Related papers: Optimal data-driven estimation of generalized Mark…
We study classical stochastic systems with discrete states, coupled to switching external environments. For fast environmental processes we derive reduced dynamics for the system itself, focusing on corrections to the adiabatic limit of…
The foundations of statistical mechanics, namely how equilibrium hypothesis emerges microscopically from quantum theory, is explored through investigating the environment-induced quantum decoherence processes. Based on the recent results on…
A new theoretical approach to non-equilibrium statistical systems has recently been proposed by the author, a co-author and others. It is based on a variational principle which is associated with the discrepancy of a path through…
A goal of data assimilation is to infer stochastic dynamical behaviors with available observations. We consider transition phenomena between metastable states for a stochastic system with (non-Gaussian) $\alpha-$stable L\'evy noise. With…
Metastability is a physical phenomenon ubiquitous in first order phase transitions. A fruitful mathematical way to approach this phenomenon is the study of rare transitions Markov chains. For Metropolis chains associated with Statistical…
Following on from our recent work, we investigate a stochastic approach to non-equilibrium quantum spin systems. We show how the method can be applied to a variety of physical observables and for different initial conditions. We provide…
With the increasing ubiquity of safety-critical autonomous systems operating in uncertain environments, there is a need for mathematical methods for formal verification of stochastic models. Towards formally verifying properties of…
Many state of the art methods for the thermodynamic and kinetic characterization of large and complex biomolecular systems by simulation rely on ensemble approaches, where data from large numbers of relatively short trajectories are…
Applying the mathematical circulation theory of Markov chains, we investigate the synchronized stochastic dynamics of a discrete network model of yeast cell-cycle regulation where stochasticity has been kept rather than being averaged out.…
When clustering molecular dynamics (MD) trajectories into a few metastable conformational states, the Markov state models (MSMs) assumption of timescale separation between fast intrastate fluctuations and rarely occurring interstate…
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…
This thesis is devoted to the study of dynamical properties of diluted models. These are mean field statistical mechanics systems, but with finite local connectivity. Among other reasons, the interest for these models arises from their deep…
Data-driven, model-free analytics are natural choices for discovery and forecasting of complex, nonlinear systems. Methods that operate in the system state-space require either an explicit multidimensional state-space, or, one approximated…
The lifetime of statistical system is introduced. It is supposed that the nonequilibrium statistical operator implicitly contains the lifetime. The operations of taking of invariant part, averaging on initial conditions used in works of…
Markov chains are fundamental models for stochastic dynamics, with applications in a wide range of areas such as population dynamics, queueing systems, reinforcement learning, and Monte Carlo methods. Estimating the transition matrix and…
We introduce a stochastic model that describes the quasi-static dynamics of an electric transmission network under perturbations introduced by random load fluctuations, random removing of system components from service, random repair times…
The paper is devoted to the construction of the superstatistical description for nonequilibrium Markovian systems. It is based on Kirchhoff's diagram technique and the assumption on the system under consideration to possess a wide variety…
This article presents a constrained policy optimization approach for the optimal control of systems under nonstationary uncertainties. We introduce an assumption that we call Markov embeddability that allows us to cast the stochastic…
A fundamental challenge is to understand nonequilibrium statistical mechanics starting from microscopic chaos in the equations of motion of a many-particle system. In this review we summarize recent theoretical advances along these lines.…
A method is proposed to identify target states that optimize a metastability index amongst a set of trial states and use these target states as milestones (or core sets) to build Markov State Models (MSMs). If the optimized metastability…