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\title[Cell-type specific analysis] % (optional, use only with long paper titles)
{Deciphering the identity, composition, and interaction of highly refined cell types within complex tissues}




\author[S. Mohammadi] % (optional, use only with lots of authors)
{Shahin Mohammadi}

\institute[Purdue] % (optional, but mostly needed)
{
  Department of Computer Science\\
  Purdue University \\
  \vspace{2em}
    \underline{Broad Fellows Program}
}

\date[June17] % (optional, should be abbreviation of conference name)
{June 6, 2017}



\pgfdeclareimage[height=0.5cm]{university-logo}{figures/purdue}
\logo{\pgfuseimage{university-logo}}


\AtBeginSubsection[]
{
  \begin{frame}<beamer>{Outline}
    \tableofcontents[currentsection,currentsubsection]
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}

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\begin{document}


\begin{frame}
  \titlepage
\end{frame}


\begin{frame}{Overview}
\begin{center}
\includegraphics[width = \textwidth]{figures/ResearchSummary}
\end{center}
\end{frame}

\section{Discovering the functional identity of cell types}


\begin{frame}{Overall Workflow}
\begin{center}
\includegraphics[width=0.95\textwidth]{figures/ACTION/main/ACTION_flow}
\end{center}
\end{frame}


\begin{frame}{Component 1}{Motivation}

\begin{block}{Underlying hypothesis}
%Transcriptional profile of cells is dominated by housekeeping genes, whereas their functional identity is determined by a combination of weakly expressed but highly preferential/selective/specific genes.
Transcriptional profile of cells is dominated by housekeeping genes, whereas their functional identity is determined by a combination of weak but preferentially expressed genes.
\end{block}
\end{frame}



\begin{frame}{Component 1}{Supporting evidence}

\begin{columns}
\column{0.45\textwidth}
\begin{figure}
\includegraphics[width = \columnwidth]{figures/ACTION/hypothesis/before_EndothelialCells.pdf}
\caption{Endothelial Cells}
\end{figure}

\column{0.45\textwidth}
\begin{figure}
\includegraphics[width = \columnwidth]{figures/ACTION/hypothesis/before_B-Cells.pdf}
\caption{B-Cells}
\end{figure}

\end{columns}

\end{frame}




\begin{frame}{Component 1}{Supporting evidence}

\begin{columns}
\column{0.45\textwidth}
\begin{figure}
\includegraphics[width = \columnwidth]{figures/ACTION/hypothesis/after_EndothelialCells.pdf}
\caption{Endothelial Cells}
\end{figure}

\column{0.45\textwidth}
\begin{figure}
\includegraphics[width = \columnwidth]{figures/ACTION/hypothesis/after_B-Cells.pdf}
\caption{B-Cells}
\end{figure}

\end{columns}

\end{frame}

\begin{frame}{Component 1}{Overall flow -- cell similarity kernel}
\begin{center}
\includegraphics[width=0.85\textwidth]{figures/ACTION/main/kernel_flow}
\end{center}

\begin{itemize}
\item  The main steps involved in identifying similarity between cells
\end{itemize}

\end{frame}


\begin{frame}{Component 1}{Reducing the noise contributed by highly expressed but uninformative genes}
\alert{Goal:} Identify the shared subspace of genes

\begin{block}{Low-rank decomposition}
\begin{equation*}
A = U_r \Sigma_r V_r = \sum_{i=1}^{r}\sigma_i u_i {v_i}^{T},
\end{equation*}
\end{block}

Example decomposition choices:

\begin{itemize}
\item Mean vector
\begin{itemize}
\item \textit{Optimal in a least-square sense when the chance of observing a gene is uniform across all cells.}
\end{itemize}
\item Singular Value Decomposition (SVD) 
\item Nonnegative Matrix Underapproximation (NMU)
\item Sparse NMU
\end{itemize}

\end{frame}


\begin{frame}{Component 1}{Reducing the noise contributed by highly expressed but uninformative genes}
	\alert{Goal:} Remove the effect of common subspace
	
	\begin{columns}
    \column{.55\textwidth}
    \begin{itemize}
    \small
		\item $\Vector{x}_i$ and $\Vector{x}_j$: tissues/cell types $i$ and $j$
		\item \emph{z}-score normalize $\Vector{x}_i$ to compute $\Vector{z}_i$
		\item $\Vector{\beta}_h$: the common signature    
		\item \emph{z}-score normalize $\Vector{\beta}_h$ to compute $\Vector{z}_h$

		
		\item Project to the orthogonal subspace:		
		\begin{eqnarray*}
			\Vector{z}_i^{\perp} &=& %\Matrix{P}^{\perp}\Vector{z}_i\\\nonumber
			%&=&(\Matrix{I} - \Matrix{P})\Vector{z}_i\\\nonumber
			%&=&
			\Big(\Matrix{I} - \frac{\Vector{z}_{h}\Vector{z}_{h}^{T}}{\| \Vector{z}_{h}\|_2^2}\Big) \Vector{z}_i.
		\end{eqnarray*}

		
    \end{itemize}
		
    \column{.45\textwidth}
		\centering 
		\includegraphics[width=0.9\columnwidth]{figures/ACTION/geo}\\
	\end{columns}

	\vspace{1em}
	Similar in nature to the partial Pearson's correlation		
\end{frame}


\begin{frame}{Component 1}{Enhancing the signal from preferentially-expressed genes}
\alert{Goal: } Estimate expression-specificity of genes across different cells

\begin{columns}[c]
\column{.35\textwidth}
\includegraphics[height=0.4\textheight]{figures/ACTION/Entropy}


\column{.65\textwidth}
\begin{itemize}
\item Entropy as a measure of expression uniformity: $H(i) = -\sum_j p_{ij} log(p_{ij})$
\item How informative observing a gene is with respect to the cell type that it came from
\item Maximum entropy when probability of a gene coming from all cell types is equal
\item For each gene $i$, compute a specificity factor \alert{$w_i$}.
\end{itemize}
\end{columns}
%
	\vspace{1em}
	Similar formulation have been previously used for marker detection.

\end{frame}


%\begin{frame}{Component 1}{Enhance signal from preferentially-expressed genes-- Changes}
%
%\begin{itemize}
%\item We work with the projection of $\mathcal{Z}^{\perp}$ onto the space of positive real values: $\mathcal{P}^{(+)}(\mathcal{Z}^{\perp})$.
%\item Compute uniformity of expression for each gene using entropy-based method
%\item Estimate the number of genes with high specificity using \textit{participation ratio ($\Loss_2^2/\Loss_4$)}.
%\item Limit the range of weights to a band of 4 order of magnitudes ($10^{[-2, 2]}$), in order to remove the effect of outliers.
%\end{itemize}
%\end{frame}
%



\begin{frame}{Component 1}{Putting pieces back together}

\begin{block}{ACTION-adjusted cell signatures}
\begin{equation*}
\Matrix{Y} = \diag(\Vector{w})\Matrix{\mathcal{Z}^{\perp}}
\end{equation*}
\end{block}

\begin{block}{ACTION metric (kernel)}
\begin{eqnarray*}
\Matrix{K}_{ACTION} &=& \Matrix{Y}^{T}\Matrix{Y}\\ &=&\big(\Matrix{\mathcal{Z}^{\perp}}\big)^{T}\diag(\Vector{w}^2)\big(\Matrix{\mathcal{Z}^{\perp}}\big)
\end{eqnarray*}

\end{block}
\end{frame}


\begin{frame}{Component 1}{Cell similarity kernel -- revisited}
\begin{center}
\includegraphics[width=0.85\textwidth]{figures/ACTION/main/kernel_flow}
\end{center}

\begin{itemize}
\item  Now we have computed the ACTION kernel
\end{itemize}

\end{frame}


\begin{frame}{Benchmark datasets}
\begin{itemize}
\small
\item \textbf{Immune:} \alert{1,522 immune cells} from mouse hematopoietic system (\alert{30 different types} of stem, progenitor, and fully differentiated cells)
\item \textbf{Melanoma:} \alert{4,645 malignant, immune, and stromal cells} isolated from 19 freshly procured human melanoma tumors (\alert{7 major types}, including T, B, NK, CAF, Endo, Macro, and Tumor)
\item \textbf{MouseBrain:} \alert{3005 cells}  from the mouse cortex and hippocampus (\alert{7 major types}, including \textit{astrocytes-ependymal, endothelial-mural, interneurons, microglia, oligodendrocytes, pyramidal CA1}, and \textit{pyramidal SS}).
\item \textbf{Pollen:} Small set of \alert{301 cells} spanning \alert{11 different cell types} in developing cerebral cortex
\end{itemize}
\end{frame}



\begin{frame}{Performance of ACTION Kernel}
  \begin{columns}[c]   
    \column{.3\textwidth}
			\includegraphics[width=\columnwidth]{figures/ACTION/kernelComp_mean_NMI}\\
			\includegraphics[width=\columnwidth]{figures/ACTION/kernelComp_mean_ARI}\\

    \column{.7\textwidth}
	\begin{itemize}
	\small
		\item Benchmarks:
		\begin{itemize}
		\item SIMLR: Specifically designed for single-cell data
		\item IsoMap,MDS: General purpose dimension reduction
		\end{itemize}
		\item Tested a range of parameters (5:5:50). Reported best case.
%		\item Used \emph{t}-test for evaluating differences
		\item Ties:
		\begin{itemize}
			\tiny
			\item \textit{Immune} (NMI: ACTION/MDS/SMLR, ARI: ACTON/MDS)
			\item \textit{Melanoma} (ARI: ACTION/SIML)
		\end{itemize}
		\item In all other cases, \textit{ACTION} metric significantly outperforms all other methods.
	\end{itemize}		
	
	\end{columns}

\vspace{1em}
\begin{itemize}
\item \underline{\textit{ACTION} metric performs equally good or better than other methods}
\end{itemize}

\end{frame}

\begin{frame}{Overall Workflow}{Component 2}
\begin{center}
\includegraphics[width=0.95\textwidth]{figures/ACTION/main/ACTION_flow}
\end{center}
\end{frame}



\begin{frame}{Component 2}{Motivation}

\begin{block}{General framework}
		\begin{equation*}
\centering
\begin{aligned}
& \underset{\Matrix{C}, \Matrix{H}}{\argmin}
& & \parallel \Matrix{Y} - \underbrace{\Matrix{Y} \Matrix{C}}_{\Matrix{W}} \Matrix{H} \parallel \\
& \text{subject to:} 
& & \parallel \Matrix{C}(:, i) \parallel_1 = 1.\\
& & & \parallel \Matrix{H}(:, i) \parallel_1 = 1.\\
&& &  0 \leq \Matrix{C},  0 \leq \Matrix{H}
\end{aligned}	
		\end{equation*}
\end{block}

Various algorithms can be cast using this formulation
\begin{itemize}
\item \alert{K-means}: $\Matrix{C} \in \R^{+}, \Matrix{H} \in\{0, 1\}$
\item \alert{K-medoids}: $\Matrix{C}  \in\{0, 1\}, \Matrix{H} \in\{0, 1\}$
\end{itemize}
\end{frame}



\begin{frame}{Component 2}{Motivations}
There are fundamental problems with K-means/medoids:

	\begin{itemize}
		\item They use hard assignment, whereas many cell types are believed to form a continuum.
		\item They are sensitive to initialization.
		\item They are dependent on $k$.
	\end{itemize}
\end{frame}




\begin{frame}{Component 2}{Convex Nonnegative Matrix Factorization (NMF) }
\begin{block}{Convex NMF}
		\begin{equation*}
\centering
\begin{aligned}
& \underset{\mathcal{K}, \Matrix{H}}{\argmin}
& & \parallel \Matrix{Y} - \Matrix{Y}(:, \mathcal{S}) \Matrix{H} \parallel \\
& \text{subject to:} 
& & \parallel \Matrix{H}(:, i) \parallel_1 = 1, \Matrix{H} \in \R^{+}.\\
\end{aligned}	
		\end{equation*}				
\end{block}

\begin{itemize}
\item It uses the same formulation as k-medoid, but relaxes the hard assignment of cells: $ \Matrix{C} \in \{0, 1\},  \Matrix{H} \in \R^{n}$
\item Unlike k-medoid and k-means, it has an \alert{optimal global solution}.
\begin{itemize}
\item Under \alert{near-separability} assumption: there exists for each cell type an ideal example in the population.
\end{itemize}
\item A modification of the \textit{Gram Schmidt} process.
\end{itemize}	
	
\end{frame}



\begin{frame}{Component 2}{Convex NMF-- Geometric interpretation}
	
  \begin{columns}[c]   
    \column{.4\textwidth}
			\includegraphics[width=\columnwidth]{figures/ACTION/polytope}\\
	    \alert{Geometry of functional space:} each point is a cell and red points are the ``pure cells''

    \column{.6\textwidth}
	\begin{itemize}
	\item Picking $k$ corner points/archetypes from the convex hull of the cells, such that they optimally "contain" the rest of cells.
	\item Each archetype is an ideal example of a cell type with a distinct set of \alert{principal functions}.
	\end{itemize}
	\end{columns}


\end{frame}





\begin{frame}{Component 2}{Preconditioning -- theorems}
	\alert{Goal:} Understand the behavior of near-separable NMF

\begin{block}{Performance guarantee}
\begin{equation*}
\max_{1 \leq  j\leq r}\min_{s \in \mathcal{S}} \parallel \Matrix{Y}(:, s)-\Matrix{W}(:, j) \parallel \leq \mathcal{O}\Big( \epsilon \kappa^2(\Matrix{W})\Big)
\end{equation*}
\end{block}	


\begin{itemize}
\item For any near-separable matrix, multiplying it with any nonsingular matrix $\Matrix{Q}$ preserved separability, where matrix $\Matrix{W}$ is replaced with $\Matrix{Q}\Matrix{W}$. 

\item In this case, we have the following modified upper bound: \alert{$\mathcal{O}\Big( \epsilon \kappa(\Matrix{W})\kappa^3(\Matrix{Q}\Matrix{W})\Big)$}.
\end{itemize}

\end{frame}

%
%
%\begin{frame}{Component 2}{Preconditioning -- Minimum volume ellipsoid method}
%	\alert{Goal:} Enhance conditioning of the problem
%
%\begin{itemize}
%\item Ideally, we would like $\Matrix{Q} = \Matrix{W}^{-1}$, but if we knew that there was nothing to solve!
%\item It turns out that we can approximate $\Matrix{W}^{-1}$ using a \textit{minimum volume ellipsoid} centered around the origin that that contains all columns of the original matrix $\Matrix{X}$.
%\item This can be solved using the following SDP to identify spd matrix $\Matrix{A^{*}}$:
%
%\begin{alignat*}{2}
%\Matrix{A}^{(*)}  &= \argmax_{\Matrix{A} \in \mathbb{S}_{+}^{k}} \textbf{det}(\Matrix{A})\\
%\mbox{S.t.} & \Matrix{X}(:, j)^{T}\Matrix{A}\Matrix{X}(:, j) \leq 1; \forall j
%\end{alignat*}
%
%\item Since $\Matrix{A^{T}}$ is s.p.d., we can compute $\Matrix{A^{T}} = \Matrix{Q}^T\Matrix{Q}$ using Cholesky factorization. 
%\end{itemize}
%
%\end{frame}
%


\begin{frame}{Component 2}{Archetypal Analysis (AA)}
\begin{itemize}
\item  It further relaxes matrix $\Matrix{C}$: $\Matrix{C}, \Matrix{H} \in \R^{+}$.
\item It can handle cases where pure pixel assumption is violated.
\item But it no longer has global convergence guarantee $\rightarrow$ it is also dependent on the initialization
\begin{itemize}
\item To address this issue, we use the solution of convex NMF for initializing A.A.
\end{itemize}
\item In essence, it allows local adjustment of the Convex NMF solution.
\item A variant of \alert{block-coordinate descent} for optimization.
\end{itemize}

\end{frame}




\begin{frame}{Component 2}{Finding the number of archetypes ($k$)}
\alert{Goal:} To identify when we should stop adding new archetypes.

\vspace{1em}

	\begin{itemize}
	\small
	\item Idea is simple: keep adding archetypes till we sense "oversampling."
	\item Oversampling happens when we start adding archetypes that are "too close" to each other.
	\item Each archetype is a cell $\rightarrow$ we can compute their similarity of using the ACTION metric.
	\end{itemize}

\end{frame}


\begin{frame}{Component 2}{Statistical significance of oversampling}
\begin{columns}[c]
    \column{.25\textwidth}
		\includegraphics[width=\columnwidth]{figures/ACTION/ER}\\

    \column{.75\textwidth}
    \footnotesize
	\begin{itemize}
	\item We build and threshold an archetype-archetype similarity graph.
	\item For each connected component in this graph, we assess its statistical significance using ER model.
	\item Probability that there exists in $\Graph{G}$ a subgraph of density $\delta(\Set{Z})$ and size 
at least $|\Set{Z}|$: 
\begin{align*}
	\Pr[\exists \Set{H} \subseteq \Graph{G}, |\Set{H}|\geq |\Set{Z}| ~:~ \delta(\Set{H}) = \delta(\Set{Z})].
\end{align*}
	
	\end{itemize}
\end{columns}

\end{frame}





\begin{frame}{Component 2}{Test 1: Identifying cell types using closest archetype}
    	\includegraphics[width=\columnwidth]{figures/ACTION/main/CellType_ID}

\vspace{4em}
	\begin{itemize}
	\item \underline{ACTION excels in identifying underlying cell types in \alert{all cases}}
	\end{itemize}
\end{frame}



\begin{frame}{Component 2}{Visualizing the functional space}
	\begin{itemize}
	\item Use matrix $\Matrix{H}$ instead of $\Matrix{Y}$ in visualization:
	\begin{itemize}
		\item We are interested in the relationship between cells and their surrounding archetypes.
	\end{itemize}	
	\item Initialize using Fiedler embedding
	\begin{itemize}
		\item Position according to the dominant eigenvectors of the Laplacian matrix: $\Matrix{L} = \mathbf{diag}(\Delta_\Matrix{Y}) - \Matrix{Y}$.
	\end{itemize}	
	\item Update using \emph{t}-SNE
	\end{itemize}
\end{frame}


\begin{frame}{Continuous view}{Case study in the Melanoma dataset}
\begin{columns}[c]
\column{0.45\textwidth}
    		\includegraphics[width=\columnwidth]{figures/ACTION/main/Melanoma_map_cox}

\column{0.5\textwidth}
\begin{itemize}
\small
\item T-cells reside in a continuum of states (\alert{Thogerson \textit{et al.}}). 
\item Tumor cells form compact groups.
\item Two subclasses of MITF-associated tumors significantly differ in terms of their survival.
\end{itemize}
\end{columns}

\vspace{0.5em}

\begin{itemize}
\item \underline{ACTION sheds light on the underlying topology of cell types}
\end{itemize}

\end{frame}


%\begin{frame}{Stats of tumor cells}
%\begin{itemize}
%\item Patients 58, 67, 72, 74 have no measured tumor cells    
%\item Patients 53, 60, 65, 75, 84, and 94 have less than 20 sampled cells
%\item There are 9 cells with sufficient tumor cell samples
%\end{itemize}
%\end{frame}

%\begin{frame}{Archetype 4}{A \textit{de novo} identified subclass of Melanoma cancer patients}
%\begin{itemize}
%\item There are a total of 4 patients with NRAS Q61L mutation among 19 total patients.
%\item Archetype 4 identifies 5 patients, 4 of which coincide with patients with NRAS Q61L mutation
%\item This has \emph{p}-value of $1.3 \times 10^{-3}$.
%\end{itemize}
%\end{frame}

\begin{frame}{Overall Workflow}{Component 3}
\begin{center}
\includegraphics[width=0.95\textwidth]{figures/ACTION/main/ACTION_flow}
\end{center}
\end{frame}


\begin{frame}{Component 3}{Constructing TRN}
\begin{center}
    		\includegraphics[width=0.95\textwidth]{figures/ACTION/main/TRN_flow}\\    		
\end{center}
\end{frame}


\begin{frame}{Component 3}{Constructing TRN}{Continued}
\alert{Goal:} Identifying key regulatory elements that drive each cell type

\vspace{1em}

\begin{enumerate}
\item \alert{Archetype Orthogonalization} ($\rightarrow$ Only over positive projection)\\
\begin{equation*}
\Vector{a}_i^{\perp} 
= \Big(\Matrix{I} - \Matrix{A}_{-i}^{} 
	(\Matrix{A}_{-i}^{T}\Matrix{A}^{}_{-i})^{-1}
    \Matrix{A}_{-i}^{T}\Big)
\Vector{a}_i
\end{equation*}

\item \alert{Assessing significance of TFs/TGs}\\
\begin{eqnarray*}
\text{\emph{p}-value} (Z = b_l(\lambda)) &=& \text{Prob}(b_l(\lambda)\leq Z) \nonumber \\
&=& \sum_{x=b_l(\lambda)}^{min(T, l)} \frac{{T \choose x} {m-T \choose l-x}} {{m \choose l}} \nonumber\\
\end{eqnarray*}
Use Dynamic Programming to compute exact \emph{p}-value.
\end{enumerate}

\end{frame}


\begin{frame}{Functional activity of transcription factors (TFs)}
\begin{block}{Key point!}
We identify ``functional activity'' of transcription factors (TFs) by aggregating transcriptional activity of their downstream targets, not the transcriptional level of TFs themselves. TFs can, and typically do, get regulated through post-translational mechanisms.
\end{block}
\end{frame}


\begin{frame}{Dissecting transcriptional controls of Melanoma subtypes}{Proliferative versus invasive status}

\begin{itemize}
\small
\item Both \textit{Subtype A} and \textit{Subtype C} exhibit high activity of \textit{MITF} and \textit{Sox10} transcription factors, which are canonical markers for melanoma cells in the ``proliferative'' (as opposed to ``invasive'') state (\alert{Verfaiilie \textit{et al.}}).
\item These two subtypes are significantly enriched for marker genes in the proliferative state:
\begin{itemize}
\item \textit{Subtype A: } $9.3 \times 10^{-14}$
\item \textit{Subtype B: } $7.9 \times 10^{-11}$
\end{itemize}
\item Subtype A has higher MITF activity (according to its activated targets):
\begin{itemize}
\item \textit{GPNMB, M1ANA, PMEL,} and \textit{TYR} are shared between two subtypes.
\item \textit{ACP5, CDK2, CTSK, DCT, KIT,} and {TRPM1/P1} are uniquely upregulated in subtype A.
\end{itemize}
\end{itemize}
\end{frame}



\begin{frame}{Dissecting transcriptional controls of Melanoma subclasses}{Case study in MITF$\upuparrows$/MYC$\uparrow$ subtype}
\begin{center}
    		\includegraphics[height=0.53\textheight]{figures/ACTION/main/TRN}\\    		    		
\end{center}

\begin{itemize}
\small
\item 19 ``functionally'' active transcription factors in subtype A (\emph{p}-value $\leq 0.05$)
\item We focus on the five most significant TFs and their targets (\emph{p}-value $\leq 10^{-3}$)
\end{itemize}
\end{frame}


\begin{frame}{Case study in MITF$\upuparrows$/MYC$\uparrow$ subtype}{Core transcription factors}
\begin{itemize}
\footnotesize
\item MITF is one of the most well-known markers for classifying melanoma patients (\alert{Hartman \textit{et al.}}: MITF in melanoma: mechanisms behind its expression and activity).
\item Overexpression of the E2F1 is common in high-grade tumors that are associated with poor survival in melanoma patients (\alert{Alla \textit{et al.}}: E2F1 in melanoma progression and metastasis).
\item Melanoma cell phenotype switching, between proliferative an invasive states, is regulated by differential expression of LEF1/TCF4 (\alert{Eichhoff \textit{et al.}}:Differential LEF1 and TCF4 expression is involved in melanoma cell phenotype switching).
\item Amplification and overexpression of the c-myc have been associated with poor outcome (\alert{Kraehn \textit{et al.}}: Extra c-myc oncogene copies in high risk cutaneous malignant melanoma and melanoma metastases).
\end{itemize}
\end{frame}


\begin{frame}{Dissecting transcriptional controls of Melanoma subtypes}{Survival analysis}
\begin{columns}[c]
\column{0.35\textwidth}
\includegraphics[width=\columnwidth]{figures/ACTION/SubtypeA_Cox}\\
\tiny \textit{Subtype A:} \emph{p}-value = $5.4 \times 10^{-10}$

\includegraphics[width=\columnwidth]{figures/ACTION/SubtypeC_Cox}\\
\tiny \textit{Subtype C:} \emph{p}-value = $ 0.31$

\column{0.6\textwidth}
\begin{itemize}
\item OncoLnc (\alert{Jordan Anaya})
\item Multivariate Cox regressions
\item Gene expression, sex, age, and grade or histology  as factors
\item Genes associated with Subclass A have significantly worse outcome, compare to the background of all genes
\end{itemize}
\end{columns}
\end{frame}


\begin{frame}{Case study in MITF$\upuparrows$/MYC$\uparrow$ subtype}{Survival analysis revisited -- Kaplan-Meier plots}
\begin{center}
    		\includegraphics[height=0.6\textheight]{figures/ACTION/TRN_Cox}\\
\end{center}
\end{frame}


\begin{frame}{Contributions}{Recap}
\begin{enumerate}
\item Developed a novel cell similarity metric that is robust to biological noise, while at the same time is sensitive enough to identify weak cell type-specific signals
\item Characterized the functional identity of cells
\begin{itemize}
\item Under the pure cell assumption, this metric induces a convex topology that embeds functional identity of cells
\end{itemize}
\item Utilized functional identity of cells to identify both discrete cell types and continuous cell states
\item Identified driving transcriptional controls that mediate the functional identity of cells
\end{enumerate}

\begin{center}
\alert{Clinical significance:} Characterization of  two MITF-associated subclasses of Melanoma patients, one of which has substantially worse outcomes, along with their underlying regulatory elements.
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\begin{frame}{Questions?}

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