Related papers: Correspondence and translation principles for the …
A solution is given to a conjecture proposed by Y. Wigderson and A. Wigderson concerning a "Heisenberg-like" uncertainty principle. This is an old article already published in 2022.
We find a sharp combinatorial bound for the metric entropy of sets in R^n and general classes of functions. This solves two basic combinatorial conjectures on the empirical processes. 1. A class of functions satisfies the uniform Central…
We prove a convolution formula for the conjugacy classes in symmetric groups conjectured by the second author. A combinatorial interpretation of coefficients is provided. As a main tool we introduce new semigroup of partial permutations. We…
Sentence embeddings from transformer models encode in a fixed length vector much linguistic information. We explore the hypothesis that these embeddings consist of overlapping layers of information that can be separated, and on which…
Let $1\leq p\leq 2$ and let $\Lambda = \{\lambda_n\}_{n\in \mathbb{N}} \subseteq \mathbb{R}$ be an arbitrary subset. We prove that for any $g\in M^p(\mathbb{R})$ with $1\leq p\leq 2$ the system of translates $\{g(x-\lambda_n)\}_{n\in…
Le but cette note est de tenter d'expliquer les liens \'etroits qui unissent la th\'eorie des empilements de cercles et des modules combinatoires, et de comparer les approches \`a la conjecture de J.W. Cannon qui en d\'ecoulent. ???? The…
The union-closed sets conjecture, attributed to P\'eter Frankl from 1979, states that for any non-empty finite union-closed family of finite sets not consisting of only the empty set, there is an element that is in at least half of the sets…
In this paper we prove the following: Take any "small Mandelbrot set" and zoom in a neighborhood of a parabolic or Misiurewicz parameter in it, then we can see a quasiconformal image of a Cantor Julia set which is a perturbation of a…
In this chapter, we present and discuss a new generalized proportional conflict redistribution rule. The Dezert-Smarandache extension of the Demster-Shafer theory has relaunched the studies on the combination rules especially for the…
In a recent work, Andrews gave analytic proofs of two conjectures concerning some variations of two combinatorial identities between partitions of a positive integer into odd parts and partitions into distinct parts discovered by Beck.…
In this paper, the recently introduced M&m sequences and associated mean-median map are studied. These sequences are built by adding new points to a set of real numbers by balancing the mean of the new set with the median of the original.…
The paper characterizes the Shannon (1948) and Tsallis (1988) entropies in a standard framework of decision theory, mixture sets. Procedural mixture sets are introduced as a variant of mixture sets in which it is not necessarily true that a…
In recent decades, it has been emphasized that the evolving structure of networks may be shaped by interaction principles that yield sparse graphs with a vertex degree distribution exhibiting an algebraic tail, and other structural traits…
The `Congruence Conjecture' was developed by the second author in a previous paper. It provides a conjectural explicit reciprocity law for a certain element associated to an abelian extension of a totally real number field whose existence…
This paper focuses on the convergence of infor- mation in distributed systems of agents communicating over a network. The information on which the convergence is sought is not represented by real numbers, rather by sets of real numbers,…
Conformal symmetry is broken in physical QCD; nevertheless, one can use conformal symmetry as a template, systematically correcting for its nonzero $\beta$ function as well as higher-twist effects. For example, commensurate scale relations…
We introduce an algorithm that conjectures the structure of a permutation class in the form of a disjoint cover of "rules"; similar to generalized grid classes. The cover is usually easily verified by a human and translated into an…
We report on a test of the Maldacena conjecture. This string/field theory correspondence has interesting applications. When combined with Rehren's theorem, it has implications for issues concerning space-time structure and Lorentz symmetry.…
Using standard techniques from combinatorics, model theory, and algebraic geometry, we prove generalized versions of several basic results in the theory of spectrally arbitrary matrix patterns. Also, we point out a counterexample to a…
A complete proof is given of relative interpretability of Adjunctive Set Theory with Extensionality in an elementary concatenation theory.