Related papers: Interaction Graphs: Graphings
We show that sums over graphs such as appear in the theory of Feynman diagrams can be seen as integrals over discrete groupoids. From this point of view, basic combinatorial formulas of the theory of Feynman diagrams can be interpreted as…
Built upon the shoulders of graph theory, the field of complex networks has become a central tool for studying real systems across various fields of research. Represented as graphs, different systems can be studied using the same analysis…
Directed mixed graphs permit directed and bidirected edges between any two vertices. They were first considered in the path analysis developed by Sewall Wright and play an essential role in statistical modeling. We introduce a matrix…
In this paper, we use the theory of Riordan matrices to introduce the notion of a Riordan graph. The Riordan graphs are a far-reaching generalization of the well known and well studied Pascal graphs and Toeplitz graphs, and also some other…
In this work, we have studied classical and quantum systems in interaction by means of geometric reduction procedure. The main target is the description in these terms of fundamental interactions. We have shown that, to describe in a…
A non-commutative, non-associative weakening of Girard's linear logic is developed for multiplicative and additive connectives. Additional assumptions capture the logic of quantic measurements.
Probabilistic graphical models combine the graph theory and probability theory to give a multivariate statistical modeling. They provide a unified description of uncertainty using probability and complexity using the graphical model.…
By interpreting a traffic scene as a graph of interacting vehicles, we gain a flexible abstract representation which allows us to apply Graph Neural Network (GNN) models for traffic prediction. These naturally take interaction between…
We propose a method for obtaining parsimonious decompositions of networks into higher order interactions which can take the form of arbitrary motifs.The method is based on a class of analytically solvable generative models, where vertices…
Graphs are used in many disciplines to model the relationships that exist between objects in a complex discrete system. Researchers may wish to compare a network of interest to a "typical" graph from a family (or ensemble) of graphs which…
Graph neural networks (GNNs) are a powerful tool to learn representations on graphs by iteratively aggregating features from node neighbourhoods. Many variant models have been proposed, but there is limited understanding on both how to…
Here I report about the modifications of and relations between graphic lambda calculus, various formalisms which appeared under the name chemlambda and a version of directed interaction combinators. This is part of the study and experiments…
Graph colouring is a combinatorial optimisation problem with applications in several important domains, including sports scheduling, cartography, street map navigation, and timetabling. It is also of significant theoretical interest and a…
This paper introduces a logical system, called BV, which extends multiplicative linear logic by a non-commutative self-dual logical operator. This extension is particularly challenging for the sequent calculus, and so far it is not achieved…
Graphs are used in almost every scientific discipline to express relations among a set of objects. Algorithms that compare graphs, and output a closeness score, or a correspondence among their nodes, are thus extremely important. Despite…
The notion of 1-planarity is among the most natural and most studied generalizations of graph planarity. A graph is 1-planar if it has an embedding where each edge is crossed by at most another edge. The study of 1-planar graphs dates back…
This paper is the second part of an introduction to linear logic and ludics, both due to Girard. It is devoted to proof nets, in the limited, yet central, framework of multiplicative linear logic and to ludics, which has been recently…
We propose representation of configurational physical quantities and microscopic structures for multicomponent system on lattice, by extending a concept of generalized Ising model (GIM) to graph theory. We construct graph Laplacian (and…
Graphs are a powerful tool for representing and analyzing unstructured, non-Euclidean data ubiquitous in the healthcare domain. Two prominent examples are molecule property prediction and brain connectome analysis. Importantly, recent works…
The relations, rather than the elements, constitute the structure of networks. We therefore develop a systematic approach to the analysis of networks, modelled as graphs or hypergraphs, that is based on structural properties of…