Related papers: Mesoscopic behavior from microscopic Markov dynami…
We present a non-isothermal mesoscopic model for investigation of the phase transition dynamics of thermoresponsive polymers. Since this model conserves energy in the simulations, it is able to correctly capture not only the transient…
We propose a simple discrete stochastic model for calcium dynamics in living cells. Specifically, the calcium concentration distribution is assumed to give rise to a set of probabilities for the opening/closing of channels which release…
In this paper, we consider semi-Markov processes whose transition times and transition probabilities depend on a small parameter $\varepsilon$. Understanding the asymptotic behavior of such processes is needed in order to study the…
Stochastic thermodynamics has largely succeeded in characterizing both equilibrium and far-from-equilibrium phenomena. Yet many opportunities remain for application to mesoscopic complex systems -- especially biological ones -- whose…
Starting at the mesoscopic level with a general formulation of stochastic thermodynamics in terms of Markov jump processes, we identify the scaling conditions that ensure the emergence of a (typically nonlinear) deterministic dynamics and…
We consider stochastic thermodynamics as a theory of statistical inference for experimentally observed fluctuating time-series. To that end, we introduce a general framework for quantifying the knowledge about the dynamical state of the…
For many stochastic dynamic systems, the Mean First Passage Time (MFPT) is a useful concept, which gives expected time before a state of interest. This work is an extension of MFPT in several ways. (1) We show that for some systems the…
The dynamics of an infinite system of point particles in $\mathbb{R}^d$, which hop and interact with each other, is described at both micro- and mesoscopic levels. The states of the system are probability measures on the space of…
A goal in the kinetic characterization of a macromolecular system is the description of its slow relaxation processes, involving (i) identification of the structural changes involved in these processes, and (ii) estimation of the rates or…
The production processes of proteins in prokaryotic cells are investigated. Most of the mathematical models in the literature study the production of {\em one} fixed type of proteins. When several classes of proteins are considered, an…
It is shown that the exact dynamics of a composite quantum system can be represented through a pair of product states which evolve according to a Markovian random jump process. This representation is used to design a general Monte Carlo…
To understand how rich dynamics emerge in neural populations, we require models exhibiting a wide range of activity patterns while remaining interpretable in terms of connectivity and single-neuron dynamics. However, it has been challenging…
Bottom-up models of functionally relevant patterns of neural activity provide an explicit link between neuronal dynamics and computation. A prime example of functional activity pattern is hippocampal replay, which is critical for memory…
Stochastic dynamical systems arise naturally across nearly all areas of science and engineering. Typically, a dynamical system model is based on some prior knowledge about the underlying dynamics of interest in which probabilistic features…
The capability of cells to form surface extensions to non-locally probe the surrounding environment plays a key role in cell migration. The existing mathematical models for migration of cell populations driven by this non-local form of…
Machine learning techniques not only offer efficient tools for modelling dynamical systems from data, but can also be employed as frontline investigative instruments for the underlying physics. Nontrivial information about the original…
The mean first-passage time (MFPT) is one standard measure for the reaction time in thermally activated barrier-crossing processes. While the relationship between MFPTs and phenomenological rate coefficients is known for systems that…
Binding and unbinding of ligands to specific sites of a macromolecule are one of the most elementary molecular interactions inside the cell that embody the computational processes of biological regulations. The interaction between…
We describe an exact approach for calculating transition probabilities and waiting times in finite-state discrete-time Markov processes. All the states and the rules for transitions between them must be known in advance. We can then…
We introduce a model of interacting Random Walk, whose hopping amplitude depends on the number of walkers/particles on the link. The mesoscopic counterpart of such a microscopic dynamics is a diffusing system whose diffusivity depends on…