Related papers: Random Relation Algebras
We provide a survey on relational models. Relational models describe complete networked {domains by taking into account global dependencies in the data}. Relational models can lead to more accurate predictions if compared to non-relational…
In this paper we explore a new method of analysis of associative algebras.
We develop a theory of toroidal vertex algebras and their modules, and we give a conceptual construction of toroidal vertex algebras and their modules. As an application, we associate toroidal vertex algebras and their modules to toroidal…
After recalling the notion of Lie algebroid, we construct these structures associated with contact forms or systems. We are then interested in particular classes of Lie Rinehart algebras.
A new method is developed to represent probabilistic relations on multiple random events. Where previously knowledge bases containing probabilistic rules were used for this purpose, here a probability distribution over the relations is…
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…
Relative algebroids provide a framework that unifies Lie algebroids with partial differential equations. In this set of notes, we explain how relative algebroids arise from geometric problems, and give an introduction to their structural…
A series of nonrepresentable relation algebras is constructed from groups. We use them to prove that there are continuum many subvarieties between the variety of representable relation algebras and the variety of coset relation algebras. We…
The validation of any database mining methodology goes through an evaluation process where benchmarks availability is essential. In this paper, we aim to randomly generate relational database benchmarks that allow to check probabilistic…
We take a categorical approach to describe ternary derivations and ternary automorphisms of triangular algebras. New classes of automorphisms and derivations of triangular algebras are also introduced and studied.
This short course offers a new perspective on randomized algorithms for matrix computations. It explores the distinct ways in which probability can be used to design algorithms for numerical linear algebra. Each design template is…
In this paper we will provide an introductory understanding of random graph models, and matchings in the case of Erdos-Renyi random graphs. We will provide a synthesis of background theory to this end. We will further examine pertinent…
We give a polymorphic account of the relational algebra. We introduce a formalism of ``type formulas'' specifically tuned for relational algebra expressions, and present an algorithm that computes the ``principal'' type for a given…
Motivated by a problem in graph theory, this article introduces an algebra called the balanced algebra. This algebra is defined by generators and relations, and the main goal is to find a minimal set of relations for it.
We develop a new framework of relative algebroids to address existence and classification problems of geometric structures subject to partial differential equations.
Random graphs are more and more used for modeling real world networks such as evolutionary networks of proteins. For this purpose we look at two different models and analyze how properties like connectedness and degree distributions are…
A quantitative model of concurrent interaction is introduced. The basic objects are linear combinations of partial order relations, acted upon by a group of permutations that represents potential non-determinism in synchronisation. This…
We introduce parallelism into the basic algebra of games to model concurrent game algebraically. Parallelism is treated as a new kind of game operation. The resulted algebra of concurrent games can be used widely to reason the parallel…
We survey some ideas from the subject of Random Algebraic Geometry, a field that introduces a probabilistic perspective on classical topics in real algebraic geometry. This offers a modern approach to classical problems, such as Hilbert's…
To any directed graph we associate an algebra with edges of the graph as generators and with relations defined by all pairs of directed paths with the same origin and terminus. Such algebras are related to factorizations of polynomials over…