Related papers: Iteration Algebras for UnQL Graphs and Completenes…

We introduces the umodules, a generalisation of the notion of graph module. The theory we develop captures among others undirected graphs, tournaments, digraphs, and $2-$structures. We show that, under some axioms, a unique decomposition…

Query graph construction aims to construct the correct executable SPARQL on the KG to answer natural language questions. Although recent methods have achieved good results using neural network-based query graph ranking, they suffer from…

We reduce the isomorphism problem for undirected graphs without loops to the isomorphism problems for a class of finite dimensional $2$-step nilpotent Lie algebras over a field and for a class of finite $p$-groups. We show that the…

A biform theory is a combination of an axiomatic theory and an algorithmic theory that supports the integration of reasoning and computation. These are ideal for formalizing algorithms that manipulate mathematical expressions. A theory…

In this paper, we propose a novel graph kernel, namely the Quantum-based Entropic Subtree Kernel (QESK), for Graph Classification. To this end, we commence by computing the Average Mixing Matrix (AMM) of the Continuous-time Quantum Walk…

We study binomiality of the steady state ideals of chemical reaction networks. Considering rate constants as indeterminates, the concept of unconditional binomiality has been introduced and an algorithm based on linear algebra has been…

In this paper, we study the task of multimodal sequence analysis which aims to draw inferences from visual, language and acoustic sequences. A majority of existing works generally focus on aligned fusion, mostly at word level, of the three…

We consider an algebraic formulation of Quantum Theory and develop a combinatorial model of the Heisenberg-Weyl algebra structure. It is shown that by lifting this structure to the richer algebra of graph operator calculus, we gain a simple…

Nested graphs have been used in different applications, for example to represent knowledge in semantic networks. On the other hand, graphs with cycles are really important in surface reconstruction, periodic schedule and network analysis.…

Oriented graph complexes, in which graphs are not allowed to have oriented cycles, govern for example the quantization of Lie bialgebras and infinite dimensional deformation quantization. It is shown that the oriented graph complex GC^or_n…

Interpretable Multi-Task Learning can be expressed as learning a sparse graph of the task relationship based on the prediction performance of the learned models. Since many natural phenomenon exhibit sparse structures, enforcing sparsity on…

In this paper we develop a structure called Link Algebra, in which we present a Set with two binary operations and an axiom system developed from the study of graph theory and set/antiset theory, sowing main theorems and definitions. Once…

Using Large Language Models (LLMs) to process graph-structured data is an active research area, yet current state-of-the-art approaches typically rely on multi-step pipelines with Graph Neural Network (GNN) encoders that compress rich…

The notion of a $k$-11-representable graph was introduced by Jeff Remmel in 2017 and studied by Cheon et al.\ in 2019 as a natural extension of the extensively studied notion of word-representable graphs, which are precisely…

We propose a new approach to text semantic analysis and general corpus analysis using, as termed in this article, a "bi-gram graph" representation of a corpus. The different attributes derived from graph theory are measured and analyzed as…

We propose the vision of a functional data model (FDM) and an associated functional query language (FQL). Our proposal has far-reaching consequences: we show a path to come up with a modern QL that solves (almost if not) all problems of SQL…

Much recent work in bilingual lexicon induction (BLI) views word embeddings as vectors in Euclidean space. As such, BLI is typically solved by finding a linear transformation that maps embeddings to a common space. Alternatively, word…

We prove that unital graph C*-algebras often admit a convenient decomposition into amalgamated free products. We use this to give a complete characterization of when a unital graph C*-algebra is residually finite-dimensional and when it is…

We introduce an approach to semantically represent and query raster data in a Semantic Web graph. We extend the GeoSPARQL vocabulary and query language to support raster data as a new type of geospatial data. We define new filter functions…

Graph-structured combinatorial challenges are inherently difficult due to their nonlinear and intricate nature, often rendering traditional computational methods ineffective or expensive. However, these challenges can be more naturally…