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There has been substantial interest in developing Markov chain Monte Carlo algorithms based on piecewise-deterministic Markov processes. However existing algorithms can only be used if the target distribution of interest is differentiable…
In this paper, we investigate a nonparametric approach to provide a recursive estimator of the transition density of a non-stationary piecewise-deterministic Markov process, from only one observation of the path within a long time. In this…
We introduce a Monte Carlo algorithm to efficiently compute transport properties of chaotic dynamical systems. Our method exploits the importance sampling technique that favors trajectories in the tail of the distribution of displacements,…
Dusty plasma medium turns out to be an ideal system for studying the strongly coupled behavior of matter. The large size and slow response make their dynamics suitable to be captured through simple diagnostic tools. Furthermore, as the…
Molecular signalling in living cells occurs at low copy numbers and is thereby inherently limited by the noise imposed by thermal diffusion. The precision at which biochemical receptors can count signalling molecules is intimately related…
The statistics of steps and dwell times in reversible molecular motors differ from those of cycle completion in enzyme kinetics. The reason is that a step is only one of several transitions in the mechanochemical cycle. As a result,…
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)…
How do we capture the breadth of behavior in animal movement, from rapid body twitches to aging? Using high-resolution videos of the nematode worm $C. elegans$, we show that a single dynamics connects posture-scale fluctuations with…
Biological transport is supported by collective dynamics of enzymatic molecules that are called motor proteins or molecular motors. Experiments suggest that motor proteins interact locally via short-range potentials. We investigate the…
The basic question in perturbation analysis of Markov chains is: how do small changes in the transition kernels of Markov chains translate to chains in their stationary distributions? Many papers on the subject have shown, roughly, that the…
Molecular motors play pivotal roles in organizing the interior of cells. A motor efficient in cargo transport would move along cytoskeletal filaments with a high speed and a minimal error in transport distance (or time) while consuming a…
Theoretical analysis, which maps single molecule time trajectories of a molecular motor onto unicyclic Markov processes, allows us to evaluate the heat dissipated from the motor and to elucidate its dependence on the mean velocity and…
The paper algorithmizes the problem of regime change point identification for data measured in a system exhibiting impulsive behaviors. This is a fundamental challenge for annotation of measurement data relevant, e.g., for designing…
We introduce a model for stochastic transport on a one-dimensional substrate with particles assuming different conformations during their stepping cycles. These conformations correspond to different footprints on the substrate: in order to…
The automated segmentation and tracking of macrophages during their migration are challenging tasks due to their dynamically changing shapes and motions. This paper proposes a new algorithm to achieve automatic cell tracking in time-lapse…
We numerically examine the driven transport of an overdamped self-propelled particle through a two-dimensional array of circular obstacles. A detailed analysis of transport quantifiers (mobility and diffusivity) has been performed for two…
Molecular motor proteins serve as an essential component of intracellular transport by generating forces to haul cargoes along cytoskeletal filaments. Two species of motors that are directed oppositely (e.g. kinesin, dynein) can be attached…
Mathematically modelling diffusive and advective transport of particles in heterogeneous layered media is important to many applications in computational, biological and medical physics. While deterministic continuum models of such…
A Markov state model is a powerful tool that can be used to track the evolution of populations of configurations in an atomistic representation of a protein. For a coarse-grained linear chain model with discontinuous interactions, the…
Recent advances in molecular biology and fluorescence microscopy imaging have made possible the inference of the dynamics of single molecules in living cells. Such inference allows to determine the organization and function of the cell. The…