Update all files

.gitattributes

@@ -37,6 +37,10 @@ saved_model/**/* filter=lfs diff=lfs merge=lfs -text
 *.pdf filter=lfs diff=lfs merge=lfs -text
 images/coke.jpg filter=lfs diff=lfs merge=lfs -text
 mtrack.png filter=lfs diff=lfs merge=lfs -text
+presentation_images/cell_fate_labelling.png filter=lfs diff=lfs merge=lfs -text
+presentation_images/cell_fate_xgboost.png filter=lfs diff=lfs merge=lfs -text
+presentation_images/feature_analysis.png filter=lfs diff=lfs merge=lfs -text
+presentation_images/model_accuracy.png filter=lfs diff=lfs merge=lfs -text
 presentation_images/nuclei_Acceleration_t_start_0_t_end_100_nuclei__distribution.png filter=lfs diff=lfs merge=lfs -text
 presentation_images/nuclei_Acceleration_t_start_200_t_end_300_nuclei__distribution.png filter=lfs diff=lfs merge=lfs -text
 presentation_images/nuclei_Acceleration_t_start_300_t_end_359.0_nuclei__distribution.png filter=lfs diff=lfs merge=lfs -text
@@ -79,5 +83,10 @@ presentation_images/nuclei_Speed_t_start_300_t_end_359.0_nuclei__distribution.pn
 presentation_images/nuclei_Surface_Area_t_start_0_t_end_100_nuclei__distribution.png filter=lfs diff=lfs merge=lfs -text
 presentation_images/nuclei_Surface_Area_t_start_200_t_end_300_nuclei__distribution.png filter=lfs diff=lfs merge=lfs -text
 presentation_images/nuclei_Surface_Area_t_start_300_t_end_359.0_nuclei__distribution.png filter=lfs diff=lfs merge=lfs -text
+presentation_images/oneat1.png filter=lfs diff=lfs merge=lfs -text
+presentation_images/oneat_arch.png filter=lfs diff=lfs merge=lfs -text
+presentation_images/overall_workflow.png filter=lfs diff=lfs merge=lfs -text
+presentation_images/seg_tra_oneat.png filter=lfs diff=lfs merge=lfs -text
 presentation_images/tm-oneat-panel.png filter=lfs diff=lfs merge=lfs -text
+presentation_images/track_oneat_metrics.png filter=lfs diff=lfs merge=lfs -text
 presentation_images/trackmate-panes-1536x495.png filter=lfs diff=lfs merge=lfs -text

chapters/collecting-trajectories.tex

@@ -1,59 +1,400 @@
-\section{Collecting Trajectories}
+\section{Overall Workflow}
 
-    \subsection{Nuclei Segmentation: VollSeg}
-    \frame{\sectionpage}
+\begin{frame}{Overall Workflow}
+
+% Large figure at the beginning
+\only<1>{
+    \begin{center}
+        \includegraphics[width=0.8\textwidth]{presentation_images/overall_workflow.png}
+    \end{center}
+}
+
+% Shrunk figure + text overlay for subsequent slides
+\only<2->{
+    \begin{columns}
+        \begin{column}{0.45\textwidth}
+            \includegraphics[width=\textwidth]{presentation_images/overall_workflow.png}
+        \end{column}
+        \begin{column}{0.55\textwidth}
+            \begin{itemize}[<+->]
+                \item A. Animal caps are cut from Xenopus embryos at NF stage 8-9. 
+                \item B. The prospective MCE undergoes morphogenetic shaping and cell fate decisions during development into differentiated tissue. 
+                \item C. Immunostained differentiated tissue at NF stage 28: acetylated $\alpha$-tubulin labels multiciliated cells (green) and lectin labels goblet cells and small secretory cells in later stages. Ionocytes are distinct for their lack of labeling.
+                \item D. Nuclei and membrane labeling (H2B-RFP and mem-mNeonGreen, respectively) of developing tissue at 0, 8, and 22 h.
+                \item E. Image analysis pipeline from live image acquisition to cell fate prediction. Single-cell features are then used to classify cell fate by using ground truth data based on cell immunolabeling.
+            \end{itemize}
+        \end{column}
+    \end{columns}
+}
+
+\end{frame}
+
+\section{Segmenation, Tracking and Action Classification}
+
+\begin{frame}{Seg Tra and Oneat}
+
+% Large figure at the beginning
+\only<1>{
+    \begin{center}
+        \includegraphics[width=0.5\textwidth]{presentation_images/seg_tra_oneat.png}
+    \end{center}
+}
+
+% Shrunk figure + text overlay for subsequent slides
+\only<2->{
+    \begin{columns}
+        \begin{column}{0.4\textwidth}
+            \includegraphics[width=\textwidth]{presentation_images/seg_tra_oneat.png}
+        \end{column}
+        \begin{column}{0.55\textwidth}
+            \begin{itemize}[<+->]
+                \item A-B. Nuclei and membrane stacks (raw for nuclei,CARE denoised for membrane) are used as inputs for StarDist (nuclei) and Cellpose (membrane)
+                \item C. Segmented nuclei and membrane object labels. 
+                \item D. Cell trajectories are generated by tracking nuclei objects, which are then assigned membrane objects based on closest object centroid matching. Tracks are initially generated with TrackMate, using StarDist labelled objects as input, and trajectory branching points are imposed at cells that are classified as dividing by Oneat, using a Fiji plugin TrackMate-Oneat.
+                \item  E. Resulting cell trajectories at 0, 10 and 20 h.
+            \end{itemize}
+        \end{column}
+    \end{columns}
+}
+
+\end{frame}
+
+
+
+\section{Trajectory feature analysis}
+
+\begin{frame}{Trajectory feature analysis}
+
+% Large figure at the beginning
+\only<1>{
+    \begin{center}
+        \includegraphics[width=0.5\textwidth]{presentation_images/feature_analysis.png}
+    \end{center}
+}
+
+% Shrunk figure + text overlay for subsequent slides
+\only<2->{
+    \begin{columns}
+        \begin{column}{0.4\textwidth}
+            \includegraphics[width=\textwidth]{presentation_images/feature_analysis.png}
+        \end{column}
+        \begin{column}{0.55\textwidth}
+            \begin{itemize}[<+->]
+                \item A. Each constructed trajectory in time consists of single cells with shape, nucleus shape, movement, and positional features.
+                \item B-C. Membrane and nucleus shapes of example trajectories at 8 and 16 h, with corresponding
+				point cloud to 16 h. 3D shape measurements of both cell membranes and nuclei are constructed from
+				a point cloud. For membranes, additional 2D shape descriptor features are calculated from the object
+				center slice.
+                \item D. 1st and 2nd principal components of membrane shape, nucleus shape, movement, and
+				all features feature space.
+                \item  E. Feature correlations with principal components. For all features, only the
+				top 5 correlating features for PC1 and PC2 are shown
+				\item  F. Selected feature trends across developmental
+				time for all cells. 
+				\item G. Spearman rank correlations of each feature with time, calculated per trajectory, and
+				a boxplot shows the distribution of correlations. 
+            \end{itemize}
+        \end{column}
+    \end{columns}
+}
+
+\end{frame}
+
+
+
+
+
+\section{Cell Fate Labelling}
+
+\begin{frame}{Cell Fate Labelling}
+
+% Large figure at the beginning
+\only<1>{
+    \begin{center}
+        \includegraphics[width=0.4\textwidth]{presentation_images/cell_fate_labelling.png}
+    \end{center}
+}
+
+% Shrunk figure + text overlay for subsequent slides
+\only<2->{
+    \begin{columns}
+        \begin{column}{0.4\textwidth}
+            \includegraphics[width=\textwidth]{presentation_images/cell_fate_labelling.png}
+        \end{column}
+        \begin{column}{0.55\textwidth}
+            \begin{itemize}[<+->]
+                \item A-B. Live imaged cells are fixed at the end
+				of the experiment and immunolabelled for MCE cell types (A). The cell fate is assigned to a track based
+				on manual annotation of the final timepoint cell type based on the presence of immunolabel in a cell
+				(B).
+                \item C. Tracks with cell fate labelling, overlaid against the last timepoint.
+                \item D. Mean and s.d. of selected features, colored by cell type.
+                \item E. Membrane shape of randomly selected cells, 1 per cell type, at 1 h, 4 h, 8, 16 h and 22 h.
+				\item F. Single cell features of randomly selected cells across time, 1 per cell type  
+			
+            \end{itemize}
+        \end{column}
+    \end{columns}
+}
+
+\end{frame}
+
+
+
+\section{Cell Fate Classification: XGBoost}
+
+\begin{frame}{Cell Fate Classification: XGBoost}
+
+% Large figure at the beginning
+\only<1>{
+    \begin{center}
+        \includegraphics[width=0.4\textwidth]{presentation_images/cell_fate_xgboost.png}
+    \end{center}
+}
+
+% Shrunk figure + text overlay for subsequent slides
+\only<2->{
+    \begin{columns}
+        \begin{column}{0.4\textwidth}
+            \includegraphics[width=\textwidth]{presentation_images/cell_fate_xgboost.png}
+        \end{column}
+        \begin{column}{0.55\textwidth}
+            \begin{itemize}[<+->]
+                \item A. Feature vectors of single
+				cells are used as independent features, and cell fate as a dependent feature, for training a classifier
+				model, based on either XGBoost or multinomial (softmax) logistic regressor. Then, each cell in the test
+				dataset is assigned a cell fate based on its feature vector.
+                \item B-C. Confusion matrices of test dataset cell
+				fate prediction vs. ground truth, for XGBoost model and logistic regression model, respectively.
+                \item  D. Example test dataset trajectories showing single-cell predictions per track.
+                \item E-F. Percent point-wise
+				accuracy difference to baseline accuracy of the XGBoost model for leaving out a feature category (E)
+				or a single feature (F, only the top feature per feature category is shown). 
+				\item  G. Feature coefficients for a
+				logistic regressor model, only the top feature per category is shown. All calculations in B, C, E, F, and
+				G are averaged out for 20 iterations of randomized test-train split, model training, and prediction
+			
+            \end{itemize}
+        \end{column}
+    \end{columns}
+}
+
+\end{frame}
 
-    \begin{frame}{VollSeg}
-    	\begin{itemize}[<+->]
-    	 
-    	 	\item VollSeg is a versatile tool built over StarDist with modular segmentation methodologies.
-    
-    		\item Xenopus: Early stage of development occupies limited space, $\rightarrow$ lots of background signal $\rightarrow$ Normalization issues. 
-    
-    		\item Train a ROI and StarDist nuclei model $\rightarrow$ nuclei segmentation in the region of signal.
-    	
-    	\end{itemize}
-    	
-    \end{frame}
     
-    \begin{frame}{VollSeg}
-    	\href{run:presentation_movies/sixth_nuclei_seg.mp4}{
-    	 \fcolorbox{blue!80!black}{blue!10}{% Border and background color
-    		\parbox[c][1.5em][c]{0.6\textwidth}{% Box size
-    			\centering\textbf{\textcolor{blue!90!black}{Nuclei Segmentation (Click)}}% Text styling
-    		}%
-    	}%
-    }
+
+
+\section{Oneat Architecture: Action Classification}
+
+\begin{frame}{Oneat Architecture: Action Classification}
+
+% Large figure at the beginning
+\only<1>{
+    \begin{center}
+        \includegraphics[width=0.4\textwidth]{presentation_images/oneat_arch.png}
+    \end{center}
+}
+
+% Shrunk figure + text overlay for subsequent slides
+\only<2->{
+    \begin{columns}
+        \begin{column}{0.4\textwidth}
+            \includegraphics[width=\textwidth]{presentation_images/oneat_arch.png}
+        \end{column}
+        \begin{column}{0.55\textwidth}
+            \begin{itemize}[<+->]
+                \item Oneat model structure. A. Training data annotations in Napari for training a mitosis
+				classifier.
+                \item B. CNN architecture. Input data is 3 timepoints, 8 x 64 x 64 pixel crop, centered around
+				the annotation ZYX+t centroid. Output is probabilities for classification as mitotic or non-mitotic
+                
+			
+            \end{itemize}
+        \end{column}
+    \end{columns}
+}
+
+\end{frame}
+
+
+\section{TrackMate-Oneat: Auto Track Correction}
+
+\begin{frame}{TrackMate-Oneat: Auto Track Correction}
+
+% Large figure at the beginning
+\only<1>{
+    \begin{center}
+        \includegraphics[width=0.4\textwidth]{presentation_images/track_oneat_metrics.png}
+    \end{center}
+}
+
+% Shrunk figure + text overlay for subsequent slides
+\only<2->{
+    \begin{columns}
+        \begin{column}{0.4\textwidth}
+            \includegraphics[width=\textwidth]{presentation_images/track_oneat_metrics.png}
+        \end{column}
+        \begin{column}{0.55\textwidth}
+            \begin{itemize}[<+->]
+                \item A-B. Cell Tracking Challenge format
+				quality estimations in Table S3 are based on an ROI of a dataset (A), where each cell is manually
+				tracked for as long it appears in the ROI.
+                \item Manual track annotations are formatted in CTC format, to
+				which automated tracking with TrackMate is then compared to estimate tracking quality. Division metrics
+				in C-J are based on a dataset where each cell division is manually annotated (B).
+                \item  C-E, I.
+				Division detections for Oneat (not connected with tracks), TrackMate-Oneat (Oneat divisions connected
+				with TrackMate tracks), TrackMate-Oneat + MARI principle (TrackMate-Oneat with max boundary set
+				for angle between mother cell and daughter cells), and TrackMate “native” track splitting, enabled in
+				TrackMate LAP linking algorithm.
+                \item H, J. Corresponding detection metrics. K. Manually annotated
+				ground truth tracks colorized by the Track ID assigned by automatic tracking used for the experiments
+			 
+			
+            \end{itemize}
+        \end{column}
+    \end{columns}
+}
+
+\end{frame}
+
+
+
+\section{XGBoost: Feature Ablation}
+
+\begin{frame}{XGBoost: Feature Ablation}
+
+% Large figure at the beginning
+\only<1>{
+    \begin{center}
+        \includegraphics[width=0.4\textwidth]{presentation_images/model_accuracy.png}
+    \end{center}
+}
+
+% Shrunk figure + text overlay for subsequent slides
+\only<2->{
+    \begin{columns}
+        \begin{column}{0.4\textwidth}
+            \includegraphics[width=\textwidth]{presentation_images/model_accuracy.png}
+        \end{column}
+        \begin{column}{0.55\textwidth}
+            \begin{itemize}[<+->]
+                \item A. Classifier
+				training dataset sample counts across dataset time.
+                \item B. Mean and s.d. prediction confidence of predicted class of
+				XGBoost-based predictions, colored by class.
+				\item C. Timewise accuracy confusion matrix of XGBoost-
+				based predictions.	
+				\item D. Percent point-wise accuracy difference to baseline accuracy of the XGBoost
+				model for leaving out a single feature
+			    \item G. Feature coefficients for a logistic regressor model. All
+				calculations in B, C, D, and E are averaged out for 20 iterations of randomized test-train split, model
+				training and prediction		
+
+            \end{itemize}
+        \end{column}
+    \end{columns}
+}
+
+\end{frame}
+
+
+\begin{frame}{Inception Model Prediction}
+	\begin{itemize}[<+->]
+		\item A totally theoretical physics based network, on ideas of non-equilibrium statistical physics (later slides).
+		\item Cell type $\rightarrow$ Track label, Motion type $\rightarrow$ Another Track label
+		\item $F$ features along channel dimension, T as other dimension: Input Data for Neural Network(s)
+		\item 1D densenet as the model for training a) Cell type/Track type b) Motion type
+		\item Not whole track in training, cut out tracklets. Feature not Vision based neural network.
+		\begin{alertblock}{Model can Predict!}
+			Given a cut-out of tracklet it can reliably predict a) \& b)
+		\end{alertblock}
+		 \end{itemize}
+  \end{frame}
   
-    	  \end{frame}
-    
-    \subsection{Mitosis Action Classification: Oneat}
-    \frame{\sectionpage}
-    \begin{frame}{Mitosis Action Classification}
-        
-        	\begin{itemize}[<+->]
-        	
-        			\item Mitosis is a process that completes in $\delta T$ time-frame $\rightarrow$ action event
-        	
-        			\item Oneat: (Osis network for event as action topology) is a network that is jointly trained to find the plane of focus and space-time location of mitotic cells (arbitrary shaped images).
-        	
-        			\item Leveraging the segmentation of nuclei $\rightarrow$ apply trained network to obtain TZYX location of mitotic cells. 
-       			\item Oneat is organism and action event type independent, extensible to Apoptosis, static cell type classification.
-        		
-        	\end{itemize}
-    \end{frame}
-    \begin{frame}{Mitosis Action Classification}
-    \href{run:presentation_movies/all_timepoints_mitosis.mp4}{
-    	 \fcolorbox{blue!80!black}{blue!10}{% Border and background color
-    		\parbox[c][1.5em][c]{0.6\textwidth}{% Box size
-    			\centering\textbf{\textcolor{blue!90!black}{Action Classification Video (Click)}}% Text styling
-    		}%
-    	}%
-    }
-    
+
+\subsection{Time Cross Correlations}
+
+\frame{\sectionpage}
+\begin{frame}{Time Cross Correlations: Motivation}
+   \begin{itemize}[<+->]
+	   
+	   \item Equilibrium statistical mechanics $\rightarrow$ thermodynamic properties: partition function of the ensemble
+	   \item Nonequilibrium systems $\rightarrow$ no unique partition function 
+	   \item System properties obtained via time cross-correlations
+   \end{itemize}
+   \uncover<+->{\begin{equation*}
+		   \langle  v(t) v(t^\prime)  \rangle_\mathrm{time} = \frac{kT}{m}\exp^{-\gamma(t-t^\prime)/m}  \label{time-cross}
+   \end{equation*}}
    
-    \end{frame}
-    
+   \uncover<+->{
+	   \begin{alertblock}{Inception Model}
+		   Can we design a neural network to learn time-cross correlations $\rightarrow$ predict cell-fate (Basal, Goblet, Radial)/action (Mitosis, Apoptosis) classfication.
+	   \end{alertblock}
+   }
+   
+\end{frame}
+
+\begin{frame}{Time Cross Correlations}
+   
+   
+   
+   \uncover<+->{
+	   Consider the vector of morphodynamic properties $\vec{A(t)}$, let us compute time average of this vector
+	   \begin{equation*}
+		   \langle \vec{A} \rangle = \frac{1}{\tau}\int_0^\tau dt \vec{A(t)}
+   \end{equation*}}
+   
+   
+   \uncover<+->{
+	   Subtract the average to get the fluctuation $\delta \vec{A}$
+	   \begin{equation*}
+		   \delta \vec{A(t)} = \vec{A(t)} - \langle \vec{A} \rangle 
+   \end{equation*}}	
+   
+   
+   \uncover<+->{
+	   The time-averaged product of two fluctuations 
+	   \begin{equation*}
+		   C(t) = \frac{1}{\tau}\int_0^\tau ds \delta \vec{A}(s)\delta \vec{A}(t + s) \label{cross-corr}
+	   \end{equation*}
+	   $C(t)$: cross-correlation of the morphodynamic feature vector.
+   }	
+   
+   
+   
+\end{frame}
+
+\begin{frame}{Neural Network: Learning cross-correlations}
+   \begin{itemize}[<+->]
+	   \item Construct a $(B,F,T)$ dimensional tensor, B: batch dimension, F: channels/features and T: time interval, take all the tracks belonging to a certain cell type $S$.
+	   \item Inception Model: Customized $1D$ Densenet model with soft attention over time 
+	   \item Convolution operations in Densenet $=$ computing the cross correlations as 1D convolutions are mathematically the same.
+	   \item Training data: several tracks of $25$ timepoints with $18$ features for each cell type $S$ 
+	   \item Data is $Z$ scored to have zero mean and are normalized by the standard deviation of the feature vector (component wise) with $S$ being the ground truth label
+	   \item Categorical Cross entropy as objective to train the network to classify trajectories as belonging to certain cell type.
+   \end{itemize}
+\end{frame}
+\begin{frame}{Neural Network: Learning cross-correlations}
+   \begin{columns} % Use columns for better layout
+	   \begin{column}{0.5\textwidth} % Adjust width as needed
+		   \includegraphics[width=0.8\linewidth, angle=-90]{presentation_images/1DCNN.png} % Use \linewidth to fit within the column
+	   \end{column}
+	   
+	   \begin{column}{0.5\textwidth} 
+		   
+		   \begin{itemize}[<+->]
+			   \item Input 1D data with features as channels $\rightarrow$ 1D Densenet: a) Convolutional, b) Dense, c) Transition, d) Attention block.
+			   \item Convolutions compute temporal correlations b/w features
+			   \item Network output class: cell type, $S$ (Goblet, Basal, Radial)/ action class, $A$ (Mitosis, Non-Mitosis)  
+		   \end{itemize}
+	   \end{column}
+   \end{columns}
+\end{frame}
+  
+  
+
+
     \subsection{Lineage tree correction: TrackMate-Oneat}
     
      \frame{\sectionpage}
@@ -107,31 +448,7 @@
      	 }
      	\end{frame}
      	
-    \subsection{Membrane Segmentation: VollSeg + CellPose}
-    \frame{\sectionpage}
-    \begin{frame}{Membrane Segmentation}
-        
-       	\begin{itemize}[<+->]
-       		
-       		\item CellPose: Slice by Slice 3D segmentation, object shape stretched, 3D features washed out.
-       		
-       		\item Mode VollSeg: Autoencoder to enhance membrane edges $\rightarrow$  Nuclei seeds perform 3D watershed.
-       		
-       		\item Computer vision methods to remove 'overflows', cellpose regions as mask.
-       		\href{run:presentation_movies/fifth_data_membrane_segmentation.mp4}{
-       		\fcolorbox{blue!80!black}{blue!10}{% Border and background color
-       			\parbox[c][1.5em][c]{0.6\textwidth}{% Box size
-       				\centering\textbf{\textcolor{blue!90!black}{Membrane Segmentation (Click)}}% Text styling
-       			}%
-       		}%
-       	}
-       		\begin{alertblock}{3D membrane leveraged segmentation}
-       			Leveraging nuclei seeds on membrane enhanced signal for 3D shape preserving segmentation
-       		\end{alertblock}
-       		
-       	\end{itemize}
-       	 
-    \end{frame}
+
     \subsection{Tracks: Nuclei $\rightarrow$ Membrane: NapaTrackMater}
     \frame{\sectionpage}
     \begin{frame}{Transfer Tracks}
@@ -198,97 +515,4 @@
         	  \end{itemize}
     \end{frame}
     
-    \begin{frame}{Inception Model Prediction}
-      \begin{itemize}[<+->]
-      	\item A totally theoretical physics based network, on ideas of non-equilibrium statistical physics (later slides).
-      	\item Cell type $\rightarrow$ Track label, Motion type $\rightarrow$ Another Track label
-      	\item $F$ features along channel dimension, T as other dimension: Input Data for Neural Network(s)
-      	\item 1D densenet as the model for training a) Cell type/Track type b) Motion type
-      	\item Not whole track in training, cut out tracklets. Feature not Vision based neural network.
-      	\begin{alertblock}{Model can Predict!}
-      		Given a cut-out of tracklet it can reliably predict a) \& b)
-      	\end{alertblock}
-      	 \end{itemize}
-    \end{frame}
-    
- 
- \subsection{Time Cross Correlations}
- 
- \frame{\sectionpage}
- \begin{frame}{Time Cross Correlations: Motivation}
- 	\begin{itemize}[<+->]
- 		
- 		\item Equilibrium statistical mechanics $\rightarrow$ thermodynamic properties: partition function of the ensemble
- 		\item Nonequilibrium systems $\rightarrow$ no unique partition function 
- 		\item System properties obtained via time cross-correlations
- 	\end{itemize}
- 	\uncover<+->{\begin{equation*}
- 			\langle  v(t) v(t^\prime)  \rangle_\mathrm{time} = \frac{kT}{m}\exp^{-\gamma(t-t^\prime)/m}  \label{time-cross}
- 	\end{equation*}}
- 	
- 	\uncover<+->{
- 		\begin{alertblock}{Inception Model}
- 			Can we design a neural network to learn time-cross correlations $\rightarrow$ predict cell-fate (Basal, Goblet, Radial)/action (Mitosis, Apoptosis) classfication.
- 		\end{alertblock}
- 	}
- 	
- \end{frame}
- 
- \begin{frame}{Time Cross Correlations}
- 	
- 	
- 	
- 	\uncover<+->{
- 		Consider the vector of morphodynamic properties $\vec{A(t)}$, let us compute time average of this vector
- 		\begin{equation*}
- 			\langle \vec{A} \rangle = \frac{1}{\tau}\int_0^\tau dt \vec{A(t)}
- 	\end{equation*}}
- 	
- 	
- 	\uncover<+->{
- 		Subtract the average to get the fluctuation $\delta \vec{A}$
- 		\begin{equation*}
- 			\delta \vec{A(t)} = \vec{A(t)} - \langle \vec{A} \rangle 
- 	\end{equation*}}	
- 	
- 	
- 	\uncover<+->{
- 		The time-averaged product of two fluctuations 
- 		\begin{equation*}
- 			C(t) = \frac{1}{\tau}\int_0^\tau ds \delta \vec{A}(s)\delta \vec{A}(t + s) \label{cross-corr}
- 		\end{equation*}
- 		$C(t)$: cross-correlation of the morphodynamic feature vector.
- 	}	
- 	
- 	
- 	
- \end{frame}
- 
- \begin{frame}{Neural Network: Learning cross-correlations}
- 	\begin{itemize}[<+->]
- 		\item Construct a $(B,F,T)$ dimensional tensor, B: batch dimension, F: channels/features and T: time interval, take all the tracks belonging to a certain cell type $S$.
- 		\item Inception Model: Customized $1D$ Densenet model with soft attention over time 
- 		\item Convolution operations in Densenet $=$ computing the cross correlations as 1D convolutions are mathematically the same.
- 		\item Training data: several tracks of $25$ timepoints with $18$ features for each cell type $S$ 
- 		\item Data is $Z$ scored to have zero mean and are normalized by the standard deviation of the feature vector (component wise) with $S$ being the ground truth label
- 		\item Categorical Cross entropy as objective to train the network to classify trajectories as belonging to certain cell type.
- 	\end{itemize}
- \end{frame}
- \begin{frame}{Neural Network: Learning cross-correlations}
- 	\begin{columns} % Use columns for better layout
- 		\begin{column}{0.5\textwidth} % Adjust width as needed
- 			\includegraphics[width=0.8\linewidth, angle=-90]{presentation_images/1DCNN.png} % Use \linewidth to fit within the column
- 		\end{column}
- 		
- 		\begin{column}{0.5\textwidth} 
- 			
- 			\begin{itemize}[<+->]
- 				\item Input 1D data with features as channels $\rightarrow$ 1D Densenet: a) Convolutional, b) Dense, c) Transition, d) Attention block.
- 				\item Convolutions compute temporal correlations b/w features
- 				\item Network output class: cell type, $S$ (Goblet, Basal, Radial)/ action class, $A$ (Mitosis, Non-Mitosis)  
- 			\end{itemize}
- 		\end{column}
- 	\end{columns}
- \end{frame}
-    
     

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-\documentclass[aspectratio=43]{beamer}
+\documentclass[aspectratio=43, 8pt]{beamer}
 \usepackage[english]{babel}
-\usepackage{amsmath,amssymb,amsfonts,bbold,bm,color,dcolumn,hhline,verbatim,rotating,epsfig,fancyhdr,graphicx,nicefrac,psfrag,pstricks,cite,subfigure,bbm,makeidx,dsfont}
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 \input{chapters/preamble}
 \title{Trajectory analysis: Xenopus} 
 \subtitle{Perspective: Non-equilibrium system}
@@ -23,7 +23,7 @@
     
     \input{chapters/collecting-trajectories.tex}
      
-    \section*{Acknowledgments} %You can remove this if you do not want to use it
+    \section*{Acknowledgments} 
         \begin{frame}{Acknowledgments}
             The author is extremely thankful to Jean-Zay supercomputing support for this project.
         \end{frame}

presentation.toc

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 \babel@toc {english}{}\relax 
-\beamer@sectionintoc {1}{Collecting Trajectories}{3}{0}{1}
-\beamer@subsectionintoc {1}{1}{Nuclei Segmentation: VollSeg}{3}{0}{1}
-\beamer@subsectionintoc {1}{2}{Mitosis Action Classification: Oneat}{8}{0}{1}
-\beamer@subsectionintoc {1}{3}{Lineage tree correction: TrackMate-Oneat}{14}{0}{1}
-\beamer@subsectionintoc {1}{4}{Membrane Segmentation: VollSeg + CellPose}{21}{0}{1}
-\beamer@subsectionintoc {1}{5}{Tracks: Nuclei $\rightarrow $ Membrane: NapaTrackMater}{26}{0}{1}
-\beamer@subsectionintoc {1}{6}{Point Cloud based morphodynamic features: NapaTrackMater}{32}{0}{1}
-\beamer@subsectionintoc {1}{7}{Trajectory Analysis: NapaTrackMater}{38}{0}{1}
-\beamer@subsectionintoc {1}{8}{Time Cross Correlations}{49}{0}{1}
+\beamer@sectionintoc {1}{Overall Workflow}{3}{0}{1}
+\beamer@sectionintoc {2}{Segmenation, Tracking and Action Classification}{8}{0}{2}
+\beamer@sectionintoc {3}{Trajectory feature analysis}{12}{0}{3}
+\beamer@sectionintoc {4}{Cell Fate Labelling}{18}{0}{4}
+\beamer@sectionintoc {5}{Cell Fate Classification: XGBoost}{23}{0}{5}
+\beamer@sectionintoc {6}{Oneat Architecture: Action Classification}{28}{0}{6}
+\beamer@sectionintoc {7}{TrackMate-Oneat: Auto Track Correction}{30}{0}{7}
+\beamer@sectionintoc {8}{XGBoost: Feature Ablation}{34}{0}{8}
+\beamer@subsectionintoc {8}{1}{Time Cross Correlations}{45}{0}{8}
+\beamer@subsectionintoc {8}{2}{Lineage tree correction: TrackMate-Oneat}{63}{0}{8}
+\beamer@subsectionintoc {8}{3}{Tracks: Nuclei $\rightarrow $ Membrane: NapaTrackMater}{70}{0}{8}
+\beamer@subsectionintoc {8}{4}{Point Cloud based morphodynamic features: NapaTrackMater}{76}{0}{8}
+\beamer@subsectionintoc {8}{5}{Trajectory Analysis: NapaTrackMater}{82}{0}{8}