Related papers: Pattern graph rewrite systems
The present paper is concerned with the concept of the one-way quantum computer, beyond binary-systems, and its relation to the concept of stabilizer quantum codes. This relation is exploited to analyze a particular class of quantum…
We introduce a general diagrammatic theory of digital circuits, based on connections between monoidal categories and graph rewriting. The main achievement of the paper is conceptual, filling a foundational gap in reasoning syntactically and…
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…
We propose a new statistical model suitable for machine learning of systems with long distance correlations such as natural languages. The model is based on directed acyclic graph decorated by multi-linear tensor maps in the vertices and…
This book objective is to develop an algebraization of graph grammars. Equivalently, we study graph dynamics. From the point of view of a computer scientist, graph grammars are a natural generalization of Chomsky grammars for which a purely…
This paper describes a new technique, called "knowledge patterns", for helping construct axiom-rich, formal ontologies, based on identifying and explicitly representing recurring patterns of knowledge (theory schemata) in the ontology, and…
Real-world networks exhibit prominent hierarchical and modular structures, with various subgraphs as building blocks. Most existing studies simply consider distinct subgraphs as motifs and use only their numbers to characterize the…
Social relationships (e.g., friends, couple etc.) form the basis of the social network in our daily life. Automatically interpreting such relationships bears a great potential for the intelligent systems to understand human behavior in…
We introduce \textit{dual graph diagrams} representing oriented knots and links. We use these combinatorial structures to define corresponding algebraic structures we call \textit{biquasiles} whose axioms are motivated by dual graph…
Gene assembly is an intricate biological process that has been studied formally and modeled through string and graph rewriting systems. Recently, a restriction of the general (intramolecular) model, called simple gene assembly, has been…
Subgraph-enhanced graph neural networks (SGNN) can increase the expressive power of the standard message-passing framework. This model family represents each graph as a collection of subgraphs, generally extracted by random sampling or with…
Quantum graphs have been introduced by Duan, Severini, and Winter to describe the zero-error behaviour of quantum channels. Since then, quantum graph theory has become a field of study in its own right. A substantial source of difficulty in…
Inference is a fundamental reasoning technique in probability theory. When applied to a large joint distribution, it involves updating with evidence (conditioning) in one or more components (variables) and computing the outcome in other…
The perturbation expansion of the solution of a fixed point equation or of an ordinary differential equation may be expressed as a power series in the perturbation parameter. The terms in this series are indexed by rooted trees and depend…
Hypergraphs allow one to encode higher-order relationships in data and are thus a very flexible modeling tool. Current learning methods are either based on approximations of the hypergraphs via graphs or on tensor methods which are only…
We revisit a concept that has been central in some early stages of computer science, that of structured programming: a set of rules that an algorithm must follow in order to acquire a structure that is desirable in many aspects. While much…
Graph compression is a data analysis technique that consists in the replacement of parts of a graph by more general structural patterns in order to reduce its description length. It notably provides interesting exploration tools for the…
We present a new graph compressor that works by recursively detecting repeated substructures and representing them through grammar rules. We show that for a large number of graphs the compressor obtains smaller representations than other…
We generalize Gopakumar's microscopic derivation of Witten diagrams in large N free quantum field theory [1] to interacting theories in perturbative expansion. For simplicity we consider a matrix scalar field with $\Phi^h$ interaction in d…
Many scientific datasets are of high dimension, and the analysis usually requires visual manipulation by retaining the most important structures of data. Principal curve is a widely used approach for this purpose. However, many existing…