相关论文: Quantitative touchdown localization for the MEMS p…

We study the problem of estimating the fixed point of a contractive operator defined on a separable Banach space. Focusing on a stochastic query model that provides noisy evaluations of the operator, we analyze a variance-reduced stochastic…

The conditioning of the linear finite volume element discretization for general diffusion equations is studied on arbitrary simplicial meshes. The condition number is defined as the ratio of the maximal singular value of the stiffness…

This paper considers facility location problems in which a firm entering a market seeks to open facilities on a subset of candidate locations so as to maximize its expected market share, assuming that customers choose the available…

This paper examines asymptotic properties of local M-estimators under three sets of high-level conditions. These conditions are sufficiently general to cover the minimum volume predictive region, conditional maximum score estimator for a…

Local adaptivity and mesh refinement are key to the efficient simulation of wave phenomena in heterogeneous media or complex geometry. Locally refined meshes, however, dictate a small time-step everywhere with a crippling effect on any…

We consider the problem of estimating latent positions in a one-dimensional torus from pairwise affinities. The observed affinity between a pair of items is modeled as a noisy observation of a function $f(x^*_{i},x^*_{j})$ of the latent…

We study the finite element approximation of the solid isotropic material with penalization method (SIMP) for the topology optimization problem of minimizing the compliance of a linearly elastic structure. To ensure the existence of a local…

We obtain upper bounds for the quenching time of the solutions of the nonlocal parabolic MEMS equation $u_t=\Delta u+\lam/(1-u)^2(1+\chi\int_{\Omega}1/(1-u) dx)^2$ in $\Omega\times (0,\infty)$, $u=0$ on $\1\Omega\times (0,\infty)$,…

This article deals with stochastic processes endowed with the Markov (memoryless) property and evolving over general (uncountable) state spaces. The models further depend on a non-deterministic quantity in the form of a control input, which…

We study the hitting times of Markov processes to target set $G$, starting from a reference configuration $x_0$ or its basin of attraction. The configuration $x_0$ can correspond to the bottom of a (meta)stable well, while the target $G$…

We present a collection of algorithms which utilize dimensional reduction to perform mesh refinement and study possibly singular solutions of time-dependent partial differential equations. The algorithms are inspired by constructions used…

We consider the problem of distributed mean estimation (DME), in which $n$ machines are each given a local $d$-dimensional vector $x_v \in \mathbb{R}^d$, and must cooperate to estimate the mean of their inputs $\mu = \frac 1n\sum_{v = 1}^n…

We consider the problem of approximating the reachability probabilities in Markov decision processes (MDP) with uncountable (continuous) state and action spaces. While there are algorithms that, for special classes of such MDP, provide a…

Automatically tuning software configuration for optimizing a single performance attribute (e.g., minimizing latency) is not trivial, due to the nature of the configuration systems (e.g., complex landscape and expensive measurement). To deal…

We consider finite element approximations of ill-posed elliptic problems with conditional stability. The notion of {\emph{optimal error estimates}} is defined including both convergence with respect to mesh parameter and perturbations in…

We introduce an end-to-end optimization strategy for quantum machine learning that directly targets performance under finite measurement resources, where learning objectives are defined directly at the level of task performance. The method…

The maximal entropy moment method (MEM) is systematic solution of the challenging problem: generating extended hydrodynamic equations valid for both dense and rarefied gases. However, simulating MEM suffers from a computational expensive…

Utility-scale quantum computers require quantum error correcting codes with large numbers of physical qubits to achieve sufficiently low logical error rates. The performance of quantum error correction (QEC) is generally predicted through…

Mesh adaption procedures for finite element approximation allows one to adapt the resolution, by local refinement in the regions of strong variation of the function of interest. This procedure plays a key role in numerous applications of…

Numerical and analytical methods are developed for the investigation of contact sets in electrostatic-elastic deflections modeling micro-electro mechanical systems. The model for the membrane deflection is a fourth-order semi-linear partial…