相关论文: Two classes of ODE models with switch-like behavio…
We study a lattice model with two body interactions that reproduces in three-dimensions many features of structural glasses, like cage effect and vanishing diffusivity. While having a crystalline state at low temperatures, it does not…
Suppose two Bayesian agents each learn a generative model of the same environment. We will assume the two have converged on the predictive distribution, i.e. distribution over some observables in the environment, but may have different…
The smooth piecewise-linear models cover a wide range of applications nowadays. Basically, there are two classes of them: models are transitional or hyperbolic according to their behaviour at the phase-transition zones. This study explored…
"Oscillations" occur in quite different kinds of many-particle-systems when two groups of particles with different directions of motion meet or intersect at a certain spot. We present a model of pedestrian motion that is able to reproduce…
A novel way of using neural networks to learn the dynamics of time delay systems from sequential data is proposed. A neural network with trainable delays is used to approximate the right hand side of a delay differential equation. We relate…
Out-of-distribution (OOD) detection is essential for model trustworthiness which aims to sensitively identify semantic OOD samples and robustly generalize for covariate-shifted OOD samples. However, we discover that the superior OOD…
Distinguishability takes a crucial rule in studying observability of hybrid system such as switched system. Recently, for two linear systems, Lou and Si gave a condition not only necessary but also sufficient to the distinguishability of…
In this paper, we study the stability of an Ordinary Differential Equation (ODE) usually referred to as Cyclic Feedback Loop, which typically models a biological network of molecules where each molecule regulates its successor in a cycle.…
A dynamical system approaching the first-order transition can exhibit a specific type of critical behavior known as self-organized bistability (SOB). It lies in the fact that the system can permanently switch between the coexisting states…
We present new results reflecting the analogies between the Kob-Andersen model and other glassy systems. Studying the stability of the blocked configurations above and below the transition we also give arguments that supports their…
Switched systems constitute an important modeling paradigm faithfully describing many engineering systems in which software interacts with the physical world. Despite considerable progress on stability and stabilization of switched systems,…
We consider the links between consistent and approximate descriptions of the quantum-classical systems, i.e. systems are composed of two interacting subsystems, one of which behaves almost classically while the other requires a quantum…
Neural ordinary differential equations (neural ODEs) are a popular type of deep learning model that operate with continuous-depth architectures. To assess how well such models perform on unseen data, it is crucial to understand their…
Neural Ordinary Differential Equations (ODE) are a promising approach to learn dynamic models from time-series data in science and engineering applications. This work aims at learning Neural ODE for stiff systems, which are usually raised…
We numerically study some of the 3-D dynamical systems which exhibit complete synchronisation as well as generalised synchronisation (GS) to show that these systems can be conveniently partitioned into equivalent classes facilitating the…
The quasi-steady state approximation and time-scale separation are commonly applied methods to simplify models of biochemical reaction networks based on ordinary differential equations (ODEs). The concentrations of the "fast" species are…
In this work, we propose a family of single-node second-order boundary schemes for the lattice Boltzmann method with general collision terms. The construction of the schemes is quite universal and simple, it does not involve concrete…
Systems with two species of active molecular motors moving on (cytoskeletal) filaments into opposite directions are studied theoretically using driven lattice gas models. The motors can unbind from and rebind to the filaments. Two motors…
Self-similarity is the property of a system being similar to a part of itself. We posit that a special class of behaviourally self-similar systems exhibits a degree of resilience to adversarial behaviour. We formalise the notions of system,…
We use a Monte Carlo bond-switching method to study systematically the thermodynamic properties of a "continuous random network" model, the canonical model for such amorphous systems as a-Si and a-SiO$_2$. Simulations show first-order…