http://hdl.handle.net/10498/6797 2026-11-06T13:45:34Z 2026-11-06T13:45:34Z García Aragón, Roberto Medina Moreno, Jesús Molina Ruiz, Samuel José http://hdl.handle.net/10498/40545 2026-11-05T05:00:15Z 2026-01-01T00:00:00Z

Computing Bonds Between Formal Contexts García Aragón, Roberto; Medina Moreno, Jesús; Molina Ruiz, Samuel José The notion of bond was introduced as a technique to aggregate information from multiple datasets without modifying the information already present in each of the datasets. This notion has been extended to several fuzzy frameworks, including the residuated lattice setting, which we also consider in this paper. While most studies on bonds have emphasized their role in aggregating contexts, relatively little attention has been given to how they can be effectively computed. In this paper, we address this gap by introducing algorithms to compute all bonds between two contexts in both the classical and residuated lattice setting.

2026-01-01T00:00:00Z Brownlowe, Nathan Clark, Lisa Orloff Pardo Espino, Enrique Sims, Aidan http://hdl.handle.net/10498/40292 2026-09-30T04:08:38Z 2026-09-29T00:00:00Z

Global and local triviality for extensions of ample groupoids: an algebraic approach Brownlowe, Nathan; Clark, Lisa Orloff; Pardo Espino, Enrique; Sims, Aidan Using the Steinberg duality between the categories of inverse semigroups and ample groupoids, we prove the triviality (global and local) of the central term of the extension in terms of twisted crossed products.

2026-09-29T00:00:00Z Ara, Pere Bosa, Joan Cantier, Laurent Pardo Espino, Enrique Vilalta, Eduard http://hdl.handle.net/10498/40257 2026-09-26T04:02:53Z 2026-09-21T00:00:00Z

Super adaptable graphs and the realization problem Ara, Pere; Bosa, Joan; Cantier, Laurent; Pardo Espino, Enrique; Vilalta, Eduard We introduce and study the family of super adaptable monoids, which includes, among many others, all conical refinement monoids that are either finitely generated, or countable, primely generated, and regular. Our main result shows that any countable super adaptable monoid can be realized by a von Neumann regular ring, thus answering affirmatively the Realization problem for this class. The result is new even for the subclass of countable, primely generated, regular conical refinement monoids, which we show can be realized by both a von Neumann regular ring and a purely infinite, real rank zero C^*-algebra. To prove this result, we develop a systematic framework that connects three fundamental structures: abstract monoids, separated graphs (a specific class of colored graphs), and von Neumann regular rings. By establishing functorial connections among these classes, we translate several algebraic properties of monoids into combinatorial and ring-theoretic notions. This allows us not only to prove the main realization result, but also to obtain several characterizations of super adaptable monoids. As a particular application, these can be used to provide a complete characterization of which regular monoids arise as graph monoids. To our knowledge, this work offers the first self-contained treatment in the literature where the complete realization process —from abstract monoids through I-systems and separated graphs to regular rings and C^∗-algebras— isdeveloped sequentially and in full detail within a single text.

2026-09-21T00:00:00Z Díaz Jiménez, Marina Pavón Domínguez, Pablo Ruiz Villalobos, Patricia Moreno Pulido, Soledad http://hdl.handle.net/10498/39673 2026-05-28T04:06:50Z 2026-03-18T00:00:00Z

Exploring multifractal geometry in directed complex networks Díaz Jiménez, Marina; Pavón Domínguez, Pablo; Ruiz Villalobos, Patricia; Moreno Pulido, Soledad Complex networks are fundamental for modelling and understanding a wide range of real-world applications or non-trivial systems. Understanding their multifractal geometry has become relevant in recent years. Various algorithms have been developed either to refine existing methods or to adapt them to different network topologies. However, multifractal analysis has never been applied to directed networks. In this work, we present a novel multifractal box-covering method for directed networks, referred as . To assess its applicability, state-of-the-art undirected networks have been used to generate the directed ones. Specifically, -flower, the generalized minimal model, scale-free and random networks are used as weakly connected networks. Krapivsky and small-world networks are used to generate the strongly connected ones. To evaluate the impact of the degree of directionality, has been evaluated with different percentages of directed edges. Results show that Krapivsky networks exhibit a clear multifractal structure, with a approximately 0.9, confirming the method’s effectiveness. In contrast, small-world networks display limited multifractality, with less than 0.16, decreasing as the rewiring probability becomes smaller. Moreover, adding directed shortcuts in small-world networks increases multifractality compared to the non-directed case. The weakly connected networks studied exhibit multifractality, which diminishes as the proportion of directed links increases. Higher directionality also increases the number of boxes required to cover the network and leads to a loss of multifractality, approaching monofractal behaviour. This loss is particularly pronounced in scale-free and random networks, whereas ring-based networks such as -flower and generalized minimal model preserve multifractality up to certain thresholds. The proposed method is further validated using two real-world directed networks, enabling a consistent multifractal analysis and distinguishing different multifractal behaviour.

2026-03-18T00:00:00Z