3 papers
math.NA2024
An improved Halton sequence for implementation in quasi-Monte Carlo methods
Nathan Kirk, Christiane Lemieux
Despite possessing the low-discrepancy property, the classical d dimensional Halton sequence is known to exhibit poorly distributed projections when d becomes even moderately large…
cs.LG2024
Message-Passing Monte Carlo: Generating low-discrepancy point sets via Graph Neural Networks
T. Konstantin Rusch, Nathan Kirk, Michael M. Bronstein +2
Discrepancy is a well-known measure for the irregularity of the distribution of a point set. Point sets with small discrepancy are called low-discrepancy and are known to efficient…
math.NT2023
Golden Ratio Nets and Sequences
Nathan Kirk, Christiane Lemieux, Jaspar Wiart
In this paper we introduce and study nets and sequences constructed in an irrational base, focusing on the case of a base given by the golden ratio . We provide a complete frame…