Merge pull request #184 from markovmodel/revision-cw

revision-cw

Author: cwehmeyer

binder/environment.yml

@@ -4,4 +4,5 @@ channels:
   - defaults
 dependencies:
   - pyemma_tutorials 
+  - nomkl
 

manuscript/manuscript.tex

@@ -67,6 +67,9 @@
 %%% ARTICLE START
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
+\hyphenation{Mar-kov}
+\setlength{\emergencystretch}{3em}
+
 \begin{document}
 
 \begin{frontmatter}
@@ -152,13 +155,13 @@ \subsection{Markov state models}
 \end{equation}
 When the ITS become approximately constant with the lag time, we say that our timescales have converged and choose the smallest lag time with the converged timescales in order to maximize the model's temporal resolution.
 
-Once we have used the ITS to choose the lag time, we can check whether a given transition probability matrix $\mathbf{P}(\tau)$ is approximately Markovian using the Chapman-Kolmogorov (CK) test~\cite{noe-folding-pathways}.
+Once we have used the ITS to choose the lag time, we can check whether a given transition probability matrix $\mathbf{P}(\tau)$ is approximately Markovian using the Chapman-Kolmogorov (CK) test~\cite{noe-folding-pathways,msm-jhp}.
 The CK property for a Markovian matrix is,
 \begin{equation}
 \mathbf{P}(k \tau) = \mathbf{P}^k(\tau),
 \end{equation}
 where the left-hand side of the equation corresponds to an MSM estimated at lag time $k\tau$, where $k$ is an integer larger than~$1$, whereas the right-hand side of the equation is our estimated MSM transition probability matrix to the $k^\textrm{th}$ power.
-By assessing how well the approximated transition probability matrix adheres to the CK property, we can validate the appropriateness of the Markovian assumption for the model.
+By assessing how well the approximated transition probability matrix adheres to the CK property, we can validate the appropriateness of the Markovian assumption for the model (see Sec.~IV.F in~\cite{msm-jhp}).
 
 Once validated, the transition matrix can be decomposed into eigenvectors and eigenvalues.
 The highest eigenvalue, $\lambda_1(\tau)$, is unique and equal to $1$.
@@ -248,7 +251,7 @@ \subsection{Variational approach and TICA}
 
 \subsection{Hidden Markov state models}
 
-\begin{figure}
+\begin{figure}[ht]
 \includegraphics[width=0.48\textwidth]{figure_1}
 \caption{The HMM transition matrix $\tilde{\mathbf{P}}(\tau)$ propagates the hidden state trajectory $\tilde{s}(t)$ (orange circles) and, at each time step $t$, the emission into the observable state $s(t)$ (cyan circles) is governed by the emission probabilities $\bm{\chi}\left( s(t) \middle| \tilde{s}(t) \right)$.}
 \label{fig:hmm-scheme}
@@ -285,7 +288,8 @@ \subsection{Hidden Markov state models}
 \subsection{Software and installation}
 
 We utilize Jupyter~\cite{jupyter} notebooks to show code examples along with figures and interactive widgets to display molecules.
-The user can install all necessary packages in one step using the \texttt{conda} command provided by the Anaconda Python stack (\url{https://anaconda.com}).
+The user can install all necessary packages in one step using the \texttt{conda} command provided by the Anaconda Python 
+stack (\url{https://conda.io/miniconda.html}).
 We recommend Anaconda because it resolves and installs dependencies as well as provides pre-compiled versions of common packages.
 The tutorial installation contains a launcher command to start the Jupyter notebook server as well as the notebook files.
 
@@ -312,7 +316,9 @@ \subsection{Software and installation}
 The tutorial software is currently supported for Python versions~$3.5$ and~$3.6$ on the operating systems Linux, OSX, and Windows.
 
 Should the user prefer not to use Anaconda, a manual installation via the pip installer is possible.
-Alternatively, one can use the Binder service (\url{https://mybinder.org}) to view and run the tutorials online in any browser.
+Alternatively, one can use the Binder service 
+(\href{https://mybinder.org/v2/gh/markovmodel/pyemma_tutorials/master?filepath=notebooks}{https://mybinder.org}) to view 
+and run the tutorials online in any browser.
 
 \section{PyEMMA tutorials}
 
@@ -325,6 +331,15 @@ \section{PyEMMA tutorials}
 
 \subsection{The PyEMMA workflow}
 
+\begin{figure}[ht]
+\includegraphics[width=0.48\textwidth]{figure_2}
+\caption{The PyEMMA workflow: MD trajectories are processed and discretized (first row).
+A Markov state model is estimated from the resulting discrete trajectories and validated (middle row).
+By iterating between data processing and MSM estimation/validation,
+a dynamical model is obtained that can be analyzed (last row).}
+\label{fig:workflowchart}
+\end{figure}
+
 In short, the workflow (Fig.~\ref{fig:workflowchart}) for a full analysis of an MD dataset might consist of,
 \begin{itemize}
 	\item extracting molecular features from the raw data (01),
@@ -351,17 +366,18 @@ \subsection{The PyEMMA workflow}
 we chose to adopt a sequential approach where only the hyper-parameters of the current stage are optimized.
 This approach is not only computationally cheaper but allows us to discuss the significance of the necessary modeling choices.
 
-\begin{figure}[bt]
-\includegraphics[width=0.48\textwidth]{figure_2}
-\caption{The PyEMMA workflow: MD trajectories are processed and discretized (first row).
-A Markov state model is estimated from the resulting discrete trajectories and validated (middle row).
-By iterating between data processing and MSM estimation/validation,
-a dynamical model is obtained that can be analyzed (last row).}
-\label{fig:workflowchart}
-\end{figure}
-
 \subsection{Feature selection}
 
+\begin{figure}[bht]
+\includegraphics{figure_3}
+\caption{Example analysis of the conformational dynamics of a pentapeptide backbone:
+(a)~The Trp-Leu-Ala-Leu-Leu pentapeptide in licorice representation~\cite{vmd}.
+(b)~The VAMP-2 score indicates which of the tested featurizations contains the highest kinetic variance.
+(c)~The sample free energy projected onto the first two time-lagged independent components (ICs) at lag time $\tau=0.5$~ns shows multiple minima and
+(d)~the time series of the first two ICs of the first trajectory show rare jumps.}
+\label{fig:io-to-tica}
+\end{figure}
+
 In Markov state modeling, our objective is to model the slow dynamics of a molecular process.
 In order to approximate the slow dynamics in a statistically efficient manner,
 a lower dimensional representation of our simulation data is necessary.
@@ -400,16 +416,6 @@ \subsection{Dimensionality reduction}
 
 We demonstrate how to apply TICA, suggest how to interpret the projected coordinates, and compare the results to other dimension reduction techniques in notebook~02.
 
-\begin{figure}
-\includegraphics{figure_3}
-\caption{Example analysis of the conformational dynamics of a pentapeptide backbone:
-(a)~The Trp-Leu-Ala-Leu-Leu pentapeptide in licorice representation~\cite{vmd}.
-(b)~The VAMP-2 score indicates which of the tested featurizations contains the highest kinetic variance.
-(c)~The sample free energy projected onto the first two time-lagged independent components (ICs) at lag time $\tau=0.5$~ns shows multiple minima and
-(d)~the time series of the first two ICs of the first trajectory show rare jumps.}
-\label{fig:io-to-tica}
-\end{figure}
-
 \subsection{Discretization}
 
 TICA yields a representation of our molecular simulation data with a reduced dimensionality,
@@ -421,7 +427,7 @@ \subsection{Discretization}
 
 \subsection{MSM estimation and validation}
 
-\begin{figure}
+\begin{figure}[ht]
 \includegraphics{figure_4}
 \caption{Example analysis of the conformational dynamics of a pentapeptide backbone:
 (a)~The convergence behavior of the implied timescales associated with the four slowest processes.
@@ -456,7 +462,7 @@ \subsection{MSM estimation and validation}
 
 \subsection{Analyzing the MSM}
 
-\begin{figure}
+\begin{figure}[ht]
 \includegraphics{figure_5}
 \caption{Example analysis of the conformational dynamics of a pentapeptide backbone:
 (a)~The reweighted free energy surface projected onto the first two independent components exhibits five minima which
@@ -467,7 +473,7 @@ \subsection{Analyzing the MSM}
 \label{fig:msm-analysis}
 \end{figure}
 
-\begin{figure}
+\begin{figure}[ht]
 \includegraphics{figure_6}
 \caption{Example analysis of the conformational dynamics of a pentapeptide backbone:
 visualization of the transition paths from $\mathcal{S}_2$ to $\mathcal{S}_4$.
@@ -537,7 +543,7 @@ \subsection{Analyzing the MSM}
 
 \subsection{Connecting the MSM with experimental data}
 
-\begin{figure}
+\begin{figure}[ht]
 \includegraphics{figure_7}
 \caption{Example analysis of the conformational dynamics of a pentapeptide backbone:
 (a)~the Trp-1 SASA autocorrelation function yields a weak signal which, however,