Related papers: Relational Characterisations of Paths
We characterize Leavitt path algebras which are exchange rings in terms of intrinsic properties of the graph and show that the values of the stable rank for these algebras are 1, 2 or $\infty$. Concrete criteria in terms of properties of…
Comparing relational languages by their logical expressiveness is well understood. Less well understood is how to compare relational languages by their ability to represent relational query patterns. Indeed, what are query patterns other…
Graphs are fundamental data structures which concisely capture the relational structure in many important real-world domains, such as knowledge graphs, physical and social interactions, language, and chemistry. Here we introduce a powerful…
We say that a graph $G$ is $(2,m)$-linked if, for any distinct vertices $a_1,\ldots, a_m, b_1,b_2$ in $G$, there exist vertex disjoint connected subgraphs $A,B$ of $G$ such that $\{a_1, \ldots, a_m\}$ is contained in $A$ and $\{b_1,b_2\}$…
Answering connectivity queries in real algebraic sets is a fundamental problem in effective real algebraic geometry that finds many applications in e.g. robotics where motion planning issues are topical. This computational problem is…
The Longest Path Problem is a question of finding the maximum length between pairs of vertices of a graph. In the general case, the problem is NP-complete. However, there is a small collection of graph classes for which there exists an…
Topology identification and inference of processes evolving over graphs arise in timely applications involving brain, transportation, financial, power, as well as social and information networks. This chapter provides an overview of graph…
Many real life networks present an average path length logarithmic with the number of nodes and a degree distribution which follows a power law. Often these networks have also a modular and self-similar structure and, in some cases -…
Owing to their versatility, graph structures admit representations of intricate relationships between the separate entities comprising the data. We formalise the notion of connection between two vertex sets in terms of edge and vertex…
The recent developments and growing interest in neural-symbolic models has shown that hybrid approaches can offer richer models for Artificial Intelligence. The integration of effective relational learning and reasoning methods is one of…
The paper gives an overview of recent advances in structural equation modeling. A structural equation model is a multivariate statistical model that is determined by a mixed graph, also known as a path diagram. Our focus is on the…
We present an algorithm to compute path homology for simple digraphs, and use it to topologically analyze various small digraphs en route to an analysis of complex temporal networks which exhibit such digraphs as underlying motifs. The…
Path calculus, or graphical linear algebra, is a string diagram calculus for the category of matrices over a base ring. It is the usual string diagram calculus for a symmetric monoidal category, where the monoidal product is the direct sum…
Cities can be seen as the epitome of complex systems. They arise from a set of interactions and components so diverse that is almost impossible to describe them exhaustively. Amid this diversity, we chose an object which orchestrates the…
When proving theorems from large sets of logical assertions, it can be helpful to restrict the search for a proof to those assertions that are relevant, that is, closely related to the theorem in some sense. For example, in the Watson…
Road network is a critical infrastructure powering many applications including transportation, mobility and logistics in real life. To leverage the input of a road network across these different applications, it is necessary to learn the…
In recent years, algebraic topology and its modern development, the theory of persistent homology, has shown great potential in graph representation learning. In this paper, based on the mathematics of algebraic topology, we propose a novel…
Document-level relation extraction (DocRE) models generally use graph networks to implicitly model the reasoning skill (i.e., pattern recognition, logical reasoning, coreference reasoning, etc.) related to the relation between one entity…
We introduce a class of algebras over a field $\mathbb{F}$ related to directed graphs in which all edges are labeled by nonzero elements of the field $\mathbb{F}$. If all labels are different from $1$, these algebras are axial algebras. We…
Distance based knowledge graph embedding methods show promising results on link prediction task, on which two topics have been widely studied: one is the ability to handle complex relations, such as N-to-1, 1-to-N and N-to-N, the other is…