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We study the coupled dynamics of primary and secondary structure formation (i.e. slow genetic sequence selection and fast folding) in the context of a solvable microscopic model that includes both short-range steric forces and and…
We present a novel approach to investigate the long-time stochastic dynamics of multi-dimensional classical systems, in contact with a heat-bath. When the potential energy landscape is rugged, the kinetics displays a decoupling of short and…
We propose a setup of an open quantum system in which the environment can be tuned such that either Markovian or non-Markovian system dynamics can be achieved. The implementation uses ultracold Rydberg atoms, relying on their strong…
In this paper, we consider the stability analysis of large-scale distributed networked control systems with random communication delays between linearly interconnected subsystems. The stability analysis is performed in the Markov jump…
In the last years, tens of thousands gene expression profiles for cells of several organisms have been monitored. Gene expression is a complex transcriptional process where mRNA molecules are translated into proteins, which control most of…
Dynamical reweighting methods permit to estimate kinetic observables of a stochastic process governed by a target potential $\tilde{V}(x)$ from trajectories that have been generated at a different potential $V(x)$. In this article, we…
State-free reversible VAMPnets (SRVs) are a neural network-based framework capable of learning the leading eigenfunctions of the transfer operator of a dynamical system from trajectory data. In molecular dynamics simulations, these…
Stochastic dynamics of chemical reactions in a mutually repressing two-gene circuit is numerically simulated. The circuit has a rich variety of different states when the kinetic change of DNA status is slow. The stochastic switching…
It is well established that gene expression can be modeled as a Markovian stochastic process and hence proper observables might be subjected to large fluctuations and rare events. Since dynamics is often more than statics, one can work with…
We propose a method to sample stationary properties of solutions of stochastic differential equations, which is accurate and efficient if there are rarely visited regions or rare transitions between distinct regions of the state space. The…
We propose a system identification method, Non-Markovian Optimization-based Modeling for Approximate Dynamics with Spatially-homogeneous memory (NOMADS), for identifying linear dynamical systems from a set of multi-dimensional time-series…
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…
Ergodicity-breaking and slow relaxation are intriguing aspects of nonequilibrium dynamics both in classical and in quantum settings. These phenomena are typically associated with phase transitions, e.g. the emergence of metastable regimes…
Computational modeling of assembly is challenging for many systems because their timescales vastly exceed those accessible to simulations. This article describes the MultiMSM, which is a general framework that uses Markov state models…
The precise characterization of dynamics in open quantum systems often presents significant challenges, leading to the introduction of various approximations to simplify a model. One commonly used strategy involves Markovian approximations,…
Based on multiple parallel short molecular dynamics simulation trajectories, we designed the reweighted ensemble dynamics (RED) method to more efficiently sample complex (biopolymer) systems, and to explore their hierarchical metastable…
Molecular ecology uses molecular genetic data to answer traditional ecological questions in biogeography and biodiversity among others. Several ecological principles, such as the niche hypothesis and the competitive exclusions, are based on…
We present a new method for inferring hidden Markov models from noisy time sequences without the necessity of assuming a model architecture, thus allowing for the detection of degenerate states. This is based on the statistical prediction…
Markov chains are simple yet powerful mathematical structures to model temporally dependent processes. They generally assume stationary data, i.e., fixed transition probabilities between observations/states. However, live, real-world…
This work presents a low-rank tensor model for multi-dimensional Markov chains. A common approach to simplify the dynamical behavior of a Markov chain is to impose low-rankness on the transition probability matrix. Inspired by the success…