Commit 4d54ed94 authored by Carlos GO's avatar Carlos GO
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vernal fig

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\documentclass[11pt]{amsart}
\usepackage{geometry} % See geometry.pdf to learn the layout options. There are lots.
\geometry{letterpaper} % ... or a4paper or a5paper or ...
\geometry{letterpaper}
% ... or a4paper or a5paper or ...
%\geometry{landscape} % Activate for for rotated page geometry
%\usepackage[parfill]{parskip} % Activate to begin paragraphs with an empty line rather than an indent
\usepackage{amssymb}
\usepackage{fdsymbol}
\usepackage{graphicx}
\usepackage{amssymb}
\usepackage{epstopdf}
\usepackage[ruled,vlined,linesnumbered,noresetcount]{algorithm2e}
\usepackage{tikz}
\usetikzlibrary{timeline}
\DeclareGraphicsRule{.tif}{png}{.png}{`convert #1 `dirname #1`/`basename #1 .tif`.png}
\graphicspath{{Figs/}}
\newcommand{\maternal}{\texttt{mateRNAl}}
\newcommand{\rnamigos}{\texttt{RNAmigos}}
\newcommand{\RNAmigos}{\texttt{RNAmigos}}
\newcommand{\vernal}{\texttt{veRNAl}}
\newcommand{\garl}{\texttt{garl}}
\newcommand{\norm}[1]{\left\lVert#1\right\rVert}
\DeclareMathOperator{\GED}{GED}
\title{PhD Proposal Exam \\ Computational Tools for Complex RNA Structure Analysis}
\author{Carlos G. Oliver}
\date{\today} % Activate to display a given date or no date
......@@ -52,12 +57,12 @@ To this end, we develop an evolutioary reactor for studying the thermodynamic an
In {\bf Projects II-IV} we build a set of tools for extracting useful patterns from RNA at the 3D level.
The main challenge addressed by these tools is the computational complexity imposed by modeling higher-order interactions which break some of the central assumptions of earlier models such as planarity of graphs and the convenience of experimental energy models.
The result is \rnamigos, \garl, and \vernal.
The result is \RNAmigos, \garl, and \vernal.
These tools respectively attempt to solve the problem of (i) building predictive models on complex RNA networks, (ii) making efficient comparisons and alignments (iii) mining recurrent structural signatures.
\begin{itemize}
\item \maternal: complex structures evolve autonomously at 2D level
\item \rnamigos: at 3D level we can learn useful functional signatures using graph representations
\item \RNAmigos: at 3D level we can learn useful functional signatures using graph representations
\item \garl: tool for automated structure matching with custom cost functions
\item \vernal: we can isolate new complex signatures using graph neural networks
......@@ -126,7 +131,7 @@ These interactions fine-tune the specificity of RNA interactions by determining
\end{figure}
\section{{\bf Project II:} \rnamigos -- Controlling RNA using drug-like molecules}
\section{{\bf Project II:} \RNAmigos -- Controlling RNA using drug-like molecules}
\subsection{Problem}
......@@ -183,35 +188,35 @@ Finally, the fingerprint is used in a similarity search to identify molecules ma
\end{figure}
\begin{algorithm}
\SetAlgoLined
\KwData{$\mathcal{D}$ graph dataset, $c$ graph cost function}
\KwResult{Trained DQN agent for graph alignment}
$\Theta \leftarrow \text{GCN network parameters}$\\
\While{episode $e=1 < E$}{
$G, G' \sim \mathcal{D} \qquad \text{i.i.d random graph pair}$ \\
$ t \leftarrow 0$\\
$\mathcal{M}_t \leftarrow \emptyset$\\
\While{$\vert \mathcal{M}_t \vert \leq \vert N_{G} \vert $}{
\[
(v, v')_t =
\begin{cases}
\text{random pair w.p} \qquad \epsilon \\
\argmax_{(v,v') \in \mathcal{\bar{M}}_t} Q(h(S_{t+1}, v, v'); \Theta)
\end{cases}
\]
$\mathcal{M}_{t+1} \leftarrow \mathcal{M}_t \cup (v, v')_t$\\
$R_t \leftarrow c(G, G', \mathcal{M}_{t+1}) -c(G, G', \mathcal{M}_t$) \\
$\Theta \leftarrow \text{TD update w. SGD over GCN}$\\
$t \leftarrow t + 1$
}
}
\Return $\Theta$
\caption{Deep Q-Learning for Graph Alignment}
\label{algo:dqn}
\end{algorithm}
%\begin{algorithm}
%\SetAlgoLined
%\KwData{$\mathcal{D}$ graph dataset, $c$ graph cost function}
%\KwResult{Trained DQN agent for graph alignment}
%$\Theta \leftarrow \text{GCN network parameters}$\\
% \While{episode $e=1 < E$}{
% $G, G' \sim \mathcal{D} \qquad \text{i.i.d random graph pair}$ \\
% $ t \leftarrow 0$\\
% $\mathcal{M}_t \leftarrow \emptyset$\\
% \While{$\vert \mathcal{M}_t \vert \leq \vert N_{G} \vert $}{
% \[
% (v, v')_t =
% \begin{cases}
% \text{random pair w.p} \qquad \epsilon \\
% \argmax_{(v,v') \in \mathcal{\bar{M}}_t} Q(h(S_{t+1}, v, v'); \Theta)
% \end{cases}
% \]
% $\mathcal{M}_{t+1} \leftarrow \mathcal{M}_t \cup (v, v')_t$\\
% $R_t \leftarrow c(G, G', \mathcal{M}_{t+1}) -c(G, G', \mathcal{M}_t$) \\
% $\Theta \leftarrow \text{TD update w. SGD over GCN}$\\
% $t \leftarrow t + 1$
% }
%
%
% }
% \Return $\Theta$
% \caption{Deep Q-Learning for Graph Alignment}
% \label{algo:dqn}
%\end{algorithm}
\section{{\bf Project IV:} \vernal -- Searching for conserved RNA structures}
......@@ -229,6 +234,23 @@ State-of-the-art techniques for mining structural motifs rely on two major const
We propose \vernal, the first tool which addresses both limitations of current methods. Our tool is built on a graph neural networks which encodes local structural information across very large sets of structures into a vector space. Similar sub-structures are thus represented as nearby vectors. The problem of comparing structures is reduced to comparing vectors, and the problem of searching the structures becomes a vector-based search. We show that this method produces richer motifs (more flexible) in a fully scalable manner.
\begin{figure}
\centering
\includegraphics[width=\textwidth]{vernal.pdf}
\end{figure}
\begin{equation}
k_L(u,v) := \sum_{l=0}^{L-1} \lambda^{l} d(R_u^l, R_v^l)
\end{equation}
\begin{equation}
d(R, R') := \frac{f_R \cap f_R'}{f_R \cup f_R'}
\end{equation}
\begin{equation}
d(R, R') := \frac{1}{|R| + |R'|}\sum_{(n,n') \in R, R'} GED(\bar{n}, \bar{n}')
\end{equation}
\begin{itemize}
\item A motif is a `subgraph level' thing.
......
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