Related papers: Markov-type state models to describe non-Markovian…
There are multiple ways in which a stochastic system can be out of statistical equilibrium. It might be subject to time-varying forcing; or be in a transient phase on its way towards equilibrium; it might even be in equilibrium without us…
We present a new method that enables the identification and analysis of both transition and metastable conformational states from atomistic or coarse-grained molecular dynamics (MD) trajectories. Our algorithm is presented and studied by…
Markov State Models (MSM) are widely used to elucidate dynamic properties of molecular systems from unbiased Molecular Dynamics (MD). However, the implementation of reweighting schemes for MSMs to analyze biased simulations, for example…
It is a challenge to obtain an accurate model of the state-to-state dynamics of a complex biological system from molecular dynamics (MD) simulations. In recent years, Markov State Models have gained immense popularity for computing…
A possibly time-dependent transition intensity matrix or generator $(Q(t))$ characterizes the law of a Markov jump process (MP). For a time homogeneous MP, the transition probability matrix (TPM) can be expressed as a matrix exponential of…
We present a maximum-caliber method for inferring transition rates of a Markov State Model (MSM) with perturbed equilibrium populations, given estimates of state populations and rates for an unperturbed MSM. It is similar in spirit to…
In this work we address the analysis of discrete-time models of structured metapopulations subject to environmental stochasticity. Previous works on these models made use of the fact that migrations between the patches can be considered…
Hidden semi-Markov Models (HSMM's) - while broadly in use - are restricted to a discrete and uniform time grid. They are thus not well suited to explain often irregularly spaced discrete event data from continuous-time phenomena. We show…
We study the long-time dynamics in non-Markovian single-population stochastic models, where one or more reactions are modelled as a stochastic process with a fat-tailed non-exponential distribution of waiting times, mimicking long-term…
We are interested in the connection between a metastable continuous state space Markov process (satisfying e.g. the Langevin or overdamped Langevin equation) and a jump Markov process in a discrete state space. More precisely, we use the…
Markov state models (MSMs) are a widely used method for approximating the eigenspectrum of the molecular dynamics propagator, yielding insight into the long-timescale statistical kinetics and slow dynamical modes of biomolecular systems.…
A number of modern sampling methods probe long time behavior in complex biomolecules using a set of relatively short trajectory segments. Markov state models (MSMs) can be useful in analyzing such data sets, but in particularly complex…
Markov chains are a common framework for individual-based state and time discrete models in ecology and evolution. Their use, however, is largely limited to systems with a low number of states, since the transition matrices involved pose…
The well-established methodology for the estimation of hidden semi-Markov models (HSMMs) as hidden Markov models (HMMs) with extended state spaces is further developed to incorporate covariate influences across all aspects of the state…
Generating synthetic financial time series that preserve the statistical properties of real market data is essential for stress testing, risk model validation, and scenario design. Existing approaches struggle to simultaneously reproduce…
Molecular simulations can provide microscopic insight into the physical and chemical driving forces of complex molecular processes. Despite continued advancement of simulation methodology, model errors may lead to inconsistencies between…
Markov state models represent a popular means to interpret molecular dynamics trajectories in terms of memoryless transitions between metastable conformational states. To provide a mechanistic understanding of the considered biomolecular…
With recent advances in structural biology, including experimental techniques and deep learning-enabled high-precision structure predictions, molecular dynamics methods that scale up to large biomolecular systems are required. Current…
Non-Markovian models have great expressive power, at the cost of complex analysis of the stochastic process. The method of Stochastic State Classes (SSCs) derives closed-form analytical expressions for the joint Probability Density…
Markov cohort state-transition models have been the standard approach for simulating the prognosis of patients or, more generally, the life trajectories of individuals over a time period. Current approaches for estimating the variance of a…