Artículos (Matemática Aplicada II)

URI permanente para esta colecciónhttps://hdl.handle.net/11441/10899

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A Banzhaf value for games with a proximity relation among the agents
(Elsevier, 2017-09) Fernández García, Julio R.; Gallego Sánchez, Inés Magdalena; Jiménez Losada, Andrés; Ordóñez Sánchez, Manuel; Universidad de Sevilla. Departamento de Matemática Aplicada II (ETSI); Ministerio de Economía y Competitividad (MINECO). España; Universidad de Sevilla. FQM237: Juegos con Estructuras Combinatorias y de Orden; Universidad de Sevilla. FQM226: Grupo de Investigación en Educación Matemática
The Banzhaf index is a function determining the power or influence in the decision of a set of agents. The extension of this index to the family of the cooperative games is named Banzhaf value. The relationships of closeness among the agents should modify their power. Games with a priori unions study situations where the closeness relations among the agents are taken into account. In this model the agents are organized in an a priori partition where each element of the partition represents a group of agents with close interests or ideas. The power is determined in two steps, first as a problem among the unions and later, inside each one, the power of each agent is determined. Proximity relations extend this model considering leveled closeness among the agents. In this paper we analyze a version of the Banzhaf value for games with a proximity relation and we show the interest of this value by applying it to the allocation of the power of the political groups in the European Parliament.
A characterization of the Shapley value for cooperative games with fuzzy characteristic function
(Elsevier, 2020-11) Gallardo Morilla, José Manuel; Jiménez Losada, Andrés; Universidad de Sevilla. Departamento de Matemática Aplicada II; Ministerio de Ciencia, Innovación y Universidades, España MTM2017-83455-P; Andalusian Regional Government under grant FQM-237; Universidad de Sevilla. FQM237: Juegos con Estructuras Combinatorias y de Orden
The characteristic function of a cooperative game determines the payment that each coalition can obtain when the players in the coalition cooperate. But there are cooperative situations in which the players have only imprecise expectations about the profit that can be achieved by each coalition. These situations are modeled through cooperative games with fuzzy characteristic function, in which the payment of each coalition is a fuzzy quantity. A value for these games assigns to each player in a game a fuzzy quantity that indicates the vaguely expected payoff for the player. There is a Shapley value for games with fuzzy characteristic function, but no characterization of this value has been given in the literature. In this paper a characterization of the Shapley value for games with fuzzy characteristic function is presented.
A comprehensive approach for discrete resilience of complex networks
(AIP Publishing, 2023) Moreno Casablanca, Rocío; Criado Herrero, Regino; Mesa López-Colmenar, Juan Antonio; Romance, Miguel; Universidad de Sevilla. Departamento de Matemática Aplicada II; European Commission (EC). Fondo Europeo de Desarrollo Regional (FEDER); Universidad Rey Juan Carlos; Universidad de Sevilla. FQM241: Optimización Matemática Aplicada (ÓPTIMA)
The research and use of the term resilience in various types of technological, physiological, and socioeconomic systems has become very topical in recent years since this term has been applied in different fields with different meanings and connotations. One of the most common meanings of resilience is related to a positive idea that addresses recovery from failures. This study proposes to establish a theoretical and mathematical framework for discrete resilience that allows different systems to be quantitatively compared from this point of view. Also, a definition and a local view of the concept of resilience applicable to different characteristic measures in the field of complex networks is provided. Furthermore, several computational experiments are presented on the values of this new parameter in different types of synthetic and real-world networks, supplying a new set of conceptual tools for network science research.
A connection-based analysis of networks using the position value: a computational approach
(Elsevier, 2024-10-01) Algaba Durán, Encarnación; Saavedra Nieves, Alejandro; Universidad de Sevilla. Departamento de Matemática Aplicada II (ETSI); Ministerio de Ciencia e Innovación (MICIN). España; Agencia Estatal de Investigación. España; Xunta de Galicia
In this paper, we introduce the position value as a centrality measure to evaluate the relevance of the edges and players in a network, with the additional advantage that this value integrates the degree measure of each player in it. In fact, in the real world, it is particularly important to consider the natural influence of connections of a player in a network. Its applications were very limited in real-world situations due to the high computational complexity of exactly obtaining this value. With the aim of solving this problem we provide a method, based on sampling theory, to estimate the position value, which is analyzed in terms of the theoretical properties of the resulting estimator. Moreover, we establish specific statistical results for bounding the absolute error in this approximation. It is important to emphasize that this approach allows for obtaining rankings not only of the nodes but also of the edges of the network. To illustrate the advantages and interest of the proposed methodology, as well as the variety of problems that can be analyzed in this framework, we applied it in three very different settings, the suburban train network of Madrid in the year 2000, the Spanish national team in a match against Portugal, and the Zerkani network responsible for the terrorist attacks of Paris (2015) and Brussels (2016).
A double-zero bifurcation in a Lorenz-like system
(Springer, 2023-12) Algaba Durán, Antonio; Domínguez-Moreno, M.C.; Merino Morlesín, Manuel; Rodríguez Luis, Alejandro José; Universidad de Sevilla. Departamento de Matemática Aplicada II (ETSI); Ministerio de Economía y Competitividad (España) MTM2017-87915- C2-1-P; Ministerio de Ciencia, Innovación y Universidades (España) PGC2018-096265-B-I00; Ministerio de Ciencia, Innovación y Universidades (España) PID2021-123200NB-I00; Consejería de Economía, Innovación, Ciencia y Empleo de la Junta de Andalucía (España) project FQM-276; Consejería de Economía, Innovación, Ciencia y Empleo de la Junta de Andalucía (España) project TIC-0130; Consejería de Economía, Innovación, Ciencia y Empleo de la Junta de Andalucía (España) project P20_01160; Consejería de Economía, Innovación, Ciencia y Empleo de la Junta de Andalucía (España) project UHU-1260150; Universidad de Sevilla. TIC130: Invenstigación en Sistemas Dinámicos en Ingeniería; Universidad de Sevilla. TIC-130: Investigación en sistemas dinámicos en ingeniería
The Lorenz system presents a double-zero bifurcation (a double-zero eigenvalue with geometric multiplicity two). However, its study by means of standard techniques is not possible because it occurs for a non-isolated equilibrium. To circumvent this difficulty, we add in the third equation a new term, Dz². In this Lorenz-like system, the analysis of the double-zero bifurcation of the equilibrium at the origin guarantees, for certain values of the parameters, the existence of a heteroclinic cycle between the two equilibria located on the z-axis. The numerical continuation in parameter space of the locus of heteroclinic connections allows to detect various degeneracies of codimension two and three, some of which have not been previously studied in the literature. These bifurcations are organizing centers of the complicated dynamics exhibited by this system. Furthermore, studying how the bifurcation sets evolve when D tends to zero, we are able to explain, in the Lorenz system, the origin of several global connections which are related to T-point heteroclinic loops.
A Game Theoretical Randomized Method for Large-Scale Systems Partitioning
(IEEE, 2018) Muros Ponce, Francisco Javier; Maestre Torreblanca, José María; Ocampo-Martínez, Carlos; Algaba Durán, Encarnación; Camacho, Eduardo F.; Universidad de Sevilla. Departamento de Ingeniería de Sistemas y Automática; Universidad de Sevilla. Departamento de Matemática Aplicada II (ETSI); European Union (UE); Ministerio de Economía y Competitividad (MINECO). España
In this paper, a game theory-based partitioning algorithm for large-scale systems (LSS) is proposed. More speci cally, a game over nodes is introduced in a model predictive control framework. The Shapley value of this game is used to rank the communication links of the control network based on their impact on the overall system performance. A randomized method to estimate the Shapley value of each node and also an ef cient redistribution of the resulting value to the links involved are considered to relieve the combinatorial explosion issues related to LSS. Once the partitioning solution is obtained, a sensitivity analysis is proposed to give a measure of its performance. Likewise, a greedy ne tuning procedure is considered to increase the optimality of the partitioning results. The full Barcelona drinking water network is analyzed as a real LSS case study, showing the effectiveness of the proposed approach in comparison with other partitioning schemes available in the literature.
A general approach for the location of transfer points on a network with a trip covering criterion and mixed distances
(Elsevier, 2017) López de los Mozos Martín, María Cruz; Mesa López-Colmenar, Juan Antonio; Schöbel, Anita; Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII); Universidad de Sevilla. Departamento de Matemática Aplicada II (ETSI)
In this paper we consider a trip covering location model in a mixed planar-network space. An embed- ded network in the plane represents an alternative transportation system in which traveling is fasterthan traveling within the plane. We assume that the demand to be covered is given by a set of origin- destination pairs in the plane, with some traffic between them. An origin-destination pair is covered bytwo facility points on the network (or transfer points), if the travel time from the origin to destinationby using the network through such points is not higher than a given acceptance level related to the traveltime without using the network. The facility location problems studied in this work consist of locatingone or two transfer points on the network such that, under several objective functions, the traffic throughthe network is maximized. Due to the continuous nature of these problems, a general approach is pro- posed for discretizing them. Since the non-convexity of the distance function on cyclic networks alsoimplies the absence of convexity of the mixed distance function, such an approach is based on a decom- position process which leads to a collection of subproblems whose solution set can be found by adaptingthe general strategy to each problem considered.
A general vertical decomposition of Euler equations: Multilayer-moment models
(Elsevier, 2023-01) Garres-Díaz, José; Escalante Sánchez, Cipriano; Morales de Luna, Tomás; Castro Díaz, Manuel Jesús; Universidad de Sevilla. Departamento de Matemática Aplicada II (ETSI); Gobierno de España; European Commission (EC). Fondo Europeo de Desarrollo Regional (FEDER); Junta de Andalucía; Universidad de Málaga; Universidad de Sevilla. FQM120: Modelado Matemático y Simulación de Sistemas Medioambientales
In this work, we present a general framework for vertical discretizations of Euler equations. It generalizes the usual moment and multilayer models and allows to obtain a family of multilayer-moment models. It considers a multilayer-type discretization where the layerwise velocity is a polynomial of arbitrary degree N on the vertical variable. The contribution of this work is twofold. First, we compare the multilayer and moment models in their usual formulation, pointing out some advantages/disadvantages of each approach. Second, a family of multilayer-moment models is proposed. As particular interesting case we shall consider a multilayer-moment model with layerwise linear horizontal velocity. Several numerical tests are presented, devoted to the comparison of multilayer and moment methods, and also showing that the proposed method with layerwise linear velocity allows us to obtain second order accuracy in the vertical direction. We show as well that the proposed approach allows to correctly represent the vertical structure of the solutions of the hydrostatic Euler equations. Moreover, the measured efficiency shows that in many situations, the proposed multilayer-moment model needs just a few layers to improve the results of the usual multilayer model with a high number of vertical layers.
A generalized model of equality measures in network location problems
(Elsevier, 2008-03) López de los Mozos Martín, María Cruz; Mesa López-Colmenar, Juan Antonio; Puerto Albandoz, Justo; Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII); Universidad de Sevilla. Departamento de Matemática Aplicada II (ETSI); Universidad de Sevilla. Departamento de Estadística e Investigación Operativa; European Commission (EC); Ministerio de Educación y Ciencia (MEC). España; Universidad de Sevilla. FQM241: Grupo de Investigacion en Localizacion; Universidad de Sevilla. FQM331: Metodos y Modelos de la Estadistica y la Investigacion Operativa
In this paper, the concept of the ordered weighted averaging operator is applied to define a model which unifies and generalizes several inequality measures. For a location x, the value of the new objective function is the ordered weighted average of the absolute deviations from the average distance from the facilities to the location x. Several kinds of networks are studied: cyclic, tree and path networks and, for each of them, the properties of the objective function are analyzed in order to identify a finite dominating set for optimal locations. Polynomial-time algorithms are proposed for these problems, and the corresponding complexity is discussed.
A logistic type equation in Rᴺ with a nonlocal reaction term via bifurcation method
(Elsevier, 2021-01-01) Delgado Delgado, Manuel; Molina Becerra, Mónica; Suárez Fernández, Antonio; Universidad de Sevilla. Departamento de Matemática Aplicada II (ETSI); Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico; European Commission (EC). Fondo Europeo de Desarrollo Regional (FEDER); Universidad de Sevilla. TIC130: Investigación en Sistemas Dinámicos en Ingeniería; Universidad de Sevilla. FQM131: Ecuaciones Diferenciales, Simulación Numérica y Desarrollo Software
We study the existence of positive solutions of a logistic equation in the entire space with a nonlocal reaction term. Mainly, we apply a bifurcation method and singular boundary equations to obtain a priori bounds of the solutions. Our results show a drastic change of behaviour of the set of positive solutions depending on the sign of the nonlocal term.
A matheuristic for optimizing skip–stop operation strategies in rail transit lines
(WIT Press, 2019) Ortega Riejos, Francisco Alonso; Mesa López-Colmenar, Juan Antonio; Piedra de la Cuadra, Ramón; Pozo Montaño, Miguel Ángel; Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII); Universidad de Sevilla. Departamento de Matemática Aplicada II (ETSI); Universidad de Sevilla. Departamento de Estadística e Investigación Operativa; Ministerio de Economía y Competitividad (MINECO). España; Ministerio de Economía y Competitividad (MINECO). España
In many transit systems, operators use skip–stop strategies to reduce travel time of particular train services by not stopping (skipping) at less densely populated stations. This decision of omitting some stops reduces the travel time for the users within the vehicle and increases the speed of operation, favouring the provision of new transit services where are more necessary. In this work, the best A/B stop–skip patterns for a set of transit services along a railway corridor are determined by means a three-phase methodology that includes the formulation of a nonlinear integer programming inspired in the multiple knapsack problem and the application of a heuristic algorithm based on mathematical properties (matheuristic).
A maximum trip covering location problem with an alternative mode of transportation on tree networks and segments
(Sociedad Española de Estadística e Investigación Operativa, 2014) Körner, Mark Christof; Mesa López-Colmenar, Juan Antonio; Perea Rojas-Marcos, Federico; Schöbel, Anita; Scholz, Daniel; Universidad de Sevilla. Departamento de Matemática Aplicada II; Universidad de Sevilla. FQM241: Grupo de Investigación en Localización
In this paper the following facility location problem in a mixed planarnetwork space is considered: We assume that traveling along a given network is faster than traveling within the plane according to the Euclidean distance. A pair of points (Ai,Aj ) is called covered if the time to access the network from Ai plus the time for traveling along the network plus the time for reaching Aj is lower than, or equal to, a given acceptance level related to the travel time without using the network. The objective is to find facilities (i.e. entry and exit points) on the network that maximize the number of covered pairs. We present a reformulation of the problem using convex covering sets and use this formulation to derive a finite dominating set and an algorithm for locating two facilities on a tree network. Moreover, we adapt a geometric branch and bound approach to the discrete nature of the problem and suggest a procedure for locating more than two facilities on a single line, which is evaluated numerically.
A mixed integer linear programming model for resolution of the antenna-satellite scheduling problem
(Institute of Electrical and Electronics Engineers, 2024-02) Linares López, Lorena; Vázquez Valenzuela, Rafael; Perea Rojas-Marcos, Federico; Galán Vioque, Jorge Francisco; Universidad de Sevilla. Departamento de Ingeniería Aeroespacial y Mecánica de Fluidos; Universidad de Sevilla. Departamento de Matemática Aplicada II (ETSI); European Union; Agencia Estatal de Investigación. España; European Commission (EC). Fondo Europeo de Desarrollo Regional (FEDER); Junta de Andalucía; Ministerio de Ciencia e Innovación (MICIN). España; Universidad de Sevilla. TEP945: Ingeniería Aeroespacial; Universidad de Sevilla. FQM241: Optimización Matemática Aplicada (Óptima); Universidad de Sevilla. TIC130: Investigación en Sistemas Dinámicos en Ingeniería
This article deals with one of the types of “Satellite Range Scheduling” problems arising in Earth Observation Satellite operations, Antenna-Satellite Scheduling. Given a set of satellites, a set of available antennas and a time horizon, the problem consists of designing an operational plan that assigns satellites to antennas in an optimal fashion. Extending a previous integer linear programming (ILP) model (shortening model, with only integer variables), we propose a mixed ILP (MILP) (shaving model, which includes both continuous and integer variables), to more efficiently solve this problem. After computing the passes generated by the satellites' windows of visibility from the antennas, the optimal planner is able to cancel a pass, move it to another antenna, or shorten its duration, in order to avoid scheduling conflicts. In contrast to the shortening model, which used intersections between passes to determine the best schedule, the shortening operation is now referred to as shaving, since the shaving model can arbitrarily adjust the duration of a pass in a razor-like fashion, giving the model its name. Computational results obtained in tests over realistic scenarios prove that the shaving model outperforms the shortening model, producing fewer cancellations, smaller shaved times, and a fairer distribution of cancelled passes among satellites, with much shorter preprocessing times.
A multiple focus-center-cycle bifurcation in 4D discontinuous piecewise linear memristor oscillators
(Springer, 2018-12) Ponce Núñez, Enrique; Amador, Andrés; Ros Padilla, Francisco Javier; Universidad de Sevilla. Departamento de Matemática Aplicada II (ETSI); Ministerio de Economía y Competitividad (MINECO). España; Consejería de Economía y Conocimiento, Junta de Andalucía; Pontificia Universidad Javeriana Cali-Colombia; Universidad de Sevilla. TIC130: Investigación en Sistemas Dinámicos en Ingeniería
The dynamical richness of 4D memristor oscillators has been recently studied in several works, showing different regimes, from stable oscillations to chaos. Typically, only numerical simulations have been reported and so there is a lack of mathematical results. We focus our analysis in the existence of multiple stable oscillations in the 4D piecewise linear version of the canonical circuit proposed by Itoh and Chua (Int J Bifurc Chaos 18(11):3183–3206, 2008). This oscillator is modeled by a discontinuous piecewise linear dynamical system. By adding one parameter that stratifies the 4D dynamics, it is shown that the dynamics in each stratum is topologically equivalent to a 3D continuous piecewise linear dynamical system. Some previous results on bifurcations in such reduced system allow to detect rigorously for the first time a multiple focus-center-cycle bifurcation in a three-parameter space, leading to the appearance of a topological sphere in the original model, completely foliated by stable periodic orbits. © 2018, Springer Nature B.V.
A new commutativity property of exceptional orthogonal polynomials
(Springer, 2024-03-29) Castro Smirnova, Mirta María; Grünbaum, Francisco Alberto; Universidad de Sevilla. Departamento de Matemática Aplicada II (ETSI); Universidad de Sevilla; European Commission (EC). Fondo Europeo de Desarrollo Regional (FEDER); Ministerio de Ciencia e Innovación (MICIN). España; Agencia Estatal de Investigación. España; Junta de Andalucía; Universidad de Sevilla. FQM262: Teoría de la Aproximación
We exhibit three examples showing that the “time-and-band limiting” commutative property found and exploited by D. Slepian, H. Landau and H. Pollak at Bell Labs in the 1960s, and independently by M. Mehta and later by C. Tracy and H. Widom in Random matrix theory, holds for exceptional orthogonal polynomials. The property in question is the existence of local operators with simple spectrum that commute with naturally appearing global ones. We illustrate numerically the advantage of having such a local operator.
A new Shapley value for games with fuzzy coalitions
(Elsevier, 2020) Basallote Galván, Manuela; Hernández Mancera, Carmen; Jiménez Losada, Andrés; Universidad de Sevilla. Departamento de Matemática Aplicada II (ETSI); Jiménez Losada, Andrés; Ministerio de Economia, Industria y Competitividad (MINECO). España; Junta de Andalucía; Universidad de Sevilla. FQM237: Juegos con Estructuras Combinatorias y de Orden
En este artículo se introduce un nuevo valor de Shapley para juegos con coaliciones difusas, identificadas con los puntos del cubo unidad N-dimensional. En los valores existentes en la literatura se usa poca información del juego para elaborar la solución, o bien los vértices del cubo o bien la diagonal. El valor propuesto mejora en el sentido de que utiliza más información de la disponible al usar todas las caras del cubo. Se da también una axiomatización del valor. Además se propone un modelo para elaborar soluciones que van usando cada vez más información.
A new simple proof for Lum–Chua's conjecture
(Elsevier, 2021-05) Carmona Centeno, Victoriano; Fernández Sánchez, Fernando; Novaes, Douglas D.; Universidad de Sevilla. Departamento de Matemática Aplicada II (ETSI); Universidad de Sevilla. TIC-130: Investigación en sistemas dinámicos en Ingeniería
The already proved Lum–Chua’s conjecture says that a continuous planar piecewise linear differential system with two zones separated by a straight line has at most one limit cycle. In this paper, we provide a new proof by using a novel characterization for Poincaré half-maps in planar linear systems. This proof is very short and straightforward, because this characterization avoids the inherent flaws of the usual methods to study piecewise linear systems (the appearance of large case-by-case analysis due to the unnecessary discrimination between the different spectra of the involved matrices, to deal with transcendental equations forced by the implicit occurrence of flight time, …). In addition, the application of the characterization allow us to prove that if a limit cycle exists, then it is hyperbolic and its stability is determined by a simple relationship between the parameters. To the best of our knowledge, the hyperbolicity of the limit cycle and this simple expression for its stability have not been pointed out before.
A non-local perturbation of the logistic equation in IR N
(Elsevier, 2019-10) Delgado Delgado, Manuel; Molina Becerra, Mónica; Rodrigues dos Santos Júnior, Joao; Suárez Fernández, Antonio; Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico; Universidad de Sevilla. Departamento de Matemática Aplicada II (ETSI); Universidad de Sevilla. FQM131: Ec.diferenciales,Simulación Num.y Desarrollo Software; Universidad de Sevilla. TIC130: Investigación en Sistemas Dinámicos en Ingeniería
A logistic equation in the whole space is considered. In this problem, a non-local perturbation is included. We establish a new sub-supersolution method forgeneral nonlocal elliptic equations and, consequently, we obtain the existence ofpositive solutions of a nonlocal logistic equation.
A nonlinear age-dependent model with spatial diffusion
(Elsevier, 2006-01-01) Delgado Delgado, Manuel; Molina Becerra, Mónica; Suárez Fernández, Antonio; Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico; Universidad de Sevilla. Departamento de Matemática Aplicada II; Ministerio de Ciencia y Tecnología (MCYT). España
The main goal of this paper is to study the existence and uniqueness of positive solution for a nonlinear age-dependent equation with spatial diffusion. For that, we mainly use properties of an eigenvalue problem related to the equation and the subsupersolution method. We justify that this method works for this kind of equation, in which appears a potential blowing-up and a non-local initial condition.
A note on the Köthe dual of Banach-valued echelon spaces
(Universitat de Barcelona. Promociones y Publicaciones Universitarias, PPU, 1988) Florencio Lora, Miguel; Paúl Escolano, Pedro José; Sáez Agulló, Carmen; Universidad de Sevilla. Departamento de Matemática Aplicada II (ETSI)
Several different ways of defining the Köthe dual of echelon spaces of Banach-valued functions are shown to be equivalent

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