Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Theoretical restrictions on longest implicit timescales in Markov state
  models of biomolecular dynamics   Markov state models (MSMs) have been widely used to analyze computer
simulations of various biomolecular systems. They can capture conformational
transitions much slower than an average or maximal length of a single molecular
dynamics (MD) trajectory from the set of trajectories used to build the MSM. A
rule of thumb claiming that the slowest implicit timescale captured by an MSM
should be comparable by the order of magnitude to the aggregate duration of all
MD trajectories used to build this MSM has been known in the field. However,
this rule have never been formally proved. In this work, we present analytical
results for the slowest timescale in several types of MSMs, supporting the
above rule. We conclude that the slowest implicit timescale equals the product
of the aggregate sampling and four factors that quantify: (1) how much
statistics on the conformational transitions corresponding to the longest
implicit timescale is available, (2) how good the sampling of the destination
Markov state is, (3) the gain in statistics from using a sliding window for
counting transitions between Markov states, and (4) a bias in the estimate of
the implicit timescale arising from finite sampling of the conformational
transitions. We demonstrate that in many practically important cases all these
four factors are on the order of unity, and we analyze possible scenarios that
could lead to their significant deviation from unity. Overall, we provide for
the first time analytical results on the slowest timescales captured by MSMs.
These results can guide further practical applications of MSMs to biomolecular
dynamics and allow for higher computational efficiency of simulations.

34
The categories of this paper are: chem-ph
35
The categories of this paper are: mtrl-th
26
The categories of this paper are: bayes-an
12
The categories of this paper are: nucl-th
16
The categories of this paper are: stat
27
The categories of this paper are: comp-gas
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The categories of this paper are: alg-geom
36
The categories of this paper are: cmp-lg
11
The categories of this paper are: hep-lat
0
The categories of this paper are: hep-ph
24
The categories of this paper are: dg-ga
5
The categories of this paper are: gr-qc
31
The categories of this paper are: ao-sci
22
The categories of this paper are: chao-dyn
9
The categories of this paper are: nlin
4
The categories of this paper are: cond-mat