http://hdl.handle.net/10498/6797 Mon, 21 Sep 2026 18:46:01 GMT 2026-09-21T18:46:01Z http://hdl.handle.net/10498/39591 Automatic computational classification of bone marrow cells for B cell pediatric leukemia using UMAP Niño López, Ana del Rosario; Martínez Rubio, Álvaro; Picón González, Rocío; Castillo Robleda, Ana; Ramírez Orellana, Manuel; Chulian García, Salvador; Rosa Durán, María B Acute Lymphoblastic Leukemia (B-ALL) accounts for approximately 80% of pediatric leukemia cases. Despite treatment advances, 15–20% of children experience relapse, highlighting the need of improved monitoring of patients and novel strategies leading to successful therapies. Flow Cytometry is an essential technique for measuring residual disease and guiding treatment. However, traditional manual gating limits its efficiency. In recent years, computational tools have been integrated to enhance these clinical processes but many mathematical techniques are underexploited. Particularly, Uniform Manifold Approximation and Projection (UMAP), together with Machine Learning, provide promising approaches for analyzing large datasets. Mathematical tools and artificial intelligence offer new perspectives on these health problems, beyond the usual approach in biomedicine. We have exploited 234 samples from 75 B-ALL patients to develop an artificial intelligence-based algorithm that can improve patient classification and therapy decisions in different patient cohorts. This implies an advancement on the routine manual analysis of the disease progression, as we identify key subpopulations automatically, distinguishing patients’ bone marrow regeneration patterns, thus improving the prediction and prognosis of the disease. Wed, 01 Jan 2025 00:00:00 GMT http://hdl.handle.net/10498/39591 2025-01-01T00:00:00Z http://hdl.handle.net/10498/39589 Roman Domination inWeighted Graphs Cera López, Martín; García Vázquez, Pedro; Valenzuela Tripodoro, Juan Carlos A Roman dominating function for a (non-weighted) graph G = (V, E) is a function f : V → {0, 1, 2} such that every vertex u ∈ V with f (u) = 0 has at least one neighbor v ∈ V such that f (v) = 2. The minimum weight åv∈V f (v) of a Roman dominating function f on G is called the Roman domination number of G and is denoted by gR(G). A graph G = (V, E), together with a positive real-valued weight-function w : V → R>0, is called a weighted graph and is denoted by (G;w). The minimum weight åv∈V f (v)w(v) of a Roman dominating function f on G is called the weighted Roman domination number of G and is denoted by gwR(G). The domination and Roman domination numbers of unweighted graphs have been extensively studied, particularly for their applications in bioinformatics and computational biology. However, graphs used to model biomolecular structures often require weights to be biologically meaningful. In this paper, we initiate the study of the weighted Roman domination number in weighted graphs. We first establish several bounds for this parameter and present various realizability results. Furthermore, we determine the exact values for several well-known graph families and demonstrate an equivalence between the weighted Roman domination number and the differential of a weighted graph. Thu, 29 Jan 2026 00:00:00 GMT http://hdl.handle.net/10498/39589 2026-01-29T00:00:00Z http://hdl.handle.net/10498/39559 Handling incomplete information in formal concept analysis - a possibilistic approach Chacón Gómez, Fernando; Cornejo Piñero, María Eugenia; Dubois, Didier; Medina Moreno, Jesús; Prade, Henri It is very common to find databases with missing information. Therefore, it is important to develop formal tools. This paper focuses on the contribution of Formal Concept Analysis to this fundamental goal. For this purpose, five forms of attribute implications are extracted from incomplete contexts, which are analyzed from two different approaches. The first approach follows the traditional recipe taking into account the well-known characterizations about the validity of attribute implications. The second approach goes further by considering possibility theory. Specifically, possibility and necessity measures are defined in order to establish the plausibility and certainty of relevant statements pertaining to an incomplete context. Thu, 01 Jan 2026 00:00:00 GMT http://hdl.handle.net/10498/39559 2026-01-01T00:00:00Z http://hdl.handle.net/10498/39385 Unit neighborhoods of zero in topological ordered rings García Pacheco, Francisco Javier A closed unit neighborhood of zero in a topological ring is an additively symmetric and multiplicatively idempotent regular closed neighborhood of zero containing the unity whose interior is multiplicatively idempotent as well. The search for nontrivial closed unit neighborhoods of zero in topological rings is an ongoing quest. A unital ordered ring is a ring endowed with a partial ordering compatible with the addition and multiplication by positive elements for which zero and the unity are comparable. A topological ordered ring is a unital ordered ring for which the order topology is a ring topology. Recently, it was posed the question whether the set of elements lying in between −1 and 1 is a closed unit neighborhood of 0 in a topological ordered ring. This question has been partially solved on topological totally ordered division rings with no holes. Here, we provide a full answer in topological ordered rings (not relying on total orderings nor on division rings). Wed, 01 Jan 2025 00:00:00 GMT http://hdl.handle.net/10498/39385 2025-01-01T00:00:00Z