Related papers: Border Avoidance: Necessary Regularity for Coeffic…

This paper conducts sensitivity analysis of random constraint and variational systems related to stochastic optimization and variational inequalities. We establish efficient conditions for well-posedness, in the sense of robust Lipschitzian…

The existence and search for thermodynamic phase transitions is of unfading interest. In this paper, we present numerical evidence of dynamical phase transitions occurring in boundary driven systems with a constrained integrated current. It…

Existing bounds on the generalization error of deep networks assume some form of smooth or bounded dependence on the input variable, falling short of investigating the mechanisms controlling such factors in practice. In this work, we…

Transporting causal information across populations is a critical challenge in clinical decision-making. Causal modeling provides criteria for identifiability and transportability, but these require knowledge of the causal graph, which…

We study a driven many particle system comprising of two identical lanes of finite lengths. On one lane, particles hop diffusively with a bias in a specific direction. On the other lane, particles hop in a specific direction obeying mutual…

We establish sharp global regularity results for solutions to nonhomogeneous, nonunifomrly elliptic systems with zero boundary conditions. In particular, we obtain everywhere Lipschitz continuity under borderline Lorentz assumptions on the…

We show that some boundary conditions assumed at a thin membrane may result in normal diffusion not being the stochastic Markov process. We consider boundary conditions defined in terms of the Laplace transform in which there is a linear…

We consider the boundary crossing problem for time-homogeneous diffusions and general curvilinear boundaries. Bounds are derived for the approximation error of the one-sided (upper) boundary crossing probability when replacing the original…

We propose a new continuum model for random genetic drift by employing a dynamic boundary condition approach. The model can be viewed as a regularized version of the Kimura equation and admits a continuous solution. We establish the…

We extend basic regularity of the free boundary of the obstacle problem to some classes of heterogeneous quasilinear elliptic operators with variable growth that includes, in particular, the $p(x)$-Laplacian. Under the assumption of…

The Lipschitz constant is an important quantity that arises in analysing the convergence of gradient-based optimization methods. It is generally unclear how to estimate the Lipschitz constant of a complex model. Thus, this paper studies an…

The aim of the present paper is to provide necessary and sufficient conditions to maintain a stochastic coupled system, with porous media components and gradient-type noise in a prescribed set of constraints by using internal controls. This…

Probabilistic control design is founded on the principle that a rational agent attempts to match modelled with an arbitrary desired closed-loop system trajectory density. The framework was originally proposed as a tractable alternative to…

Overparameterized neural networks often show a benign overfitting property in the sense of achieving excellent generalization behavior despite the number of parameters exceeding the number of training examples. A promising direction to…

This article studies the expected occupancy probabilities on an alphabet. Unlike the standard situation, where observations are assumed to be independent and identically distributed (iid), we assume that they follow a regime switching…

We investigate the role of the boundary in the symmetric simple exclusion process with competing nonlocal and local hopping events. With open boundaries, the system undergoes a first order phase transition from a finite density phase to an…

We study the probability of arbitrary density profiles in conserving diffusive fields which are driven by the boundaries. We demonstrate the existence of singularities in the large-deviation functional, the direct analog of the free-energy…

Inspired by classical sensitivity results for nonlinear optimization, we derive and discuss new quantitative bounds to characterize the solution map and dual variables of a parametrized nonlinear program. In particular, we derive explicit…

Barrier crossing is a widespread phenomenon across natural and engineering systems. While an abundant cross-disciplinary literature on the topic has emerged over the years, the stochastic underpinnings of the process are yet to be linked…

In this article we reconsider high Reynolds number boundary layer flows of fluids with viscoelastic properties. We show that a number of previous studies that have attempted to address this problem are, in fact, incomplete. We correctly…