Related papers: Random Relation Algebras
We give an historical survey of some of the original basic algebraic and combinatorial results on Temperley-Lieb algebras, with a focus on certain results that have become folklore.
We develop a graphical notation to introduce classical Lie algebras. Although this paper deals with well-known results, our pictorial point of view is slightly different to the traditional one. Our graphical notation is fairly elementary…
Random graph (RG) models play a central role in the complex networks analysis. They help to understand, control, and predict phenomena occurring, for instance, in social networks, biological networks, the Internet, etc. Despite a large…
Starting from a description of various generalized function algebras based on sequence spaces, we develop the general framework for considering linear problems with singular coefficients or non linear problems. Therefore, we prove…
Let $A$ and $B$ be two connected graded algebras finitely generated in degree one. If $A$ is isomorphic to $B$ as ungraded algebras, then they are also isomorphic to each other as graded algebras.
We develop here the algebra of the differential field of transseries and of related valued differential fields. This book contains in particular our recently obtained decisive positive results on the model theory of these structures.
We introduce the notion of amenability for affine algebras. We characterize amenability by Folner-sequences, paradoxicality and the existence of finitely invariant dimension-measures. Then we extend the results of Rowen on ranks, from…
Primarily this paper presents an expository report on alternatives to the traditional methods of classifying representations of finite dimensional algebras. Some new results illustrating such alternatives for algebras with only finitely…
Relation linking is essential to enable question answering over knowledge bases. Although there are various efforts to improve relation linking performance, the current state-of-the-art methods do not achieve optimal results, therefore,…
An infinite dimensional algebra, which is useful for deriving exact solutions of the generalized pairing problem, is introduced. A formalism for diagonalizing the corresponding Hamiltonian is also proposed. The theory is illustrated with…
This paper presents an investigation on the structure of conditional events and on the probability measures which arise naturally in this context. In particular we introduce a construction which defines a (finite) {\em Boolean algebra of…
We begin by defining Temperley-Lieb algebra, in two different ways: as a presented algebra or as a diagrammatic algebra. Next, we look for a basis algorithmically, using rewriting theory. Finally, we introduce a generalization of the…
A new algebraic treatment of dependent type theory is proposed using ideas derived from topos theory and algebraic set theory.
The purpose of this paper is to introduce Hom-alternative algebras and Hom-Jordan algebras. We discuss some of their properties and provide construction procedures using ordinary alternative algebras or Jordan algebras. Also, we show that a…
We summarize our recent findings, where we proposed a framework for learning a Kolmogorov model, for a collection of binary random variables. More specifically, we derive conditions that link outcomes of specific random variables, and…
We describe the role of algebraic extensions in the theory of commutative, unital normed algebras, with special attention to uniform algebras. We shall also compare these constructions and show how they are related to each other.
We propose a new formalism for specifying and reasoning about problems that involve heterogeneous "pieces of information" -- large collections of data, decision procedures of any kind and complexity and connections between them. The essence…
In this article the idea of random variables over the set theoretic universe is investigated. We explore what it can mean for a random set to have a specific probability of belonging to an antecedently given class of sets.
We review a collection of models of random simplicial complexes together with some of the most exciting phenomena related to them. We do not attempt to cover all existing models, but try to focus on those for which many important results…
We study links between first-order formulas and arbitrary properties for families of theories, classes of structures and their isomorphism types. Possibilities for ranks and degrees for formulas and theories with respect to given properties…