Related papers: Randomstrasse101: Open Problems of 2024
The 2012 logic blog has focussed on the following: Randomness and computable analysis/ergodic theory; Systematizing algorithmic randomness notions; Traceability; Higher randomness; Calibrating the complexity of equivalence relations from…
This year's logic blog has focussed on: 1. Demuth randomness 2. traceability 3. The connection of computable analysis and randomness 4. $K$-triviality in metric spaces.
Increasing availability and quality of actual, as opposed to scheduled, open transport data offers new possibilities for capturing the spatiotemporal dynamics of the railway and other networks of social infrastructure. One way to describe…
We describe a list of open problems in random matrix theory and integrable systems which was presented at the conference ``Integrable Systems, Random Matrices, and Applications'' at the Courant Institute in May 2006.
In this paper we study random optimization problems where random functions are investigated in sample paths. Some sufficient conditions ensuring the existence of random solutions to random optimization problems are proposed.
The 2013 logic blog has focussed on the following: 1. Higher randomness. Among others, the Borel complexity of $\Pi^1_1$ randomness and higher weak 2 randomness is determined. 2. Reverse mathematics and its relationship to randomness. For…
This short course offers a new perspective on randomized algorithms for matrix computations. It explores the distinct ways in which probability can be used to design algorithms for numerical linear algebra. Each design template is…
We present and discuss a list of some interesting points that are currently open in nonextensive statistical mechanics. Their analytical, numerical, experimental or observational advancement would naturally be very welcome.
Lecture notes of a master course given at Orsay between 2019-2024. Topics covered include Part I: One-dimensional random walks, cycle lemma and Bienaym\'e--Galton--Watson random trees. Part II: Erd\"os--R\'enyi random graphs, three proofs…
These notes constitute the basis for the lectures given by the author at Centre de recherches math\'ematiques (CRM) at Universit\'e de Montreal, as part of the thematic semester on "Mathematical challenges in many-body physics and quantum…
We discuss a connection between two areas of mathematics which until recently seemed to be rather distant from each other: (1) noncommutative harmonic analysis on groups and (2) some topics in probability theory related to random point…
The blog has several entries on group theory interacting with computability and wider logic, several open questions, and an entry on undecidability in physics.
The blog is somewhat shorter than in previous years, It contains new insights in a variety of areas, including computability, quantum algorithmic version of the SMB theorem, descriptions of groups (both discrete and profinite), metric…
Statistics 101, 201, and 202 are three open-source interactive web applications built with R \citep{R} and Shiny \citep{shiny} to support the teaching of introductory statistics and probability. The apps help students carry out common…
The aim of this paper is to share with the mathematical community a list of 33 problems that I have found along the years during my research. I believe that it is worth to think about them and, hopefully, it will be possible either to solve…
This document is a brief summary of progress that has been made on the problems posed in the document "Twenty Open Problems in Enumeration of Matchings" (also available from this server as math.CO/9801060). NOTE: This article has now been…
This text presents an unified approach of probability and statistics in the pursuit of understanding and computation of randomness in engineering or physical or social system with prediction with generalizability. Starting from elementary…
We review mathematically tractable models for connected networks on random points in the plane, emphasizing the class of proximity graphs which deserves to be better known to applied probabilists and statisticians. We introduce and motivate…
We give new results for problems in computational and statistical machine learning using tools from high-dimensional geometry and probability. We break up our treatment into two parts. In Part I, we focus on computational considerations in…
Combinatorics is a powerful tool for dealing with relations among objectives mushroomed in the past century. However, an more important work for mathematician is to apply combinatorics to other mathematics and other sciences not merely to…