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Gradient schemes is a framework that enables the unified convergence analysis of many numerical methods for elliptic and parabolic partial differential equations: conforming and non-conforming Finite Element, Mixed Finite Element and Finite…
We study the stability of non-conservative deterministic cross diffusion models and prove that they are approximated by stochastic population models when the populations become locally large. In this model, the individuals of two species…
The paper is concerned with the equilibrium distributions of continuous-time density dependent Markov processes on the integers. These distributions are known typically to be approximately normal, and the approximation error, as measured in…
In this paper, we investigate the convergence performance of a cooperative diffusion Gauss-Newton (GN) method, which is widely used to solve the nonlinear least squares problems (NLLS) due to the low computation cost compared with Newton's…
A method for adaptive model order reduction for nonsmooth discrete element simulation is developed and analysed in numerical experiments. Regions of the granular media that collectively move as rigid bodies are substituted with rigid bodies…
Theoretical analyses of evolution strategies are indispensable for gaining a deep understanding of their inner workings. For constrained problems, rather simple problems are of interest in the current research. This work presents a…
Coalescent theory combined with statistical modeling allows us to estimate effective population size fluctuations from molecular sequences of individuals sampled from a population of interest. When sequences are sampled serially through…
We study the fixed design segmented regression problem: Given noisy samples from a piecewise linear function $f$, we want to recover $f$ up to a desired accuracy in mean-squared error. Previous rigorous approaches for this problem rely on…
Several problems in modeling and control of stochastically-driven dynamical systems can be cast as regularized semi-definite programs. We examine two such representative problems and show that they can be formulated in a similar manner. The…
This article is concerned with numerical methods to approximate effective coefficients in stochastic homogenization of discrete linear elliptic equations, and their numerical analysis --- which has been made possible by recent contributions…
In distributed optimization problems, a technique called gradient coding, which involves replicating data points, has been used to mitigate the effect of straggling machines. Recent work has studied approximate gradient coding, which…
We study solution techniques for an evolution equation involving second order derivative in time and the spectral fractional powers, of order $s \in (0,1)$, of symmetric, coercive, linear, elliptic, second-order operators in bounded domains…
We provide the detailed asymptotic behavior for first-order aggregation models of heterogeneous oscillators. Due to the dissimilarity of natural frequencies, one could expect that all relative distances converge to definite positive value…
A stochastic algorithm for the recursive approximation of the location $\theta$ of a maximum of a regression function was introduced by Kiefer and Wolfowitz [Ann. Math. Statist. 23 (1952) 462--466] in the univariate framework, and by Blum…
We present a novel Newton-type method for distributed optimization, which is particularly well suited for stochastic optimization and learning problems. For quadratic objectives, the method enjoys a linear rate of convergence which provably…
We initiate the study of game dynamics in the population protocol model: $n$ agents each maintain a current local strategy and interact in pairs uniformly at random. Upon each interaction, the agents play a two-person game and receive a…
A new approach to estimate population size based on a stratified link-tracing sampling design is presented. The method extends on the Frank and Snijders (1994) approach by allowing for heterogeneity in the initial sample selection…
In this paper, we propose a new numerical strategy for the stabilization of evolution systems. The method is based on the methodology given by Ammari, Nicaise andPignotti in ''Stabilization by switching time-delay, Asymptot. Anal., 83…
Distributed Nash equilibrium seeking of aggregative games is investigated and a continuous-time algorithm is proposed. The algorithm is designed by virtue of projected gradient play dynamics and distributed average tracking dynamics, and is…
We consider compartmental models in epidemiology. For the study of the divergence of the stochastic model from its corresponding deterministic limit (i.e., the solution of an ODE) for long time horizon, a large deviations principle suggests…