Related papers: On Languages Describing Large Graph Classes
Despite the superior performance of large language models to generate natural language texts, it is hard to generate texts with correct logic according to a given task, due to the difficulties for neural models to capture implied rules from…
The vast amount of data and increase of computational capacity have allowed the analysis of texts from several perspectives, including the representation of texts as complex networks. Nodes of the network represent the words, and edges…
Pretrained Language Models (PLMs) such as BERT have revolutionized the landscape of Natural Language Processing (NLP). Inspired by their proliferation, tremendous efforts have been devoted to Pretrained Graph Models (PGMs). Owing to the…
The notion of word-representable graphs is a generalization of comparability graphs, in which graphs are represented by words. The complexity of word-representation of a word-representable graph is captured through the representation…
Graph-based text representation focuses on how text documents are represented as graphs for exploiting dependency information between tokens and documents within a corpus. Despite the increasing interest in graph representation learning,…
In this paper I survey the sources of inspiration for my own and co-authored work in trying to develop a general theory of graph polynomials. I concentrate on meta-theorems, i.e., theorem which depend only on the form infinite classes of…
We study the question of whether, for a given class of finite graphs, one can define, for each graph of the class, a linear ordering in monadic second-order logic, possibly with the help of monadic parameters. We consider two variants of…
A categorical formalism for directed graphs is introduced, featuring natural notions of morphisms and subgraphs, and leading to two elementary descriptions of the free-properad monad, first in terms of presheaves on elementary graphs,…
Discovering the underlying structures present in large real world graphs is a fundamental scientific problem. In this paper we show that a graph's clique tree can be used to extract a hyperedge replacement grammar. If we store an ordering…
GF(2)-grammars are a recently introduced grammar family with some unusual algebraic properties. They are closely connected to unambiguous grammars. By using the method of formal power series, we establish strong conditions that are…
Consider multiple experts with overlapping expertise working on a classification problem under uncertain input. What constitutes a consistent set of opinions? How can we predict the opinions of experts on missing sub-domains? In this paper,…
This article is intended as a reference guide to various notions of monoidal categories and their associated string diagrams. It is hoped that this will be useful not just to mathematicians, but also to physicists, computer scientists, and…
We present a formal semantics and proof of soundness for shapes schemas, an expressive schema language for RDF graphs that is the foundation of Shape Expressions Language 2.0. It can be used to describe the vocabulary and the structure of…
Fixed points ${\bf u}=\varphi({\bf u})$ of marked and primitive morphisms $\varphi$ over arbitrary alphabet are considered. We show that if ${\bf u}$ is palindromic, i.e., its language contains infinitely many palindromes, then some power…
We demonstrate that graph-based models are fully capable of representing higher-order interactions, and have a long history of being used for precisely this purpose. This stands in contrast to a common claim in the recent literature on…
In recent years, concepts and methods of complex networks have been employed to tackle the word sense disambiguation (WSD) task by representing words as nodes, which are connected if they are semantically similar. Despite the increasingly…
We present the basic ideas of forms (a generalization of Ehresmann's sketches) and their theories and models, more explicitly than in previous expositions. Forms provide the ability to specify mathematical structures and data types in any…
A graph $G=(V,E)$ is word-representable if there exists a word $w$ over the alphabet $V$ such that letters $x$ and $y$ alternate in $w$ if and only if $xy\in E$. Word-representable graphs generalize several important classes of graphs such…
The search for linguistic patterns, stylometry and forensic linguistics have in the theory of complex networks, their structures and associated mathematical tools, allies with which to model and analyze texts. In this paper we present a new…
Graph-structured data are the commonly used and have wide application scenarios in the real world. For these diverse applications, the vast variety of learning tasks, graph domains, and complex graph learning procedures present challenges…