Related papers: Random Relation Algebras
We characterize vertex algebras (in a suitable sense) as algebras over a certain graded co-operad. We also discuss some examples and categorical implications of this characterization.
In this paper, we propose Latent Relation Language Models (LRLMs), a class of language models that parameterizes the joint distribution over the words in a document and the entities that occur therein via knowledge graph relations. This…
This is in some sense an addendum to the book Relational Mathematics by the first-named author. It originated from work on diverse other topics during which a lot of purely relational results with broad applicability have been produced.…
We introduce the notion of ends for algebras. The definition is analogous to the one in geometric group theory. We establish some relations to growth conditions and cyclic cohomology.
A novel approach for creating ER conceptual models and an algorithm for transforming them to the relational model has been developed by modifying and extending the existing methods. A part of the new algorithm has previously been presented.…
We define a new cohomology for associative algebras which we compute for algebras with units.
In this paper we investigate the problem of which Lie algebras appear as the derived algebra of a Lie algebra. We present new results that further develop this study and address two questions raised in a paper concerned with the…
In extending results from Lie to Leibniz algebras, it is helpful to have techniques which translate results from the former to the latter without having to repeat the (perhaps modified) arguments. Such a technique is developed in this work,…
In a general algebraic setting, we state some properties of commutators of reflexive admissible relations.
This paper is a sequel to [3]. We formulate a natural algebraic geometry conjecture, give some of its number theoretic and analytical consequences, and show that those can be used to get further advances in wave turbulence theory.
In this paper we define the basic concepts for left or right Leibniz algebras and prove some of the main results. Our proofs are often variations of the known proofs and several results seem to be new.
We discuss various aspects of the statistical formulation of the theory of random graphs, with emphasis on results obtained in a series of our recent publications.
In this work we study the connection between iterated tilted algebras and m-cluster tilted algebras. We show that an iterated tilted algebra induces an m-cluster tilted algebra. This m-cluster tilted algebra can be seen as a trivial…
In relational approach to general rough sets, ideas of directed relations are supplemented with additional conditions for multiple algebraic approaches in this research paper. The relations are also specialized to representations of general…
The Jacobian algebras are introduced and their various properties are studied.
The relationship between belief networks and relational databases is examined. Based on this analysis, a method to construct belief networks automatically from statistical relational data is proposed. A comparison between our method and…
Enveloping algebras of Hom-Lie and Hom-Leibniz algebras are constructed.
Consider the set of solutions to a system of polynomial equations in many variables. An algebraic manifold is an open submanifold of such a set. We introduce a new method for computing integrals and sampling from distributions on algebraic…
Large matrices arise in many machine learning and data analysis applications, including as representations of datasets, graphs, model weights, and first and second-order derivatives. Randomized Numerical Linear Algebra (RandNLA) is an area…
We study the limit theory of large threshold graphs and apply this to a variety of models for random threshold graphs. The results give a nice set of examples for the emerging theory of graph limits.