相关论文: Two classes of ODE models with switch-like behavio…

Glasses are traditionally characterized by their rugged landscape of disordered low-energy states and their slow relaxation towards thermodynamic equilibrium. Far from equilibrium, dynamical forms of glassy behavior with anomalous algebraic…

Bayesian networks, and especially their structures, are powerful tools for representing conditional independencies and dependencies between random variables. In applications where related variables form a priori known groups, chosen to…

Optical lattice systems provide exceptional platforms for quantum simulation of many-body systems. We focus on the doubly modulated Bose-Hubbard model driven by both time-dependent on-site energy and interaction, and predict the emergence…

Motivated by sensor networks and other distributed settings, several models for distributed learning are presented. The models differ from classical works in statistical pattern recognition by allocating observations of an independent and…

The standard lattice Boltzmann equation (LBE) method usually fails to capture the physical equilibrium state of a two-phase fluid system, i.e., zero velocity and constant chemical potential. Consequently, spurious velocities and…

We show that the standard discrete update rule of transformer layers can be naturally interpreted as a forward Euler discretization of a continuous dynamical system. Our Transformer Flow Approximation Theorem demonstrates that, under…

Characterization of classes of switching signals that ensure stability of switched systems occupies a significant portion of the switched systems literature. This article collects a multitude of stabilizing switching signals under an…

Two classifications of second order ODE's cubic with respect to the first order derivative are compared in the case of general position, which is common for both classifications. The correspondence of vectorial, pseudovectorial, scalar, and…

We consider systems of backward stochastic differential equations with c\`adl\`ag upper barrier $U$ and oblique reflection from below driven by an increasing continuous function $H$. Our equations are defined on general probability spaces…

It is shown that for a $N$-boson system the parity of $N$ can be responsible for a qualitative difference in the system response to variation of a parameter. The nonlinear boson model is considered, which describes tunneling of boson pairs…

We consider a stochastic process driven by a linear ordinary differential equation whose right-hand side switches at exponential times between a collection of different matrices. We construct planar examples that switch between two matrices…

We investigate error of the Euler scheme in the case when the right-hand side function of the underlying ODE satisfies nonstandard assumptions such as local one-sided Lipschitz condition and local H\"older continuity. Moreover, we assume…

Discrete dynamical models underpin systems biology, but we still lack substrate-agnostic diagnostics for identifying finite-horizon dynamical signatures that may be relevant to open-ended evolution (OEE), such as the recurrent production of…

In two different classes of network models, namely, the Watts Strogatz type and the Euclidean type, subtle changes have been introduced in the randomness. In the Watts Strogatz type network, rewiring has been done in different ways and…

Data-driven modelling and scientific machine learning have been responsible for significant advances in determining suitable models to describe data. Within dynamical systems, neural ordinary differential equations (ODEs), where the system…

In this paper the problem of {\em learning} appropriate domain-specific bias is addressed. It is shown that this can be achieved by learning many related tasks from the same domain, and a theorem is given bounding the number tasks that must…

We revisit the results on admissible transformations between normal linear systems of second-order ordinary differential equations with an arbitrary number of dependent variables under several appropriate gauges of the arbitrary elements…

In this paper we introduce an observer design framework for ordinary differential equation (ODE) systems based on various types of existing or even novel one-parameter symmetries (exact, asymptotic and variational) ending up with a certain…

Many physical systems are governed by ordinary or partial differential equations (see, for example, Chapter ''Differential equations'', ''System of Differential Equations''). Typically the solution of such systems are functions of time or…

A model for the joint evolution of opinions and how much the agents trust each other is presented. The model is built using the framework of the Continuous Opinions and Discrete Actions (CODA) model. Instead of a fixed probability that the…