We present a calculation of the ground state energy of massive spinor fields and massive scalar fields in the background of an inhomogeneous magnetic string with potential given by a delta function. The zeta functional regularization is used and the lowest heat kernel coefficients are calculated. The rest of the analytical calculation adopts the Jost function formalism. In the numerical part of...

Let X = G/K be a symmetric space of noncompact type and let ∆ be the Laplacian associated with a G-invariant metric on X . We show that the resolvent kernel of ∆ admits a holomorphic extension to a Riemann surface depending on the rank of the symmetric space. This Riemann surface is a branched cover of the complex plane with a certain part of the real axis removed. It has a branching point at t...

We introduce an alternative to reservoir sampling, a classic and popular algorithm for drawing a fixed-size subsample from streaming data in a single pass. Rather than draw a random sample, our approach performs an online optimization which aims to select the subset that provides the best overall approximation to the full data set, as judged using a kernel two-sample test. This produces subsets...

We study the problem of completing a binary matrix in an online learning setting. On each trial we predict a matrix entry and then receive the true entry. We propose a Matrix Exponentiated Gradient algorithm [1] to solve this problem. We provide a mistake bound for the algorithm, which scales with the margin complexity [2, 3] of the underlying matrix. The bound suggests an interpretation where ...

Homecare, i.e., supportive care provided at the patients’ homes, is established as a prevalent alternative to unnecessary hospitalization or institutional care (e.g., in a rest home or a nursing home). These activities are provided either by healthcare professional or by nonmedical caregivers, depending on the patient’s needs (e.g., medical care or just instrumental activities of daily living)....

This paper considers a constraint-based scheduling approach to the flexible jobshop, a generalization of the traditional jobshop scheduling where activities have a choice of machines. It studies both large neighborhood (LNS) and adaptive randomized decomposition (ARD) schemes, using random, temporal, and machine decompositions. Empirical results on standard benchmarks show that, within 5 minute...

In this paper, we study the two-point Weyl Law for Laplace–Beltrami operator on a smooth, compact Riemannian manifold M with no conjugate points. That is, find asymptotic behavior of Schwartz kernel, E λ (x,y), projection from L 2 (M) onto direct sum eigenspaces eigenvalue smaller than as λ→∞. regime where x,y are restricted to neighborhood diagonal in M×M, obtain uniform logarithmic improvemen...

We investigate the statistical complexity of estimating parameters a discrete-state Markov chain kernel from single long sequence state observations. In finite case, we characterize (modulo logarithmic factors) minimax sample estimation with respect to operator infinity norm, while in countably infinite analyze problem natural entry-wise norm derived total variation. show that both cases, is go...

A special class of four-point correlation functions in the maximally supersymmetric Yang-Mills theory is given by square Fredholm determinant a generalized Bessel kernel. In this note, we re-express its logarithmic derivatives terms two-dimensional Riemann-Hilbert problem. We solve latter null limit making use Deift-Zhou steepest descent. reproduce exact octagonal anomalous dimension 't Hooft c...