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Large collections of high-dimensional data have become nearly ubiquitous across many academic fields and application domains, ranging from biology to the humanities. Since working directly with high-dimensional data poses challenges, the…

The Bayesian approach to inverse problems is widely used in practice to infer unknown parameters from noisy observations. In this framework, the ensemble Kalman inversion has been successfully applied for the quantification of uncertainties…

This short note describes the tentative form of a finite-dimensional optimization problem that may be of use in a second-generation proof of the Kepler conjecture. In the original 1998 proof of the Kepler conjecture, the form of the…

Poissonian pair correlations have sparked interest within the mathematical community, because of their number theoretic properties, and their connections to quantum physics and probability theory, particularly uniformly distributed random…

This article is an introductory review of random matrix theory (RMT) and its applications, with special focus on quantum chaos. Random matrices were first used by Wigner to understand the spectra of complex nuclei from a statistical…

Higher-dimensional orthogonal packing problems have a wide range of practical applications, including packing, cutting, and scheduling. In the context of a branch-and-bound framework for solving these packing problems to optimality, it is…

This is a presentation of recent work on quantum permutation groups, complex Hadamard matrices, and the connections between them. A long list of problems is included. We include as well some conjectural statements, about matrix models.

Cuckoo search (CS) was introduced in 2009, and it has attracted great attention due to its promising efficiency in solving many optimization problems and real-world applications. In the last few years, many papers have been published…

The possible existence of black holes has fascinated scientists at least since Michell and Laplace's proposal that a gravitating object could exist from which light could not escape. In the 20th century, in light of the general theory of…

In this work, we propose a novel topic consisting of two dual tasks: 1) given a scene, recommend objects to insert, 2) given an object category, retrieve suitable background scenes. A bounding box for the inserted object is predicted in…

Bayesian persuasion and its derived information design problem has been one of the main research agendas in the economics and computation literature over the past decade. However, when attempting to apply its model and theory, one is often…

Sequential search models provide a powerful framework for studying consumer search using rich data that records the sequence of consumer actions taken during the search process. In existing empirical applications, their implementation often…

Research on fractal networks is a dynamically growing field of network science. A central issue is to analyze fractality with the so-called box-covering method. As this problem is known to be NP-hard, a plethora of approximating algorithms…

Quantum algorithms are demonstrated to outperform classical algorithms for certain problems and thus are promising candidates for efficient information processing. Herein we aim to provide a brief and popular introduction to quantum…

Random matrices have their roots in multivariate analysis in statistics, and since Wigner's pioneering work in 1955, they have been a very important tool in mathematical physics. In functional analysis, random matrices and random structures…

When exploring a new dataset, Data Scientists often apply analysis queries, look for insights in the resulting dataframe, and repeat to apply further queries. We propose in this paper a novel solution that assists data scientists in this…

Recent advances in computing have changed not only the nature of mathematical computation, but mathematical proof and inquiry itself. While artificial intelligence and formalized mathematics have been the major topics of this conversation,…

We discuss recent progress many problems in random matrix theory of a combinatorial nature, including several breakthroughs that solve long standing famous conjectures.

Erd\H{o}s first introduced the idea of covering systems in 1950. Since then, much of the work in this area has concentrated on identifying covering systems that meet specific conditions on their moduli. Among the central open problems in…

We consider the problem of a decision-maker searching for information on multiple alternatives when information is learned on all alternatives simultaneously. The decision-maker has a running cost of searching for information, and has to…