Related papers: Remarks on the Levi core
We present a simple and clear foundation for finite inference that unites and significantly extends the approaches of Kolmogorov and Cox. Our approach is based on quantifying lattices of logical statements in a way that satisfies general…
Over any partially ordered abelian group whose positive cone is closed in an appropriate sense and has finitely many faces, modules that satisfy a weak finiteness condition admit finite primary decompositions. This conclusion rests on the…
I discuss some aspects of a lattice approach to canonical quantum gravity in a connection formulation, discuss how it differs from the continuum construction, and compare the spectra of geometric operators - encoding information about…
The charged lepton masses obey to high precision the so-called Koide relation. We propose a generalization of this relation to quarks. It includes up and down quarks of the three generations and is numerically reasonably close to the Koide…
We consider countable linear orders and study the quasi-order of convex embeddability and its induced equivalence relation. We obtain both combinatorial and descriptive set-theoretic results, and further extend our research to the case of…
I prove lower bounds of some parameters of elliptic curve over finite field. There parameters are closely interrelated with cryptographic stability of elliptic curve.
The ultimate limits of computation are not just logical, but physical. We investigate the physical resources -- time, energy, entropy, and free energy -- required to perform computational work. We apply the resulting measures of physical…
In this note we prove a decomposition related to the affine fundamental group and the projective fundamental group of a line arrangement and a reducible curve with a line component. We give some applications to this result.
This survey describes some recent work, by the authors and others, on the existence of algebraic fibrations of group extensions, as well as the finiteness properties of their algebraic fibers, in the realm of both abstract and pro-$p$…
We present an algorithm for the classification of linear codes over finite fields, based on lattice point enumeration. We validate a correct implementation of our algorithm with known classification results from the literature, which we…
We consider the problem of counting the number of answers to a first-order formula on a finite structure. We present and study an extension of first-order logic in which algorithms for this counting problem can be naturally and conveniently…
Some contemporary views of the universe assume information and computation to be key in understanding and explaining the basic structure underpinning physical reality. We introduce the Computable Universe exploring some of the basic…
We use different approaches to study a generalization of a result of Levin and Ste\v{c}kin concerning an inequality analogous to Hardy's inequality. Our results lead naturally to the study of weighted remainder form of Hardy-type…
These lecture notes focus on the application of ideas of locality, in particular Lieb-Robinson bounds, to quantum many-body systems. We consider applications including correlation decay, topological order, a higher dimensional…
We interpret homogenousness as a second order property and base it on the same principle as nonmonotonic logic: there might be a small set of exceptions. We use this idea to analyse fundamental questions about defeasible inheritance…
In this short survey we concern ourselves with minimal codes, a classical object in coding theory. We will explain the relation between minimal codes and various other mathematical domains, in particular with finite projective geometry.…
We prove the Levin-Ste\v{c}kin inequality using Chebyshev's inequality and symmetrization. Symmetry and slightly modified Chebyshev's inequality are also the key to an elementary proof of Clausing's inequality .
Some of the important inequalities associated with quantum entropy are immediate algebraic consequences of the Hansen-Pedersen-Jensen inequality. A general argument is given using matrix perspectives of operator convex functions. A matrix…
The notion of differentiation index for DAE systems of arbitrary order with generic second members is discussed by means of the study of the behavior of the ranks of certain Jacobian associated sub-matrices. As a by-product, we obtain upper…
Some particular examples of classical and quantum systems on the lattice are solved with the help of orthogonal polynomials and its connection to continuous models are explored.