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In uncertainty quantification for parametric partial differential equations (PDEs), it is common to model uncertain random field inputs using countably infinite sequences of independent and identically distributed random variables. The…

Numerical Analysis · Mathematics 2025-12-15 Philipp A. Guth , Vesa Kaarnioja

When the state space of a discrete state space positive recurrent Markov chain is infinite or very large, it becomes necessary to truncate the state space in order to facilitate numerical computation of the stationary distribution. This…

Probability · Mathematics 2025-05-07 Peter W. Glynn , Zeyu Zheng

The Chemical Master Equation (CME) provides a highly accurate, yet extremely resource-intensive representation of a stochastic chemical reaction network and its kinetics due to the exponential scaling of its possible states with the number…

Quantum Physics · Physics 2024-04-16 Tilas Kabengele , Yash M. Lokare , J. B. Marston , Brenda M. Rubenstein

We consider linear reaction-diffusion equations posed on unbounded domains, and discretized by adaptive Lagrange finite elements. To obtain finite-dimensional spaces, it is necessary to introduce a truncation boundary, whereby only a…

Numerical Analysis · Mathematics 2025-11-13 Théophile Chaumont-Frelet , Gregor Gantner

We propose a method for eliminating the truncation error associated with any subspace diagonalization calculation. The new method, called stochastic error correction, uses Monte Carlo sampling to compute the contribution of the remaining…

High Energy Physics - Lattice · Physics 2009-10-31 Dean Lee , Nathan Salwen , Mark Windoloski

For a multipart quantum system, a locally maximally entangled (LME) state is one where each elementary subsystem is maximally entangled with its complement. This paper is a sequel to arXiv:1708.01645, which gives necessary and sufficient…

Quantum Physics · Physics 2019-03-12 Jim Bryan , Samuel Leutheusser , Zinovy Reichstein , Mark Van Raamsdonk

The Chemical Master Equation (CME) is well known to provide the highest resolution models of a biochemical reaction network. Unfortunately, even simulating the CME can be a challenging task. For this reason more simple approximations to the…

Optimization and Control · Mathematics 2015-10-21 Aivar Sootla , James Anderson

The recently introduced method of excess collisions (MEC) is modified to estimate diffusion-controlled reaction times inside systems of arbitrary size. The resulting MEC-E equations contain a set of empirical parameters, which have to be…

Biological Physics · Physics 2009-11-11 Holger Merlitz , Konstantin V. Klenin , Chen-Xu Wu , Jörg Langowski

Here we develop an effective approach to simplify two-time-scale Markov chains with infinite state spaces by removal of states with fast leaving rates, which improves the simplification method of finite Markov chains. We introduce the…

Molecular Networks · Quantitative Biology 2017-09-13 Chen Jia

Context: Mutation Testing (MT) is an important tool in traditional Software Engineering (SE) white-box testing. It aims to artificially inject faults in a system to evaluate a test suite's capability to detect them, assuming that the test…

Software Engineering · Computer Science 2023-01-16 Florian Tambon , Foutse Khomh , Giuliano Antoniol

Distributed state estimation (DSE) is considered as a more robust and reliable alternative for centralized state estimation (CSE) in power system. Especially, taking into account the future power grid, so called smart grid in which…

Systems and Control · Electrical Eng. & Systems 2021-04-12 Sajjad Asefi , Elena Gryazina , Helder Leite

The reaction-diffusion master equation (RDME) is a model that allows for efficient on-lattice simulation of spatially resolved stochastic chemical kinetics. Compared to off-lattice hard-sphere simulations with Brownian Dynamics (BD) or…

Numerical Analysis · Mathematics 2017-09-06 Stefan Hellander , Andreas Hellander , Linda Petzold

This paper introduces a new algorithm for numerically computing equilibrium (i.e. stationary) distributions for Markov chains and Markov jump processes with either a very large finite state space or a countably infinite state space. The…

Probability · Mathematics 2022-08-31 Alex Infanger , Peter W. Glynn

We consider stochastic descriptions of chemical reaction networks in which there are both fast and slow reactions, and for which the time scales are widely separated. We develop a computational algorithm that produces the generator of the…

Dynamical Systems · Mathematics 2015-12-11 Xingye Kan , Chang Hyeong Lee , Hans G. Othmer

We consider probabilistic model checking for continuous-time Markov chains (CTMCs) induced from Stochastic Reaction Networks (SRNs) against a fragment of Continuous Stochastic Logic (CSL) extended with reward operators. Classical numerical…

Logic in Computer Science · Computer Science 2018-04-25 Luca Bortolussi , Luca Cardelli , Marta Kwiatkowska , Luca Laurenti

We develop a convergent reaction-drift-diffusion master equation (CRDDME) to facilitate the study of reaction processes in which spatial transport is influenced by drift due to one-body potential fields within general domain geometries. The…

Numerical Analysis · Mathematics 2025-01-22 Samuel A. Isaacson , Ying Zhang

The application of the quasi-steady-state approximation to the Michaelis-Menten reaction embedded in large open chemical reaction networks is a popular model reduction technique in deterministic and stochastic simulations of biochemical…

Statistical Mechanics · Physics 2013-05-28 Philipp Thomas , Arthur V. Straube , Ramon Grima

Multipartite entanglement is an essential resource for quantum information theory and technologies, but its quantification has been a persistent challenge. Recently, Concentratable Entanglement (CE) has been introduced as a promising…

Quantum Physics · Physics 2024-06-27 Xiaoyu Liu , Johannes Knörzer , Zherui Jerry Wang , Jordi Tura

There exist several methods for simulating biological and physical systems as represented by chemical reaction networks. Systems with low numbers of particles are frequently modelled as discrete-state Markov jump processes and are typically…

Quantitative Methods · Quantitative Biology 2022-10-24 Joshua C. Kynaston , Christian A Yates , Anna Hekkink , Chris Guiver

Renormalization Group (RG) theory provides the theoretical framework to define Effective Theories (ETs), i.e. systematic low-resolution approximations of arbitrary microscopic models. Markov State Models (MSMs) are shown to be rigorous ETs…

Statistical Mechanics · Physics 2016-11-03 Simone Orioli , Pietro Faccioli