A key challenge across many disciplines is to extract meaningful information from data which is often obscured by noise. These datasets are typically represented as large matrices. Given the current trend of ever-increasing data volumes, with datasets grow ...
We prove global in time well-posedness for perturbations of the 2D stochastic Navier-Stokes equations partial derivative( t)u + u center dot del u = Delta u - del p + sigma + xi, u(0, center dot ) = u(0),div (u) = 0, driven by additive space-time white noi ...
We study the hitting probabilities of the solution to a system of d stochastic heat equations with additive noise subject to Dirichlet boundary conditions. We show that for any bounded Borel set with positive (d-6)\documentclass[12pt]{minimal} \usepackage{ ...
Information theory has allowed us to determine the fundamental limit of various communication and algorithmic problems, e.g., the channel coding problem, the compression problem, and the hypothesis testing problem. In this work, we revisit the assumptions ...
Linear-Quadratic-Gaussian (LQG) control is a fundamental control paradigm that is studied in various fields such as engineering, computer science, economics, and neuroscience. It involves controlling a system with linear dynamics and imperfect observations ...
Mechanisms used in privacy-preserving machine learning often aim to guarantee differential privacy (DP) during model training. Practical DP-ensuring training methods use randomization when fitting model parameters to privacy-sensitive data (e.g., adding Ga ...
We consider nonlinear parabolic stochastic PDEs on a bounded Lipschitz domain driven by a Gaussian noise that is white in time and colored in space, with Dirichlet or Neumann boundary condition. We establish existence, uniqueness and moment bounds of the r ...
We study the compact support property for solutions of the following stochastic partial differential equations: partial derivative tu=aijuxixj(t,x)+biuxi(t,x)+cu+h(t,x,u(t,x))F-center dot(t,x),(t,x)is an element of(0,infinity)xRd,where F-center dot is a sp ...
A multi-agent system consists of a collection of decision-making or learning agents subjected to streaming observations from some real-world phenomenon. The goal of the system is to solve some global learning or optimization problem in a distributed or dec ...
In this thesis we address various factors that contribute both theoretically and practically to mitigating supply demand mismatches. The thesis is composed of three chapters, where each chapter is an independent scientific paper. In the first paper, we dev ...
