Centro de Investigación e Tecnoloxía Matemática de Galicia (CITMAga)

Permanent URI for this collectionhttps://hdl.handle.net/10347/34293

O Centro de Investigación e Tecnoloxía Matemática de Galicia (CITMAga) créase mediante convenio das tres universidades públicas de Galicia, co obxecto de integrar as capacidades científicas do ámbito das Matemáticas, compartindo visión e estratexia e cunha clara aposta pola transferencia de coñecemento. Coa motivación de fomentar unha cultura colaborativa, que busque a excelencia na investigación, a innovación e a formación, CITMAga aspira a converterse nun centro de referencia nacional e internacional, constituíndo unha contorna atractiva para o desenvolvemento científico e profesional.

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Gonosomal algebras and operators associated to genetic systems with a single male genotype
(2025-02-10) Cabrera Casado, Yolanda; Ladra González, Manuel; Pérez Rodríguez, Andrés; Universidade de Santiago de Compostela. Departamento de Matemáticas
This article is devoted to studying gonosomal algebras and operators with a single male genotype. We compute the limit points of the trajectories of the corresponding normalised gonosomal operators, describing the development of specific populations and providing the corresponding biological interpretations.
Derivations and lower cohomology of Lie algebra crossed modules
(University of Niš, Faculty of Sciences and Mathematics, 2026-04-15) Ladra González, Manuel; Pérez Rodríguez, Andrés; Universidade de Santiago de Compostela. Departamento de Matemáticas; Universidade de Santiago de Compostela. Centro de Investigación e Tecnoloxía Matemática de Galicia (CITMAga)
In this paper, we define the derivation of a Lie algebra crossed module and prove that it can be represented by the augmentation ideal of a crossed module. Additionally, we introduce the first cohomology groups for n = 0,1, of a crossed module with coefficients, and we establish their connection to the classical Chevalley-Eilenberg Lie algebra cohomology.
Álxebras de evolución e grafos
(Centro de Investigación e Tecnoloxía Matemática de Galicia (CITMAga), 2022-03-23) Pérez Rodríguez, Andrés; Universidade de Santiago de Compostela. Departamento de Matemáticas
Actas do Seminario de Iniciación á Investigación. Curso 2023-2024
(Centro de Investigación e Tecnoloxía Matemática de Galicia (CITMAga), 2024) Universidade de Santiago de Compostela. Centro de Investigación e Tecnoloxía Matemática de Galicia (CITMAga); Universidade de Santiago de Compostela. Departamento de Matemáticas; Cora Calvo, Víctor; Lorenzo Naveiro, Juan Manuel; Pérez Rodríguez, Andrés; Picos Maiztegui, Miguel; Vidal García, María
A Frattini theory for evolution algebras
(Springer-Verlag Italia, 2025-11-16) Ladra González, Manuel; Pérez Rodríguez, Andrés; Universidade de Santiago de Compostela. Departamento de Matemáticas; Universidade de Santiago de Compostela. Centro de Investigación e Tecnoloxía Matemática de Galicia (CITMAga)
This paper develops a Frattini theory for evolution algebras defining the Frattini subalgebra as the intersection of all maximal subalgebras, and the Frattini ideal as the largest ideal contained in it. To this end, we revisit the notion of nilradical, whose classical definition is not directly applicable in this setting, and propose the supersolvable nilradical as a suitable alternative. This leads to necessary and sufficient conditions for the triviality of the Frattini subalgebra and ideal. Finally, we also briefly examine the relevance of the Frattini ideal in the study of dually atomistic evolution algebras.
A note on complete evolution algebras
(Springer, 2026-04-22) García-Martínez, Xabier; Pérez Rodríguez, Andrés; Universidade de Santiago de Compostela. Departamento de Matemáticas
This short note provides positive answers to two conjectures of Camacho, Khudoyberdiyev, and Omirov on the classification of complete evolution algebras. Our approach is based on analysing the solution set of a generic non-linear polynomial system of equations using elementary tools from algebraic geometry. We also obtain new results on subalgebras and idempotents of evolution algebras, and conclude by proposing a conjecture that may characterise solvable evolution algebras.
Regular evolution algebras are closed under subalgebras
(Académie des Sciences, 2025-11-28) Ladra González, Manuel; Pérez Rodríguez, Andrés; Universidade de Santiago de Compostela. Departamento de Matemáticas
The main goal of this note is to show that subalgebras of regular evolution algebras are themselves evolution algebras. This allows us to assume, without loss of generality, that every subalgebra in the regular setting has a basis consisting of vectors with disjoint supports. Finally, we use this result to characterise the existence of codimension-one subalgebras in regular evolution algebras.
Unsupervised clustering based coronary artery segmentation
(BioMed Central, 2025-03-07) Serrano Antón, Belén; Insúa Villa, Manuel; Pendón-Minguillón, Santiago; Paramés Estévez, Santiago; Otero Cacho, Alberto; López Otero, Diego; Díaz Fernández, Brais; Bastos-Fernández, María; González Juanatey, José Ramón; Pérez Muñuzuri, Alberto; Universidade de Santiago de Compostela. Departamento de Física de Partículas
Background: The acquisition of 3D geometries of coronary arteries from computed tomography coronary angiography (CTCA) is crucial for clinicians, enabling visualization of lesions and supporting decision-making processes. Manual segmentation of coronary arteries is time-consuming and prone to errors. There is growing interest in automatic segmentation algorithms, particularly those based on neural networks, which require large datasets and significant computational resources for training. This paper proposes an automatic segmentation methodology based on clustering algorithms and a graph structure, which integrates data from both the clustering process and the original images. Results: The study compares two approaches: a 2.5D version using axial, sagittal, and coronal slices (3Axis), and a perpendicular version (Perp), which uses the cross-section of each vessel. The methodology was tested on two patient groups: a test set of 10 patients and an additional set of 22 patients with clinically diagnosed lesions. The 3Axis method achieved a Dice score of 0.88 in the test set and 0.83 in the lesion set, while the Perp method obtained Dice scores of 0.81 in the test set and 0.82 in the lesion set, decreasing to 0.79 and 0.80 in the lesion region, respectively. These results are competitive with current state-of-the-art methods. Conclusions: This clustering-based segmentation approach offers a robust framework that can be easily integrated into clinical workflows, improving both accuracy and efficiency in coronary artery analysis. Additionally, the ability to visualize clusters and graphs from any cross-section enhances the method’s explainability, providing clinicians with deeper insights into vascular structures. The study demonstrates the potential of clustering algorithms for improving segmentation performance in coronary artery imaging.
A fast and automated approach for urban CFD simulations: validation with meteorological predictions and its application to drone flights
(Elsevier, 2025-12) Suárez Vázquez, Marcos; Varela Ballesta, Sylvana; Otero Cacho, Alberto; Pérez Muñuzuri, Alberto; Mira Pérez, Jorge; Universidade de Santiago de Compostela. Departamento de Física Aplicada; Universidade de Santiago de Compostela. Instituto de Materiais (iMATUS); Universidade de Santiago de Compostela. Departamento de Física de Partículas
In past years, several studies have proposed new methods and applications for urban wind simulations, including geometry reconstruction from urban data sources or improved boundary condition definition. In this article, we present a fast and automated methodology for reconstructing airflows within urban environments using LiDAR and cadastral data coupled with Computational Fluid Dynamics (CFD) simulations. Our approach integrates meteorological predictions with computational techniques to simulate the complex interactions between wind currents, buildings, vegetation, water zones and terrain morphology within urban environments. Accurate boundary conditions based on meteorological predictions are introduced into a coupled methodology that directly creates the terrain shape inside the simulation environment, simplifying the geometry creation process, which is one of the most prevalent problems in CFD urban simulations. The simulation results are confronted against ground-truth real data obtained from a meteorological station, showing strong agreement with the outcomes generated by the proposed CFD model, with a concordance correlation coefficient up to ρ and ρ c c =0.985 for the wind direction =0.853 for the wind speed. The results from these simulations are then used for validating a wind tunnel approach that mimics the interaction between a moving drone and the extracted wind currents, demonstrating a great improvement in computation times when compared to the most straightforward approach that consists in embedding the drone within the full urban landscape. This research contributes to the advancement of urban CFD modeling, and it has significant implications for various applications, providing valuable insights for urban development.
Numerical reconstruction of the kernel function in generalized non-convolutional fractional operators
(Elsevier, 2026-05-15) Al-Shdaifat, Hamza; Rodríguez López, Rosana
This paper deals with the numerical reconstruction of the kernel function 𝜅(𝑡,𝑧) for a new class of generalized non-convolutional fractional operators. These operators are defined in integral form of Volterra type and the general kernel is not always reducible to classical convolutiontype expressions. The work focuses on the reconstruction of the kernel starting from the generalized Sonin condition, which connects the kernel of the integral operator with that of the corresponding differential operator. Taking the generalized Sonin condition as the starting point, we propose a constructive numerical method by approximating the functional identity obtained from the integration of the product of both kernels, operation that is achieved by proper integration on segment lines of the domain. By casting the theoretical requirements as one-dimensional integral estimations on parameterized trajectories (segment lines), the problem becomes a nonlinear inverse problem for the determination of one of the kernels, 𝜅, provided that the other one is known. Our approach is based on the selection of a proper partition of the domain, and the consideration of the auxiliary functions 𝜑𝑡,𝑧 and 𝜙𝑡,𝑧, which are combined in such a way that it is possible to compute the unknown functions 𝜓𝑡,𝑧 and 𝛹𝑡,𝑧, provided that the given restrictions on the integrals in the generalized Sonin condition are fulfilled. The feasibility of reconstructing the kernel in some chosen test examples is illustrated by some numerical procedures, as a first step toward the implementation of generalized fractional models in numerical simulations, and also as a tool for the selection of proper kernels in the definition of generalized fractional operators.
Effect of fear and refuge in eco-epidemiological model with predator supported by additional food
(Springer, 2026-02-24) Kar, Raktim; Biswas, Santosh; Pal, Amit Kumar; Nieto Roig, Juan José; Universidade de Santiago de Compostela. Departamento de Estatística, Análise Matemática e Optimización
We propose a three-compartment eco-epidemiological model in which prey experience fear from susceptible predators and may seek refuge, predator follows a modified Leslie–Gower growth. The predator population is divided into susceptible and infected class, with disease transmission occurring horizontally together with saturated treatment of infected class. We analyze positivity and boundedness, compute biologically feasible equilibria, and derive the basic reproduction number (R0) along with conditions for local and global stability. Sensitivity is explored by partial rank correlation coefficient (PRCC) method; bifurcation behaviours are illustrated analytically and numerically. Furthermore, we formulate and numerically solve an optimal control problem aimed at minimizing infected predator biomass and treatment cost using the forward–backward sweep method. The results reveal that larger refuge size and stronger treatment efforts effectively reduce infection prevalence, while fear on prey species control by the refuge. Additionally, the system exhibits parameter-dependent bi-stability and multi-stability, as demonstrated through bifurcation diagrams.
An arbitrary Lagrangian-Eulerian semi-implicit hybrid method for continuum mechanics with GLM cleaning
(Elsevier, 2026-05-01) Busto Ulloa, Saray; Universidade de Santiago de Compostela. Departamento de Matemática Aplicada
This paper proposes a novel semi-implicit arbitrary Lagrangian-Eulerian (ALE) method for the solution of the unified Godunov-Peshkov-Romenski (GPR) model of continuum mechanics. To handle the curl-free-type involutions arising in the solid limit of the model, the original system is augmented by adopting a thermodynamically compatible generalized Lagrangian multiplier (GLM) approach. Next, an operator splitting strategy decouples the computation of fast pressure waves from the bulk velocity of the medium yielding a transport subsystem, containing convective terms and non-conservative products, and a Poisson-type subsystem, for the pressure. A second splitting yields an ODE subsystem comprising only the potentially stiff source terms, responsible for the relaxation of the model between its fluid and solid limits. The mesh motion can be driven by two sources: the local fluid velocity and a prescribed boundary displacement. For the spatial discretisation, we employ unstructured staggered grids, with the pressure defined on the primal mesh and all remaining variables on the dual grid. The transport subsystem is advanced via an explicit finite volume method, in which integration over closed space-time control volumes ensures verification of the geometric conservation law (GCL). On the other hand, implicit continuous finite elements are used for the discretisation of the pressure subsystem and an implicit DIRK scheme is employed to solve the ODE subsystem. Consequently, the proposed approach is well suited to address all Mach number flows. A comprehensive set of benchmarks is employed to assess the accuracy and robustness of the proposed methodology in tackling both fluid and solid mechanics problems.
Four-dimensional Lorentzian algebraic Ricci solitons
(Cambridge University Press, 2026-03-27) García Río, Eduardo; Rodríguez Gigirey, Rosalía; Vázquez Lorenzo, Ramón; Universidade de Santiago de Compostela. Departamento de Matemáticas
We describe four-dimensional Lorentzian algebraic Ricci solitons. In sharp contrast with the Riemannian situation, any four-dimensional Lie group admits a left-invariant Lorentz metric which is a Ricci soliton.
Personalized medicine to treat refractory benign paroxysmal positional vertigo, through computational fluid dynamics analysis from magnetic resonance image reconstructions
(Frontiers Media, 2025) Rossi Izquierdo, Marcos; Santos Pérez, Sofía María de la Soledad; Arán Tapia, Ismael; Blanco Ulla, Miguel; Arán González, Ismael; Vaamonde Sánchez-Andrade, Isabel; Franco-Gutiérrez, Virginia; Pérez Muñuzuri, Vicente; Pérez Muñuzuri, Alberto; Soto Varela, Andrés; Universidade de Santiago de Compostela. Departamento de Cirurxía e Especialidades Médico-Cirúrxicas; Universidade de Santiago de Compostela. Departamento de Física de Partículas; Universidade de Santiago de Compostela. Centro Interdisciplinar de Investigación en Tecnoloxías Ambientais (CRETUS)
Background: Benign paroxysmal positional vertigo (BPPV) is the most common cause of vertigo, often effectively treated with standard canalith repositioning maneuvers (CRMs). However, approximately 12.5% of cases remain refractory, leading to persistent symptoms and increased healthcare burden. Variations in the anatomical orientation of the semicircular canals (SCCs) may explain the resistance to conventional maneuvers. This study explores a personalized medicine approach, utilizing computational fluid dynamics (CFD) based on MRI reconstructions to tailor CRMs with the help of mechanical rotation chair according to individual inner ear anatomy. Methods: We conducted a randomized, multicenter, open-label study targeting patients with refractory posterior canal BPPV. Participants were allocated to either a control group (receiving repeated standard CRMs and Brandt-Daroff exercises) or an intervention group (receiving personalized CRMs based on CFD simulations derived from MRI scans). The intervention group’s maneuvers were executed using a mechanical rotational chair designed for precise angulation. Primary outcomes included resolution of nystagmus and vertigo symptoms, while secondary outcomes measured the reduction in healthcare visits and improved quality of life (Dizziness Handicap Inventory score). Discussion: Personalized CRMs based on CFD models may enhance treatment efficacy for refractory BPPV by optimizing maneuver angles according to the specific SCC orientation. This approach could significantly reduce symptom persistence, decrease the need for repeated healthcare visits, and improve patient outcomes. The use of non-invasive MRI and CFD techniques represents a novel step toward individualized treatment in vestibular disorders, with potential for broader application in personalized otoneurology. Further analysis will determine the extent of clinical benefit and cost-effectiveness of this approach. Clinical trial registration: ClinicalTrials.gov, Identifier: NCT06725966.
Semiparametric regression for circular responsewith application in ecology
(Wiley, 2025) Ameijeiras Alonso, José; Gijbels, Irène
A regression model for a circular response variabledepending on a linear or a circular predictor is pre-sented in this paper. The conditional density belongsto a parametric flexible family that allows for asymme-try and varying peakedness around the modal direction.The modal direction and concentration depend on thecovariate and are nonparametrically modeled via localpolynomial fitting with a kernel weight. The asymp-totic normality of the estimators for the conditionalmodal direction and concentration is established. Fur-thermore, from these theoretical results, the expressionof the optimal smoothing parameter and a proposeddata-driven estimator are derived. An application con-cerns the orientation of migratory birds according to theflight altitude and the wind direction.
The Peano–Sard theorem for fractional operators with Mittag-Leffler kernel and application in classical numerical approximation
(Elsevier, 2025-03-15) Jornet, Marc; Nieto Roig, Juan José; Universidade de Santiago de Compostela. Departamento de Estatística, Análise Matemática e Optimización
We investigate fractional Peano kernels for continuous linear functionals, in the context of differintegral operators with Mittag-Leffler kernel. New bounds for polynomial interpolation are obtained and numerical computations are shown, indicating improvements.
Representation and inequalities involving continuous linear functionals and fractional derivatives
(Springer, 2024-10-29) Jornet, Marc; Nieto Roig, Juan José; Universidade de Santiago de Compostela. Departamento de Estatística, Análise Matemática e Optimización
We investigate how continuous linear functionals can be represented in terms of generic operators and certain kernels (Peano kernels), and we study lower bounds for the operators as a consequence, in the space of square-integrable functions. We apply and develop the theory for the Riemann–Liouville fractional derivative (an inverse of the Riemann–Liouville integral), where inequalities are derived with the Gaussian hypergeometric function. This work is inspired by the recent contributions by Fernandez and Buranay (J Comput Appl Math 441:115705, 2024) and Jornet (Arch Math, 2024).
Displacement Lipschitz Spaces and Rectifiability
(Springer, 2024-12-13) Fernández Tojo, Fernando Adrián; Universidade de Santiago de Compostela. Departamento de Estatística, Análise Matemática e Optimización
In this article, we introduce the notion of displacement Lipschitz spaces based on a divided difference approach. After studying rectifiability and arc length in displacement spaces, we apply Lipschitz functions to the study of convexity by measuring the allowed curvature of paths.
Influence of Abutment Shape on Implant Marginal Bone Remodeling: A Double-Blind, Randomized 24-Month Clinical Study
(Wiley, 2025-12-30) Seijas Naya, Flavio; Bernabeu Mira, Juan C.; Pérez Jardón, Alba; Conde Amboage, Mercedes; Peñarrocha Oltra, David; Camacho Alonso, Fabio; Pérez-Sayáns García, Mario; Universidade de Santiago de Compostela. Departamento de Estatística, Análise Matemática e Optimización; Universidade de Santiago de Compostela. Instituto de Materiais (iMATUS); Universidade de Santiago de Compostela. Departamento de Cirurxía e Especialidades Médico-Cirúrxicas
Objective This study follows a 2-year evaluation to verify marginal bone remodeling (MBR) trends associated with different abutment designs. Methods A balanced, randomised, double-blind clinical trial with two parallel experimental arms. 68 implants were placed in 9 men and 12 women, 48.5% using the straight abutment and 51.5% the concave abutment. The primary variable was peri-implant tissue stability, measured by marginal bone loss (MBL) or gain (MBG) through digital radiology. Mixed linear regression models and Additive Generalized Additive Models were constructed to estimate MBR, simultaneously considering the variables abutment height, group, and time. Results At 24 months, linear mixed-effects regression models revealed that the concave abutment group exhibited significantly less MBL than the straight abutment group across mesial, distal, and average measurements (p = 0.006–0.026). Significant interactions between abutment type and time at 8 weeks and 6 months suggest early and sustained benefits of the concave design. At 24 months, this effect remained significant except in the mesial model (p = 0.072). Abutment height was positively associated with MBL, particularly in the straight group; however, in the concave group, greater height mitigated bone loss (p < 0.01). Conclusion Concave abutments demonstrated a potential advantage in reducing early marginal bone loss and promoting mid-term bone stability compared to straight abutments. Their design may enhance soft tissue adaptation, contributing to improved peri-implant bone preservation. While increased abutment height showed a protective effect in the concave group, these findings require confirmation. Further long-term studies are warranted to validate these results and clarify their clinical relevance.
Artificial Intelligence in Science and Society: The Vision of USERN
(Institute of Electrical and Electronics Engineers, 2025) Dorigo, Tommaso; Nieto Fontarigo, Juan José; Yazdanpanah, Niloufar; Universidade de Santiago de Compostela. Departamento de Estatística, Análise Matemática e Optimización
The recent rise in relevance and diffusion of Artificial Intelligence (AI)-based systems and the increasing number and power of applications of AI methods invites a profound reflection on the impact of these innovative systems on scientific research and society at large. The Universal Scientific Education and Research Network (USERN), an organization that promotes initiatives to support interdisciplinary science and education across borders and actively works to improve science policy, collects here the vision of its Advisory Board members, together with a selection of AI experts, to summarize how we see developments in this exciting technology impacting science and society in the foreseeable future. In this review, we first attempt to establish clear definitions of intelligence and consciousness, then provide an overview of AI's state of the art and its applications. A discussion of the implications, opportunities, and liabilities of the diffusion of AI for research in a few representative fields of science follows this. Finally, we address the potential risks of AI to modern society, suggest strategies for mitigating those risks, and present our conclusions and recommendations.

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