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Stochastic dynamical systems often contain nonlinearities which make it hard to compute probability density functions or statistical moments of these systems. For the moment computations, nonlinearities in the dynamics lead to unclosed…
We present approximate algorithms for performing smoothing in a class of high-dimensional state-space models via sequential Monte Carlo methods ("particle filters"). In high dimensions, a prohibitively large number of Monte Carlo samples…
Living systems produce "persistent" copies of information-carrying polymers, in which template and copy sequences remain correlated after physically decoupling. We identify a general measure of the thermodynamic efficiency with which these…
In this paper we continue the study of the derivation of different types of kinetic equations which arise from scaling limits of interacting particle systems. We began this study in \cite{NVW}. More precisely, we consider the derivation of…
We establish a general framework for developing approximation algorithms for a class of counting problems. Our framework is based on the cluster expansion of abstract polymer models formalism of Koteck\'y and Preiss. We apply our framework…
We initiate a systematic study of utilizing predictions to improve over approximation guarantees of classic algorithms, without increasing the running time. We propose a systematic method for a wide class of optimization problems that ask…
The Hamiltonian dynamics of chains of nonlinearly coupled particles is numerically investigated in two and three dimensions. Simple, off-lattice homopolymer models are used to represent the interparticle potentials. Time averages of…
While the characteristics of the driven translocation for asymptotically long polymers are well understood, this is not the case for finite-sized polymers, which are relevant for real-world experiments and simulation studies. Most notably,…
Particle smoothers are widely used algorithms allowing to approximate the smoothing distribution in hidden Markov models. Existing algorithms often suffer from slow computational time or degeneracy. We propose in this paper a way to improve…
We solve the Chapman-Kolmogorov equation and study the exact splitting probabilities of the general stochastic process which describes polymer translocation through membrane pores within the broad class of Markov chains. Transition…
The new method of the mean-field approximation is extended. An approach which enables to estimate some parameters of the transition from the isotropic state of hard sticks to the nematic ordering phase is suggested. An technique of the…
We introduce polynomial couplings, a generalization of probabilistic couplings, to develop an algorithm for the computation of equivalence relations which can be interpreted as a lifting of probabilistic bisimulation to polynomial…
In this review we provide an organized summary of the theoretical and computational results which are available for polymers subject to spatial or topological constraints. Because of the interdisciplinary character of the topic, we provide…
Many practical approximations in physics and engineering invoke a relatively long physical domain with a relatively thin cross-section. In this scenario we typically expect the system to have structures that vary slowly in the long…
Partitioning of (bio)materials in polymeric mixtures is a key phenomenon both in cellular environments, as well as in industrial applications. In cells, several macromolecules are suspended within different biomolecular phases. On the other…
We investigate polymer partitioning from polymer mixtures into nanometer size cavities by formulating an equation of state for a binary polymer mixture assuming that only one (smaller) of the two polymer components can penetrate the cavity.…
The simulation of viscoelastic time-evolution problems described by a large number of internal variables and with a large spectrum of relaxation times requires high computational resources for their resolution. Furthermore, the internal…
We study the dynamics of an ideal polymer chain in a crowded, viscoelastic medium and in the presence of active forces. The motion of the centre of mass and of individual monomers is calculated. On time scales that are comparable to the…
Linear polymers are represented as chains of hopping reptons and their motion is described as a stochastic process on a lattice. This admittedly crude approximation still catches essential physics of polymer motion, i.e. the universal…
We present the results of analytic calculations and numerical simulations of the behaviour of a new class of chain molecules which we call thick polymers. The concept of the thickness of such a polymer, viewed as a tube, is encapsulated by…