Related papers: Mesoscopic behavior from microscopic Markov dynami…
Computational studies of the thermodynamic properties of materials at the mesoscopic and macroscopic scales -- involving lengths and times of at least $\mu$m and $\mu$s, respectively -- rely on a coarse-graining approximation such that only…
Complex systems are often characterized by the interplay of multiple interconnected dynamical processes operating across a range of temporal scales. This phenomenon is widespread in both biological and artificial scenarios, making it…
Increasing the number of particles in a system often leads to qualitative changes in its properties, such as breaking of symmetries and the appearance of phase transitions. This renders a macroscopic system fundamentally different from its…
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)…
We consider a stochastic individual based model where each predator searches during a random time and then manipulates its prey or rests. The time distributions may be non-exponential. An age structure allows to describe these interactions…
Most of the functions performed by astrocytes in brain information processing are related to calcium waves. Experimental studies involving calcium waves present discrepant results, leading to gaps in the full understanding of the functions…
Traditional chemical kinetics may be inappropriate to describe chemical reactions in micro-domains involving only a small number of substrate and reactant molecules. Starting with the stochastic dynamics of the molecules, we derive a…
In present paper we suggest a new universal approach to study complex systems by microscopic, mesoscopic and macroscopic methods. We discuss new possibilities of extracting information on nonstationarity, unsteadiness and non-Markovity of…
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,…
The properties of excited nuclear matter and the quest for a phase transition which is expected to exist in this system are the subject of intensive investigations. High energy nuclear collisions between finite nuclei which lead to matter…
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 provide a numerical study of the macroscopic model of [3] derived from an agent-based model for a system of particles interacting through a dynamical network of links. Assuming that the network remodelling process is very fast, the…
This thesis is dedicated to the study of stochastic processes; non-deterministic physical phenomena that can be well described by classical physics. The stochastic processes we are interested in are akin to Brownian Motion and can be…
Applications of first passage times in stochastic processes arise across a wide range of length and time scales in biological settings. After an initial technical overview, we survey representative applications and their corresponding…
Coarse-grained descriptions of collective motion of flocking systems are often derived for the macroscopic or the thermodynamic limit. However, many real flocks are small sized (10 to 100 individuals), called the mesoscopic scales, where…
We present a novel characterization of slow variables for continuous Markov processes that provably preserve the slow timescales. These slow variables are known as reaction coordinates in molecular dynamical applications, where they play a…
Markov models are widely used to describe processes of stochastic dynamics. Here, we show that Markov models are a natural consequence of the dynamical principle of Maximum Caliber. First, we show that when there are different possible…
Background: Mechanotransduction in bone cells plays a pivotal role in osteoblast differentiation and bone remodelling. Mechanotransduction provides the link between modulation of the extracellular matrix and intracellular actions. By…
We elucidate the physics of the dynamical transition via 10-100ns molecular dynamics simulations at temperatures spanning 160-300K. By tracking the energy fluctuations, we show that the protein dynamical transition is marked by a cross-over…
The dynamics of biological systems, from proteins to cells to organisms, is complex and stochastic. To decipher their physical laws, we need to bridge between experimental observations and theoretical modeling. Thanks to progress in…