Related papers: Error Breakdown and Sensitivity Analysis of Dynami…

The variational principle for conformational dynamics has enabled the systematic construction of Markov state models through the optimization of hyperparameters by approximating the transfer operator. In this note we discuss why lag time of…

Rate processes are often modeled using Markov-State Models (MSM). Suppose you know a prior MSM, and then learn that your prediction of some particular observable rate is wrong. What is the best way to correct the whole MSM? For example,…

State-space models (SSMs) have recently emerged as a compelling alternative to Transformers for sequence modeling tasks. This paper presents a theoretical generalization analysis of selective SSMs, the core architectural component behind…

Direct simulation of biomolecular dynamics in thermal equilibrium is challenging due to the metastable nature of conformation dynamics and the computational cost of molecular dynamics. Biased or enhanced sampling methods may improve the…

With increasingly available computer-based or online assessments, researchers have shown keen interest in analyzing log data to improve our understanding of test takers' problem-solving processes. In this paper, we propose a multi-state…

The problem of real-time remote tracking and reconstruction of a two-state Markov process is considered here. A transmitter sends samples from an observed information source to a remote monitor over an unreliable wireless channel. The…

In this paper we present elementary computations for some Markov modulated counting processes, also called counting processes with regime switching. Regime switching has become an increasingly popular concept in many branches of science. In…

Markov Decision Processes (MDPs) are mathematical models of sequential decision-making under uncertainty that have found applications in healthcare, manufacturing, logistics, and others. In these models, a decision-maker observes the state…

This work attempts to approximate a linear Gaussian system with a finite-state hidden Markov model (HMM), which is found useful in solving sophisticated event-based state estimation problems. An indirect modeling approach is developed,…

Environmental time series data observed at high frequencies can be studied with approaches such as hidden Markov and semi-Markov models (HMM and HSMM). HSMMs extend the HMM by explicitly modeling the time spent in each state. In a…

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…

Multiple sampling strategies commonly used in molecular dynamics, such as umbrella sampling and alchemical free energy methods, involve sampling from multiple thermodynamic states. Commonly, the data are then recombined to construct…

State space models (SSMs) provide a flexible framework for modeling complex time series via a latent stochastic process. Inference for nonlinear, non-Gaussian SSMs is often tackled with particle methods that do not scale well to long time…

Non-equilibrium Markov State Modeling (MSM) has recently been proposed [Phys. Rev. E 94, 053001 (2016)] as a possible route to construct a physical theory of sliding friction from a long steady state atomistic simulation: the approach…

State space models (SSMs) are a flexible approach to modeling complex time series. However, inference in SSMs is often computationally prohibitive for long time series. Stochastic gradient MCMC (SGMCMC) is a popular method for scalable…

The bisimulation metric (BSM) is a powerful tool for analyzing state similarities within a Markov decision process (MDP), revealing that states closer in BSM have more similar optimal value functions. While BSM has been successfully…

We consider risk-sensitive Markov decision processes (MDPs), where the MDP model is influenced by a parameter which takes values in a compact metric space. We identify sufficient conditions under which small perturbations in the model…

For additive actuator and sensor faults, we propose a systematic method to design a state-space fault estimation filter directly from Markov parameters identified from fault-free data. We address this problem by parameterizing a…

Molecular Dynamics (MD) is a powerful computational microscope for probing protein functions. However, the need for fine-grained integration and the long timescales of biomolecular events make MD computationally expensive. To address this,…

This work studies remote state estimation of multiple linear time-invariant systems over shared wireless time-varying communication channels. We model the channel states by a semi-Markov process which captures both the random holding period…