Related papers: High-dimensional integration on $\mathbb{R}^d$, we…

Weighted discrete Hilbert transforms $(a_n)_n \mapsto \big(\sum_n a_n v_n/(\lambda_j-\gamma_n)\big)_j$ from $\ell^2_v$ to $\ell^2_w$ are considered, where $\Gamma=(\gamma_n)$ and $\Lambda=(\lambda_j)$ are disjoint sequences of points in the…

Building upon recent work by the author, we prove that multivariate integration in the following subspace of the Wiener algebra over $[0,1)^d$ is strongly polynomially tractable: \[ F_d:=\left\{ f\in C([0,1)^d)\:\middle| \:…

This paper proposes a new importance sampling (IS) that is tailored to quasi-Monte Carlo (QMC) integration over $\mathbb{R}^s$. IS introduces a multiplicative adjustment to the integrand by compensating the sampling from the proposal…

In this paper, we are interested in investigating a weighted variant of Hermite-Hadamard type inequalities involving convex functionals. The approach undertaken makes it possible to refine and reverse certain inequalities already known in…

We introduce the notion of an orthocomplemented subspace of a Hilbert space H, that is, a pair of orthogonal closed subspaces of H, as a two-dimensional counterpart to the one-dimensional notion of a closed subspace of H. Orthocomplemented…

Monte Carlo methods play a central role in particle physics, where they are indispensable for simulating scattering processes, modeling detector responses, and performing multi-dimensional integrals. However, traditional Monte Carlo methods…

For large-scale eigenvalue problems requiring many mutually orthogonal eigenvectors, traditional numerical methods suffer substantial computational and communication costs with limited parallel scalability, primarily due to explicit…

Matrices are typically considered over fields or rings. Motivated by applications in parametric differential equations and data-driven modeling, we suggest to study matrices with entries from a Hilbert space and present an elementary theory…

Hierarchical modeling provides a framework for modeling the complex interactions typical of problems in applied statistics. By capturing these relationships, however, hierarchical models also introduce distinctive pathologies that quickly…

In this paper we investigate quasi-Monte Carlo (QMC) integration using digital nets over $\mathbb{Z}_b$ in reproducing kernel Hilbert spaces. The tent transformation, or the baker's transformation, was originally used for lattice rules by…

Learning low-dimensional numerical representations from symbolic data, e.g., embedding the nodes of a graph into a geometric space, is an important concept in machine learning. While embedding into Euclidean space is common, recent…

Higher-dimensional orthogonal packing problems have a wide range of practical applications, including packing, cutting, and scheduling. Previous efforts for exact algorithms have been unable to avoid structural problems that appear for…

This is basically a review of the field of Quasi-Monte Carlo intended for computational physicists and other potential users of quasi-random numbers. As such, much of the material is not new, but is presented here in a style hopefully more…

Let $(\mathcal{X},\rho)$ be a metric space and $\lambda$ be a Borel measure on this space defined on the $\sigma$-algebra generated by open subsets of $\mathcal{X}$; this measure $\lambda$ defines volumes of Borel subsets of $\mathcal{X}$.…

The entanglement entropy probing novel phases and phase transitions numerically via quantum Monte Carlo has made great achievements in large-scale interacting spin/boson systems. In contrast, the numerical exploration in interacting fermion…

We consider a transformation of a normalized measure space such that the image of any point is a finite set. We call such transformation $m$-transformation. In this case the orbit of any point looks like a tree. In the study of…

We study multivariate integration of functions that are invariant under the permutation (of a subset) of their arguments. Recently, in Nuyens, Suryanarayana, and Weimar (Adv. Comput. Math. (2016), 42(1):55--84), the authors derived an upper…

This paper mainly dedicates to prove a plethora of weighted estimates on Morrey spaces for bilinear fractional integral operators and their general commutators with BMO functions of the form…

We discuss a method called quasi-sparse eigenvector diagonalization which finds the most important basis vectors of the low energy eigenstates of a quantum Hamiltonian. It can operate using any basis, either orthogonal or non-orthogonal,…

The geometric construction of the functional integral over coset spaces ${\cal M}/{\cal G}$ is reviewed. The inner product on the cotangent space of infinitesimal deformations of $\cal M$ defines an invariant distance and volume form, or…