Related papers: Une liste de probl\`emes
The paper proposes open problems in classical Kolmogorov complexity. Each problem is presented with background information and thus the article also surveys some recent studies in the area.
With the advancements of Large Language Models (LLMs), an increasing number of open-source software projects are using LLMs as their core functional component. Although research and practice on LLMs are capturing considerable interest, no…
We give a survey of work on the number of vertices of the convex hull of integer points defined by the system of linear inequalities. Also, we present our improvement of some of these.
Numerical simulations are ubiquitous in mathematics and computational science. Several industrial and clinical applications entail modeling complex multiphysics systems that evolve over a variety of spatial and temporal scales. This study…
In this lecture I will talk about three mathematical puzzles involving mathematics and computation that have preoccupied me over the years. The first puzzle is to understand the amazing success of the simplex algorithm for linear…
A sequence of positive integers is introduced, that is proved to simultaneously solve an infinite family of related puzzles, one of which was recently featured on the popular YouTube sudoku channel \emph{Cracking the Cryptic}.
This document is both a synthesis of current notions about complex systems, and a practical approach description. A disambiguation is proposed and exposes possible reasons for controversies related to causation and emergence. Theoretical…
This article presents a general solution to the problem of computational complexity. First, it gives a historical introduction to the problem since the revival of the foundational problems of mathematics at the end of the 19th century.…
It is shown the construction of a module structure [2] with universe over a set of a particular kind of mathematical proofs, the base ring of this module will be built on a maximal consistent extension of a set of propositions, this…
This paper addresses problems on the structural design of control systems taking explicitly into consideration the possible application to large-scale systems. We provide an efficient and unified framework to solve the following major…
A method for converting the geometrical problem of rectangle packing to an algebraic problem of solving a system of polynomial equations is described.
Following an orginal idea by Kn\"odel, an online bin-packing problem is considered where the the large items arrive in double-packs. The dual problem where the small items arrive in double-packs is also considered. The enumerations have a…
Compared with constraint satisfaction problems, counting problems have received less attention. In this paper, we survey research works on the problems of counting the number of solutions to constraints. The constraints may take various…
Contains various tools for preferential and related logics
In this small paper we bring together various open problems on geometric multidimensional continued fractions.
A collection of short expository essays by the author on various topics in quantum mechanics, quantum cosmology, and physics in general.
Quantum graphs have become in this century a favorite playground for mathematicians, mathematical physicists, and chemists, due to their manifold applications as models of thin structures, as well as presenting sometimes simpler playground…
"Clarithmetic" is a generic name for formal number theories similar to Peano arithmetic, but based on computability logic (see http://www.cis.upenn.edu/~giorgi/cl.html) instead of the more traditional classical or intuitionistic logics.…
MathRepo, located at https://mathrepo.mis.mpg.de, is an online repository for mathematical research data. In mathematics, research data comes in many different flavours. For instance, in computer algebra it most often takes the form of…
This is an introductory article to the theory of multiple gaps.