[manuscript] unify notation for notebook numbers

Author: thempel

manuscript/manuscript.tex

@@ -318,11 +318,11 @@ \subsection{Software and installation}
 \section{PyEMMA tutorials}
 
 This tutorial consists of nine Jupyter notebooks which introduce the basic features of PyEMMA.
-The first notebook (00), which we will summarize in the following, showcases the entire estimation,
+The first notebook~00, which we will summarize in the following, showcases the entire estimation,
 validation, and analysis workflow for a small example system.
-The goal of this introductory notebook (00) is to provide the user with the typical steps required to obtain a validated MSM analysis of protein or peptide simulation data.
-The seven subsequent notebooks (01--07) provide in-depth lessons on specific topics,
-and the last notebook (08) contains guidelines on how to deal with common problems during MSM estimation.
+The goal of this introductory notebook~00 is to provide the user with the typical steps required to obtain a validated MSM analysis of protein or peptide simulation data.
+The seven subsequent notebooks~01--07 provide in-depth lessons on specific topics,
+and the last notebook~08 contains guidelines on how to deal with common problems during MSM estimation.
 
 \subsection{The PyEMMA workflow}
 
@@ -338,12 +338,12 @@ \subsection{The PyEMMA workflow}
 	\item coarse-graining the MSM using a hidden Markov model approach (07).
 \end{itemize}
 
-For the remainder of this manuscript we will walk through the first notebook (00).
+For the remainder of this manuscript we will walk through the first notebook~00.
 In notebook~00 we analyze a dataset of the Trp-Leu-Ala-Leu-Leu pentapeptide (Fig.~\ref{fig:io-to-tica}a),
 consisting of~$25$ independent MD trajectories conducted in implicit solvent with frames saved at an interval of~$0.1$~ns.
 We present the results obtained in this notebook,
 thereby providing an example of how results generated using PyEMMA can be integrated into research publications.
-The figures that will be displayed in the following are created in the showcase notebook (00) and can be easily reproduced.
+The figures that will be displayed in the following are created in the showcase notebook~00 and can be easily reproduced.
 
 Note that the modeler has to select hyper-parameters at most stages throughout the workflow.
 This selection must be done carefully as poor choices make it hard, or even impossible, to build a good MSM.
@@ -371,15 +371,15 @@ \subsection{Feature selection}
 and the more general variational approach for Markov processes (VAMP)~\cite{vamp-preprint}
 provide a systematic means to quantitatively compare multiple representations of the simulation data.
 In particular, we can use a scalar score obtained using VAMP to directly compare the ability of certain features to capture slow dynamical modes in a particular molecular system.
-In Notebook (01), we present in detail how to extract features from MD datasets and how to systematically compare them.
+In notebook~01, we present in detail how to extract features from MD datasets and how to systematically compare them.
 
 Throughout this tutorial, we utilize the VAMP-2 score, which maximizes the kinetic variance contained in the features~\cite{kinetic-maps}.
 We should always evaluate the score in a cross-validated manner to ensure that we neither include too few features (under-fitting) or too many features (over-fitting)~\cite{gmrq,vamp-preprint}.
 To choose among three different molecular features reflecting protein structure,
-we compute the (cross-validated) VAMP-2 score (notebook 00).
+we compute the (cross-validated) VAMP-2 score (notebook~00).
 Although we cannot MSM optimize lag times with a variational score\cite{husic2017note}, such as VAMP-2,
 it is important to ensure that properties that we optimize are robust as a function of lag time. 
-Consequently, we compute the VAMP-2 score at several lag times (notebook 00). 
+Consequently, we compute the VAMP-2 score at several lag times (notebook~00). 
 We find that the relative rankings of the different molecular features are highly robust as a function of lag time. 
 We show one example of this ranking and the absolute VAMP-2 scores for lag time~$0.5$~ns in Fig.~\ref{fig:io-to-tica}b. 
 We find that backbone torsions contain more kinetic variance than the backbone heavy atom positions or the distances between them (Fig.~\ref{fig:io-to-tica}b).
@@ -399,7 +399,7 @@ \subsection{Dimensionality reduction}
 Discrete jumps between the minima can be observed by visualizing the transformation of the first trajectory into these ICs (Fig.~\ref{fig:io-to-tica}d).
 We thus assume that our TICA-transformed backbone torsion features describe one or more metastable processes.
 
-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).
+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}
@@ -417,8 +417,8 @@ \subsection{Discretization}
 which can greatly facilitate the decomposition of our system into the discrete Markovian states necessary for MSM estimation.
 Here, we use the $k$-means algorithm to segment the four dimensional TICA space into $k=75$ cluster centers.
 The number of cluster centers has been chosen to optimize the VAMP-2 score in a manner identical to how the feature selection was carried out above,
-which is shown in the showcase Notebook (00).
-A detailed comparison between different clustering techniques is provided in Notebook (02).
+which is shown in the showcase notebook~00.
+A detailed comparison between different clustering techniques is provided in notebook~02.
 
 \subsection{MSM estimation and validation}
 
@@ -451,7 +451,7 @@ \subsection{MSM estimation and validation}
 and shows that the MSM we have estimated at lag time $\tau=0.5$~ns indeed predicts the
 long-timescale behavior of our system within error (blue/shaded area).
 
-In Notebook (03), we demonstrate in detail how to estimate and validate MSMs with PyEMMA.
+In notebook~03, we demonstrate in detail how to estimate and validate MSMs with PyEMMA.
 
 \subsection{Analyzing the MSM}
 
@@ -532,7 +532,7 @@ \subsection{Analyzing the MSM}
 The transition network can be additionally visualized by plotting representative structures of the five metastable states $\mathcal{S}_{(1-5)}$ according to their committor probability (Fig.~\ref{fig:tpt-network}).
 It is easy to see from this depiction that the dominant pathway from $\mathcal{S}_2$ to $\mathcal{S}_4$ proceeds through $\mathcal{S}_5$.
 
-More details about (spectral) properties of MSMs and how to analyze them with PyEMMA are discussed in Notebook (04) and Notebook (05).
+More details about (spectral) properties of MSMs and how to analyze them with PyEMMA are discussed in notebook~04 and notebook~05.
 
 \subsection{Connecting the MSM with experimental data}
 
@@ -568,12 +568,12 @@ \subsection{Connecting the MSM with experimental data}
 We see that the predicted relaxation signal has a much larger amplitude for the nonequilibrium initialization,
 making it more likely to be experimentally measurable.
 
-In addition to a detailed demonstration of the above, Notebook (06) demonstrates how to compute J-couplings and dynamic fingerprints from MSMs.
+In addition to a detailed demonstration of the above, notebook~06 demonstrates how to compute J-couplings and dynamic fingerprints from MSMs.
 
 \subsection{Summary}
 
 In this section, we have summarized how to conduct an MSM-based analysis of biomolecular dynamics data using PyEMMA.
-For the full analysis, please refer to the first notebook (00).
+For the full analysis, please refer to the first notebook~00.
 All notebooks as well as detailed installation instructions are available on \githubrepository{}.
 
 \subsection{Modeling large systems}
@@ -597,7 +597,7 @@ \subsection{Modeling large systems}
 we explain how to deal with those in the tutorials (notebook~01).
 
 More details on how to model complex systems with the techniques presented here are described, e.g., by~\cite{plattner_protein_2015,plattner_complete_2017}.
-We further examine some symptoms that may indicate problematic or difficult datasets, and demonstrate how to deal with them in Notebook (08).
+We further examine some symptoms that may indicate problematic or difficult datasets, and demonstrate how to deal with them in notebook~08.
 
 \subsection{Advanced Methods}