Related papers: Partial Cartesian Graph Product
Topological algebras have properties that extend naturally to those of topological groups [8, 9], but is it the case that semi-direct products exist as in the category of groups? Firstly, we express concepts in categorical language that…
The notion of quasicrossed product is introduced in the setting of G-graded quasialgebras, i.e., algebras endowed with a grading by a group G, satisfying a "quasiassociative" law. The equivalence between quasicrossed products and…
We introduce a simple initial working system in which relations (such as part-whole) are directly represented via an architecture with operating and learning rules fundamentally distinct from standard artificial neural network methods.…
In this paper, we describe {\sc quantitative graph theory} and argue it is a new graph-theoretical branch in network science, however, with significant different features compared to classical graph theory. The main goal of quantitative…
This paper studies the structure of graphs with given tree-width and excluding a fixed complete bipartite subgraph, which generalises the bounded degree setting. We give a new structural description of such graphs in terms of so-called…
We introduce a notion of complexity of diagrams (and in particular of objects and morphisms) in an arbitrary category, as well as a notion of complexity of functors between categories equipped with complexity functions. We discuss several…
In this paper we investigate undirected discrete graphical tree models when all the variables in the system are binary, where leaves represent the observable variables and where all the inner nodes are unobserved. A novel approach based on…
We define a free product of connected simple graphs that is equivalent to several existing definitions when the graphs are vertex-transitive but differs otherwise. The new definition is designed for the automorphism group of the free…
The paper gives some criteria for partial sums of rational number sequences to be not rational functions and to be not algebraic functions. As an application, we study partial sums of some famous rational number sequences in mathematical…
With the increased interest in machine learning, and deep learning in particular, the use of automatic differentiation has become more wide-spread in computation. There have been two recent developments to provide the theoretical support…
This paper generalizes the normally ordered tensor product from Tate vector spaces to Tate objects over arbitrary exact categories. We show how to lift bi-right exact monoidal structures, duality functors, and construct external Homs. We…
We introduce priors and algorithms to perform Bayesian inference in Gaussian models defined by acyclic directed mixed graphs. Such a class of graphs, composed of directed and bi-directed edges, is a representation of conditional…
This paper describes a method for the recovering of software architectures from a set of similar (but unrelated) software products in binary form. One intention is to drive refactoring into software product lines and combine architecture…
We introduce the notion of the action of a group on a labeled graph and the quotient object, also a labeled graph. We define a skew product labeled graph and use it to prove a version of the Gross-Tucker theorem for labeled graphs. We then…
In this paper a general theory of semi-classical matrix orthogonal polynomials is developed. We define the semi-classical linear functionals by means of a distributional equation $D(u A) = u B,$ where $A$ and $B$ are matrix polynomials.…
In this paper, we introduce a new concept namely degree polynomial for vertices of a simple graph. This notion leads to a concept namely degree polynomial sequence which is stronger than the concept of degree sequence. After obtaining the…
Graphical (Linear) Algebra is a family of diagrammatic languages allowing to reason about different kinds of subsets of vector spaces compositionally. It has been used to model various application domains, from signal-flow graphs to Petri…
We determine all the ways in which a direct product of two finite groups can be expressed as the set-theoretical union of proper subgroups in a family of minimal cardinality.
We present the operator semigroups approach to first- and second-order dynamical systems taking place on metric graphs. We briefly survey the existing results and focus on the well-posedness of the problems with standard vertex conditions.…
The performance of codes defined from graphs depends on the expansion property of the underlying graph in a crucial way. Graph products, such as the zig-zag product and replacement product provide new infinite families of constant degree…