-
Notifications
You must be signed in to change notification settings - Fork 8
/
heritability_rbc.html
201 lines (153 loc) · 5.3 KB
/
heritability_rbc.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
<!DOCTYPE html>
<html>
<head>
<title>Heritability</title>
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8" />
<link rel="stylesheet" href="fonts/quadon/quadon.css">
<link rel="stylesheet" href="fonts/gentona/gentona.css">
<link rel="stylesheet" href="slides_style_i.css">
<script type="text/javascript" src="assets/plotly/plotly-latest.min.js"></script>
</head>
<body>
<textarea id="source">
### Heritablity of Human Structural Connectomes
Jaewon Chung
---
### What is Heritability?
- .ye[Heritability]: phenotypic variations due to genetic variations
- understand effects of genes (+environment) on brain circuitry
- understand neurologic diseases
Question: Are the connectivity patterns in human brains heritable?
---
### What is a graph?
(aka networks or connectomes)
- Vertex = a region of interest
- Edges = connectivity measure between a pair of vertices
- Diffusion MRI = # of estimated neuronal fibers
---
### What data will we be using?
- Human Connectome Project dataset
- Identical twins (monozygotic), fraternal twins (dizygotic), siblings
- $N\approx 1200$ individuals recruited
- Most have diffusion and functional MRI
---
### Overview
<center>
</center>
---
### Hypothesis testing: distance correlation (DCorr)
- Tests whether $X$ and $Y$ are independent.
- Key idea: measures correlation between distance matrices $D^X$ and $D^Y$
- $D_{ij}^X = \delta_X(x_i, x_j), D_ij^Y = \delta_Y(y_i, y_j)$
<br><br>
Are differences in pairs of connectomes indepedent of genetics?
- Need to compute $D^X$ and $D^Y$
---
### Distance between graphs: Step 1
- Compute adj. spectral embedding (ASE) on graphs $G, H$
- Embeddings = latent positions
- ASE$(G) = \hat{X}$, ASE$(H) = \hat{Y}$
- $\hat{X}, \hat{Y}\in\mathbb{R}^{N\times d}$
<center>
</center>
---
### Distance between graphs: Step 2
- Distance = Frobenius norm of difference in latent positions
- $\delta_X(G, H) = ||\hat{X}R - \hat{Y}||_F$
<center></center>
High distance: pair of graphs are less similar (or more dissimilar)
---
### What is genetic distance?
- Encode via labels
- $\delta_Y(y_i, y_j) = 0$ if monozygotic (or self)
- $\delta_Y(y_i, y_j) = 1$ if dizygotic/sibling
- $\delta_Y(y_i, y_j) = 2$ if unrelated
<center></center>
---
### Are the connectome and genetics distances independent?
<center></center>
--
<br><br>
<center>No</center>
---
class: middle
.center[questions?]
---
### Acknowledgements
<div class="small-container">
<img src="faces/jovo.png"/>
<div class="centered">Josh Vogelstein</div>
</div>
<div class="small-container">
<img src="faces/cep.png" />
<div class="centered">Carey Priebe</div>
</div>
<div class="small-container">
<img src="faces/ebridge.jpg" />
<div class="centered">Eric</div>
</div>
<div class="small-container">
<img src="faces/jesus.jpg"/>
<div class="centered">Jesus</div>
</div>
<div class="small-container">
<img src="faces/jayanta.jpg"/>
<div class="centered">Jayanta</div>
</div>
<div class="small-container">
<img src="faces/pedigo.jpg"/>
<div class="centered">Ben</div>
</div>
<div class="small-container">
<img src="faces/loftus.jpg"/>
<div class="centered">Alex</div>
</div>
<div class="small-container">
<img src="faces/ross.jpg"/>
<div class="centered">Ross</div>
</div>
<img src="images/funding/nsf_fpo.png" STYLE="HEIGHT:95px;"/>
<img src="images/funding/nih_fpo.png" STYLE="HEIGHT:95px;"/>
<img src="images/funding/darpa_fpo.png" STYLE=" HEIGHT:95px;"/>
<img src="images/funding/iarpa_fpo.jpg" STYLE="HEIGHT:95px;"/>
<img src="images/funding/KAVLI.jpg" STYLE="HEIGHT:95px;"/>
<img src="images/funding/schmidt.jpg" STYLE="HEIGHT:95px;"/>
</textarea>
<!-- <script src="https://gnab.github.io/remark/downloads/remark-latest.min.js"></script> -->
<!-- <script src="remark-latest.min.js"></script> -->
<script src="remark-latest.min.js"></script>
<script src="https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.5.1/katex.min.js"></script>
<script src="https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.5.1/contrib/auto-render.min.js"></script>
<link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.5.1/katex.min.css">
<script type="text/javascript">
var options = {};
var renderMath = function () {
renderMathInElement(document.body);
// or if you want to use $...$ for math,
renderMathInElement(document.body, {
delimiters: [ // mind the order of delimiters(!?)
{ left: "$$", right: "$$", display: true },
{ left: "$", right: "$", display: false },
{ left: "\\[", right: "\\]", display: true },
{ left: "\\(", right: "\\)", display: false },
]
});
}
remark.macros.scale = function (percentage) {
var url = this;
return '<img src="' + url + '" style="width: ' + percentage + '" />';
};
// var slideshow = remark.create({
// Set the slideshow display ratio
// Default: '4:3'
// Alternatives: '16:9', ...
// {
// ratio: '16:9',
// });
var slideshow = remark.create(options, renderMath);
</script>
</body>
</html>