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The Discrepancy of a hypergraph is the minimum attainable value, over two-colorings of its vertices, of the maximum absolute imbalance of any hyperedge. The Hereditary Discrepancy of a hypergraph, defined as the maximum discrepancy of a…

Data Structures and Algorithms · Computer Science 2014-07-24 Aleksandar Nikolov , Kunal Talwar

Generation of pseudorandom numbers from different probability distributions has been studied extensively in the Monte Carlo simulation literature. Two standard generation techniques are the acceptance-rejection and inverse transformation…

Computational Finance · Quantitative Finance 2014-03-25 Nguyet Nguyen , Giray Ökten

Low isometric distortion is often required for mesh parameterizations. A configuration of some vertices, where the distortion is concentrated, provides a way to mitigate isometric distortion, but determining the number and placement of…

Graphics · Computer Science 2019-11-05 Shuangming Chai , Xiao-Ming Fu , Ligang Liu

We study computing geometric problems on uncertain points. An uncertain point is a point that does not have a fixed location, but rather is described by a probability distribution. When these probability distributions are restricted to a…

Computational Geometry · Computer Science 2012-05-03 Allan Jorgensen , Maarten Löffler , Jeff M. Phillips

Although the applications of Non-Homogeneous Poisson Processes to model and study the threshold overshoots of interest in different time series of measurements have proven to provide good results, they needed to be complemented with an…

Applications · Statistics 2023-09-15 Biviana Marcela Suárez-Sierra , Arrigo Coen , Carlos Alberto Taimal

We establish the existence of $N$-point sets in dimension $d$ whose star-discrepancy is bounded above by $2.4631832 \sqrt{\frac{d}{N}}$, where the numerical constant improves upon all previously known bounds. This improvement is obtained by…

Number Theory · Mathematics 2026-01-08 Christian Weiß

Efficiently computing low discrepancy colorings of various set systems, has been studied extensively since the breakthrough work by Bansal (FOCS 2010), who gave the first polynomial time algorithms for several important settings, including…

Data Structures and Algorithms · Computer Science 2022-11-28 Kasper Green Larsen

Star-shaped bodies are an important nonconvex generalization of convex bodies (e.g., linear programming with violations). Here we present an efficient algorithm for sampling a given star-shaped body. The complexity of the algorithm grows…

Data Structures and Algorithms · Computer Science 2009-04-06 Karthekeyan Chandrasekaran , Daniel Dadush , Santosh Vempala

We present two main contributions to the expected star discrepancy theory. First, we derive a sharper expected upper bound for jittered sampling, improving the leading constants and logarithmic terms compared to the state-of-the-art [Doerr,…

Statistics Theory · Mathematics 2026-01-09 Xiaoda Xu , Jun Xian

Message-Passing Monte Carlo (MPMC) was recently introduced as a novel low-discrepancy sampling approach leveraging tools from geometric deep learning. While originally designed for generating uniform point sets, we extend this framework to…

Machine Learning · Computer Science 2025-03-28 Nathan Kirk , T. Konstantin Rusch , Jakob Zech , Daniela Rus

We investigate the expected star discrepancy under a newly designed class of convex equivolume partition models. The main contributions are two-fold. First, we establish a strong partition principle for the star discrepancy, showing that…

Probability · Mathematics 2026-01-09 Xiaoda Xu , Jun Xian

Anomaly detection has important applications in biosurveilance and environmental monitoring. When comparing measured data to data drawn from a baseline distribution, merely, finding clusters in the measured data may not actually represent…

Computational Geometry · Computer Science 2016-08-31 Deepak Agarwal , Jeff M. Phillips , Suresh Venkatasubramanian

We introduce genetic algorithms as a means to estimate the accuracy required to discriminate among different models using experimental observables. We exemplify the technique in the context of the minimal supersymmetric standard model. If…

High Energy Physics - Phenomenology · Physics 2009-11-10 B. C. Allanach , D. Grellscheid , F. Quevedo

The Covariance Matrix Adaptation Evolution Strategy (CMA-ES) is one of the most successful examples of a derandomized evolution strategy. However, it still relies on randomly sampling offspring, which can be done via a uniform distribution…

Neural and Evolutionary Computing · Computer Science 2024-09-25 Jacob de Nobel , Diederick Vermetten , Thomas H. W. Bäck , Anna V. Kononova

We establish sharp non-asymptotic probabilistic bounds for the star discrepancy of double-infinite random matrices -- a canonical model for sequences of random point sets in high dimensions. By integrating the recently proved…

Statistics Theory · Mathematics 2026-01-09 Xiaoda Xu , Jun Xian

Importance sampling Monte-Carlo methods are widely used for the approximation of expectations with respect to partially known probability measures. In this paper we study a deterministic version of such an estimator based on quasi-Monte…

Computation · Statistics 2024-12-20 Josef Dick , Daniel Rudolf , Houying Zhu

A flood of reliable seismic data will soon arrive. The migration to larger telescopes on the ground may free up 4-m class instruments for multi-site campaigns, and several forthcoming satellite missions promise to yield nearly uninterrupted…

Astrophysics · Physics 2007-05-23 Travis S. Metcalfe

We describe a framework in which is possible to develop and implement algorithms for the approximation of invariant measures of dynamical systems with a given bound on the error of the approximation. Our approach is based on a general…

Dynamical Systems · Mathematics 2017-10-05 Stefano Galatolo , Isaia Nisoli

The hereditary discrepancy of a set system is a certain quantitative measure of the pseudorandom properties of the system. Roughly, hereditary discrepancy measures how well one can $2$-color the elements of the system so that each set…

Data Structures and Algorithms · Computer Science 2024-04-23 Greg Bodwin , Chengyuan Deng , Jie Gao , Gary Hoppenworth , Jalaj Upadhyay , Chen Wang

The L_2-discrepancy measures the irregularity of the distribution of a finite point set. In this note we prove lower bounds for the L_2 discrepancy of arbitrary N-point sets. Our main focus is on the two-dimensional case. Asymptotic upper…

Numerical Analysis · Mathematics 2014-02-19 Aicke Hinrichs , Lev Markhasin