Related papers: Graph Grammars, Insertion Lie Algebras, and Quantu…
In recent years, diagrammatic languages have been shown to be a powerful and expressive tool for reasoning about physical, logical, and semantic processes represented as morphisms in a monoidal category. In particular, categorical quantum…
Recent years have witnessed rapid advances in graph representation learning, with the continuous embedding approach emerging as the dominant paradigm. However, such methods encounter issues regarding parameter efficiency, interpretability,…
This book collects the lectures about graph theory and its applications which were given to students of mathematical departments of Moscow State University and Peking University. Graph theory is a very wide field with a lot of applications…
We report on implementing graph grammars for intelligence analysis in OCaml. Graph grammars are represented as elements of an algebraic data type in OCaml. In addition to algebraic data types, we use other concepts from functional…
We show how graph theory can be combined with quantum theory to calculate the electronic structure of large complex systems. The graph formalism is general and applicable to a broad range of electronic structure methods and materials,…
We have designed a new logic programming language called LM (Linear Meld) for programming graph-based algorithms in a declarative fashion. Our language is based on linear logic, an expressive logical system where logical facts can be…
We introduce a novel compositional description of Feynman diagrams, with well-defined categorical semantics as morphisms in a dagger-compact category. Our chosen setting is suitable for infinite-dimensional diagrammatic reasoning,…
Graph-language models (GLMs) have demonstrated great potential in graph-based semi-supervised learning. A typical GLM consists of two key stages: graph generation and text embedding, which are usually implemented by inferring a latent graph…
The Lie algebra of Feynman graphs gives rise to two natural representations, acting as derivations on the commutative Hopf algebra of Feynman graphs, by creating or eliminating subgraphs. Insertions and eliminations do not commute, but…
We demonstrate the complementary natures of neural knowledge graph embedding, fine-grain entity type prediction, and neural language modeling. We show that a language model-inspired knowledge graph embedding approach yields both improved…
While Language Models (LMs) are the workhorses of NLP, their interplay with structured knowledge graphs (KGs) is still actively researched. Current methods for encoding such graphs typically either (i) linearize them for embedding with LMs…
We develop the Lie theory of Lie-admissible algebras whose product is enriched with higher operations modeled on directed graphs with a view to apply it to the deformation theories controlled by this kind of Lie algebras. We produce…
The theory of finite automata concerns itself with words in a free monoid together with concatenation and without further structure. There are, however, important applications which use alphabets which are structured in some sense. We…
We investigate three formalisms to specify graph languages, i.e. sets of graphs, based on type graphs. First, we are interested in (pure) type graphs, where the corresponding language consists of all graphs that can be mapped…
Process theories combine a graphical language for compositional reasoning with an underlying categorical semantics. They have been successfully applied to fields such as quantum computation, natural language processing, linear dynamical…
We investigate the applicability of the formalism of quantum mechanics to everyday life. It seems to be directly relevant for situations in which the very act of coming to a conclusion or decision on one issue affects one's confidence about…
Graph theory provides fundamental concepts for many fields of science like statistical physics, network analysis and theoretical computer science. Here we give a pedagogical introduction to graph theory, divided into three sections. In the…
In recent years enormous progress has been made in perturbative quantum field theory by applying methods of algebraic geometry to parametric Feynman integrals for scalar theories. The transition to gauge theories is complicated not only by…
Grammar inference deals with determining (preferable simple) models/grammars consistent with a set of observations. There is a large body of research on grammar inference within the theory of formal languages. However, there is surprisingly…
An analog of Kreimer's coproduct from renormalization of Feynman integrals in quantum field theory, endows an analog of Kontsevich's graph complex with a dg-coalgebra structure. The graph complex is generated by orientation classes of…