相关论文: Asymptotic convergence of heterogeneous first-orde…

We consider a first-order aggregation model in both discrete and continuum formulations and show rigorously how it can be obtained as zero inertia limits of second-order models. In the continuum case the procedure consists in a macroscopic…

The phase reduction technique is essential for studying rhythmic phenomena across various scientific fields. It allows the complex dynamics of high-dimensional oscillatory systems to be expressed by a single phase variable. This paper…

An interesting situation occurs when the linearized dynamics of the shape of a formally stable Hamiltonian relative equilibrium at nongeneric momentum 1:1 resonates with a frequency of the relative equilibrium's generator. In this case some…

Complex interactions leading to phase transitions continue to hold a due interest in the scientific community. We charactersize a phase transition in a coupled oscillators model where interactions are not local in nature. At a first order…

We extend a well-studied ODE model for collective behaviour by considering anisotropic interactions among individuals. Anisotropy is modelled by limited sensorial perception of individuals, that depends on their current direction of motion.…

This paper investigates the quantitative homogenization of first-order ODEs. For single-scale scalar ODEs, we obtain a sharp $O(\varepsilon)$ convergence rate and characterize the effective constant. In the multi-scale setting, our results…

We propose a general strategy for reduced order modeling of systems that display highly nonlinear oscillations. By considering a continuous family of forced periodic orbits defined in relation to a stable fixed point and subsequently…

In the framework of the concordance cosmological model the first-order scalar and vector perturbations of the homogeneous background are derived in the weak gravitational field limit without any supplementary approximations. The sources of…

This paper is devoted to the study of the asymptotic behavior of solutions to multi-order fractional cooperative systems. First, we demonstrate the boundedness of solutions to fractional-order systems under certain conditions imposed on the…

The long time effect of nonlinear perturbation to oscillatory linear systems can be characterized by the averaging method, and we consider first-order averaging for its simplest applicability to high-dimensional problems. Instead of the…

In this paper an asymptotic homogenization method for the analysis of composite materials with periodic microstructure in presence of thermodiffusion is described. Appropriate down-scaling relations correlating the microscopic fields to the…

We examine a model in which a nonequilibrium phase transition from an active to an extinct state is observed. The order of this phase transition has been shown to be either continuous or first-order, depending on the parameter values and…

First-order operator splitting methods are ubiquitous among many fields through science and engineering, such as inverse problems, signal/image processing, statistics, data science and machine learning, to name a few. In this paper, we…

We propose a family of optimization methods that achieve linear convergence using first-order gradient information and constant step sizes on a class of convex functions much larger than the smooth and strongly convex ones. This larger…

A heterogeneous medium of constituents with vastly different mechanical properties, whose inhomogeneities are in close proximity to each other, is considered. The gradient of the solution to the corresponding problem exhibits singular…

In the context of the multi-dimensional infinite horizon optimal consumption-investment problem with proportional transaction costs, we provide the first order expansion in small transact costs. Similar to the one-dimensional derivation in…

We consider a class of models describing an ensemble of identical interacting agents subject to multiplicative noise. In the thermodynamic limit, these systems exhibit continuous and discontinuous phase transitions in a, generally,…

Coordinate descent methods have considerable impact in global optimization because global (or, at least, almost global) minimization is affordable for low-dimensional problems. Coordinate descent methods with high-order regularized models…

A unified framework for first-order optimization algorithms fornonconvex unconstrained optimization is proposed that uses adaptivelypreconditioned gradients and includes popular methods such as full anddiagonal AdaGrad, AdaNorm, as well as…

Gradient methods are widely used in optimization problems. In practice, while the smoothness parameter can be estimated utilizing techniques such as backtracking, estimating the strong convexity parameter remains a challenge; moreover, even…