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arxiv.org arXiv
arxiv.org › abs › 2505.16286v2
Quantum simulation has emerged as a powerful framework for investigating complex many - body phenomena. A key requirement for emulating these dynamics is the realization of fully controllable quantum ...
arxiv.org arXiv
arxiv.org › abs › 1909.10508v1
This is a small contribution to the (September 15, 2019) Liber Amicorum Richard "Dick" Allen Askey. At the end a positivity conjecture related to the First and Second Borwein Conjectures is offered......
arxiv.org arXiv
arxiv.org › abs › 1203.4322v1
Higher order nets were introduced by Dick as a generalisation of classical $(t,m,s)$-nets, which are point sets frequently used in quasi-Monte Carlo integration algorithms. Essential tools in finding ...
arxiv.org arXiv
arxiv.org › abs › 1203.5157v1
In this paper we study reproducing kernel Hilbert spaces of arbitrary smoothness on the sphere $\mathbb{S}^d \subset \mathbb{R}^{d+1}$. The reproducing kernel is given by an integral representation us...
arxiv.org arXiv
arxiv.org › abs › 1602.07363v1
We analyze combined Quasi-Monte Carlo quadrature and Finite Element approximations in Bayesian estimation of solutions to countably-parametric operator equations with holomorphic dependence on the par...
arxiv.org arXiv
arxiv.org › abs › 1601.07281v2
The $L_p$-discrepancy is a quantitative measure for the irregularity of distribution modulo one of infinite sequences. In 1986 Proinov proved for all $p>1$ a lower bound for the $L_p$-discrepancy of g...
arxiv.org arXiv
arxiv.org › abs › 1704.04998v1
Symbolic regression via genetic programming is a flexible approach to machine learning that does not require up-front specification of model structure. However, traditional approaches to symbolic regr...
arxiv.org arXiv
arxiv.org › abs › 1301.6441v3
Higher order scrambled digital nets are randomized quasi-Monte Carlo rules which have recently been introduced in [J. Dick, Ann. Statist., 39 (2011), 1372--1398] and shown to achieve the optimal rate ...
arxiv.org arXiv
arxiv.org › abs › 1207.5189v2
We show that the $\mathcal{L}_2$ discrepancy of the explicitly constructed infinite sequences of points $(\boldsymbol{x}_0,\boldsymbol{x}_1, \boldsymbol{x}_2,...)$ in $[0,1)^s$ over $\mathbb{F}_2$ int...
arxiv.org arXiv
arxiv.org › abs › 1409.2180v2
We analyze the convergence of higher order Quasi-Monte Carlo (QMC) quadratures of solution-functionals to countably-parametric, nonlinear operator equations with distributed uncertain parameters takin...