> - Different approaches to mining dynamic graphs</span></p><p class="P2"><span class="T3"> </span><span class="T17">It is common to treat dynamic graphs in one of three ways:</span></p><ul><li><p class="P60" style="margin-left:0cm;"><span class="Bullet_20_Symbols" style="display:block;float:left;min-width:0.635cm;">•</span>Aggregation: <span class="odfLiEnd"/> </p><p class="P63" style="margin-left:0cm;"><span class="Bullet_20_Symbols" style="display:block;float:left;min-width:0cm"><!-- --></span><span class="T3">All instances are combined into one, for example by using a weighted average of the edge weights across instances. This has the advantage of reducing the size of the data and </span><span class="T20">can </span><span class="T3">be a way of addressing changes in individual edges over long period of times. This is also a good approach to take when assuming that the instances </span><span class="T19">are</span><span class="T3"> not different from each other </span><span class="T19">(</span><span class="T18">as, </span><span class="T19">for example, in</span><span class="T18"> the kernel-based integration </span><span class="T19">approach seen earlier)</span><span class="T3">. However, this approach could reveal patterns that don't exist if nodes belong to different clusters in different instances and any temporal pattern or correlation is lost.</span><span class="odfLiEnd"/> </p></li><li><p class="P61" style="margin-left:0cm;"><span class="Bullet_20_Symbols" style="display:block;float:left;min-width:0.635cm;">•</span>Splitting:<span class="odfLiEnd"/> </p><p class="P64" style="margin-left:0cm;"><span class="Bullet_20_Symbols" style="display:block;float:left;min-width:0cm"><!-- --></span><span class="T3">In this case, each </span><span class="T22">graph </span><span class="T3">instance is treated in isolation. Patterns found in each instance are then linked and analysed in post-processing steps. </span><span class="T22">In addition to the difficulty in devising adequate post-processing steps, t</span><span class="T3">he </span><span class="T43">problem</span><span class="T3"> here is that there is no guarantee that a structure inferred in one instance is the same in another. </span><span class="odfLiEnd"/> </p></li><li><p class="P62" style="margin-left:0cm;"><span class="Bullet_20_Symbols" style="display:block;float:left;min-width:0.635cm;">•</span>Evolutionary clustering:<span class="odfLiEnd"/> </p><p class="P65" style="margin-left:0cm;"><span class="Bullet_20_Symbols" style="display:block;float:left;min-width:0cm"><!-- --></span><span class="T21">T</span><span class="T3">his approach assumes that </span><span class="T23">there's continuity between instances, i.e. structures do not change dramatically between instances. Therefore, one can constrain analysis of one instance on </span><span class="T24">the analysis result from another instance or analyse two aggregated consecutive instances. </span><span class="T25">This </span><span class="T26">approach c</span><span class="T25">an work in some cases but the continuity assumption is generally not realistic. Abrupt changes in patterns </span><span class="T26">will make it fail and it is unsuitable for analysis of temporal patterns over long periods.</span><span class="odfLiEnd"/> </p></li></ul><p class="P15"> </p><p class="P52"><span class="T3">All the above treat time or experimental conditions separately from the nodes. A global approach treating time/conditions and nodes simultaneously would better capture evolving patterns. </span><span class="T33">One of the</span><span class="T30"> first </span><span class="T3">such </span><span class="T30">approach did so by </span><span class="T32">extending the modularity coefficient </span><span class="T28">[</span><span class="T29">1</span><span class="T28">] </span><span class="T32">to </span><span class="T27">multiple instances of a graph [</span><span class="T29">2</span><span class="T27">,</span><span class="T29">3</span><span class="T27">] by defining links between </span><span class="T31">graph</span><span class="T27"> instances. </span><span class="T34">Here, we'll introduce another global approach which treats genes, time and conditions as multiple dimensions </span><span class="T35">of</span><span class="T34"> the data.</span></p><p class="P53"> </p><p class="P26">Tensors</p><p class="P12"><span> <span class="T37">- What is a tensor ?</span></span></p><p class="P12"><span> <span class="T38">There are different definitions of tensors used in different fields but they all come down to the same concept that tensors are a generalization of scalars, vectors and matrices: a scalar is a rank zero tensor, a vector is a rank one tensor, a matrix a rank two tensor... Therefore for most practical purposes, a tensor is a multidimensional array. It's easy to see that a dynamic graph represented as a series of adjacency matrices is a three-dimensional tensor.</span></span></p><p class="P12"> </p><p class="P12"><span> - <span class="T40">Terminology and notation:</span></span></p><p class="P14"><span> <span class="T42">Although the notation and terminology are not fully standardized, many papers now </span><span class="T42">follow the conventions in [4] which we also adopt here. A tensor will be denoted using underlined bold face e.g. </span><span class="T44">X</span><span class="T42"> to distinguish it from the matrix </span><span class="T49">X</span><span class="T42">.</span></span></p><p class="P12"><span> <span class="T40">The order of a tensor is its number of dimensions also called modes (or sometimes ways). The equivalent of matrix rows and columns are fibers and when used as vectors, they are assumed to be column vectors. Slices are 2D sections of a tensor. See Figure 1 for a graphical representation of these terms for third-order tensors.</span></span></p><!--Next 'div' was a 'text:p'.--><div class="P12"><!--Next 'div' is emulating the top hight of a draw:frame.--><!--Next '
div' is a draw:frame.
--><div style="width:6.6929in; padding:0; float:left; position:relative; left:0cm; " class="fr1" id="Frame1"><!--Next 'div' was a 'draw:text-box'.--><div style="min-height:5.3665in;"><!--Next 'div' was a 'text:p'.--><div class="Caption"><!--Next 'div' is emulating the top hight of a draw:frame.--><!--Next '
div' is a draw:frame.
--><div style="height:4.6583in;width:6.8744in; padding:0; float:left; position:relative; left:0cm; " class="fr2" id="Image1"><img style="height:11.8321cm;width:17.461cm;" alt="" src="data:image/*;base64,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"/></div><!--Next 'div' added for floating.--><div style="position:relative; left:0cm;">Figure 1: Tensor terminology</div></div><div style="clear:both; line-height:0; width:0; height:0; margin:0; padding:0;"> </div></div></div></div><div style="clear:both; line-height:0; width:0; height:0; margin:0; padding:0;"> </div><p class="P13"><span> - <span class="T41">Working with tensors:</span></span></p><p class="P12"><span> <span class="T41">Most of the tasks we're interested in rely on transforming tensors into matrices using a process called matricization or unfolding. Matricization consists in rearranging the elements of the tensor into a matrix. The most commonly used way of doing this is called mode-n matricization which takes the mode-n fibers of the tensors and arranges them as columns of a matrix (Figure 2). The mode-n unfolding of </span><span class="T45">Z</span><span class="T41"> is denoted </span><span class="T50">Z</span><span class="T52">(n)</span><span class="T41">. The order of columns is not important as long as it is consistent across calculations. Sometimes it can be useful to represent a tensor as a vector, in a process called vectorization. Ordering of </span><span class="T41">the elements in the vector is also not important as long as it is consistent.</span></span></p><p class="P12"><span> <span class="T42">Although tensors can be multiplied together, we will only need the mode-n multiplication of a tensor with a matrix in which the mode-n fibers of the tensor are multiplied by the matrix. This is written </span><span class="T44">Z</span><span class="T42"> = </span><span class="T44">Y</span><span class="T42"> x</span><span class="T53">n</span><span class="T42"> </span><span class="T49">V</span><span class="T42"> and can be expressed in matricized form: </span><span class="T49">Z</span><span class="T54">(</span><span class="T53">n)</span><span class="T42"> = </span><span class="T49">VY</span><span class="T53">(n)</span><span class="T59">. </span><span class="T60">See Figure 3 for an intuitive graphical example.</span></span></p><p class="P12"><span class="T57"> </span><span class="T61">Working with matricized tensors also makes use of</span><span class="T58"> </span><span class="T62">various</span><span class="T58"> matrix products: the Kronecker product, the Khatri-Rao </span><span class="T62">product </span><span class="T58">and </span><span class="T62">the </span><span class="T58">Hadamard products. </span><span class="T68">See paragraphs 1 and 2 of [5] and chapter 1.4 of [6] for a more detailed introduction to tensor algebra.</span></p><!--Next 'div' was a 'text:p'.--><div class="P12"><!--Next 'div' is emulating the top hight of a draw:frame.--><!--Next '
div' is a draw:frame.
--><div style="width:6.6929in; padding:0; float:left; position:relative; left:0cm; " class="fr1" id="Frame2"><!--Next 'div' was a 'draw:text-box'.--><div style="min-height:3.4098in;"><!--Next 'div' was a 'text:p'.--><div class="Caption"><!--Next 'div' is emulating the top hight of a draw:frame.--><!--Next '
div' is a draw:frame.
--><div style="height:3.4098in;width:6.6929in; padding:0; float:left; position:relative; left:0cm; " class="fr3" id="Image2"><img style="height:8.6609cm;width:17cm;" alt="" src="data:image/*;base64,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"/></div><!--Next 'div' added for floating.--><div style="position:relative; left:0cm;">Figure 2: Matricization of a tensor</div></div><div style="clear:both; line-height:0; width:0; height:0; margin:0; padding:0;"> </div></div></div></div><div style="clear:both; line-height:0; width:0; height:0; margin:0; padding:0;"> </div><!--Next 'div' was a 'text:p'.--><div class="P12"><!--Next 'div' is emulating the top hight of a draw:frame.--><!--Next '
div' is a draw:frame.
--><div style="width:6.6929in; padding:0; float:left; position:relative; left:0cm; " class="fr1" id="Frame3"><!--Next 'div' was a 'draw:text-box'.--><div style="min-height:2.2929in;"><!--Next 'div' was a 'text:p'.--><div class="Caption"><!--Next 'div' is emulating the top hight of a draw:frame.--><!--Next '
div' is a draw:frame.
--><div style="height:2.2929in;width:6.6929in; padding:0; float:left; position:relative; left:0cm; " class="fr3" id="Image3"><img style="height:5.824cm;width:17cm;" alt="" src="data:image/*;base64,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"/></div><!--Next 'div' added for floating.--><div style="position:relative; left:0cm;">Figure 3: Mode-n multiplication with a matrix</div></div><div style="clear:both; line-height:0; width:0; height:0; margin:0; padding:0;"> </div></div></div></div><div style="clear:both; line-height:0; width:0; height:0; margin:0; padding:0;"> </div><p class="P27"><span class="T103">Graph nodes </span>clustering by matrix factorization</p><p class="P41"><span class="T71"> </span><span class="T72">Nodes of static graphs can be clustered by applying clustering methods to the adjacency matrix. Among these methods, matrix factorization approaches have already been successfully applied to some computational biology questions (see [</span><span class="T73">7</span><span class="T72">] for a review on non-negative matrix factorization (NMF) in computational biology, [</span><span class="T73">8</span><span class="T72">,</span><span class="T73">9</span><span class="T72">] for examples of spectral clustering). Spectral clustering and NMF solve a problem of the form: </span><span class="T86">A</span><span class="T72"> = </span><span class="T86">W</span><span class="T85"> </span><span class="T84">* </span><span class="T86">H</span><span class="T85"> </span><span class="T72">+ </span><span class="T85">E</span><span class="T72">. </span><span class="T70">A more general form of factorization is the singular value decomposition (SVD): </span><span class="T86">A</span><span class="T69"> = </span><span class="T101">U </span><span class="T102">*</span><span class="T101"> S </span><span class="T102">*</span><span class="T101"> V</span><span class="T107">T</span><span class="T63"> </span><span class="T66">where </span><span class="T65">columns of </span><span class="T67">U</span><span class="T65"> and </span><span class="T67">V</span><span class="T108">T</span><span class="T65"> are constrained to be orthogonal.</span><span class="T63"> </span><span class="T64">SVD corresponds to the decomposition of the matrix into the sum of outer products of vectors (Figure 4) </span></p><!--Next 'div' was a 'text:p'.--><div class="P44"><!--Next 'div' is emulating the top hight of a draw:frame.--><!--Next '
div' is a draw:frame.
--><div style="width:6.6929in; padding:0; float:left; position:relative; left:0cm; " class="fr1" id="Frame4"><!--Next 'div' was a 'draw:text-box'.--><div style="min-height:1.7583in;"><!--Next 'div' was a 'text:p'.--><div class="Caption"><!--Next 'div' is emulating the top hight of a draw:frame.--><!--Next '
div' is a draw:frame.
--><div style="height:1.6283in;width:6.6929in; padding:0; float:left; position:relative; left:0cm; " class="fr4" id="Image4"><img style="height:4.1359cm;width:17cm;" alt="" src="data:image/*;base64,iVBORw0KGgoAAAANSUhEUgAAAxUAAADACAYAAAByBk4LAAAKL2lDQ1BJQ0MgcHJvZmlsZQAASMedlndUVNcWh8+9d3qhzTDSGXqTLjCA9C4gHQRRGGYGGMoAwwxNbIioQEQREQFFkKCAAaOhSKyIYiEoqGAPSBBQYjCKqKhkRtZKfHl57+Xl98e939pn73P32XuftS4AJE8fLi8FlgIgmSfgB3o401eFR9Cx/QAGeIABpgAwWempvkHuwUAkLzcXerrICfyL3gwBSPy+ZejpT6eD/0/SrFS+AADIX8TmbE46S8T5Ik7KFKSK7TMipsYkihlGiZkvSlDEcmKOW+Sln30W2VHM7GQeW8TinFPZyWwx94h4e4aQI2LER8QFGVxOpohvi1gzSZjMFfFbcWwyh5kOAIoktgs4rHgRm4iYxA8OdBHxcgBwpLgvOOYLFnCyBOJDuaSkZvO5cfECui5Lj25qbc2ge3IykzgCgaE/k5XI5LPpLinJqUxeNgCLZ/4sGXFt6aIiW5paW1oamhmZflGo/7r4NyXu7SK9CvjcM4jW94ftr/xS6gBgzIpqs+sPW8x+ADq2AiB3/w+b5iEAJEV9a7/xxXlo4nmJFwhSbYyNMzMzjbgclpG4oL/rfzr8DX3xPSPxdr+Xh+7KiWUKkwR0cd1YKUkpQj49PZXJ4tAN/zzE/zjwr/NYGsiJ5fA5PFFEqGjKuLw4Ubt5bK6Am8Kjc3n/qYn/MOxPWpxrkSj1nwA1yghI3aAC5Oc+gKIQARJ5UNz13/vmgw8F4psXpjqxOPefBf37rnCJ+JHOjfsc5xIYTGcJ+RmLa+JrCdCAACQBFcgDFaABdIEhMANWwBY4AjewAviBYBAO1gIWiAfJgA8yQS7YDApAEdgF9oJKUAPqQSNoASdABzgNLoDL4Dq4Ce6AB2AEjIPnYAa8AfMQBGEhMkSB5CFVSAsygMwgBmQPuUE+UCAUDkVDcRAPEkK50BaoCCqFKqFaqBH6FjoFXYCuQgPQPWgUmoJ+hd7DCEyCqbAyrA0bwwzYCfaGg+E1cBycBufA+fBOuAKug4/B7fAF+Dp8Bx6Bn8OzCECICA1RQwwRBuKC+CERSCzCRzYghUg5Uoe0IF1IL3ILGUGmkXcoDIqCoqMMUbYoT1QIioVKQ21AFaMqUUdR7age1C3UKGoG9QlNRiuhDdA2aC/0KnQcOhNdgC5HN6Db0JfQd9Dj6DcYDIaG0cFYYTwx4ZgEzDpMMeYAphVzHjOAGcPMYrFYeawB1g7rh2ViBdgC7H7sMew57CB2HPsWR8Sp4sxw7rgIHA+XhyvHNeHO4gZxE7h5vBReC2+D98Oz8dn4Enw9vgt/Az+OnydIE3QIdoRgQgJhM6GC0EK4RHhIeEUkEtWJ1sQAIpe4iVhBPE68QhwlviPJkPRJLqRIkpC0k3SEdJ50j/SKTCZrkx3JEWQBeSe5kXyR/Jj8VoIiYSThJcGW2ChRJdEuMSjxQhIvqSXpJLlWMkeyXPKk5A3JaSm8lLaUixRTaoNUldQpqWGpWWmKtKm0n3SydLF0k/RV6UkZrIy2jJsMWyZf5rDMRZkxCkLRoLhQWJQtlHrKJco4FUPVoXpRE6hF1G+o/dQZWRnZZbKhslmyVbJnZEdoCE2b5kVLopXQTtCGaO+XKC9xWsJZsmNJy5LBJXNyinKOchy5QrlWuTty7+Xp8m7yifK75TvkHymgFPQVAhQyFQ4qXFKYVqQq2iqyFAsVTyjeV4KV9JUCldYpHVbqU5pVVlH2UE5V3q98UXlahabiqJKgUqZyVmVKlaJqr8pVLVM9p/qMLkt3oifRK+g99Bk1JTVPNaFarVq/2ry6jnqIep56q/ojDYIGQyNWo0yjW2NGU1XTVzNXs1nzvhZei6EVr7VPq1drTltHO0x7m3aH9qSOnI6XTo5Os85DXbKug26abp3ubT2MHkMvUe+A3k19WN9CP16/Sv+GAWxgacA1OGAwsBS91Hopb2nd0mFDkqGTYYZhs+GoEc3IxyjPqMPohbGmcYTxbuNe408mFiZJJvUmD0xlTFeY5pl2mf5qpm/GMqsyu21ONnc332jeaf5ymcEyzrKDy+5aUCx8LbZZdFt8tLSy5Fu2WE5ZaVpFW1VbDTOoDH9GMeOKNdra2Xqj9WnrdzaWNgKbEza/2BraJto22U4u11nOWV6/fMxO3Y5pV2s3Yk+3j7Y/ZD/ioObAdKhzeOKo4ch2bHCccNJzSnA65vTC2cSZ79zmPOdi47Le5bwr4urhWuja7ybjFuJW6fbYXd09zr3ZfcbDwmOdx3lPtKe3527PYS9lL5ZXo9fMCqsV61f0eJO8g7wrvZ/46Pvwfbp8Yd8Vvnt8H67UWslb2eEH/Lz89vg98tfxT/P/PgAT4B9QFfA00DQwN7A3iBIUFdQU9CbYObgk+EGIbogwpDtUMjQytDF0Lsw1rDRsZJXxqvWrrocrhHPDOyOwEaERDRGzq91W7109HmkRWRA5tEZnTdaaq2sV1iatPRMlGcWMOhmNjg6Lbor+wPRj1jFnY7xiqmNmWC6sfaznbEd2GXuKY8cp5UzE2sWWxk7G2cXtiZuKd4gvj5/munAruS8TPBNqEuYS/RKPJC4khSW1JuOSo5NP8WR4ibyeFJWUrJSBVIPUgtSRNJu0vWkzfG9+QzqUvia9U0AV/Uz1CXWFW4WjGfYZVRlvM0MzT2ZJZ/Gy+rL1s3dkT+S453y9DrWOta47Vy13c+7oeqf1tRugDTEbujdqbMzfOL7JY9PRzYTNiZt/yDPJK817vSVsS1e+cv6m/LGtHlubCyQK+AXD22y31WxHbedu799hvmP/jk+F7MJrRSZF5UUfilnF174y/ariq4WdsTv7SyxLDu7C7OLtGtrtsPtoqXRpTunYHt897WX0ssKy13uj9l4tX1Zes4+wT7hvpMKnonO/5v5d+z9UxlfeqXKuaq1Wqt5RPXeAfWDwoOPBlhrlmqKa94e4h+7WetS212nXlR/GHM44/LQ+tL73a8bXjQ0KDUUNH4/wjowcDTza02jV2Nik1FTSDDcLm6eORR67+Y3rN50thi21rbTWouPguPD4s2+jvx064X2i+yTjZMt3Wt9Vt1HaCtuh9uz2mY74jpHO8M6BUytOdXfZdrV9b/T9kdNqp6vOyJ4pOUs4m3924VzOudnzqeenL8RdGOuO6n5wcdXF2z0BPf2XvC9duex++WKvU++5K3ZXTl+1uXrqGuNax3XL6+19Fn1tP1j80NZv2d9+w+pG503rm10DywfODjoMXrjleuvyba/b1++svDMwFDJ0dzhyeOQu++7kvaR7L+9n3J9/sOkh+mHhI6lH5Y+VHtf9qPdj64jlyJlR19G+J0FPHoyxxp7/lP7Th/H8p+Sn5ROqE42TZpOnp9ynbj5b/Wz8eerz+emCn6V/rn6h++K7Xxx/6ZtZNTP+kv9y4dfiV/Kvjrxe9rp71n/28ZvkN/NzhW/l3x59x3jX+z7s/cR85gfsh4qPeh+7Pnl/eriQvLDwG/eE8/vMO7xsAAAABmJLR0QA/wD/AP+gvaeTAAAACXBIWXMAAAsTAAALEwEAmpwYAAAAB3RJTUUH3wwJCzgOazbYzAAAIABJREFUeNrt3X1cVGX+//H3xDCjECgWlZatllb6++pu1lcrwbvWm9JvIBjad9UWb9M03LQ2U9pS0l3TNlO78ybFthXvK21D86bAynZ1SzeoNKG1tGC/oENMDs54fn+AzAw3wgACg6/n4zEPZ845g+dc13XOXJ/rXNd1TIZhGAIAAACAGrqMJAAAAABAUAEAAACAoAIAAAAAQQUAAAAAggoAAAAAIKgAAAAAQFABAAAAgKACAAAAAEEFAAAAABBUAAAAACCoAAAAANB4mUkCAABwKTCZTE3+GA3DIKMpDw1ShggqAAAAFSYqyZQH1KoMEVQAAABQcSRgQK0wpgIAAOASk5iYqHPnzskwjCb5AkEFAAAALrKDBw/qySefpAIOggoAAADUzIYNG5SZmanp06fr3LlzJAgIKgAAAOCb5s2bKyUlRd99950SEhIILEBQAQDAxWIymap8Af7KarXqjTfeUF5eniZNmiSn00mioObXS+Mid6bjgls5+jECQOMPKi50ra7OejSe37+q8qupl9fKtjt79qwmTpwok8mkV155RYGBgZdEWjT18lDf50i9BBVkGOlS3R9Xygr5DTS1oIJy3njShKCi8u2cTqcmT54su92uVatWyWKxEFRwfhJUcFFtuj/O8J+KOfl9aeU31y2u9QQV/h1USNK5c+f0yCOPKDc3V2vWrFGzZs0IKjg/CSq4qPLjTJqS3+Q3KMeUY4IK37Y7d+6cZsyYoezsbP3lL39R8+bNCSo4P6uFgdoAAAAorhhedpkWLVqkm266Sffff78KCwtJFBBUAAAAwDcmk0nz589Xt27dFBsbq4KCAhIFBBUAAADwPbCYM2eOIiIiFBUVJZvNRqKAoAIAAAC+mz17tu655x7de++9ys/PJ0FQKTNJAAAAgMo89thjslgsGjRokN59911dccUVJAoIKgAAqE9Mj4ymICEhQVarVf3791dqaqrCw8NJFBBUAABQH5iuEk3JQw89JKvVqr59++r999/XNddcQ6KAoAL+iRY/8hsA0HDi4+NlsVjUr18/7dy5U9deey2JAoIK+Bda/MhvAEDD+81vfiOz2aw+ffpo165duv7660kUMPsTAAAAfDN8+HA999xz6tu3r7Kzsy+wpUt2m002m012exEJV4WjW6bJZDJd+DV8vRrjIwkJKgAAAOCz6OhoLV68WL1799bRo0fLrLXrn1uXqZfZrOAWLdSiRQsFB1tlGjZNKXsz1ZSf0/2vtWNksvSSydJLm4/aq9i6SDuTYmUymXRZ6FhlnrtSiohQTEyMYmIi3JtFxpYuu6tjcKM8bpNxkfsYmEwmujGQLtU6ZsoK+Q1QjsFv78U/vrpOh9TUVI0fP147d+7UzTffLMmmDWNbKG5V5d95NcOmCZ1CGjQtLlZ5OHVgucJun1D8YdYeOZP6KKCyjXP2qVebCKW5JPVbrrxd4xTmEZhtGBus4RvG6F+5K9XZ2rjPEe5UAAAAoMYGDhyo1atX6+6771ZGRoZ+2POiV0DxxPIUpaZu0bK58aXLmjXh9GjZLVov9S758PxS/eMCzwz819sriwMKSc8kDvYIKIpZSv51Ohv/cRNUAAAAoFb69eunN998U/3799fuHbuLFwZGatcJp+aPi9OAAdGaPHuVCk8c0KzLpTNNOTFM4brvsZnF73/epJe3f1nxdo4jWpnwevFXWibogTtbV/onA/3gsAkqAAAAUGu9evXShg1r9NBze4orysHd1Dbcu+NPUOtuSjrl0NiL2PWpMbi2zyiNLbkdk5yQrKwK7jT88FGKXigZchG1cKw6Wv37mAkqAAAAUCfuuuvXeu3xwZIk49RiPf7i3vKDsgMslY8xaCqCO+nhhTHF6ZA3Xxv353qvN/K1/ZnE4veBkZp6X2e/P2SCCgAAANSZQVH3lL7fOr2vLh+7SAdO2i+5dOg6dErp+8dffE+eQyvsR3do3AclH6b8Xj3D/T/MIqgAAABAnWnZ4yEdXOMelK1VM3R7m2AlrNih3EvoURUBbXpoe0LJh/Wjtad0etkiffT6iNLt1sT3krUJHC9BBQAAAOqyOq1bR69SZupSr6Uvjh+oq68cq/STl0pkEaTIMcmln2JXfyqXJOX9XXMWFC8ztV6qe7pUPr7kfEqdJagAAADApeiWAQ/LeTpLCyb8unSZUbBKvW6epAP5rksiDUK6DNJL5+eJfX6pPiuUvt3pnkZ2yorBCr/A9y0hkgJC/GL2Jx5+11AJz8PvSBPym/wG5Rj89jbA8TVEOux/+2XdFTVZ584vWLRfxqPdGzQt6isdvt/xpK4bOF+S9Nuly9UmZbzmpUmmkDH67ORKdQ1uGucIQQUXNn6cQX4DlGPyk6Diosv8cKW69B5X3AUoLkWnU+IUegkEFSrM1LgrO2tlmYdz3Llovz66iIFVfZ8jdH8CAABAncnemaL0k+W7N3XqNUqvxJV8ePsv+tFxiSSIx/Synp6M+1WTOkyCCgAAANQZ1w/rFXnjcKUeLfBeUfiNvthW8t7Yrw/Xr71k0sRzellJUlyKel1nIagAAAAAKmRpK/28SYM6hiomaYV27PtUe7ev0LCwzqVPkL7tieV64bnntGrVqksiSQLa9HRPLytpyfS+F63rV0MxU/IBAABQZ5VLjwb4LYnjtaXMelPLBK197H905cN3aODAgXI4HJo0aVJTj7SKp5ddPFqm8LmK6hbe5I6QOxUAAACoM78YukjHD2xTUnxEuXW/XbhF337/gjoFS+Hh4Xr//fe1evVqLV68uMmnS0iXQVrUUrpv6TC1bYLN+sz+1FAJz+xPpAn5TX6Dcgx+exvg+OozHVxFdtkLHXJKsgaHKsgSUG6bU6dOaciQIYqOjtaMGTPqLS04f+s2TQgquLDx4wzyG6Ack58EFQ3KZrPpvvvuU//+/TVr1iyCCj88RxhTAQAAGpwr96BeX/+xZLVWua3DId0RM1q3tbaQcE1EaGiotm3bppiYGDkcDj3zzDMymUwkjD8FJNyp8L9IsKkeM2WF/AYox5cue+ZaBXceXe3tXz1k04QuIfz21uD4GnM62O12xcXFqUuXLpo3b16NAwvuVNR//ZQ7FQCAplQ1VfbB/frs36clBapFm+v1X506KzwkgKRp5MzNWik2KELGoKuq3DZ3h0lXNidPm6KgoCBt2LBBDzzwgKZPn66FCxfqssuYV8gvAhLuVPhfJNhUj5myQn4DteLI1vMD2mv6h+VXPbMjS0/1b0c55rrEnQo/SQeHw6FRo0bp6quv1uLFi30OLLhTUf/nCEGFP2SaM1fvrl6vLFll9fGEbHNXnIbeWrO5kItys/XRp5/p1FkpMKilrr/p/6lzu3AFXKRjpqw0tLpt4SW/Ud++SRmjDiNeL/0c0VNK31f8PmptpraOvIVyzG8vQYUfpUNRUZHi4+N1+eWXa9myZTKbzXWaFpy/dZsml0b3J+OkXr6ijSbnS3cu2q+PHu3uX/vv+I82T52ilWd8/2r0irtrFFRk71io9gMfK1/Ywufqm+Oz1d7KidekXIQWXsA3Lv1r6yva+q98hf3XvXooulsNGjBKnk8bGKm07z9URLhUkHtEu199Qh+3akYSN/YSUHhSn39xXKpGxdHplFp3+qXaNni3tiLtTLpbAxLTZQqfq6+Oz1ZH64Wvtc8OaK/ZH0p3zdqmHUmDFUzWV8pisWj16tWaOHGiJk6cqFdeeUWBgYEkTCN1SQQVBYe3aXJ+8fuPZy/QgXEbdZtfPRvdqVOumn3zB52tQQUzU0lRHgFFRISUnl78/kyWCpySCCqaVIXsm61zvAIKzxbegz+WiWaL7LKdcSogOFTBdGluIpXxRhHZKvMvU5S4UVLcLzQqupt8v0zbiv85m6bIuCR9sjZBPa7rqKjZmxRFQWn8JeDf7+u2Hhd3oPZF+X3Ocv8+/lzV76PzZ2V9Wvz2oyOFcpHtVQoMDNRrr72myZMnKz4+XqtWrZLFwqxfjdElMPLFrt2rJrg//rxJS9770r8OIfhmvZCRoYwavDbE3Fyr//rOReky0tJkOE/ryCfrFHN7ezU3e6fvW2NNMg1fr0LOp4avkCUmaspfv6hBXni08OYYSks3ZMv5WlvnxuiW8y28jly9u2yaTNZgtWjRQpc376WlO4+S9H6f942HpTSKsNYoMGrXf4rGnr8hsTdRd7QNVcyzW3WyiFLiF8y+VRSbNZJmUc+9rrIN3SyFeNS8aJepZtEwm/XKK6+oZcuWGj16tBwOB4nSGPOpqR+g68R+RZd58nvypGT9IWae2vvN0Vt0XYdODfI/fzw9QnOv26+EuO7q0GO4Nu7mpGmaFbKqW3jtx97T4CkeJ9PZNE0d0FGWQ3ma0CWMDPDjynijU8M7yQGtumnFjxnqPKazpm8qXrZl9lBtfX6mPjs6V13DyqaOS3ZboczBobJQu2twQR2HyVFYWO3uT9YgWqsvJZdddplefPFFTZ8+XSNGjNCbb76p5s2bkzCNKY+a+gEe2rK03DIjb77Wpp8k9ytjvUkPvxpf+vGp4T3UMnSsthwkzZpqhaxaLbzGGanfch077ZRhOHQwOUGSNPH1j0SbkZ/mvatINptNhZX1wXDZZbPZZC+q4fqq/nuXq/Qlw6EC2/kY16GisuurnQad9OhGhzJ3JysywH3N/+Xv3ysup45M/S7YJNOwaRobaVZwixayhgzTun/mUn4aXIAsQUGyWCxVvoKCLLTyX6KBxfPPP6+bb75Z999/vwoL6SNBUFFfCjO1bMZmSZLp6oU69PmW0lV/mLtd/vQTUmS3yWbz/VVUow6bAbp19CodSX3OXZ8sWKWY29po5tbDnDWNRF1WyM638C6KdS/bMnuorm39pA7lF3/f3PoenXhnnNqHBkiy6NaYscWByPeFBBX+mPfO7/T8lVa1aNFCIdcu0nFnRetLurpdl6QsX9dXwX4kRWazufRluqyVRm0sWbl+tFqZTF7rk7+0V5UqOrpvhw7nFkmy6Ja+o/Rh4deaFlS81rRhp/7tWVA3LVa7qek6kLZOsc5N+t/eTyiT+gnQ6JlMJs2fP1/dunVTbGysCgoKSBSCiovv+31rS2dMum/hYHXpOkBrh5Ws3D1efzvsJwXRkanJV7RQixa+v+L+WvPxIx0GzJAjJ0NrZ0aULvvj0K7anE0H5YZW9xUyVdnCawm7Tq2DPLb36KJAi6Ef5r0jXxnnx+DbM5TvuMD6M1kq8HV9VZy+XUfOnK0qOHZo/6yB6nqVVQkvbdXh7JPK/uoLHahgvwrOSdErDikxrqe6RQzXn9bGU7AAPwss5syZo4iICEVFRclms5EoBBUXkZGrt+fNL34fGKkZAztKCtKQGe7uUA8u2eUfgxqdNf9qyxp8x2U7oh17M4srkuGdNHJemrI3J5Su3/vZvzlzGrxM1GWFzMcW3hJfbn1VK89Iv3+wO1Mi+mPeW8PU+XyXt6DOCis7Y431St3Woxbrq2C9NlJ7UlO1Z88e7dmzR+m71yn2/CjX5rFat3tP6brU1D3qe11QlX/TUjJ79osPD1XX9m3U/pdDlVZy+Ebi/V5TfbawMi0l4O9mz56te+65R/fee6/y8/NJkAbWZAdqFxx+T5M/KH5/59NzFBFe3JbasnucXuo9pXjd8qFKf8qhgdc18sFe5ubqPDhCMcZVvkXyuTm6sQZzszu+/0QD+46Wes/U5mcf0B03hOiLLw6Urrdxo6LBna+QqWRavUDjR/154AhtOltSIds+RVebirctKpLaX7BCVtzCO/ID6ZFlWzTu3h4KsVXcwnteUdZ2dRqxWKbwuXp4QDsyxB/z3nydHv1PoeLzHLK0Cis/PbC5tSbtdWhEfqGCwsLKz5LpsT44NMzngc4Boe3Ux6vsuHR6srRpsaSRIxXdt4+PM1cHadCC/VrW8U96eP5mrzWPLN+jp8f19Fp2iqIENAmPPfaYLBaLBg0apHfffVdXXHEFiUJQUZeKlLbKPdf1x8eOat8+6exZyTBL+f90b/nM+r9r4KM9G3ktop0e3ZimR+utVJQEWR/MV0zEfO91gZEa17c9Z04Dq+sKmWcL74tl1pVt4VVhpuZ0HSJJevvTR9XWTH74bd4HBCks/EIBp0VhYZZarPepOUNnz/dIPV2kmjwOJ6R9d02et0mTn7aroNAhpwJkDQ4VkwQBTVtCQoKsVqv69++v1NRUhYeHkygNoEl2f3Kd2KfBntPIrhyviIi+6tu3r/pF9tUsj653H8/+sw7QFc9LUMd7tH/zUsVGlFnRe6bey3ir9K4PGpPyFTIfcry4hXdmTLk1jyzfozzPoNvI1Ru/7axnf5Je3Z+jIe2CSHq/zvtGqrYPJ7UEKSQsTGFhFQcUIZdJLS3uaNiwhFKMUGOlN+8DQmT42MjCw+/qzkMPPaSpU6eqX79+KiqqfpcKk8nEy+NVG02yjfHQ9qXV37jkYXir427hjPT4Re8+9GFtHPqw7DabHC6XAsxWhYZQgWyqFbLqtfDa9f7smNJBwalvPqv9rxZIp75Wu7GvK/HeDqS9v1fGG7pydr6BJ+si/ifWTvpzoeG1qMPQF3RuKMUHNSpQurZ9hKR0GacW61juAnW+UJdqx886frbk/bXBPt+Nw4XFx8crMDBQhw9Xb6ZKwzBItDrU9IIKR6aSp5VMI9syQX//ep66BJcd62yW6//2Kf7Gftp01h8fhld/gkJDVa1Qgoa+plEhswQpxFJxjn+/PUn956UXf+gpbV7svh344HAnGdDUK+MX/2qjmDV5ynnJKXOzFgz+h58I0NUdb5NUfG3cuPeYhoysvJHyy78lF49/kvTgHTc3aFBR21ZpoFyZMi5ymGYymeo1Evx+R5KuG5goSYp+6YC2TOpWyZYufZTURz0Tiy8Ez+w5oaf6tK7Xk/lSi5CrOuZLMU3qksuer7zC4gpZWIiF/CbvQTlGPeRXUdZ2WW8YUvp5yZ4sTenTrlydIzv9dbWPHF+6ZFOWQzHtLI3++IBLM6gwcvVy36uKZ3YKjNSub/eoX+vK+/+7jm+X+fqSC0G/5crZNU71NbSHoII0Ib/Jb1CO4f9BhVSk95+0qr/nvCaxCUoeea9ubtNS9tyvtHPVaM3znJRs1g6dSepf53cqKI8gqKgjBYfWKvSXJbM+/W6bzjw/uIoT1q63xgYrelXxp1cP5WlClzCCCn6cQX4DlGOCiupz5uqtp2IUPT+9yk3vmrVFW5+J1sWY84TyiIbUpGZ/OvrpntL3a+J7VaMFIEj9pieXfvpb2hFKBAAA8I05XFHz0nQiY7cWJsRUuEnMtIXanXFC+5IuTkABNHjQ3tTGVPhNwnOngjQhv8lvUI7RJH97XUV22QrdTxAtnk0voMkcH1BhbE0SAAAA1J0AS5DCLEzDjkvLZSQBAAAAAIIKAAAAAAQVAAAAAAgqAAAAABBUAAAAAABBBQAAAACCCgAAAAAEFQAAAAAIKgAAAACAoAIAAAAAQQUAAAAAggoAAAAABBUAAAAAQFABAAAAgKACAAAAAEEFAAAAAIIKAAAAACCoAAAAAEBQAQAAAICgAgAAAABBBQAAAACCCgAAAAAgqAAAAABAUAEAAACAoAIAAAAAQQUAAAAAEFQAAAAAIKgAAAAAQFABAAAAgKACAAAAAAgqAAAAABBUAAAAACCoAAAAAEBQAQAAAAAEFQAAAAAIKgAAAAAQVAAAAAAgqAAAAABAUAEAAAAABBUAAAAACCoAAAAAEFQAAAAAIKgAAAAAgOozkwQAAOBSYTKZSASAoAIAAKBmDMMgEYCLhO5PAAAAAAgqAAAAABBUAAAAACCoAAAAAEBQAQAAAAA+qpfZn5i+DQDgr/gNA4BGEFQwfRsAwF/xGwYAjSSoADzR4kd+AwCAJvibb9AMAwAAAKAWGKgNAAAAgKACAAAAAEEFAAAAAIIKAAAAAAQVAAAAAEBQAQAAAICgAgAAAABBBQAAAACCCgAAAAAgqAAAAABAUAEAAACAoAIAAAAAQQUAAAAAEFQAAAAAIKgAAAAAQFABAAAAgKACAAAAAAgqAAAAABBUAAAAACCoAAAAAEBQAQAAAICgAgAAAAAIKgAAAAAQVAAAAADwL2aSAACAhlVkt+mMs7q/3M0UGmQh0QA0KibDMAySAQCAhmLXhvuDFbexmpv3S9bpXaMUSsIBaES4UwGgfrnsys05LWdt/kazFmodFkRa4tJ0pRRAKgBoZLhTAaBe2Y+sVfBNo2v3R2ipRVOLtYvscpyPtM1W2f75ilrfMUWmkDH6+JslujVY7kDcbFWQhbACQOPCnQoA9Yy+4EBZAZYgeQ6TMLe6svR9aFCQLEGcOQAIKgDUtSK7bCWjOoNDQ/2qK4S52eUVLn8ieYtuVYEcVf4FhyzX3K5gSgEuMleRXbbC4hIZYLUqOCio3s41J8kPgKACwEWu6uj9p4PVf37xpwX7c/RY93C/2XtL28E6snmmOsbM91peaL1FcXG3kL2oXlydtV2/7jhExp0RSjdH69h709XeWp1v2rUzaZQGpOYo8uN09X87S4n3tvPaouD4Qa19+Vk9PH+z91ebx+q51yZoeNTdahsSINkOatzVt+mr2yNk+oc07tN3NbpLSLX2335kiwZ1fV7G7dK+z2/Sx9+8ph7hdGkC4L94TgXgb/I+0ZwF7o+PL3pPNj87hA5Dn9be5yK8li0Z3klz9n5H/qJanM6flOaS0tPTZTqQoQIfmvZPZW2W0tOV5pK+yTvjte7o9iSFXn9b+YBCkn7epMdGDdQvrp2gDIekkLa6s0fxPqSdSdeDS3apsJoNA39/PUZpZ9KVnp4uXd5NbQkoABBUAKhPX25fqTSXx4L1o/XuUbufHYVFvadv1tph3kv/0LetNvvdsaAxCPSp9FXMfiRFHYckVjOokWQK1+A/POdeuHyo0k+6qtEwcECJng0DK6LUhiwEQFABoN44s/XG5NfLLX5g9T65/O1YTOEauTpDs8oMsRjWbaoO2Mhq1De7dv5xhEeUEqk16Ud02uGUYThly8nSnuS55YKYa+6K8irDT285UI2GgVdKGwZMIWP0YO/rSH4ABBUA6s9/PtmoZ3+qYMWCufo41+V/BxTcSc9k7FakR88Po2CVbo9ephP1UY3MP6ns7GxlZ2frZG6+iqqbhC6XXC6XilyuC2zikstVJFejyBaXXEXV2R+Xis5vd8kF7Hn6xqPH05L0tzS6ZweFWgIkBSgkvJ36jJotx4/7Nc0qnT2/obWjRr4UX/q9/U+8qkOF1W8Y6PHHierErAMAmgAGagP+wsjXWy88VvG6s2la9PbnihjbrRaVqly9u3q9smSV1YevORwOtbkrTkNvrdlg8YC2ffX2/tcUdvsE98I9U3Tt7Jt0Jqm/T/tSbbYjWvnUGI1bnO69PDBSM194VJN+G622lT5bz663JgQrelXxp78eKdSIDt4bF2VtkfWGmOIPcSn6KSWuQWer+iZlujqMWCxJMoXP1TcnZqt9uau/TRvub+F+qvOz6TKe7Ol74Ht4u1I+zJbV6lMpksPUTkN/O1htGmpogaNAGR7DK65sVfH+W67qrudzu3stu2XwWEUGvK40V3FQ/OYHiepaZvB3ZQ0DT9/3K65tAJpIPQWAXyj8erMhqfS1JuOEsW9uROlnU8gYI+OnWvwHP2UYY5vJ6/+o7it6RWatjy9zXUK5vzs1JbPuE/LMcWNRywsfz6uHbBfKCWPrGM98sFWQV+vcf29civFTA5cd5/epXse3IP1EuW0cx7aVSYO8muVjcnyNypCaxxqf/+TL+bCuhmXfO/8eXFtSxs5mGbMudy+/a9YW43S198Zh7Jzp/q7p6oXG9xVud9pYO8zjmMdvqbRsnD++Wp/XAFBP6P4E+IXi2WLOM4XPVd9bWuv24VPcDQQFq/TyB9m1+D+cOlXDPi8/uDuD1Ngtwxdo79zyM0K99mlunaak/dgeTT/l/hwzbaGSk5fryXj3/93MoxX/h4NbteilrTruqOF/6DU+pEi5332n3IKiei09AW36aHuC+/PjT21Xfpny9Y9Nf3SXr9ZLNbRLWA3397R/nmLmtuo/1f3xo2eHqsW4Fcqq1rwBFt0Vv859Lv44Q9sOF5Tbqihrl0Zt9CjfD/Wu1h2sswIAP7iMkgSAHygzW8zopSPU1iSpwwCtHabSisrSMZv02Mnpxet8FXyzXsjI0Nwa1GBCrrmxDg7Sot6zNmvFZ1dp3Cb30okRsep47H31va6Onidsdv8dU6uZeuH5kvQaNU6z/nREm+fNlzmwpA+OI1NT7hiqTWeltNBMbR1Zu+dofLvtcbX7n8VSv2T9tGtUPXaJsqjPxHXS4pKByLvHK/XL/9WIW0q6bdkytCrR3RXs8TVRCq/h/t4wZLEyDiX5/utiCtENDTq2IEARU3ZL8/u5F60crxtWjteS7YcUf2+XCx5/UIcBWhGr0rI7ccku/ea1aI/vuPTxX573ahiI6hpWeTE9/5DIgBCfZrYCgAbDzRqg8fPqUtI81vjEo2dK7idLvbqRLNmf498HezrDqxuKJMPUaqaRcbpu/rxX1yTJGJq0xTjhqGTjczml3VXWlHYH8rH7U5y7+1P2OzOLl/VLrv8uUefyjBW9PdL10R3GmfP7tdnd9czUMsH44kwj2N/67v5UwnZoXcXds3olGKmZFz63Tu5+zus7751wepTrA0ZsoEfXvvVHuLABoPsTgHpUZraYO2dP0e0eDZxXdo/Ropbuz1P98GF4XkI7KfYPZZads8te4bRFvnfPCWrfw2sK0C2zh6rN5b20fGemyvVwMoVr5AZDTqeh0V3Can1ovxgyVznHjyvvnf+t/4HbpjBFJXk8U2HJXO3LlWSc1KYxi0sXRy0cq87WRrC/DSSky3AV/jtd08oO1P9wsQZ2ukrxKz+tdGasayKHlZle9vPS99/8LVmbzt8FbB6rBwd24NoGoEmARfG1AAAJE0lEQVQhqAAaubKzxdz+y2tky8/Vydxc5Z48qfwCs26b5PGFWjwMr8huk83m+6uoDucf/XZ7krp5THJlapmgz469oNvCyk8L9O22x3VV27a6Kjqlmk8ylmRup2f+fcj7+Rhn0zRhQGc165ukzHyXV9Cyb22Sps9IUvrJ2o+DcOV/rU//8Q/9/V/HfZqy9YfDO/TstFhF9orVsF6Rih2XpB2HT/r8/195h0el92yaXkz9UgVH3nePMQmM1PT7Otduf11FNSpDNntRoznngtr21J8LC3XwnYXl1q0e10Nj3zhcadnynl52mTILJRnfKWWCO3DTrCn6VSjXNgBNDDdrgEbdF8h7tpjqvma5u7ZU25maz/4UtbZuZmnKSp3r3e2pZYLx+QUmIapV95yzJ4ytc2PKHYspZIzxSY6jtKvM+mFluznVvPtTYUZy6f5WrzeX0zi4xqPrW0SEEdHTs+vOIZ/T+GgFs2xVVm5831/DOLrOT2d/qiwHTmcZa2dGlNvfvx4prPgL/7ffiAxwb/f7PScM2+eveX13U1YhlzYAdH8CUH/KzhZTbQvmap+vD8Nz1nw/W9bBsWbvSFL7gYnl7lBcYCxr7brnmFsravYm5X+drqQYj4aWglW6Y9a7pV2hLFW0KFtMPjxY4fwg8Rusqs63XMd3qduDr0uBkdqcmScjLU1p6YZOHiieaWjNqK7a9p1vLfw33jNasZWM/P3ryJ7ezwXxcX9rw2RuUfMvB4TIqO7AcGeevvDhnAoIbaeR8/bqYHKC1/IHVlfSDarVbZr7uPvjn56aqviHPZ7BEpesvu2CuLgBaHKY/QlotLxni5GkiIiIC34jPb1kBp+zaVqy8XP1m+TDw/DMzdV5cIRijKt8qwzm5ujGVs3qPaCQznfP+UqBbX6lu7u3q1bFtyj/pP7PfJVahxRv3bJjT83aVKi+y6eo54TisSumDXt17M/RlT7p2LMa/x+bQ1KZSuKZKir61Rz08kPmp5Kk6JeXaegt7sS4pttwHV6eqi7jX1f2idPSdT48eDC0m37/5xhtmrLZe3m/5Rp4S1Ct9leSmoV1VkRkjK7y8VmIOQGdFVLDXyTj1GIdO7lAndtVY4Yw18865pE9N1x9eXVCC906apH2fntAfc7PknUkR4WSQivY9r/j10nzS2baStskj8nM9MykXyuMixsAggoA9SbvgJbMcU/zGb3ikLaM7XLBIOSDpD6llZ63fr9Mh0avVNfqNuFb2+nRjWl6tJ4Ps6YBhSQ5fviHhgwdLfVL1uld7VSdburHtk1Rp7G5em37Mg3v3UWhFkkK0k2/uMYjKQsu+GwAS4j7/dTlO/Wb7nGlFcWik5/qke6j6yRtnEXFY2NaWMvfWjCX3FL42e77LaZuQydKZYKKZxIH10ll99oBM5Q2oB5+vMzewcCmXV9pyAXPj5JA7aO3tNLjydk3tW9V8s6unS9vUocxo9TeWnFg8d+xEySPqXcrC2LLTi9bWrZbzdQDd7bm2gagSaL7E9BIfbnzTfdsMWUG0FYsQHc++ETpJ6NglVa8n92oj7E2AUVxzdL37jmBlrYlA7O7qoXVpGlJy/RS0hiFD5zvsdHVCrFW9heCdHv/me6PK4arVZ8nlbJ9h9Yve1LWNj28Kq210fqXPSVJaybMVupR9+PqTmVu14T44rsqN7a7wue/W/ZheKZWMzXKzyq7lvaRWjvM/Xn1uK567dMLD163Z+3RlIHuWQBM4XPV06Mr0qndo3XDPcsqfeBd7rFvy4TxlTCFKWrac+UWRy14QB2tXNsAEFQAqC/ObL0xzmO2mMcT9d/hVVebLW37ausY9+el49/QcWfjPMRaBxSefOieYy7TQ2Zx4hQ9nPi617I/vT1V7S9wH/fagVP1kud+fjBfI4YM1PAp8yvcvqaTY1na9tfe5yKknzdpUMdWihg7TdPGRCqs8xCluaQ7F6Urql1NHgpY8jC8EqMXj66kdb4xC9WQGUu9lkzs0UYJL23XkZP5Xmluz8/WzuVPKviGfu5AXdKU5SPV1iOfLaGS9kzRDVcOU/K+TNlKu0nZdXTPMrUbkuhRCIJ1oSTzmmmrpGFgapUNAwDgxxirDjQ+ZR9o99fM6s8WY/s82eu7Cxrhw/B8neWpyhmAPGZYqnpCpdPG4dR1xrTYiAofcPbOoRMVzhRUbpann44bKXPLzHQUGGnMSdlvHP96m3sGoPFb3LM/1WR/DYdxeNtSrxmF1DzWeG1HhuGsTSacfxheYKTXwxRrnb71ymnsWxpT6YxSMTExXrNleb1+t6XMjFbumb48XxExMd5pX/J657ijyr3zemjl77b5PiMbAPgRggqgsTmX5z2NbL/lhk/17XM5xkueT06OSzbyGtHhHamjgKIuKr2OwtNGXk6OkZOTY+TlVRS4FRrrx1Q+daxhGIaz8LSRk5Nj5OTkGQ5n9ffX9weEO4zC06eN04WFtQsmvPY9zziRc/oi7W99cRiHty30afraJ9amV1BenMbB5IRqfX/O9mo+Ddtjetk1h2xc2wA0aXR/Ahqb/CPa+pb7o88DaE3hGvoHj/7c77ylL3JdjePYCjP1hGcXEhXP3DMnKlImk8mn1yNbj9Z6dyxBoQoLD1d4eLjCwiqe+ej8oGxLYMXdzwKCQhUeHq7w8DBZquyhZintOuP7FK0WBYWGKjQoqM6mdw0IClPr8NCLtL/1xaL/GjxdztPHtSd5YaXT5SowUnOWb9PXeQ7NH9mzgimIA3TrqBdUeOKQUhYmKLKCA+45dqE+ybIp8d5qPg27ZHpZU+uluqdLCNc2AE2ayTAMg2QAUC8cmfpdq856wV77P/Xg2ky91ONzBd80QopL0U8pcb4/qwJNkEt2m02FhWckc/GACbPZqtCwUN8CI1eRCmyFOuN0Sk7J3KKFwoJqMH7FVaQiWaoRcAKAf2NKWQD1xykdP1s3f+orx9kyVUlAkgIUFBqmoNDa/hmLQsIsqvX9hQCLLGQKAIIKAKhDwTfp5a+ztLDWwYlT1quul34s6QLVqLvnAADQ9NH9CQAAAECtMFAbAAAAAEEFAAAAAIIKAAAAAAQVAAAAAAgqAAAAAICgAgAAAEB9+v+ix/Dkx0b5fgAAAABJRU5ErkJggg=="/></div><!--Next 'div' added for floating.--><div style="position:relative; left:0cm;">Figure 4: Singular value decomposition</div></div><div style="clear:both; line-height:0; width:0; height:0; margin:0; padding:0;"> </div></div></div></div><div style="clear:both; line-height:0; width:0; height:0; margin:0; padding:0;"> </div><p class="P28"><span class="T110">Tensor</span> factorization</p><p class="P8"><span> <span class="T110">Tensor factorization can be seen as a natural extension of SVD to an arbitrary number of dimensions (Figure 5).</span></span></p><!--Next 'div' was a 'text:p'.--><div class="P10"><!--Next 'div' is emulating the top hight of a draw:frame.--><!--Next '
div' is a draw:frame.
--><div style="width:6.6929in; padding:0; float:left; position:relative; left:0cm; " class="fr1" id="Frame5"><!--Next 'div' was a 'draw:text-box'.--><div style="min-height:2.3693in;"><!--Next 'div' was a 'text:p'.--><div class="Caption"><!--Next 'div' is emulating the top hight of a draw:frame.--><!--Next '
div' is a draw:frame.
--><div style="height:2.3693in;width:6.6929in; padding:0; float:left; position:relative; left:0cm; " class="fr3" id="Image5"><img style="height:6.018cm;width:17cm;" alt="" src="data:image/*;base64,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"/></div><!--Next 'div' added for floating.--><div style="position:relative; left:0cm;">Figure 5: <span class="T122">A h</span>igher order SVD</div></div><div style="clear:both; line-height:0; width:0; height:0; margin:0; padding:0;"> </div></div></div><!--Next 'div' added for floating.--><div style="position:relative; left:0cm; clear:both">The general form is the Tucker decomposition which factorizes a tensor into a small core tensor and a set of matrices (<span class="T116">See </span>Figure 6). <span class="T112">See [</span><span class="T111">5</span><span class="T112">] for a </span><span class="T111">general</span><span class="T112"> introduction </span><span class="T111">and [6] for non-negative factorizations.</span></div></div><div style="clear:both; line-height:0; width:0; height:0; margin:0; padding:0;"> </div><p class="P10"><span class="T113"> The Tucker decomposition can be written in terms of matrix unfolding </span><span class="T114">of the tensor </span><span class="T47">X</span><span class="T113"> </span><span class="T114">(of size I x J x K):</span></p><p class="P40"><span class="T87">X</span><span class="T55">(1)</span><span class="T75"> ≈ </span><span class="T87">AG</span><span class="T55">(1)</span><span class="T75">(</span><span class="T87">C</span><span class="T75"> ⊗ </span><span class="T87">B</span><span class="T75">)</span><span class="T115">T</span><span class="T75"> </span></p><p class="P40"><span class="T87">X</span><span class="T55">(</span><span class="T56">2</span><span class="T55">)</span><span class="T75"> ≈ </span><span class="T88">B</span><span class="T87">G</span><span class="T55">(</span><span class="T56">2</span><span class="T55">)</span><span class="T75">(</span><span class="T87">C</span><span class="T75"> ⊗ </span><span class="T88">A</span><span class="T75">)</span><span class="T115">T</span><span class="T75"> </span></p><p class="P40"><span class="T87">X</span><span class="T55">(</span><span class="T56">3</span><span class="T55">)</span><span class="T75"> ≈ </span><span class="T88">C</span><span class="T87">G</span><span class="T55">(</span><span class="T56">3</span><span class="T55">)</span><span class="T75">(</span><span class="T88">B</span><span class="T75"> ⊗ </span><span class="T88">A</span><span class="T75">)</span><span class="T115">T</span><span class="T75"> </span></p><p class="P42"><span class="T75">where ⊗ is the Kronecker product and </span><span class="T87">A</span><span class="T75">, </span><span class="T87">B</span><span class="T75"> and </span><span class="T87">C</span><span class="T75"> are </span><span class="T77">factor matrices </span><span class="T79">of size I x R, J x S and K x T respectively where R,S and T are the number</span><span class="T83">s</span><span class="T79"> of </span><span class="T82">f</span><span class="T79">actor</span><span class="T82">s</span><span class="T79"> desired for each dimension. The factor matrices are u</span><span class="T75">sually constrained to have orthogonal columns. </span></p><p class="P42"><span class="T77">Like PCA and other matrix decompositions, the Tucker decomposition is not unique as the core can be modified without affecting the quality of the </span><span class="T78">solution </span><span class="T77">as long as the inverse modification is applied to the matrices. </span><span class="T74">Restricting the core tensor to a diagonal gives the CP (or PARAFAC) decomposition </span><span class="T75">(Figure 7, </span><span class="T81">which is equivalent to Figure 5</span><span class="T75">) </span><span class="T80">in which the same R factors are shared across the matrices. The CP decomposition</span><span class="T76"> can also be expressed in terms of matrices:</span></p><p class="P40"><span class="T87">X</span><span class="T55">(1)</span><span class="T75"> ≈ </span><span class="T87">A</span><span class="T75">(</span><span class="T87">C</span><span class="T75"> </span><span class="T76">⊙</span><span class="T75"> </span><span class="T87">B</span><span class="T75">)</span><span class="T115">T</span><span class="T75"> </span></p><p class="P40"><span class="T87">X</span><span class="T55">(</span><span class="T56">2</span><span class="T55">)</span><span class="T75"> ≈ </span><span class="T88">B</span><span class="T75">(</span><span class="T87">C</span><span class="T75"> </span><span class="T76">⊙</span><span class="T75"> </span><span class="T88">A</span><span class="T75">)</span><span class="T115">T</span><span class="T75"> </span></p><p class="P40"><span class="T87">X</span><span class="T55">(</span><span class="T56">3</span><span class="T55">)</span><span class="T75"> ≈ </span><span class="T88">C</span><span class="T75">(</span><span class="T88">B</span><span class="T75"> </span><span class="T76">⊙</span><span class="T75"> </span><span class="T88">A</span><span class="T75">)</span><span class="T115">T</span><span class="T75"> </span></p><p class="P40"><span class="T76">where ⊙ is the Khatri-Rao product. A form of non-negative tensor factorisation is obtained by </span><span class="Emphasis"><span class="T100">constraining</span></span><span class="T76"> </span><span class="T87">A</span><span class="T75">, </span><span class="T87">B</span><span class="T75"> and </span><span class="T87">C</span><span class="T75"> </span><span class="T76">to have non-negative entries.</span></p><!--Next 'div' was a 'text:p'.--><div class="P9"><!--Next 'div' is emulating the top hight of a draw:frame.--><!--Next '
div' is a draw:frame.
--><div style="width:6.6929in; padding:0; float:left; position:relative; left:0cm; " class="fr1" id="Frame6"><!--Next 'div' was a 'draw:text-box'.--><div style="min-height:3.8126in;"><!--Next 'div' was a 'text:p'.--><div class="Caption"><!--Next 'div' is emulating the top hight of a draw:frame.--><!--Next '
div' is a draw:frame.
--><div style="height:3.8126in;width:6.6929in; padding:0; float:left; position:relative; left:0cm; " class="fr3" id="Image6"><img style="height:9.683999999999999cm;width:17cm;" alt="" src="data:image/*;base64,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"/></div><!--Next 'div' added for floating.--><div style="position:relative; left:0cm;">Figure 6: Tucker decomposition of a third order tensor</div></div><div style="clear:both; line-height:0; width:0; height:0; margin:0; padding:0;"> </div></div></div></div><div style="clear:both; line-height:0; width:0; height:0; margin:0; padding:0;"> </div><!--Next 'div' was a 'text:p'.--><div class="P17"><!--Next 'div' is emulating the top hight of a draw:frame.--><!--Next '
div' is a draw:frame.
--><div style="width:6.6929in; padding:0; float:left; position:relative; left:0cm; " class="fr1" id="Frame7"><!--Next 'div' was a 'draw:text-box'.--><div style="min-height:3.7091in;"><!--Next 'div' was a 'text:p'.--><div class="Caption"><!--Next 'div' is emulating the top hight of a draw:frame.--><!--Next '
div' is a draw:frame.
--><div style="height:3.7091in;width:6.6929in; padding:0; float:left; position:relative; left:0cm; " class="fr3" id="Image7"><img style="height:9.421099999999999cm;width:17cm;" alt="" src="data:image/*;base64,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"/></div><!--Next 'div' added for floating.--><div style="position:relative; left:0cm;">Figure 7: The CP decomposition</div></div><div style="clear:both; line-height:0; width:0; height:0; margin:0; padding:0;"> </div></div></div></div><div style="clear:both; line-height:0; width:0; height:0; margin:0; padding:0;"> </div><p class="P29">Non-negative tensor factorisation of dynamic graphs</p><p class="P18"><span> This can be though<span class="T118">t</span> of as an extension of spectral clustering to more than one adjacency matrix. Our dynamic graph is represented by a third order tensor <span class="T46">G</span><span class="T118"> </span>of genes x genes x time<span class="T119"> points</span> (or experimental conditions) in which each frontal slice is <span class="T120">the</span> genes x genes adjacency matrix <span class="T118">of a weighted undirected graph</span>. <span class="T118">The edge weights are also assumed to be non-negative (≥ 0). Using a non-negative CP decomposition, we can factorize </span><span class="T46">G</span><span class="T118"> into non-negative factor matrices </span><span class="T51">A</span><span class="T118">, </span><span class="T51">B</span><span class="T118"> and </span><span class="T51">C</span><span class="T118">. Because the graph is undirected, the adjacency matrices are symmetric which leads to </span><span class="T51">A</span><span class="T118"> = </span><span class="T51">B</span><span class="T118">. </span><span class="T51">A</span><span class="T118"> is a genes x factors matrix and </span><span class="T51">C</span><span class="T118"> is a factors x time points matrix. Therefore, if we think of the factors as representing clusters, elements of </span><span class="T51">A</span><span class="T118"> can be interpreted as gene cluster memberships and elements of </span><span class="T51">C</span><span class="T118"> as measuring the temporal activity of the clusters.</span></span></p><p class="P18"> </p><p class="P30">Tools</p><p class="P45">- MATLAB toolboxes: tensor, nway (compatible with Octave)</p><p class="P5"><span class="T126">- R packages</span><span class="T125">*</span><span class="T126">: PTak, ThreeWay, rTensor</span></p><p class="P5"><span class="T126">- perl: Algorithms::Cube (</span><a href="https://github.com/jkh1/Perlstuff" class="Internet_20_link"><span class="T127">https://github.com/jkh1/Perlstuff</span></a><span class="T126">)</span></p><p class="P5"><span class="T126">- python</span><span class="T125">*</span><span class="T126">: scikit-tensor (</span><a href="https://github.com/mnick/scikit-tensor" class="Internet_20_link"><span class="T127">https://github.com/mnick/scikit-tensor</span></a><span class="T126">)</span></p><p class="P49"> </p><p class="P46">* non-negativity constraint is not available in R and python packages <span class="T130">(December 2015).</span></p><p class="P46"> </p><p class="P47">Example in R</p><p class="P55">## Load required package</p><p class="P55">library(<span class="T128">rTensor</span>)</p><p class="P55"> </p><p class="P56">## Where the data is</p><p class="P56">## This is a simulated dynamic graph with 30 nodes and 6 time points</p><p class="P56">dataDir <- "<span class="T129">~/Documents/Bio-IT/courses/Data_integration_and_mining_with_graphs/</span>dynamic_graph"</p><p class="P56"> </p><p class="P56">## Get list of adjacency matrices</p><p class="P56">## Each matrix is in a csv file</p><p class="P56">fileList <- dir(path=dataDir,pattern = ".csv")</p><p class="P56"> </p><p class="P56">## Read all adjacency matrices into an array</p><p class="P56">A <- array(as.numeric(NA),dim=c(30,30,6)) # There are 6 matrices of size 30 x 30 </p><p class="P56">for (i in 1:length(fileList)){</p><p class="P56"> A[,,i] <- as.matrix(read.delim(file.path(dataDir,fileList[i]), sep = ';', header=TRUE, row.names=1))</p><p class="P56">}</p><p class="P56"> </p><p class="P56">## Convert list of adjacency matrices to a tensor</p><p class="P56">G <- as.tensor(A)</p><p class="P56"> </p><p class="P56">## Perform CP factorization</p><p class="P56">cpG <- cp(G,num_components = 4)</p><p class="P56">## View the factor matrices</p><p class="P56">## Note that the first two are identical (up to numerical accuracy)</p><p class="P56">## due to the fact that the graph adjacency matrices are symmetric</p><p class="P56">cpG$U</p><p class="P55"> </p><p class="P47"> </p><p class="P47"> </p><p class="P48">Example in <span class="T131">perl</span></p><p class="P57">#!/usr/bin/perl</p><p class="P57">use strict;</p><p class="P57">use warnings;</p><p class="P57">use Algorithms::Matrix;</p><p class="P57">use Algorithms::Cube;</p><p class="P57"> </p><p class="P57"># Where the data is</p><p class="P57">my $dataDir = "$ENV{'HOME'}<span class="T129">/Documents/Bio-IT/courses/Data_integration_and_mining_with_graphs/dynamic_graph</span>";</p><p class="P57"> </p><p class="P57"># Number of time points</p><p class="P57">my $T = 6;</p><p class="P57"> </p><p class="P57"># Read dynamic graph from files as series of adjacency matrices</p><p class="P57">my @<span class="T135">G</span>;</p><p class="P57">foreach my $t(0..$T-1) {</p><p class="P59"> my ($r<span class="T134">ow</span>Labels,$colLabels);</p><p class="P58"> ($<span class="T135">G</span>[$t], <span class="T132">$rowLabels, $colLabels</span>) = </p><p class="P58"><span> Algorithms::Matrix->load_matrix("<span class="T133">$dataDir/</span>A$t.csv",";",1,1);</span></p><p class="P57">}</p><p class="P57"># Create Cube (i.e. third order tensor) object from matrices</p><p class="P54">my $<span class="T135">G</span> = Algorithms::Cube->new(@<span class="T135">G</span>);</p><p class="P54"> </p><p class="P54"># CP factorization with non-negativity constraint</p><p class="P54">my $r = 4; # Number of components</p><p class="P54">my ($A,$B,$C,@norms) = $<span class="T135">G</span>->nncp($r,symmetry=>1,norms=>1);</p><p class="P54"> </p><p class="P51"> </p><p class="P31">References:</p><p class="P7">1. Newman MEJ, Girvan M (2004) <a href="http://arxiv.org/pdf/cond-mat/0308217.pdf" class="Internet_20_link">Finding and evaluating community structure in networks</a>. Phys. Rev. E 69, 026113.</p><p class="P12"><span class="T39">2</span>. <a id="pone.0086028-Mucha1"/>Mucha PJ, Richardson T, Macon K, Porter MA, Onnela JP (2010) <a href="https://www.sciencemag.org/content/328/5980/876.full" class="Internet_20_link">Community structure in timedependent, multiscale, and multiplex networks</a>. Science 328: 876–878.</p><p class="P12"><span class="T39">3</span>. <a id="pone.0086028-Bassett1"/>Bassett DS, Porter MA, Wymbs NF, Grafton ST, Carlson JM, et al. (2013) <a href="https://people.maths.ox.ac.uk/porterm/papers/dani-chaos-final.pdf" class="Internet_20_link">Robust detection of dynamic community structure in networks</a>. Chaos 23: 013142. </p><p class="P16">4. Kiers HAL (2000) <a href="http://www.wiley.com/legacy/wileychi/chemometrics/582_ftp.pdf" class="Internet_20_link"><span class="T136">http://www.wiley.com/legacy/wileychi/chemometrics/582_ftp.pdf</span></a>. J. Chemometrics 14: 105-122.</p><p class="P36"><span class="T93">5</span><span class="T92">. Kolda TG, Bader BW (2009) </span><a href="http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.153.2059&rep=rep1&type=pdf" class="Internet_20_link">Tensor decompositions and applications</a><span class="T92">.</span><span class="T89"> </span><span class="T90">SIAM Rev., 51(3), 455–500. </span></p><p class="P43"><span class="T94">6.</span><span class="T91"> </span><span class="T123">Cichocki A, Zdunek R, Phan AH, Amari SI (2009) </span><a href="http://www.bsp.brain.riken.jp/~cia/NMF_NTF_book/NMF-NTF-book-Chapter1_2-contents.pdf" class="Internet_20_link"><span class="T69">Nonnegative matrix and tensor factorizations: applications to exploratory multi-way data analysis and blind source separation</span></a><span class="T124">. John Wiley & Sons.</span></p><p class="P39"><span class="T95">7</span><span class="T98">. </span><span class="T97">Devarajan K (2008) </span><a href="http://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1000029" class="Internet_20_link"><span class="T97">Nonnegative matrix factorization: an analytical and interpretive tool in computational biology</span></a><span class="T97">. PLoS Comput Biol 4(7):e1000029.</span></p><p class="P35"><span class="T104">8</span><span class="T106">. </span><span class="T105">Kluger Y, Basri R, Chang JT, et al. </span><span class="T106">(2003) </span><a href="http://www.ncbi.nlm.nih.gov/pmc/articles/PMC430175/" class="Internet_20_link"><span class="T105">Spectral biclustering of microarray data: coclustering genes and conditions</span></a><span class="T105">. Genome Res. 13(4):703–16.</span></p><p class="P38"><span class="T99">9</span><span class="T98">. Imangaliyev S, Keijser B, Crielaard W, Tsivtsivadze E (2015) </span><a id="tm005"/><a href="http://www.sciencedirect.com/science/article/pii/S1046202315001231" class="Internet_20_link"><span class="T96">Personalized microbial network inference via co-regularized spectral clustering</span></a><span class="T96">. </span><span class="T98">Methods 83:28-35.</span></p><p class="P37"><a href="https://github.com/mnick/scikit-tensor" class="Internet_20_link"/></p></body></html>