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We demonstrate that the concept of a conservation law can be naturally extended from deterministic to probabilistic cellular automata (PCA) rules. The local function for conservative PCA must satisfy conditions analogous to conservation…

Cellular Automata and Lattice Gases · Physics 2009-11-10 Henryk Fukś

A risk-aware decision-making problem can be formulated as a chance-constrained linear program in probability measure space. Chance-constrained linear program in probability measure space is intractable, and no numerical method exists to…

Optimization and Control · Mathematics 2023-11-21 Xun Shen , Satoshi Ito

We introduce a general theory on stationary approximations for locally stationary continuous-time processes. Based on the stationary approximation, we use $\theta$-weak dependence to establish laws of large numbers and central limit type…

Probability · Mathematics 2022-03-01 Robert Stelzer , Bennet Ströh

Asymptotic expansion is constructed and justified for the solution to a nonuniform Neumann boundary-value problem for the Poisson equation with the right-hand side that depends both on longitudinal and transversal variables in a thin…

Analysis of PDEs · Mathematics 2013-04-30 Arsen V. Klevtsovskiy , Taras A. Mel'nyk

This paper has two main goals: (a) establish several statistical properties---consistency, asymptotic distributions, and convergence rates---of stationary solutions and values of a class of coupled nonconvex and nonsmoothempirical risk…

Statistics Theory · Mathematics 2019-10-08 Zhengling Qi , Ying Cui , Yufeng Liu , Jong-Shi Pang

Cellular automata (CA) are discrete-time dynamical systems with local update rules on a lattice. Despite their elementary definition, CA support a wide spectrum of macroscopic phenomena central to statistical physics: equilibrium and…

Statistical Mechanics · Physics 2026-03-31 Mihir Metkar , Neha Sah , Yichen Zhou

Flexible Time is a new formalism for calculations about one-dimensional cellular automata. It unifies the states of a finite number of cells into a single object, even if they occur at different times. This gives greater flexibility to…

Cellular Automata and Lattice Gases · Physics 2014-03-04 Markus Redeker

We consider the problem of minimising the number of states in a multiplicity tree automaton over the field of rational numbers. We give a minimisation algorithm that runs in polynomial time assuming unit-cost arithmetic. We also show that a…

Formal Languages and Automata Theory · Computer Science 2019-03-14 Stefan Kiefer , Ines Marusic , James Worrell

Timed automata are a convenient mathematical model for modelling and reasoning about real-time systems. While they provide a powerful way of representing timing aspects of such systems, timed automata assume arbitrary precision and…

Formal Languages and Automata Theory · Computer Science 2020-07-09 Emily Clement , Thierry Jéron , Nicolas Markey , David Mentré

The main theme of this paper is the enumeration of the occurrence of a pattern in words and permutations. We mainly focus on asymptotic properties of the sequence $f_r^v(k,n),$ the number of $n$-array $k$-ary words that contain a given…

Combinatorics · Mathematics 2019-05-15 Toufik Mansour , Reza Rastegar , Alexander Roitershtein

Probabilistic Cellular Automata are a generalization of Cellular Automata. Despite their simple definition, they exhibit fascinating and complex behaviours. The stationary behaviour of these models changes when model parameters are varied,…

Cellular Automata and Lattice Gases · Physics 2024-08-20 E. N. M. Cirillo , G. Lancia , C. Spitoni

Reciprocal space methods for solving Poisson's equation for finite charge distributions are investigated. Improvements to previous proposals are presented, and their performance is compared in the context of a real-space density functional…

Computational Physics · Physics 2007-05-23 Alberto Castro , Angel Rubio , M. J. Stott

We propose a new second-order accurate lattice Boltzmann scheme that solves the quasi-static equations of linear elasticity in two dimensions. In contrast to previous works, our formulation solves for a single distribution function with a…

Numerical Analysis · Mathematics 2022-12-14 Oliver Boolakee , Martin Geier , Laura De Lorenzis

We study the asymptotic behavior, uniform-in-time, of a non-linear dynamical system under the combined effects of fast periodic sampling with period $\delta$ and small white noise of size $\varepsilon,\thinspace 0<\varepsilon,\delta \ll 1$.…

Probability · Mathematics 2025-02-18 Shivam Singh Dhama , Konstantinos Spiliopoulos

Metric Temporal Logic can express temporally evolving properties with time-critical constraints or time-triggered constraints for real-time systems. This paper extends the Metric Interval Temporal Logic with a distribution eventuality…

Formal Languages and Automata Theory · Computer Science 2021-05-12 Lening Li , Jie Fu

Sampled semantics of timed automata is a finite approximation of their dense time behavior. While the former is closer to the actual software or hardware systems with a fixed granularity of time, the abstract character of the latter makes…

Formal Languages and Automata Theory · Computer Science 2015-07-01 Pavel Krcal , Parosh Aziz Abdulla , Wang Yi

We consider self-loops and multiple edges in the configuration model as the size of the graph tends to infinity. The interest in these random variables is due to the fact that the configuration model, conditioned on being simple, is a…

Probability · Mathematics 2017-02-06 Omer Angel , Remco van der Hofstad , Cecilia Holmgren

We use Stein's method to obtain bounds on the rate of convergence for a class of statistics in geometric probability obtained as a sum of contributions from Poisson points which are exponentially stabilizing, i.e. locally determined in a…

Probability · Mathematics 2007-05-23 Mathew D. Penrose , J. E. Yukich

For many measure preserving dynamical systems $(\Omega,T,m)$ the successive hitting times to a small set is well approximated by a Poisson process on the real line. In this work we define a new process obtained from recording not only the…

Dynamical Systems · Mathematics 2018-03-20 Françoise Pène , Benoit Saussol

We consider Ewens random permutations of length $n$ conditioned to have no cycle longer than $n^\beta$ with $0<\beta<1$ and to study the asymptotic behaviour as $n\to\infty$. We obtain very precise information on the joint distribution of…

Probability · Mathematics 2020-04-22 Volker Betz , Julian Mühlbauer , Helge Schäfer , Dirk Zeindler