Related papers: Randomstrasse101: Open Problems of 2024
In connection to the development of the field of Combinatorics on Words, we present a list of open problems and conjectures that were stated during the ten last meetings WORDS. We wish to continually update the present document by adding…
Existing macroscopic traffic control methods often struggle to strictly regulate rare, safety-critical extreme events under stochastic disturbances. In this paper, we develop a rare chance-constrained optimal control framework for…
In this short expository note, we describe a unified algorithmic perspective on several classical problems which have traditionally been studied in different communities. This perspective views the main characters -- the problems of Optimal…
In recent years, random matrices have come to play a major role in computational mathematics, but most of the classical areas of random matrix theory remain the province of experts. Over the last decade, with the advent of matrix…
The aim of this article is to promote the use of probabilistic methods in the study of problems in mathematical general relativity. Two new and simple singularity theorems, whose features are different from the classical singularity…
We present a question bank consisting of over 250 multiple-choice and true-false questions covering a broad range of material typically taught in an introductory undergraduate course in numerical analysis or scientific computing. The…
My ten-week Massive Open Online Course "Statistical Mechanics: Algorithms and Computations", in early 2014, focused on subjects such as Monte Carlo sampling, molecular dynamics, transition phases in hard-sphere liquids, simulated annealing,…
For over two decades, detecting rare events has been a challenging task among researchers in the data mining and machine learning domain. Real-life problems inspire researchers to navigate and further improve data processing and algorithmic…
Can machine learning help discover new mathematical structures? In this article we discuss an approach to doing this which one can call "mathematical data science". In this paradigm, one studies mathematical objects collectively rather than…
Throughout this book, we discuss some open problems in various branches of science, including mathematics, theoretical physics, astro-physics, geophysics etc. It is of our hope that some of the problems discussed in this book will find…
Classifying network traffic is the basis for important network applications. Prior research in this area has faced challenges on the availability of representative datasets, and many of the results cannot be readily reproduced. Such a…
This document collects contributions to the Open Problem List in Billiards and Quantitative Symplectic Geometry, compiled following discussions during the workshop ``Billiards and quantitative symplectic geometry'' that took place at the…
Randomized rounding is a technique that was originally used to approximate hard offline discrete optimization problems from a mathematical programming relaxation. Since then it has also been used to approximately solve sequential stochastic…
These are the notes for a set of lectures delivered by the two authors at the Les Houches Summer School on `Complex Systems' in July 2006. They provide an introduction to the basic concepts in modern (probabilistic) coding theory,…
In today's content-centric Internet, blogs are becoming increasingly popular and important from a data analysis perspective. According to Wikipedia, there were over 156 million public blogs on the Internet as of February 2011. Blogs are a…
Inverse problems in physical or biological sciences often involve recovering an unknown parameter that is random. The sought-after quantity is a probability distribution of the unknown parameter, that produces data that aligns with…
Latent space models are powerful statistical tools for modeling and understanding network data. While the importance of accounting for uncertainty in network analysis has been well recognized, the current literature predominantly focuses on…
The emergent field of probabilistic numerics has thus far lacked clear statistical principals. This paper establishes Bayesian probabilistic numerical methods as those which can be cast as solutions to certain inverse problems within the…
The scenario-based optimization approach (`scenario approach') provides an intuitive way of approximating the solution to chance-constrained optimization programs, based on finding the optimal solution under a finite number of sampled…
Appeals to randomness in various number-theoretic constructions appear regularly in modern scientific publications. Such famous names as V.I. Arnold, M. Katz, Ya.G. Sinai, and T. Tao are just a few examples. Unfortunately, all of these…