The inverse of the star-discrepancy problem and the generation of pseudo-random numbers
School of Mathematics and Statistics, The University of New South Wales（新南威尔士大学数学与统计学院）；Department of Financial Mathematics, Johannes Kepler University（约翰·开普勒大学金融数学系）
The inverse of the star-discrepancy problem asks for point sets $P_{N,s}$ of size $N$ in the $s$-dimensional unit cube $[0,1]^s$ whose star-discrepancy $D^\ast(P_{N,s})$ satisfies $$D^\ast(P_{N,s}) \le C \sqrt{s/N},$$ where $C> 0$ is a constant independent of $N$ and $s$. The first existence results in this direction were shown by Heinrich, Novak, Wasilkowski, and Woźniakowski in 2001, and a number of improvements have been shown since then. Until now only proofs that such point sets exist are known. Since such point sets would be useful in applications, the big open problem is to find explicit constructions of suitable point sets $P_{N,s}$.
We review the current state of the art on this problem and point out some connections to pseudo-random number generators.
The inverse of the star discrepancy of a union of randomly shifted Korobov rank-1 lattice point sets depends polynomially on the dimension
School of Mathematics, South China University of Technology（华南理工大学数学学院）；School of Mathematics and Statistics, The University of New South Wales（新南威尔士大学数学与统计学院）
Constructing Low Star Discrepancy Point Sets with Genetic Algorithms
LIAFA, Université Paris Diderot - Paris 7（巴黎第七大学 LIAFA）；Max Planck Institute for Informatics（马克斯·普朗克计算机科学研究所）；Laboratoire de vision et systèmes numériques Département de génie électrique et de génie informatique, Université Laval（拉瓦尔大学电气与计算机工程系的视觉与系统实验室）
Learned Discrepancy Reconstruction and Benchmark Dataset for Magnetic Particle Imaging
Center for Industrial Mathematics, University of Bremen（不来梅大学工业数学中心）；Section for Biomedical Imaging, University Medical Center Hamburg-Eppendorf（汉堡埃彭多夫大学医学中心生物医学影像科）；Institute for Biomedical Imaging, Hamburg University of Technology（汉堡工业大学生物医学影像研究所）；Fraunhofer Research Institution for Individualized and Cell-Based Medical Engineering IMTE（弗劳恩霍夫个性化与基于细胞的医学工程研究所IMTE）
Deep regularization networks for inverse problems with noisy operators
1.25mm 1 Department of Civil, Environmental \& Architectural Engineering, University of Colorado Boulder, USA；1mm 2 Department of Applied Mathematics, University of Colorado Boulder, USA
