Artículos (Instituto de Matemáticas de la Universidad de Sevilla (Antonio de Castro Brzezicki))

URI permanente para esta colecciónhttps://hdl.handle.net/11441/10979

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Mostrando 1 - 20 de 219

Local null controllability of a quasi-linear system and related numerical experiments
(EDP Sciences S A, 2023-04-26) Fernández Cara, Enrique; Límaco, Juan; Thamsten, Yuri; Menezes, Denilson; Ecuaciones Diferenciales y Análisis Numérico; FQM131: Ecuaciones diferenciales, Simulación Num. y Desarrollo Software
This paper concerns the null control of quasi-linear parabolic systems where the diffusion coefficient depends on the gradient of the state variable. In our main theoretical result, with some assumptions on the regularity and growth of the diffusion coefficient and regular initial data, we prove that local null controllability holds. To this purpose, we consider the null controllability problem for the linearized system, we deduce new estimates on the control and the state and, then, we apply a Local Inversion Theorem. We also formulate an iterative algorithm of the quasi-Newton kind for the computation of a null control and an associated state. We apply this method to some numerical approximations of the problem and illustrate the results with several experiments.
Local exact controllability of the Navier-Stokes system
(Elsevier Science BV, 2004-11-13) Fernández Cara, Enrique; Guerrero, Sergio; Imanuvilov, Oleg Yu; Puel, Jean-Pierre; Ecuaciones Diferenciales y Análisis Numérico; FQM131: Ecuaciones diferenciales, Simulación Num. y Desarrollo Software
In this paper we deal with the local exact controllability of the Navier–Stokes system with distributed controls supported in small sets. In a first step, we present a new Carleman inequality for the linearized Navier–Stokes system, which leads to null controllability at any time T>0. Then, we deduce a local result concerning the exact controllability to the trajectories of the Navier–Stokes system.
The ball fixed point property in spaces of continuous functions
(Springer, 2025-06-22) Avilés, Antonio; Japón Pineda, María de los Ángeles; Lennard, Christopher J.; Martínez Cervantes, Gonzalo; Stawski, Adam; Análisis Matemático; FQM127: Análisis Funcional no Lineal
A Banach space X has the ball fixed point property (BFPP) if for every closed ball B and for every nonexpansive mapping T:B→B, there is a fixed point. We study the BFPP for C(K)-spaces. Our goal is to determine topological properties over K that may determine the failure or fulfillment of the BFPP for the space of continuous functions C(K). We prove that the class of compact spaces K for which the BFPP holds lies between the class of extremally disconnected compact spaces and the class of compact F-spaces. We give a family of examples of F-spaces K for which the BFPP fails. As a result, we prove that for every cardinal κ, κ-order completeness or κ-hyperconvexity of C(K) are not enough for the BFPP and we obtain that ℓ∞/c0=C(N∗) fails BFPP under the Continuum Hypothesis. The space C([0,+∞)∗) is also analyzed. It is left as an open problem whether all compact spaces for which the BFPP holds are in fact the extremally disconnected compact sets.
Short proofs of Cambern's 1968 theorem and its generalizations applicable to fixed point theory
(Akademicka Platforma Czasopism, 2026-03-01) Japón Pineda, María de los Ángeles; Malec, Marek; Piasecki, Lukasz; Análisis Matemático; FQM127: Análisis Funcional no Lineal
First we provide short, elementary and self-contained proofs of all known results concerning the lower bounds of the Banach–Mazur distances between the space 𝑐0 of sequences converging to 0 and other ℓ1-preduals isomorphic to 𝑐0. Then, we use our technique to obtain lower bounds for the Banach–Mazur distances between any two ℓ1-preduals 𝑋 and 𝑌. Our estimate depends only on the smallest radiuses 𝑟∗⁡(𝑋) and 𝑟∗⁡(𝑌) of the closed balls in ℓ1 containing, respectively, all 𝜎⁡(ℓ1,𝑋)-cluster points and all 𝜎⁡(ℓ1,𝑌)-cluster points of the set of all extreme points of the closed unit ball in ℓ1, and for any values of 𝑟∗⁡(𝑋) and 𝑟∗⁡(𝑌) it is sharp. We apply this result to show that for every ℓ1-predual 𝑋 with 𝑟∗⁡(𝑋) <1, every ℓ1-predual 𝑌 with the distance from 𝑋 strictly less than 3−𝑟∗⁡(𝑋) 1+𝑟∗⁡(𝑋) induces a weak∗ topology on ℓ1 such that ℓ1 has the 𝜎⁡(ℓ1,𝑌)-fixed point property for nonexpansive mappings. If we additionally assume that the standard basis in ℓ1 is 𝜎⁡(ℓ1,𝑋)-convergent, then the estimate is precise. The same holds if the standard basis in ℓ1 has a finite number of 𝜎⁡(ℓ1,𝑋)-cluster points and each of them has a finite number of non-zero coordinates. It should be emphasized that the value of this constant was known only for the space 𝑐0 so far.
Generalized convexity in non-regular programming problems with inequality-type constraints
(Elsevier, 2008-11-12) Hernández Jiménez, B.; Rojas Medar, Marko Antonio; Osuna Gómez, Rafaela; Beato Moreno, Antonio; Estadística e Investigación Operativa; FQM153: Estadística e Investigación Operativa
Convexity plays a very important role in optimization for establishing optimality conditions. Different works have shown that the convexity property can be replaced by a weaker notion, the invexity. In particular, for problems with inequality-type constraints, Martin defined a weaker notion of invexity, the Karush–Kuhn–Tucker-invexity (hereafter KKT-invexity), that is both necessary and sufficient to obtain Karush–Kuhn–Tucker-type optimality conditions. It is well known that for this result to hold the problem has to verify a constraint qualification, i.e., it must be regular or non-degenerate. In non-regular problems, the classical optimality conditions are totally inapplicable. Meaningful results were obtained for problems with inequality-type constraints by Izmailov. They are based on the 2-regularity condition of the constraints at a feasible point. In this work, we generalize Martin's result to non-regular problems by defining an analogous concept, the 2-KKT-invexity, and using the characterization of the tangent cone in the 2-regular case and the necessary optimality condition given by Izmailov.
Zeros of Linear Combinations of Orthogonal Polynomials
(Springer, 2026-06-18) Durán Guardeño, Antonio José; Análisis Matemático; FQM262: Teoría de la Aproximación
Given a sequence of orthogonal polynomials (pn)n with respect to a positive measure in the real line, we study the real zeros of finite combinations of K+1 consecutive orthogonal polynomials of the form qn(x)=K∑j=o yjPn-j(x), n≥K, where yj,J=0,...,K, are real numbers with y0=1,yK=0 (which do not depend on n). We prove that for every positive measure µ there always exists a sequence of orthogonal polynomials with respect to µ such that all the zeros of the polynomial qn above are real and simple for n≥n0, where n0 is a positive integer depending on K and the yj’s.
Wasserstein support vector machine: Support vector machines made fair
(Elsevier, 2025-10-27) Carrizosa Priego, Emilio José; Halskov, Thomas; Romero Morales, Dolores; Estadística e Investigación Operativa; FQM329: Optimización
In this paper, a novel model combining Support Vector Machines (SVM) and equity is introduced. Assuming that a group of individuals need to be protected against discrimination, we address the problem of training the classifier by jointly maximizing the classification performance (SVM margin) and equity (closeness between the distribution of the predictions in the protected group and the remaining individuals). Training makes an efficient use of the available information, since the margin is evaluated on individuals for which the class label is known, whereas the equity is measured on individuals for whom we know whether they belong to the protected group or not, and thus their class label is not required. We modify the dual SVM formulation with a penalization of the Wasserstein distance between the empirical distribution of the SVM scores from the two groups. In our approach, predictions are made by reweighting the records, and we show that these weights can be found by training an SVM with a modified kernel. Numerical results are presented on classic benchmark datasets in the Fair Machine Learning literature, where we investigate the tradeoff between accuracy and unfairness for different values of the decision threshold. With a mild penalization of the Wasserstein distance, we can dramatically reduce the unfairness while keeping a similar level of accuracy.
Testing for the zero-altered Poisson distribution with positive data
(Wiley, 2025-08-25) Jiménez Gamero, María Dolores; Puig, Pedro; Ngatchou-Wandji, Joseph; Estadística e Investigación Operativa; FQM153: Estadística e Investigación Operativa
This article proposes three new goodness-of-fit tests for the zero-altered Poisson distribution, or equivalently for the positive Poisson distribution, based on positive data, that is, data truncated at 0, whose test statistic is built using a characterization of this law. It is shown that the proposed tests are consistent against any fixed alternative and that the parametric bootstrap method can accurately approximate their null distributions. The power of these tests is investigated through a large simulation study, where it is also compared with some existing tests, showing a very competitive behavior. Several applications to real datasets illustrate the usefulness of the tests.
Stochastic differential equation driven by the Rosenblatt process
(Springer, 2026-03-31) Benkaddour, Sakina; Kandouci, Abdeldjebber; Kebiri, Omar; Caraballo Garrido, Tomás; Ecuaciones Diferenciales y Análisis Numérico; FQM314: Análisis Estocástico de Sistemas Diferenciales
The Rosenblatt process is a non-Gaussian self-similar process residing in the second Wiener chaos. It emerges as the limit of correlated random sequences in "non-central limit theorems." It shares the same covariance function as fractional Brownian motion. In this paper, we studied a class of one-dimensional stochastic differential equations driven by the Rosenblatt process with Hurst parameter 1/2 < H < 1. We proved the existence and uniqueness of solution to this kind of equation under the linear growth and Lipschitz conditions. Additionally, using the Gronwall inequality lemma, we provide the continuous dependency of solutions on the initial value. We solve numerically our SDE using Euler Maruyama method. Finally the approximation solution are compared with the exact solution for different sample paths in an example.
Special issue on "Goodness-of-Fit, Change Point and Related Problems"
(Springer, 2025-05-19) Meintanis, Simos G.; Jiménez Gamero, María Dolores; Estadística e Investigación Operativa; FQM153: Estadística e Investigación Operativa
Some distributions related to double records in iid sequences
(Springer, 2025-05-08) López Blázquez, Fernando; Piliszek, Agnieszka; Salamanca Miño, Begoña; Estadística e Investigación Operativa; FQM331: Métodos y Modelos de la Estadística y la Investigación Operativa
We are concerned with the appearance of double records (two records in a row) in a sequence of independent and identically distributed (iid) random variables with absolutely continuous distribution, say F. We investigate distributions associated to the position of double records both within the original sequence and among the sequence of records. These distributions are free in the sense that they do not depend on the common distribution F. In fact, these distributions can be obtained by using a connection between iid samples and random permutations. We also study distributions associated to the values of double records. These statistics are not distribution free, so without loss of generality we consider the case in which F is the distribution function of a random variable uniformly distributed in (0, 1). As far as we know these statistics has not been studied before.
Soft decision trees for survival analysis
(Elsevier, 2026-01-08) Consolo, Antonio; Amaldi, Edoardo; Carrizosa Priego, Emilio José; Estadística e Investigación Operativa
Decision trees are popular in survival analysis for their interpretability and ability to model complex relationships. Survival trees, which predict the timing of singular events using censored historical data, are typically built through heuristic approaches. Recently, there has been growing interest in globally optimized trees, where the overall tree is trained by minimizing the error function over all its parameters. We propose a new soft survival tree model (SST), with a soft splitting rule at each branch node, trained via a nonlinear optimization formulation amenable to decomposition. Since SSTs provide for every input vector a specific survival function associated to a single leaf node, they satisfy the conditional computation property and inherit the related benefits. SST and the training formulation combine flexibility with interpretability: any smooth survival function (parametric, semiparametric, or nonparametric) estimated through maximum likelihood can be used, and each leaf node of an SST yields a cluster of distinct survival functions which are associated to the data points routed to it. Numerical experiments on 15 well-known datasets show that SSTs, with parametric and spline-based semiparametric survival functions, trained using an adaptation of the node-based decomposition algorithm proposed by Consolo et al. (2024) for soft regression trees, outperform three benchmark survival trees in terms of four widely-used discrimination and calibration measures. SSTs can also be extended to consider group fairness.
Robust counterfactual explanations in classification and regression
(Elsevier, 2026-06-02) Carrizosa Priego, Emilio José; Navas Orozco, Antonio; Estadística e Investigación Operativa; FQM329: Optimización
We prove that the word problem in an Artin group G based on a diagram without A3 or B3 subdiagrams can be solved using a system of length preserving rewrite rules which, together with free reduction, can be used to reduce any word over the standard generators of G to a geodesic word in G in quadratic time. This result builds on work of Holt and Rees, and of Blasco-García, Cumplido and Morris-Wright. Those articles prove the same result for all Artin groups that are either sufficiently large or 3-free, respectively.
Pareto-optimal trees and Pareto forest: a bi-objective optimization model for binary classification
(Springer, 2026-06-09) Santis, Marianna de; Patria, Daniele; Puerto Albandoz, Justo; Estadística e Investigación Operativa; FQM331: Métodos y Modelos de la Estadística y la Investigación Operativa
Asinherentlytransparentmodels,classificationtreesplayacentralroleininterpretable machinelearningbyprovidingeasilytraceabledecisionpaths that allowuserstounderstand how input features contribute to specific predictions. In this work, we introduce a new class of interpretable binary classification models, named Pareto-optimal trees, which aim at combining the complementary strengths of Optimal Classification Trees with Hyperplane-based splits (OCT-H) and Support Vector Machines (SVM). We formulate a bi-objective mixed-integer quadratic optimization problem, whose nondominated solutions represent trade-offs between these two different classification techniques. To further enhance robustness and performance, we propose the Pareto forest, an ensemble method based on the Pareto-optimal trees, aggregated through majority voting. Extensive experiments on benchmark datasets demonstrate that our models can outperform standard methods such as CART and OCT, underscoring the improvements gained through the bi-objective perspective. In particular, Paretooptimal trees unify the ability of OCT-HandSVMwithinasingleframework,resulting in enhanced classification performance relative to either method alone. Embracing a multiobjective perspective allows the construction of multiple “high quality" trees. Our comparison between Pareto forests and random forests shows that building shallow ensembles from a small number of such optimized trees outperforms relying on a large set of random trees with variable depth.
Ordered Median Traveling Salesman Problem
(Wiley, 2026-07) Ljubic, Ivana; Marín, Alfredo; Puerto Albandoz, Justo; Temprano, Francisco; Estadística e Investigación Operativa; FQM331: Métodos y Modelos de la Estadística y la Investigación Operativa
This paper introduces a novel combinatorial optimization problem with ordering constraints, termed the Ordered Median Traveling Salesman Problem (OMTSP). The OMTSP integrates key elements from both the classic Traveling Salesman Problem (TSP) and the Ordered Median Location Problem. Specifically, the objective is to identify a tour that minimizes a weighted sum of the sorted arc lengths within the tour. This flexible framework enables the modeling of a wide range of combinatorial optimization problems related to the traditional TSP, like the bottleneck TSP, the balanced TSP, or other TSP variants in which fairness measures are applied to the arcs of the tour. In this work, we present new mathematical formulations for the OMTSP across different variable spaces, which are solved using a branch-and-cut approach. Leveraging several newly derived structural properties, we enhance these formulations through advanced preprocessing strategies, variable bounding and variable fixing techniques, as well as through the introduction of new valid inequalities. A comprehensive computational study is conducted to evaluate the effectiveness of the proposed formulations and their associated improvements.
Operations on the de Rham cohomology of Poisson and Jacobi manifolds
(Springer, 2025-10-10) Guan, Ai; Muro Jiménez, Fernando; Álgebra; FQM218: Singularidades, Geometría Algebraica Aritmética, Grupos y Homotopía
We prove that the (homotopy) hypercommutative algebra structure on the de Rham cohomology of a Poisson or Jacobi manifold defined by several authors is (homotopically) trivial, i.e. it reduces to the underlying (homotopy) commutative algebra structure. We do so by showing that the DG operads which codify the algebraic structure on the de Rham complex of Poisson and Jacobi manifolds, generated by the exterior product and the interior products with the structure polyvector fields, are quasi-isomorphic to the commutative suboperad. We proceed similarly with the commutative BV∞-algebra structure on the de Rham complex of a generalized Poisson supermanifold.
On contextual inverse multiobjective problems
(Elsevier, 2025-12-07) Blanquero Bravo, Rafael; Carrizosa Priego, Emilio José; Gómez Vargas, Nuria; Estadística e Investigación Operativa; FQM329: Optimización
We introduce a novel framework for Contextual Inverse Multiobjective Optimization, where the goal is to recover multiple objective functions and the preferences among them from observed context-decision pairs. Assuming that each decision arises from minimizing a weighted distance to an ideal outcome, we develop a mathematical programming model that infers context-dependent linear objectives consistent with observed data. Our approach accommodates different norm-based scalarizations, including ℓ1, ℓ2, ℓ∞ and Ordered Weighted Averages, and enforces interpretability through structured sparsity. By characterizing the conditions under which observed decisions are provably optimal, we formulate a tractable Mixed-Integer Quadratic Program that reveals how contextual features influence decision-making criteria. Numerical experiments on real-world data demonstrate the method’s ability to recover interpretable, sparse models while maintaining strong generalization performance.
New results on the existence of positive periodic solutions for second-order nonlinear neutral differential equations with mixed delays
(University of Niš Faculty of Science and Mathematics, 2026-04-15) Benhadri, Mimia; Caraballo Garrido, Tomás; Ecuaciones Diferenciales y Análisis Numérico; FQM314: Análisis Estocástico de Sistemas Diferenciales
The present paper is devoted to study second-order neutral differential equations with variable coefficients and mixed delays. By using the theory of fixed point index in cones as well as some properties of a suitable Green function, several sufficient conditions for the existence of one and twin positive periodic solutions are obtained. Our results are a further expansion of previous research results of Khemis et al. [13]. Finally, two examples are exhibited to show the efficiency and application of our findings which are completely new and enrich the existing literature.
Modularity for hypergraph clustering: Methodologies and applications
(ScienceDirect, 2025-08-20) Benati, Stefano; Puerto Albandoz, Justo; Temprano García, Francisco; Estadística e Investigación Operativa; FQM331: Métodos y Modelos de la Estadística y la Investigación Operativa
We consider the problem of detecting communities of the vertices of data structures defined as hypergraphs. There are many methods that were devised to find communities on simple graphs, one of the most important being modularity maximization. Therefore we extend the definition of modularity to deal with hypergraphs, too. The new definition considers whether a hyperedge as internal or not to a community, and in the affirmative case, the hyperedge is assigned with a weight defining the level of cohesiveness of their vertices. Next, we formulate a mixed-integer linear programming model to hypergraph modularity maximization, whose optimal solutions consist in the best vertex partitions of the hypergraph. Previous attempts of partitioning hypergraphs did suggest the projection of hyperedges onto simple graphs, replacing every hyperedge with a complete subgraph. So, we compare our proposal with the previous methodologies, including other hypergraph modularity definitions, and we find that we improve the quality of the partition. Finally, we apply the methodology to the analysis of survey data, and we show how hypergraph modularity clustering highlights some peculiar data structures that otherwise would remain hidden to researchers.
Glowinski and numerical control problems
(Académie des sciences, 2023-04-06) Fernández Cara, Enrique; Ecuaciones Diferenciales y Análisis Numérico; FQM131: Ecuaciones diferenciales, Simulación Num. y Desarrollo Software
This paper is devoted to recall several contributions to the numerical control of PDE’s that have origin in Glowinski’s work. I will consider null controllability problems for linear and nonlinear heat equations and some free-boundary systems. We will also deal with some bi-objective optimal control problems. Additionally, some new methods and results will be announced.

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