Related papers: Optimized Markov State Models for Metastable Syste…
Multi-state models are commonly used for intermittent observations of a state over time, but these are generally based on the Markov assumption, that transition rates are independent of the time spent in current and previous states. In a…
Glass-forming systems, which are characterized by a highly disordered energy landscape, have been studied in physics by a simulation-based state space aggregation. The purpose of this article is to develop a path-independent approach within…
Equilibrium statistical mechanics is intended to link the microscopic dynamics of particles to the thermodynamic laws for macroscopic quantities. However, the modern statistical theory is faced with significant difficulties, as applied to…
A Markov decision process-based state switching is devised, implemented, and analyzed for proximity operations of various autonomous vehicles. The framework contains a pose estimator along with a multi-state guidance algorithm. The unified…
Metadynamics is a commonly used and successful enhanced sampling method. By the introduction of a history dependent bias which depends on a restricted number of collective variables(CVs) it can explore complex free energy surfaces…
We consider the optimization of Markovian dynamics to pursue the fastest convergence to the stationary state. The brachistochrone method is applied to the continuous-time master equation for finite-size systems. The principle of least…
We study the problem of identifying dynamically distinct basins of attraction in high dimensional time-homogeneous Markov processes using only trajectory sampling. This problem is fundamental in the analysis of metastable dynamical systems,…
The decay of unstable states when several metastable states are available for occupation is investigated using path-integral techniques. Specifically, a method is described which allows the probabilities with which the metastable states are…
Markov community models have been applied to sessile organisms because such models facilitate estimation of transition probabilities by tracking species occupancy at many fixed observation points over multiple periods of time. Estimation of…
State aggregation is a popular model reduction method rooted in optimal control. It reduces the complexity of engineering systems by mapping the system's states into a small number of meta-states. The choice of aggregation map often depends…
Experiments, in particular on biological systems, typically probe lower-dimensional observables which are projections of high-dimensional dynamics. In order to infer consistent models capturing the relevant dynamics of the system, it is…
Many sequence computations are easier to study as movement through internal states than as isolated local circuits. We introduce Markovian Circuit Tracing (MCT), a diagnostic pipeline for testing whether transformer activations contain…
This paper addresses the problem of verifying discrete-time stochastic systems against omega-regular specifications using finite-state abstractions. Omega-regular properties allow specifying complex behavior and encompass, for example,…
This article is divided into two parts. In the first part, we study the hierarchical phenomenon of metastability in low-temperature lattice models in the most general setting. Given an abstract dynamical system governed by a Hamiltonian…
In this paper, we consider an integrated MSP-MDP framework which captures features of Markov decision process (MDP) and multistage stochastic programming (MSP). The integrated framework allows one to study a dynamic decision-making process…
We present a general method to derive the metastable behavior of weakly mixing Markov chains. This approach is based on properties of the resolvent equations and can be applied to metastable dynamics which do not satisfy the mixing…
We study a class of Markov chains that describe reversible stochastic dynamics of a large class of disordered mean field models at low temperatures. Our main purpose is to give a precise relation between the metastable time scales in the…
The problem of state tracking with active observation control is considered for a system modeled by a discrete-time, finite-state Markov chain observed through conditionally Gaussian measurement vectors. The measurement model statistics are…
By generalising concepts from classical stochastic dynamics, we establish the basis for a theory of metastability in Markovian open quantum systems. Partial relaxation into long-lived metastable states - distinct from the asymptotic…
Molecular dynamics simulations allow to study the structure and dynamics of single biomolecules in microscopic detail. However, many processes occur on time scales beyond the reach of fully atomistic simulations and require coarse-grained…