相关论文: Robust Localization of the Best Error with Finite …

A space discrete approximation to a highly nonlinear reaction-diffusion system endowed with a stochastic dynamical boundary condition is analyzed and the convergence of the discrete scheme to the solution to the corresponding continuum…

Maintaining stability in an uncertain environment is essential for proper functioning of living systems. Robust perfect adaptation (RPA) is a property of a system that generates an output at a fixed level even after fluctuations in input…

We use a continued fraction approximation to calculate the RPA response function of nuclear matter. The convergence of the approximation is assessed by comparing with the numerically exact response function obtained with a typical effective…

We consider a reaction-diffusion system where some components react and diffuse on the boundary of a region, while other components diffuse in the interior and react with those on the boundary through mass transport. We establish criteria…

Parametric estimation for diffusion processes is considered for high frequency observations over a fixed time interval. The processes solve stochastic differential equations with an unknown parameter in the diffusion coefficient. We find…

Distributionally robust offline reinforcement learning (RL), which seeks robust policy training against environment perturbation by modeling dynamics uncertainty, calls for function approximations when facing large state-action spaces.…

We propose an adaptive finite element algorithm to approximate solutions of elliptic problems whose forcing data is locally defined and is approximated by regularization (or mollification). We show that the energy error decay is…

In this work, a complete error analysis is presented for fully discrete solutions of the subdiffusion equation with a time-dependent diffusion coefficient, obtained by the Galerkin finite element method with conforming piecewise linear…

In this article we propose a locally adaptive strategy for estimating a function from its Exponential Radon Transform (ERT) data, without prior knowledge of the smoothness of functions that are to be estimated. We build a non-parametric…

We give a method for proactively identifying small, plausible shifts in distribution which lead to large differences in model performance. These shifts are defined via parametric changes in the causal mechanisms of observed variables, where…

We consider systems of reaction-diffusion equations coupled in zero order terms, with general homogeneous boundary conditions in domains with a particular geometry (annular type domains). We establish Lipschitz stability estimates in L^2…

We study the diffusion-limited process $A+A\to A$ in one dimension, with finite reaction rates. We develop an approximation scheme based on the method of Inter-Particle Distribution Functions (IPDF), which was formerly used for the exact…

Local decision rules are commonly understood to be more explainable, due to the local nature of the patterns involved. With numerical optimization methods such as gradient boosting, ensembles of local decision rules can gain good predictive…

We expand on a previous study of fronts in finite particle number reaction-diffusion systems in the presence of a reaction rate gradient in the direction of the front motion. We study the system via reaction-diffusion equations, using the…

We consider mixing problems in the form of transient convection--diffusion equations with a velocity vector field with multiscale character and rough data. We assume that the velocity field has two scales, a coarse scale with slow spatial…

We present a spatially-extended system of chemical reactions exhibiting adaptation to time-dependent influxes of reactants. Here adaptation is defined as improved reproductive success, namely the ability of one of the many locally stable…

We study the fundamental problems of (i) uniformity testing of a discrete distribution, and (ii) closeness testing between two discrete distributions with bounded $\ell_2$-norm. These problems have been extensively studied in distribution…

Adaptive networks are suitable for decentralized inference tasks, e.g., to monitor complex natural phenomena. Recent research works have intensively studied distributed optimization problems in the case where the nodes have to estimate a…

We analyze a stochastic approximation algorithm for decision-dependent problems, wherein the data distribution used by the algorithm evolves along the iterate sequence. The primary examples of such problems appear in performative prediction…

The main aim of this paper is to document the performance of $p$-refinement with respect to maximum principles and the non-negative constraint. The model problem is (steady-state) anisotropic diffusion with decay (which is a second-order…