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

Maximum entropy models provide the least constrained probability distributions that reproduce statistical properties of experimental datasets. In this work we characterize the learning dynamics that maximizes the log-likelihood in the case…

We prove local well-posedness for the Muskat problem on the half-plane, which models motion of an interface between two fluids of distinct densities (e.g., oil and water) in a porous medium (e.g., an aquifer) that sits atop an impermeable…

Interface problems have long been a major focus of scientific computing, leading to the development of various numerical methods. Traditional mesh-based methods often employ time-consuming body-fitted meshes with standard discretization…

The accuracy of finite element solutions is closely tied to the mesh quality. In particular, geometrically nonlinear problems involving large and strongly localized deformations often result in prohibitively large element distortions. In…

A semilinear parabolic equation with constraint modeling the dynamics of a microelectromechanical system (MEMS) is studied. In contrast to the commonly used MEMS model, the well-known pull-in phenomenon occurring above a critical potential…

Assessing whether a noisy quantum device can potentially exhibit quantum advantage is essential for selecting practical quantum utility tasks that are not efficiently verifiable by classical means. For optimization, a prominent candidate…

Boolean programs with multiple recursive threads can be captured as pushdown automata with multiple stacks. This model is Turing complete, and hence, one is often interested in analyzing a restricted class that still captures useful…

When dedicated positioning systems, such as GPS, are unavailable, a mobile device has no choice but to fall back on its cellular network for localization. Due to random variations in the channel conditions to its surrounding base stations…

These lectures advocate the idea that quantum entanglement provides a unifying foundation for both statistical physics and high-energy interactions. I argue that, at sufficiently long times or high energies, most quantum systems approach a…

Quantum parameter estimation holds the promise of quantum technologies, in which physical parameters can be measured with much greater precision than what is achieved with classical technologies. However, how to obtain a best precision when…

In Monte Carlo simulations of lattice field theory with a $\theta$ term, one confronts the complex weight problem, or the sign problem. This is circumvented by performing the Fourier transform of the topological charge distribution $P(Q)$.…

Many problems in quantum information theory can be formulated as optimizations over the sequential outcomes of dynamical systems subject to unpredictable external influences. Such problems include many-body entanglement detection through…

We study the integration problem over the $s$-dimensional unit cube on four types of Banach spaces of integrands. First we consider Haar wavelet spaces, consisting of functions whose Haar wavelet coefficients exhibit a certain decay…

Quantum labeling tasks ask one to recover the missing associations between classical outcome labels and the effects forming the POVM. We study labeling in the multiple-shot regime, allowing a finite number of uses of the device and the most…

We study the asymptotic error between the finite element solutions of nonlocal models with a bounded interaction neighborhood and the exact solution of the limiting local model. The limit corresponds to the case when the horizon parameter,…

The approximation ratio has become one of the dominant measures in mechanism design problems. In light of analysis of algorithms, we define the \emph{smoothed approximation ratio} to compare the performance of the optimal mechanism and a…

The moment measure problem consists in finding a convex function $\psi$ whose moment measure, i.e., the pushforward by $\nabla \psi$ of the measure with density $e^{-\psi(\,\cdot\,)}$, is prescribed. It is highly non-linear and less…

We consider the standard optimistic bilevel optimization problem, in particular upper- and lower-level constraints can be coupled. By means of the lower-level value function, the problem is transformed into a single-level optimization…

We construct a quenching solution to the parabolic MEMS model \[ u_t = \Delta u - \frac{1}{u^2} \quad \text{in } \mathcal{B} \times (0,T), \quad u|_{\partial \mathcal{B}} = 1, \] where $\mathcal{B}$ is the unit disc in $\mathbb{R}^2$, and…

We generalize the string method, originally designed for the study of thermally activated rare events, to the calculation of quantum tunneling rates. This generalization is based on the analogy between quantum mechanics and statistical…