Related papers: Three lemmas on the dynamic cavity method

We introduce a new equation that describes the spatio-temporal evolution of arbitrary pulses propagating in a fiber-ring cavity. This model is a significant extension of the traditionally used Lugiato-Lefever model. We demonstrate…

The dynamics of a one dimensional Ising spin system is investigated using three families of local update rules, the Galam majority rules, Glauber inflow influences and Sznadj outflow drives. Given an initial density p of up spins the…

Two standard models for probabilistic systems are Markov chains (MCs) and Markov decision processes (MDPs). Classic objectives for such probabilistic models for control and planning problems are reachability and stochastic shortest path.…

We introduce and apply a novel efficient method for the precise simulation of stochastic dynamical processes on locally tree-like graphs. Networks with cycles are treated in the framework of the cavity method. Such models correspond, for…

Flow Matching has recently emerged as a popular class of generative models for simulating a target distribution $\mu_1$ from samples drawn from a source distribution $\mu_0$. This framework relies on a fixed coupling between $\mu_0$ and…

Model updating of engineering systems inevitably involves handling both aleatory or inherent randomness and epistemic uncertainties or uncertainities arising from a lack of knowledge or information about the system. Addressing these…

How do update rules affect the dynamical and steady state properties of a flock? In this study, we have explored the active Ising spins (s = +-1) in one dimension, where spin updates its orientation according to the Metropolis algorithm…

The dynamical invariant, whose expectation value is constant, is generalized to open quantum system. The evolution equation of dynamical invariant (the dynamical invariant condition) is presented for Markovian dynamics. Different with the…

Standard dynamical systems theory is centred around the coordinate-invariant asymptotic-time properties of autonomous systems. We identify three limitations of this approach. Firstly, we discuss how the traditional approach cannot take into…

This study investigates the dynamics of alternating minimization applied to a bilinear regression task with normally distributed covariates, under the asymptotic system size limit where the number of parameters and observations diverge at…

We develop a linear systems theory that coincides with the existing theories for continuous and discrete dynamical systems, but that also extends to linear systems defined on nonuniform time domains. The approach here is based on…

The three-state Ising neural network with synchronous updating and variable dilution is discussed starting from the appropriate Hamiltonians. The thermodynamic and retrieval properties are examined using replica mean-field theory.…

Dirac-delta distributions are often crucial components of the solid-fluid coupling operators in immersed solution methods for fluid-structure interaction (FSI) problems. This is certainly so for methods like the Immersed Boundary Method…

This paper is a continuation of Akahori-Barsotti-Imamura (2017) and where the authors i) showed that a payment at a random time, which we call timing risk, is decomposed into an integral of static positions of knock-in type barrier options,…

This paper explores the dependence modeling of financial assets in a dynamic way and its critical role in measuring risk. Two new methods, called Accelerated Moving Window method and Bottom-up method are proposed to detect the change of…

This paper deals with the problems of stochastic stability and sliding mode control for a class of continuous-time Markovian jump systems with mode-dependent time-varying delays and partly unknown transition probabilities. The design method…

We study the metastable behavior of the two-dimensional Ising model in the case of an alternate updating rule: parallel updating of spins on the even (odd) sublattice are permitted at even (odd) times. We show that although the dynamics is…

We discuss a few mathematical aspects of random dynamical decoupling, a key tool procedure in quantum information theory. In particular, we place it in the context of discrete stochastic processes, limit theorems and CPT semigroups on…

The predictive simulation of fluid dynamics in densely packed microfluidic devices, such as Deterministic Lateral Displacement (DLD) arrays, stagnates with standard iterative solvers. We show that this failure is not algorithmic but rooted…

We propose a parallel algorithm for the numerical solution of a class of second order semi-linear equations coming from stochastic optimal control problems, by means of a dynamic domain decomposition technique. The new method is an…