Near-term quantum computers will be limited in the number of qubits on which they can process information as well as the depth of the circuits that they can coherently carry out. To date, experimental demonstrations of algorithms such as the Variational Quantum Eigensolver (VQE) have been limited… read more about this publication »
Fibrin gelation involves the enzymatic conversion of the plasma protein fibrinogen to fibrin monomers which then polymerize to form the gel that is a major structural component of a blood clot. Because fibrinogen provides the material from which fibrin is made, it is generally regarded as promoting… read more about this publication »
A new efficient ensemble prediction strategy is developed for a multiscale turbulent model framework with emphasis on the nonlinear interactions between large and small-scale variables. The high computational cost in running large ensemble simulations of high-dimensional equations is effectively… read more about this publication »
We study the Langevin dynamics of a physical system with manifold structure M⊂Rp based on collected sample points {xi}i=1n⊂M that probe the unknown manifold M. Through the diffusion map, we first learn the reaction coordinates {yi}i=1n⊂N corresponding to {xi}i=1n, where N is a manifold… read more about this publication »
Let H=F be a finite abelian extension of number fields with F totally real and H a CM field. Let S and T be disjoint finite sets of places of F satisfying the standard conditions. The Brumer-Stark conjecture states that the Stickelberger element ΦH/FS,T annihilates the T-smoothed class group ClT(H… read more about this publication »
We study the statistically invariant structures of the nonlinear generalized Langevin equation (GLE) with a power-law memory kernel. For a broad class of memory kernels, including those in the subdiffusive regime, we construct solutions of the GLE using a Gibbsian framework, which does not rely on… read more about this publication »
This study examines Cho & Demmans Epp’s short-form adaptation of Rovai’s well-known Classroom Community Scale (CCS-SF) as a measure of classroom community among introductory undergraduate math and statistics students. A series of statistical analyses were conducted to investigate the validity… read more about this publication »
The Poisson-Nernst-Planck-Bikermann (PNPB) model, in which the ions and water molecules are treated as different species with non-uniform sizes and valences with interstitial voids, can describe the steric and correlation effects in ionic solution neglected by the Poisson-Nernst-Planck and Poisson-… read more about this publication »
Spectral Barron spaces have received considerable interest recently, as it is the natural function space for approximation theory of two-layer neural networks with a dimension-free convergence rate. In this paper, we study the regularity of solutions to the whole-space static Schrödinger equation… read more about this publication »
Detecting an abrupt distributional shift of a data stream, known as change-point detection, is a fundamental problem in statistics and machine learning. We introduce a novel approach for online change-point detection using neural net-works. To be specific, our approach is training neural net-works… read more about this publication »
The Gaussian kernel and its traditional normalizations (e.g., row-stochastic) are popular approaches for assessing similarities between data points. Yet, they can be inaccurate under high-dimensional noise, especially if the noise magnitude varies considerably across the data, e.g., under… read more about this publication »
This paper reinterprets the Freidlin-Wentzell variational construction of the rate function in the large deviation principle for invariant measures from the weak KAM perspective. Through a one-dimensional irreversible diffusion process on a torus, we explicitly characterize essential concepts in… read more about this publication »
Chemical reactions can be modeled by a random time-changed Poisson process on countable states. The macroscopic behaviors, such as large fluctuations, can be studied via the WKB reformulation. The WKB reformulation for the backward equation is Varadhan's discrete nonlinear semigroup and is also a… read more about this publication »
Most single-cell RNA sequencing (scRNA-seq) analyses begin with cell clustering; thus, the clustering accuracy considerably impacts the validity of downstream analyses. In contrast with the abundance of clustering methods, the tools to assess the clustering accuracy are limited. We propose a new… read more about this publication »
For each n, let An= (σij) be an n× n deterministic matrix and let Xn= (Xij) be an n× n random matrix with i.i.d. centered entries of unit variance. In the companion article (Cook et al. in Electron J Probab 23:Paper No. 110, 61, 2018), we considered the empirical spectral distribution μnY of the… read more about this publication »
Intracellular transport processes are essential to the healthy development of many organisms as well as more generally to healthy cellular function. The complex dynamics and interactions between protein molecules and filaments on different time and spatial scales generate many opportunities for… read more about this publication »
We study symmetry breaking in the mean field solutions to the electronic structure problem for the 2 electron hydrogen molecule within the Kohn Sham (KS) local spin density functional theory with Dirac exchange (the XLDA model). This simplified model shows behavior related to that of the (KS) spin… read more about this publication »
Chan, Durrett, and Lanchier introduced a multitype contact process with temporal heterogeneity involving two species competing for space on the d-dimensional integer lattice. Time is divided into two seasons. They proved that there is an open set of the parameters for which both species can coexist… read more about this publication »
We study the spectral convergence of graph Laplacians to the Laplace-Beltrami operator when the kernelized graph affinity matrix is constructed from N random samples on a d-dimensional manifold in an ambient Euclidean space. By analyzing Dirichlet form convergence and constructing candidate… read more about this publication »
Most biochemical reactions in living cells are open systems interacting with environment through chemostats to exchange both energy and materials. At a mesoscopic scale, the number of each species in those biochemical reactions can be modeled by a random time-changed Poisson processes. To… read more about this publication »
As a counterpoint to recent numerical methods for crystal surface evolution, which agree well with microscopic dynamics but suffer from significant stiffness that prevents simulation on fine spatial grids, we develop a new numerical method based on the macroscopic partial differential equation,… read more about this publication »
The main mathematical result in this paper is that change of variables in the ordinary differential equation (ODE) for the competition of two infections in a Susceptible-Infected-Removed (SIR) model shows that the fraction of cases due to the new variant satisfies the logistic differential equation… read more about this publication »
For a fixed quadratic polynomial p in n non-commuting variables, and n independent N × N complex Ginibre matrices XN1, ⋯, XNn, we establish the convergence of the empirical measure of the eigenvalues of PN = p(XN1, ⋯, XNn) to the Brown measure of p evaluated at n freely independent circular… read more about this publication »