From d35173389b0b9661046c91a1f4106c484316c53f Mon Sep 17 00:00:00 2001
From: Justin Bedo <cu@cua0.org>
Date: Mon, 5 Dec 2022 16:50:43 +1100
Subject: add results from datasets available on mavedb

---
 slides.tex | 124 +++++++++++++++++++++++++++++++++++++++++++++++++++++++------
 1 file changed, 112 insertions(+), 12 deletions(-)

(limited to 'slides.tex')

diff --git a/slides.tex b/slides.tex
index 52f6f7a..8af2bff 100644
--- a/slides.tex
+++ b/slides.tex
@@ -29,6 +29,46 @@
 \addbibresource{slides.bib}
 \AtBeginBibliography{\small}
 
+%% Tikz relative positioning https://tex.stackexchange.com/questions/89588/positioning-relative-to-page-in-tikz
+\makeatletter
+\def
+\parsecomma#1,#2
+\endparsecomma{\def
+  \page@x{#1}
+  \def
+  \page@y{#2}}
+\tikzdeclarecoordinatesystem{page}{\parsecomma#1
+  \endparsecomma
+  \pgfpointanchor{current page}{north east}
+  \pgf@xc=
+  \pgf@x
+  \pgf@yc=
+  \pgf@y
+  \pgfpointanchor{current page}{south west}
+  \pgf@xb=
+  \pgf@x
+  \pgf@yb=
+  \pgf@y
+  \pgfmathparse{(\pgf@xc-
+    \pgf@xb)/2.*
+    \page@x+(
+    \pgf@xc+
+    \pgf@xb)/2.}
+  \expandafter
+  \pgf@x
+  \expandafter=
+  \pgfmathresult pt
+  \pgfmathparse{(\pgf@yc-
+    \pgf@yb)/2.*
+    \page@y+(
+    \pgf@yc+
+    \pgf@yb)/2.}
+  \expandafter
+  \pgf@y
+  \expandafter=
+  \pgfmathresult pt}
+\makeatother
+
 \usepackage{acronym}
 \usepackage{xspace}
 \renewcommand*{\acsfont}[1]{\textsc{#1}}
@@ -59,7 +99,7 @@
 
   \begin{frame}{Basics}
     \begin{definition}[Compositional data] Data \(X \in \R^{n \times d}\) is compositional if rows \(\bx_i\) are in the simplex
-      \[S^d=\{\,\bx \in \R^d : \forall j,x_j > 0 ; \sum_{j=1}^d x_j = \kappa\,\} \]
+      \[S^d=\{\,\bx \in \R^d : \forall j,x_j > 0 ; \sum_{j=1}^d x_j = \kappa\,\}  \]
       for constant \(\kappa > 0\).
     \end{definition} Information is therefore given only by the ratios of components and any composition can be normalised to the standard simplex where \(\kappa = 1\) (c.f., dividing by library size).
   \end{frame}
@@ -67,10 +107,10 @@
   \begin{frame}{Isomorphisms to Euclidean vector spaces} The simplex forms a \(d-1\) dimensional Euclidean vector space
     \footfullcite{Aitchison1982}:
     \begin{definition}[\ac{alr}]
-      \[\alr(\bx)_i = \log \frac{x_i}{x_0} \]
+      \[\alr(\bx)_i = \log \frac{x_i}{x_0}  \]
     \end{definition}
     \begin{definition}[\ac{clr}]
-      \[\clr(\bx)_i = \log \frac{x_i}{\left(\prod_{j=1}^d x_j\right)^{\frac 1 d}} \]
+      \[\clr(\bx)_i = \log \frac{x_i}{\left(\prod_{j=1}^d x_j\right)^{\frac 1 d}}  \]
     \end{definition}
   \end{frame}
 
@@ -108,7 +148,7 @@
 
   \begin{frame}{Traditional
       \ac{pca}} Given \(\X\in \R^{n\times d}\) minimise loss
-    \[\ell_{\textsc{pca}} \triangleq {\lVert \X - \V\A \rVert}^2_{\textrm{F}}      \]
+    \[\ell_{\textsc{pca}} \triangleq {\lVert \X - \V\A \rVert}^2_{\textrm{F}}       \]
     s.t.
     \(\V \in \R^{n \times k}\), \(\A \in \R^{k \times d}\), and \(\V^\intercal \V = \I\).
 
@@ -121,39 +161,99 @@
       \ac{pca}}
     \begin{definition}{Bregman Divergence} Let \(\varphi \colon \R^d \to \R\) be a smooth ($C^1$) convex function on convex set \(\Omega\).
       The Bregman divergence \(D_\varphi\) with generator \(\varphi\) is
-      \[ D_\varphi\left(\bu\,\Vert\,\bv\right) \triangleq \varphi(\bu)-\varphi(\bv)-\langle \nabla\varphi(\bv),\bu-\bv\rangle.      \]
+      \[ D_\varphi\left(\bu\,\Vert\,\bv\right) \triangleq \varphi(\bu)-\varphi(\bv)-\langle \nabla\varphi(\bv),\bu-\bv\rangle.       \]
     \end{definition}
 
     Denote the convex conjugate of \(\varphi\) as \(\varphi^*(\bu) \triangleq \sup_\bv\left\{\langle \bu,\bv\rangle-\varphi(\bv)\right\}\).
     The exponential family
     \ac{pca} is then given by minimising loss
-    \[\ell_{\varphi} \triangleq D_\varphi\left(\X\,\Vert\,\nabla\varphi^*\left(\V\A\right)\right)      \]
+    \[\ell_{\varphi} \triangleq D_\varphi\left(\X\,\Vert\,\nabla\varphi^*\left(\V\A\right)\right)       \]
     under the same constraints as previously, approximating \(\X \sim \nabla\varphi^*\left(\V\A\right)\).
   \end{frame}
 
   \begin{frame}{Aitchison's simplex and exponential
       \ac{pca}} Aitchison's log-transformation is a dual affine coordinate space made explicit with
-    \[\varphi(z) = z\log(z) - z \Leftrightarrow \varphi^*(z) = e^z,   \]
+    \[\varphi(z) = z\log(z) - z \Leftrightarrow \varphi^*(z) = e^z,    \]
     but what about normalisation?
 
     Consider
     \ac{alr}:
-    \[\alr(\bx) \triangleq x_0 \sum_{i=1}^d\varphi\left(\frac{x_i}{x_0}\right) \Leftrightarrow \alr^*(\bx) = x_0\sum_{i=1}^d e^{\frac{x_i}{x_0}} \]
+    \[\alr(\bx) \triangleq x_0 \sum_{i=1}^d\varphi\left(\frac{x_i}{x_0}\right) \Leftrightarrow \alr^*(\bx) = x_0\sum_{i=1}^d e^{\frac{x_i}{x_0}}  \]
 
   \end{frame}
 
-  \begin{frame}
+  \begin{frame}{Scaled Bregman}
     \begin{theorem}{Scaled Bregman
         \footfullcite{nock2016scaled}} Let \(\varphi \colon \mathcal{X} \to \R\) be convex differentiable and \(g \colon \mathcal{X} \to \R\) be differentiable.
       Then
-      \[g(\bx)\cdot D_\varphi\left(\frac{\bx}{g(\bx)}\,\middle\Vert\,\frac{\by}{g(\by)}\right) =  D_{\breve{\varphi}}\left(\bx\,\middle\Vert\,\by\right) \]
+      \[g(\bx)\cdot D_\varphi\left(\frac{\bx}{g(\bx)}\,\middle\Vert\,\frac{\by}{g(\by)}\right) =  D_{\breve{\varphi}}\left(\bx\,\middle\Vert\,\by\right)  \]
       where
-      \[\breve{\varphi} \triangleq g(\bx) \cdot \varphi\left(\frac{x}{g(\bx)}\right)  \]
+      \[\breve{\varphi} \triangleq g(\bx) \cdot \varphi\left(\frac{x}{g(\bx)}\right)   \]
     \end{theorem}
 
     Avalos et al.
     \footfullcite{avalos2018representation}
-    \ considered a relaxed form for \ac{clr} recently.
+    \ considered a relaxed form for
+    \ac{clr} recently.
+  \end{frame}
+
+  \begin{frame}{Activation-Induced Deaminase
+      \footfullcite{Gajula2014}}
+    \begin{tikzpicture}[remember picture,overlay]
+      \node[scale=0.85] at (page cs:0,0.08){\input{106-samples.tikz}};
+    \end{tikzpicture}
+  \end{frame}
+
+  \begin{frame}{Activation-Induced Deaminase}
+    \begin{tikzpicture}
+      \node at (page cs:-0.5,0.08){\input{106-Leu113.tikz}};
+      \node at (page cs:0.5,0.5){\includegraphics{gku689fig3-a.pdf}};
+      \node at (page cs:0.5,-0.25){\includegraphics{gku689fig3-key.pdf}};
+    \end{tikzpicture}
+  \end{frame}
+
+  \begin{frame}{Activation-Induced Deaminase}
+    \begin{tikzpicture}
+      \node at (page cs:-0.5,0.08){\input{106-Phe115.tikz}};
+      \node at (page cs:0.5,0.5){\includegraphics{gku689fig3-b.pdf}};
+      \node at (page cs:0.5,-0.25){\includegraphics{gku689fig3-key.pdf}};
+    \end{tikzpicture}
+  \end{frame}
+
+  \begin{frame}{Activation-Induced Deaminase}
+    \begin{tikzpicture}
+      \node at (page cs:-0.5,0.08){\input{106-Glu117.tikz}};
+      \node at (page cs:0.5,0.5){\includegraphics{gku689fig3-c.pdf}};
+      \node at (page cs:0.5,-0.25){\includegraphics{gku689fig3-key.pdf}};
+    \end{tikzpicture}
+  \end{frame}
+
+  \begin{frame}{Activation-Induced Deaminase}
+    \begin{tikzpicture}
+      \node at (page cs:-0.7,0.9){\textbf{Bregman}};
+      \node at (page cs:0.3,0.9){\textbf{+1-log
+          \ac{pca}}};
+      \node[scale=0.9] at (page cs:-0.5,0.08){\input{106-samples.tikz}};
+      \node[scale=0.9] at (page cs:0.5,0.08){\input{106-samples-log.tikz}};
+    \end{tikzpicture}
+  \end{frame}
+
+  \begin{frame}{\textsc{Erbb2}
+      \footfullcite{Elazar2016}}
+    \begin{tikzpicture}
+      \node[scale=0.8] at (page cs: -0.5,0){\input{helix-erbb2.tikz}};
+      \node at (page cs: 0.5,0.07){\includegraphics[width=0.4
+          \textwidth]{helix-erbb2-pub.jpg}};
+    \end{tikzpicture}
+  \end{frame}
+
+  \begin{frame}{\textsc{Brca1}
+      \footfullcite{Findlay2018}}
+    \begin{tikzpicture}[remember picture,overlay]
+      \node[inner sep=0pt] at (5,0.5){\input{brca1-density.tikz}};
+
+      \node[inner sep=0pt] at (11,1.25){\includegraphics{brca1-hist-pub.jpg}};
+    \end{tikzpicture}
   \end{frame}
 
 \end{document}
-- 
cgit v1.2.3

