Related papers: Exact Solutions for Small Systems: Urns Models

The work [8] established memory loss in the time-dependent (non-random) case of uniformly expanding maps of the interval. Here we find conditions under which we have convergence to the normal distribution of the appropriately scaled…

We find the Euler-Lagrangian equation by maximising the total entropy. Hence we obtain an expression for mass of the spherically symmetric system by solving the Euler-Lagrangian equation where the Homotopy Perturbation Method has been…

We provide a general method to analyze the asymptotic properties of a variety of estimators of continuous time diffusion processes when the data are not only discretely sampled in time but the time separating successive observations may…

Macroscopic models for spatially extended systems under random influences are often described by stochastic partial differential equations (SPDEs). Some techniques for understanding solutions of such equations, such as estimating…

Three models from statistical physics can be analyzed by employing space-time determinantal processes: (1) crystal facets, in particular the statistical properties of the facet edge, and equivalently tilings of the plane, (2)…

While there are numerous results on minimizers or stable solutions of the Bernoulli problem proving regularity of the free boundary and analyzing singularities, much less in known about critical points of the corresponding energy. Saddle…

Consider a balanced non triangular two-color P\'olya-Eggenberger urn process, assumed to be large which means that the ratio sigma of the replacement matrix eigenvalues satisfies 1/2<sigma <1. The composition vector of both discrete time…

Since the 1990s, RANS practitioners have observed spontaneous unsteadiness in RANS simulations. Some have suggested deliberately using this as a method of resolving large turbulent structures. However, to date, no one has produced a…

We introduce an effective algorithmic method for the computation of a lower bound for uniform expansion in one-dimensional dynamics. The approach employs interval arithmetic and thus provides a rigorous numerical result (computer-assisted…

We demonstrate the use of spatially encoded magnetic resonance to quantify ensemble dynamics of microscopic particles below the spatial resolution. By evaluating time series of k-space data-points, k-dependent motion patterns can be…

We propose a computer-assisted approach to studying the effective continuum behavior of spatially discrete evolution equations. The advantage of the approach is that the "coarse model" (the continuum, effective equation) need not be…

A linear growth-diffusion equation is studied in a time-dependent interval whose location and length both vary. We prove conditions on the boundary motion for which the solution can be found in exact form, and derive the explicit expression…

Deriving the time evolution of a distribution of probability (or a probability density matrix) is a problem encountered frequently in a variety of situations: for physical time, it could be a kinetic reaction study, while identifying time…

A method of representation of a solution as segments of the series in powers of the step of the independent variable is expanded for solving complex systems of ordinary differential equations (ODE): the Lorenz system and other systems. A…

For continuous-time linear stochastic dynamical systems driven by Wiener processes, we consider the problem of designing ensemble filters when the observation process is randomly time-sampled. We propose a continuous-discrete McKean--Vlasov…

We consider a mean-field dynamical urn model, defined by rules which give the rate at which a ball is drawn from an urn and put in another one, chosen amongst an assembly. At equilibrium, this model possesses a fluid and a condensed phase,…

Building on VeriX (Verified eXplainability, arXiv:2212.01051), a system for producing optimal verified explanations for machine learning models, we present VeriX+, which significantly improves both the size and the generation time of formal…

Extended Thermodynamics is a very important theory: for example, it predicts hyperbolicity, finite speeds of propagation waves as well as continuous dependence on initial data. Therefore, it constitutes a significative improvement of…

This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…

We consider the (complete) Euler system describing the motion of a compressible perfect fluid. We propose a platform suitable for constructing the statistical solutions. The main ingredients of our approach include: 1. The concept of…