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While large language models (LLMs) have made considerable advancements in understanding and generating unstructured text, their application in structured data remains underexplored. Particularly, using LLMs for complex reasoning tasks on…
Computing layer similarities is an important way of characterizing multiplex networks because various static properties and dynamic processes depend on the relationships between layers. We provide a taxonomy and experimental evaluation of…
Geometric modeling by constraints leads to large systems of algebraic equations. This paper studies bipartite graphs underlaid by systems of equations. It shows how these graphs make possible to polynomially decompose these systems into…
We study the tailoring of structured random graph ensembles to real networks, with the objective of generating precise and practical mathematical tools for quantifying and comparing network topologies macroscopically, beyond the level of…
Recent advances in computational methods for intractable models have made network data increasingly amenable to statistical analysis. Exponential random graph models (ERGMs) emerged as one of the main families of models capable of capturing…
Many real-world complex networks actually have a bipartite nature: their nodes may be separated into two classes, the links being between nodes of different classes only. Despite this, and despite the fact that many ad-hoc tools have been…
The toric Hilbert scheme parametrizes all algebras isomorphic to a given semigroup algebra as a multigraded vectorspace. All components of the scheme are toric varieties, and among them, there is a fairly well understood coherent component.…
Knowledge Graphs (KGs) often have two characteristics: heterogeneous graph structure and text-rich entity/relation information. Text-based KG embeddings can represent entities by encoding descriptions with pre-trained language models, but…
We assume some standard choices for the branch cuts of a group of functions and consider the problem of then calculating the branch cuts of expressions involving those functions. Typical examples include the addition formulae for inverse…
Online social systems are multiplex in nature as multiple links may exist between the same two users across different social networks. In this work, we introduce a framework for studying links and interactions between users beyond the…
We describe online collaborative communities by tripartite networks, the nodes being persons, items and tags. We introduce projection methods in order to uncover the structures of the networks, i.e. communities of users, genre families...…
This paper studies the form and complexity of inference in graphical models using the abstraction offered by algebraic structures. In particular, we broadly formalize inference problems in graphical models by viewing them as a sequence of…
The package numericalsgps performs computations with and for numerical semigroups. Recently also affine semigroups are admitted as objects for calculations. This manuscript is a survey of what the package does, and at the same time of the…
This paper presents a query evaluation technique for positive relational algebra queries with aggregates on a representation system for probabilistic data based on the algebraic structures of semiring and semimodule. The core of our…
Multilayer relationships among entities and information about entities must be accompanied by the means to analyze, visualize, and obtain insights from such data. We present open-source software (muxViz) that contains a collection of…
We report on a package of routines for the computer algebra system Maple which supports the explicit determination of the geometric quantities, field equations, equations of motion, and conserved quantities of General Relativity in the…
These are expanded lecture notes of a series of expository talks surveying basic aspects of group cohomology and homology. They were written for someone who has had a first course in graduate algebra but no background in cohomology. You…
Different graph generalizations have been recently used in an ad-hoc manner to represent multilayer networks, i.e. systems formed by distinct layers where each layer can be seen as a network. Similar constructions have also been used to…
Algebraic connectivity, the second eigenvalue of the Laplacian matrix, is a measure of node and link connectivity on networks. When studying interconnected networks it is useful to consider a multiplex model, where the component networks…
For more than a decade, graphs have been used to model the voting behavior taking place in parliaments. However, the methods described in the literature suffer from several limitations. The two main ones are that 1) they rely on some…