Related papers: Piggybacking over unbounded distributive lattices
A unified model is addressed for general optimization problems in multi-scale complex systems. Based on necessary conditions and basic principles in physics, the canonical duality-triality theory is presented in a precise way to include…
This paper explores the potential of Lagrangian duality for learning applications that feature complex constraints. Such constraints arise in many science and engineering domains, where the task amounts to learning optimization problems…
Brauer and Thrall conjectured that a finite-dimensional algebra over a field of bounded representation type is actually of finite representation type and a finite-dimensional algebra (over an infinite field) of infinite representation type…
This document is an informal bibliography of the papers dealing with distributed approximation algorithms. A classic setting for such algorithms is bounded degree graphs, but there is a whole set of techniques that have been developed for…
The aim of this paper is to extend the structure theory for infinitely generated modules over tame hereditary algebras to the more general case of modules over concealed canonical algebras. Using tilting, we may assume that we deal with…
Part I of this paper introduced the infinite dimensional Lagrange-Dirac theory for physical systems on the space of differential forms over a smooth manifold with boundary. This approach is particularly well-suited for systems involving…
One of the traditional applications of relation algebras is to provide a setting for infinite-domain constraint satisfaction problems. Complexity classification for these computational problems has been one of the major open research…
The need of fast distributed solvers for optimization problems in networked systems has motivated the recent development of the Fast-Lipschitz optimization framework. In such an optimization, problems satisfying certain qualifying…
In this book i treat linear algebra over division ring. A system of linear equations over a division ring has properties similar to properties of a system of linear equations over a field. However, noncommutativity of a product creates a…
The categorified theories known as "doctrines" specify a category equipped with extra structure, analogous to how ordinary theories specify a set with extra structure. We introduce a new framework for doctrines based on double category…
We study splittings, or lack of them, in lattices of subvarieties of some logic-related varieties. We present a general lemma, the Non-Splitting Lemma, which when combined with some variety-specific constructions, yields each of our…
We prove that the universal theory and the quasi-equational theory of bounded residuated distributive lattice-orderegroupoids are both EXPTIME-complete. Similar results areproven for bounded distributive lattices with a unary or binary…
An equivalence between Lu's bialgebroids, Xu's bialgebroids with an anchor and Takeuchi's $\times_{A}$-bialgebras is explicitly proven. A new class of examples of bialgebroids is constructed. A (formal) dual of a bialgebroid, termed…
Lattices induced by coverings arise naturally in matroid theory and combinatorial optimization, providing a structured framework for analyzing relationships between independent sets and closures. In this paper, we explore the structural…
There is an unproven duality theory hypothesizing that random discrete trees and their poissonized embeddings in continuous time share fundamental properties. We give additional evidence in favor of this theory by showing that several…
Let G' be a connected reductive group over the complex numbers. We show that the set of conjugacy classes of G' is in natural bijection with the set of two-sided cells associated to a certain algebra.
We first present a Priestley-style dualitiy for the classes of algebras that are the algebraic counterpart of some congruential, finitary and filter-distributive logic with theorems. Then we analyze which properties of the dual spaces…
An attempt is made to formulate Gaiotto's S-duality relations in an explicit quantitative form. Formally the problem is that of evaluation of the Racah coefficients for the Virasoro algebra, and we approach it with the help of the matrix…
Looking at some monoids and (semi)rings (natural numbers, integers and p-adic integers), and more generally, residually finite algebras (in a strong sense), we prove the equivalence of two ways for a function on such an algebra to behave…
We construct a canonical extension for strong proximity lattices in order to give an algebraic, point-free description of a finitary duality for stably compact spaces. In this setting not only morphisms, but also objects may have distinct…