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manuscript/manuscript.tex

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@@ -160,7 +160,8 @@ \subsection{Markov state models}
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\begin{equation}
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\mathbf{P}(k \tau) = \mathbf{P}^k(\tau),
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\end{equation}
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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.
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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~$1$,
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whereas the right-hand side of the equation is our estimated MSM transition probability matrix to the $k^\textrm{th}$ power.
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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}).
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Once validated, the transition matrix can be decomposed into eigenvectors and eigenvalues.
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we can similarly compute the metastable kinetics, apply TPT, visualize the network, and obtain physical observables.
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For an extensive discussion of details about HMM properties and the estimation algorithm in general, we suggest Ref.~\cite{hmm-tutorial}.
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For its specific application to the discretization of MSMs using HMMs, we suggest Ref.~\cite{noe-proj-hid-msm}. A generalized extension for estimating this type of low-dimensional projection from the data is given in Ref.~\cite{wu2015projected}.
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For its specific application to the discretization of MSMs using HMMs, we suggest Ref.~\cite{noe-proj-hid-msm}.
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A generalized extension for estimating this type of low-dimensional projection from the data is given in Ref.~\cite{wu2015projected}.
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\subsection{Software and installation}
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The underlying software stack for running the tutorial consists of:
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\begin{itemize}
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\item \textbf{PyEMMA} -- MSM/HMM estimation, validation, analysis, and visualization, and its dependencies~\cite{pyemma}
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\item mdshare -- A downloader for MD data from a public server
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\item notebook -- The Jupyter~\cite{jupyter} notebook tool used for running the tutorials, along with extension packages jupyter\_contrib\_nbextensions and nbexamples
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\item matplotlib -- A plotting library~\cite{matplotlib}
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\item nglview -- Widget for active viewing of molecular structures in Jupyter environments~\cite{nglview}
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\item \textbf{PyEMMA} -- MSM/HMM estimation, validation, analysis, and visualization, and its dependencies~\cite{pyemma}
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\item mdshare -- A downloader for MD data from a public server
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\item notebook -- The Jupyter~\cite{jupyter} notebook tool used for running the tutorials, along with extension packages jupyter\_contrib\_nbextensions and nbexamples
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\item matplotlib -- A plotting library~\cite{matplotlib}
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\item nglview -- Widget for active viewing of molecular structures in Jupyter environments~\cite{nglview}
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\end{itemize}
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The tutorial software is currently supported for Python versions~$3.5$ and~$3.6$ on the operating systems Linux, OSX, and Windows.

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