Related papers: Random Relation Algebras
This contribution derives from a rather extensive study on the foundations of probability. We start by discussing critically the two main models of the random event in Probability Theroy and cast light over a number of incongruities. We…
Advances in information technology have increased the availability of time-stamped relational data such as those produced by email exchanges or interaction through social media. Whereas the associated information flows could be aggregated…
We introduce and study a relative cancellation property for associative algebras. We also prove a characterization result for polynomial rings which partially answers a question of Kraft.
This is survey of some recent results connecting random matrices, non-colliding processes and queues.
Fork algebras are an extension of relation algebras obtained by extending the set of logical symbols with a binary operator called fork. This class of algebras was introduced by Haeberer and Veloso in the early 90's aiming at enriching…
After briefly reviewing the methods that allow us to derive consistently new Lie (super)algebras from given ones, we consider enlarged superspaces and superalgebras, their relevance and some possible applications.
In this paper we develop a structure called Link Algebra, in which we present a Set with two binary operations and an axiom system developed from the study of graph theory and set/antiset theory, sowing main theorems and definitions. Once…
We construct a geometric system from which the Hall algebra can be recovered. This system inherently satisfies higher associativity conditions and thus leads to a categorification of the Hall algebra. We then suggest how to use this…
New notions are introduced in algebra in order to better study the congruences in number theory. For example, the <special semigroups> makes an important such contribution.
Computation of polynomial relative invariants is a classical tool in algebra. Relative differential invariants are central for the equivalence problem of geometric structures. We address the fundamental problem of finite generation of their…
We study a class of algebras that can be used as recognisers for regular languages of infinite trees.
We study higher depth algebras. We introduce several examples of such structures starting from the notion of $N$-differential graded algebras and build up to the concept of $A_{\infty}^N$-algebras.
Analyzing social networks is challenging. Key features of relational data require the use of non-standard statistical methods such as developing system-specific null, or reference, models that randomize one or more components of the…
We introduce a notion of Pre-structurable Algebras based upon triality relations and study its relation to structurable algebra of Allison, as well as to Lie algebras satisfying triality.
We survey old and new approaches to the study of symbolic powers of ideals. Our focus is on the symbolic Rees algebra of an ideal, viewed both as a tool to investigate its symbolic powers and as a source of challenging problems in its own…
The goal of this paper is to present an algebraic approach to the basic results of the theory of linear recurrence relations. This approach is based on the ideas from the theory of representations of one endomorphisms (a special case of…
Interactions and time shape many aspects of life. Everyday activities -- like conversations, emails, money transfers, citations, and even acts of violence -- are relational events: interactions between a sender and a receiver at a specific…
The database community lacks a unified relational query language for subset selection and optimisation queries, limiting both user expression and query optimiser reasoning about such problems. Decades of research (latterly under the rubric…
Algebraic statistics uses tools from algebra (especially from multilinear algebra, commutative algebra and computational algebra), geometry and combinatorics to provide insight into knotty problems in mathematical statistics. In this survey…
We search for a possible mathematical formulation of some of the key ideas of the relational interpretation of quantum mechanics and study their consequences. We also briefly overview some proposals of relational quantum mechanics for an…