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Markov-chain Monte Carlo (MCMC), the field of stochastic algorithms built on the concept of sampling, has countless applications in science and technology. The overwhelming majority of MCMC algorithms are time-reversible and satisfy the…
The transport of organelles and vesicles in living cells can be well described by a kinetic tug-of-war model advanced by M\"uller, Klumpp and Lipowsky. In which, the cargo is attached by two motor species, kinesin and dynein, and the…
It is known that state-dependent, multi-step Lyapunov bounds lead to greatly simplified verification theorems for stability for large classes of Markov chain models. This is one component of the "fluid model" approach to stability of…
Slow manifolds are important geometric structures in the state spaces of dynamical systems with multiple time scales. This paper introduces an algorithm for computing trajectories on slow manifolds that are normally hyperbolic with both…
A joint degree matrix (JDM) specifies the number of connections between nodes of given degrees in a graph, for all degree pairs and uniquely determines the degree sequence of the graph. We consider the space of all balanced realizations of…
Matroid theory provides a unifying framework for studying dependence across combinatorics, geometry, and applications ranging from rigidity to statistics. In this work, we study circuit varieties of matroids, defined by their minimal…
We study solution discovery, where the goal is to obtain a feasible solution to a problem from an initial configuration by a bounded sequence of local moves. In many applications, however, the graph that defines which vertex sets are…
The paper studies identification of linear systems with multiplicative noise from multiple-trajectory data. An algorithm based on the least-squares method and multiple-trajectory data is proposed for joint estimation of the nominal system…
A transverse knot is a knot that is transverse to the planes of the standard contact structure on real 3-space. In this paper we prove the Markov Theorem for transverse braids, which states that two transverse closed braids that are…
Many sequence computations are easier to study as movement through internal states than as isolated local circuits. We introduce Markovian Circuit Tracing (MCT), a diagnostic pipeline for testing whether transformer activations contain…
This article is divided into two parts. In the first part, we study the hierarchical phenomenon of metastability in low-temperature lattice models in the most general setting. Given an abstract dynamical system governed by a Hamiltonian…
Current fluctuations are a powerful tool to unravel the underlying physics of the observed transport process. This work discusses some general properties of the third and the fourth current cumulant (skewness and kurtosis) related to…
While one-dimensional Markov processes are well understood, going to higher dimensions there are only a few analytically solved Ising-like models, in practice requiring to use relatively costly, uncontrollable and inaccurate Monte-Carlo…
After three decades of computational multibody system (MBS) dynamics, current research is centered at the development of compact and user friendly yet computationally efficient formulations for the analysis of complex MBS. The key to this…
The Maslov index is a powerful tool for assessing the stability of solitary waves. Although it is difficult to calculate in general, a framework for doing so was recently established for singularly perturbed systems. In this paper, we apply…
We show that certain mixed displacement/traction problems (including live pressure tractions) of nonlinear elastostatics that are solved by a homogeneous deformation, admit no other classical equilibrium solution under suitable constitutive…
Perturbation theory for Markov chains addresses the question how small differences in the transitions of Markov chains are reflected in differences between their distributions. We prove powerful and flexible bounds on the distance of the…
A Markov state model of the dynamics of a protein-like chain immersed in an implicit hard sphere solvent is derived from first principles for a system of monomers that interact via discontinuous potentials designed to account for local…
In Hamiltonian systems subjected to periodic perturbations the stable and unstable manifolds of the unstable periodic orbits provide the dynamical "skeleton" that drives the mixing process and bounds the chaotic regions of the phase space.…
We construct a class of exact commensurate and incommensurate standing wave (SW) solutions in a piecewise smooth analogue of the discrete non-linear Schr\"{o}dinger (DNLS) model and present their linear stability analysis. In the case of…