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 106

Reduced Basis modelling of turbulence with well-developed inertial range
(Elsevier, 2024-02-01) Bandera Moreno, Alejandro; Caravaca García, Cristina; Chacón Rebollo, Tomás; Delgado Ávila, Enrique; Gómez Mármol, María Macarena; Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico; Universidad de Sevilla. FQM120: Modelado Matemático y Simulación de Sistemas Medioambientales
In this work, we introduce a Reduced Basis model for turbulence at statistical equilibrium. This is based upon an a-posteriori error estimation procedure that measures the distance from a trial solution to the K41 theory energy spectrum. We apply this general idea to build a Reduced Basis Smagorinsky turbulence model through a Greedy Algorithm. We derive some error estimates that make apparent the role of the energy spectrum in the ROM approximation. We carry on some tests for some academic unsteady 2D flows at large Reynolds number, that present well developed inertial spectrum. The methods presents a high efficiency, as the error achieved with the reduced method is 3 to 4 times the ones achieved if the exact error is used in the Greedy Algorithm.
Undominated Sequences of Integrable Functions
(Springer Nature, 2020-10-20) Bernal González, Luis; Calderón Moreno, María del Carmen; Murillo Arcila, Marina; Prado Bassas, José Antonio; Universidad de Sevilla. Departamento de Análisis Matemático
In this paper, we investigate to what extent the conclusion of the Lebesgue dominated convergence theorem holds if the assumption of dominance is dropped. Speci cally, we study both topological and algebraic genericity of the family of all null sequences of functions that, being continuous on a locally compact space and integrable with respect to a given Borel measure in it, are not controlled by an integrable function.
The soft-margin Support Vector Machine with ordered weighted average
(Elsevier, 2021) Marín, Alfredo; Martínez Merino, Luisa Isabel; Puerto Albandoz, Justo; Rodríguez Chía, Antonio Manuel; Universidad de Sevilla. Departamento de Estadística e Investigación Operativa
This paper deals with a cost sensitive extension of the standard Support Vector Machine (SVM) using an ordered weighted sum of the deviations of misclassified individuals with respect to their corresponding supporting hyperplanes. In contrast with previous heuristic approaches, an exact method that applies the ordered weighted average operator in the classical SVM model is proposed. Specifically, when weights are sorted in non-decreasing order, a quadratic continuous formulation is developed. For general weights, a mixed integer quadratic formulation is proposed. In addition, our results prove that nonlinear kernel functions can be also applied to these new models extending its applicability beyond the linear case. Extensive computational results reported in the paper show that the predictive performance provided by the proposed exact solution approaches are better than the ones provided by the classical models (linear and nonlinear kernel) and similar or better than the previous ones provided by the heuristic solution by Maldonado et al. (2018).
On sparse optimal regression trees
(Elsevier, 2021-12-18) Blanquero Bravo, Rafael; Carrizosa Priego, Emilio José; Molero del Río, María Cristina; Romero Morales, María Dolores; Universidad de Sevilla. Departamento de Estadística e investigación operativa; Universidad de Sevilla. FQM329: Optimización
In this paper, we model an optimal regression tree through a continuous optimization problem, where a compromise between prediction accuracy and both types of sparsity, namely local and global, is sought. Our approach can accommodate important desirable properties for the regression task, such as cost-sensitivity and fairness. Thanks to the smoothness of the predictions, we can derive local explanations on the continuous predictor variables. The computational experience reported shows the outperformance of our approach in terms of prediction accuracy against standard benchmark regression methods such as CART, OLS and LASSO. Moreover, the scalability of our approach with respect to the size of the training sample is illustrated.
Real-Analytic Non-Integrable Functions on the Plane with Equal Iterated Integrals
(Springer, 2021-12-16) Bernal González, Luis; Calderón Moreno, María del Carmen; Jung, Andreas; Universidad de Sevilla. Departamento de Análisis matemático; Universidad de Sevilla. FQM127: Análisis Funcional no Lineal
In this note, a vector space of real-analytic functions on the plane is explicitly constructed such that all its nonzero functions are non-integrable but yet their two iterated integrals exist as real numbers and coincide. Moreover, it is shown that this vector space is dense in the space of all real continuous functions on the plane endowed with the compact-open topology.
Average radial integrability spaces of analytic functions
(Academic Press Inc., 2022) Aguilar-Hernández, Tanausú; Contreras Márquez, Manuel Domingo; Rodríguez Piazza, Luis; Universidad de Sevilla. Departamento de Matemática Aplicada II (ETSI); Universidad de Sevilla. Departamento de Análisis Matemático
In this paper we introduce the family of spaces RM(p, q), 1 ≤ p, q ≤ +∞. They are spaces of holomorphic functions in the unit disc with average radial integrability. This family contains the classical Hardy spaces (when p = ∞) and Bergman spaces (when p = q). We characterize the inclusion between RM(p1, q1) and RM(p2, q2) depending on the parameters. For 1 < p, q < ∞, our main result provides a characterization of the dual spaces of RM(p, q) by means of the boundedness of the Bergman projection. We show that RM(p, q) is separable if and only if q < +∞. In fact, we provide a method to build isomorphic copies of ∞ in RM(p, ∞).
Extended eigenvalues of composition operators
(Elsevier, 2021-12-15) Lacruz Martín, Miguel Benito; León Saavedra, Fernando; Petrovic, Srdjan; Rodríguez Piazza, Luis; Universidad de Sevilla. Departamento de Análisis matemático; Universidad de Sevilla. FQM104: Analisis Matematico
A complex scalar λ is said to be an extended eigenvalue of a bounded linear operator A on a complex Hilbert space if there is a nonzero operator X such that AX=λXA. The results in this paper provide a full solution to the problem of computing the extended eigenvalues for those composition operators Cφ induced on the Hardy space H2(D) by linear fractional transformations φ of the unit disk.
Optimisation of Aiming Strategies in Solar Tower Power Plants
(AIP, 2018-11-08) Ashley, Thomas Ian; Carrizosa Priego, Emilio José; Fernández Cara, Enrique; Universidad de Sevilla. Departamento de Estadística e Investigación Operativa; Universidad de Sevilla. FQM329: Optimizacion
Inclement weather effects have a direct impact on the efficiency of a Solar Power Tower plant and have the potential to damage the receiver by flash heating. An optimised aiming strategy for the heliostat field mitigates the risk of receiver damage and maximises plant efficiency. A stochastic integer programming approach is applied to optimise the aiming strategy of the heliostat field, with uncertainty in the cloud location, size and density. The optimisation technique is demonstrated with a test case and results are presented for near real-time simulation of the optimal aiming strategy.
Sparsity in optimal randomized classification trees
(ELSEVIER SCIENCE BV, 2019-12-16) Blanquero Bravo, Rafael; Carrizosa Priego, Emilio José; Molero Río, Cristina; Romero Morales, María Dolores; Universidad de Sevilla. Departamento de Estadística e Investigación Operativa; Universidad de Sevilla. FQM329: Optimización
Decision trees are popular Classification and Regression tools and, when small-sized, easy to interpret. Traditionally, a greedy approach has been used to build the trees, yielding a very fast training process; however, controlling sparsity (a proxy for interpretability) is challenging. In recent studies, optimal decision trees, where all decisions are optimized simultaneously, have shown a better learning performance, especially when oblique cuts are implemented. In this paper, we propose a continuous optimization approach to build sparse optimal classification trees, based on oblique cuts, with the aim of using fewer predictor variables in the cuts as well as along the whole tree. Both types of sparsity, namely local and global, are modeled by means of regularizations with polyhedral norms. The computational experience reported supports the usefulness of our methodology. In all our data sets, local and global sparsity can be improved without harming classification accuracy. Unlike greedy approaches, our ability to easily trade in some of our classification accuracy for a gain in global sparsity is shown.
rs-Sparse principal component analysis: A mixed integer nonlinear programming approach with VNS
(PERGAMON-ELSEVIER SCIENCE LTD, 2013-05-03) Carrizosa Priego, Emilio José; Guerrero Lozano, Vanesa; Universidad de Sevilla. Departamento de Estadística e Investigación Operativa; Universidad de Sevilla. FQM329: Optimización
Principal component analysis is a popular data analysis dimensionality reduction technique, aiming to project with minimum error for a given dataset into a subspace of smaller number of dimensions. In order to improve interpretability, different variants of the method have been proposed in the literature, in which, besides error minimization, sparsity is sought. In this paper we formulate as a mixed integer nonlinear program the problem of finding a subspace with a sparse basis minimizing the sum of squares of distances between the points and their projections. Contrary to other attempts in the literature, with our model the user can fix the level of sparseness of the resulting basis vectors. Variable neighborhood search is proposed to solve the problem obtained this way. Our numerical experience on test sets shows that our procedure outperforms benchmark methods in the literature, both in terms of sparsity and errors.
Spotting Key Members in Networks: Clustering-Embedded Eigenvector Centrality
(IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC, 2020-11-03) Carrizosa Priego, Emilio José; Marín Pérez, Alfredo; Pelegrín García, Mercedes; Universidad de Sevilla. Departamento de Estadística e Investigación Operativa; Universidad de Sevilla. FQM329: Optimización
Identifying key members in a social network is critical to understand the underlying system behavior. Whereas there are several measures designed to discern the most central member, they fail to identify a central set of members and at the same time reveal the spheres of influence of the individuals in such central set. Here, we combine eigenvector centrality with clustering to design a mathematical programming formulation capable of detecting key members while preventing their spheres of influence from overlapping. Our computational experience reproduces these two features as different aspects of the same phenomenon. The optimal set of key members and their spheres of influence are identified in real-life networks and synthetic ones. For the former, community structures are consistent with existing knowledge about the instances. For the latter, network underlying organization is known a priori and it is perfectly uncovered. Experiments further reveal previously neglected nodes to be optimal key members. The size of the instances tested reach several hundreds of nodes and thousands of links.
Selection of time instants and intervals with Support Vector Regression for multivariate functional data
(PERGAMON-ELSEVIER SCIENCE LTD, 2020-07-19) Blanquero Bravo, Rafael; Carrizosa Priego, Emilio José; Jiménez Cordero, María Asunción; Martín Barragán, Belén; Universidad de Sevilla. Departamento de Estadística e Investigación Operativa; Universidad de Sevilla. FQM329: Optimización
When continuously monitoring processes over time, data is collected along a whole period, from which only certain time instants and certain time intervals may play a crucial role in the data analysis. We develop a method that addresses the problem of selecting a finite and small set of short intervals (or instants) able to capture the information needed to predict a response variable from multivariate functional data using Support Vector Regression (SVR). In addition to improving interpretability, storage requirements, and monitoring cost, feature selection can potentially reduce overfitting by mitigating data autocorrelation. We propose a continuous optimization algorithm to fit the SVR parameters and select intervals and instants. Our approach takes advantage of the functional nature of the data by formulating a new bilevel optimization problem that integrates selection of intervals and instants, tuning of some key SVR parameters and fitting the SVR. We illustrate the usefulness of our proposal in some benchmark data sets.
Threshold robustness in discrete facility location problems: a bi-objective approach
(Springer, 2015-04-24) Carrizosa Priego, Emilio José; Ushakov, Anton; Vasilyev, Igor; Universidad de Sevilla. Departamento de Estadística e Investigación Operativa; Universidad de Sevilla. FQM329: Optimización
The two best studied facility location problems are the p-median problem and the uncapacitated facility location problem (Daskin, Network and discrete location: models, algorithms, and applications. Wiley, New York, 1995; Mirchandani and Francis, Discrete location theory. Wiley, New York, 1990). Both seek the location of the facilities minimizing the total cost, assuming no uncertainty in costs exists, and thus all parameters are known. In most real-world location problems the demand is not certain, because it is a long-term planning decision, and thus, together with the minimization of costs, optimizing some robustness measure is sound. In this paper we address bi-objective versions of such location problems, in which the total cost, as well as the robustness associated with the demand, are optimized. A dominating set is constructed for these bi-objective nonlinear integer problems via the ε-constraint method. Computational results on test instances are presented, showing the feasibility of our approach to approximate the Pareto-optimal set.
Visualization of complex dynamic datasets by means of mathematical optimization
(PERGAMON-ELSEVIER SCIENCE LTD, 2019-07-01) Carrizosa Priego, Emilio José; Guerrero Lozano, Vanesa; Romero Morales, María Dolores; Universidad de Sevilla. Departamento de Estadística e Investigación Operativa; Universidad de Sevilla. FQM329: Optimización
In this paper we propose an optimization model and a solution approach to visualize datasets which are made up of individuals observed along different time periods. These individuals have attached a time-dependent magnitude and a dissimilarity measure, which may vary over time. Difference of convex optimization techniques, namely, the so-called Difference of Convex Algorithm, and nonconvex quadratic binary optimization techniques are used to heuristically solve the optimization model and develop this visualization framework. This way, the so-called Dynamic Visualization Map is obtained, in which the individuals are represented by geometric objects chosen from a catalogue. A Dynamic Visualization Map faithfully represents the dynamic magnitude by means of the areas of the objects, while it trades off three different goodness of fit criteria, namely the correct match of the dissimilarities between the individuals and the distances between the objects representing them, the spreading of such objects in the visual region, and the preservation of the mental map by ensuring smooth transitions along snapshots. Our procedure is successfully tested on dynamic geographic and linguistic datasets.
On support vector machines under a multiple-cost scenario
(Springer, 2018-07-31) Benítez Peña, Sandra; Blanquero Bravo, Rafael; Carrizosa Priego, Emilio José; Ramírez Cobo, Josefa; Universidad de Sevilla. Departamento de Estadística e Investigación Operativa; Universidad de Sevilla. FQM329: Optimización
Support vector machine (SVM) is a powerful tool in binary classification, known to attain excellent misclassification rates. On the other hand, many realworld classification problems, such as those found in medical diagnosis, churn or fraud prediction, involve misclassification costs which may be different in the different classes. However, it may be hard for the user to provide precise values for such misclassification costs, whereas it may be much easier to identify acceptable misclassification rates values. In this paper we propose a novel SVM model in which misclassification costs are considered by incorporating performance constraints in the problem formulation. Specifically, our aim is to seek the hyperplane with maximal margin yielding misclassification rates below given threshold values. Such maximal margin hyperplane is obtained by solving a quadratic convex problem with linear constraints and integer variables. The reported numerical experience shows that our model gives the user control on the misclassification rates in one class (possibly at the expense of an increase in misclassification rates for the other class) and is feasible in terms of running times.
The Markovian arrival process: A statistical model for daily precipitation amounts
(ELSEVIER SCIENCE BV, 2013-12-21) Ramírez Cobo, Josefa; Marzo Artigas, Xavier; Olivares Nadal, Alba Victoria; Alvarez Francoso, José; Carrizosa Priego, Emilio José; Pita López, María Fernanda; Universidad de Sevilla. Departamento de Estadística e Investigación Operativa; Universidad de Sevilla. FQM329: Optimización
The Markovian arrival process (MAP) is a stochastic process that allows for modeling dependent and non-exponentially distributed observations. Due to its versatility, it has been widely applied in different contexts, from reliability to teletraffic. In this work we show the suitability of the MAP for modeling daily precipitation data, which are often characterized by a non-negligible correlation structure. Specifically, a set of daily precipitation amounts series from the region of Andalusia (Spain) is shown to be correctly fitted with a two-state MAP.
On Building Online Visualization Maps for News Data Streams by Means of Mathematical Optimization
(Mary Ann Liebert, INC, 2018-06-01) Carrizosa Priego, Emilio José; Guerrero Lozano, Vanesa; Hardt, Daniel; Romero Morales, María Dolores; Universidad de Sevilla. Departamento de Estadística e Investigación Operativa; Universidad de Sevilla. FQM329: Optimización
In this article we develop a novel online framework to visualize news data over a time horizon. First, we perform a Natural Language Processing analysis, wherein the words are extracted, and their attributes, namely the importance and the relatedness, are calculated. Second, we present a Mathematical Optimization model for the visualization problem and a numerical optimization approach. The model represents the words using circles, the time-varying area of which displays the importance of the words in each time period. Word location in the visualization region is guided by three criteria, namely, the accurate representation of semantic relatedness, the spread of the words in the visualization region to improve the quality of the visualization, and the visual stability over the time horizon. Our approach is flexible, allowing the user to interact with the display, as well as incremental and scalable. We show results for three case studies using data from Danish news sources.
Variable selection in classification for multivariate functional data
(ELSEVIER SCIENCE INC, 2019-05-01) Blanquero Bravo, Rafael; Carrizosa Priego, Emilio José; Jiménez Cordero, María Asunción; Martín Barragán, Belén; Universidad de Sevilla. Departamento de Estadística e Investigación Operativa; Universidad de Sevilla. FQM329: Optimización
When classification methods are applied to high-dimensional data, selecting a subset of the predictors may lead to an improvement in the predictive ability of the estimated model, in addition to reducing the model complexity. In Functional Data Analysis (FDA), i.e., when data are functions, selecting a subset of predictors corresponds to selecting a subset of individual time instants in the time interval in which the functional data are measured. In this paper, we address the problem of selecting the most informative time instants in multivariate functional data, a case much less studied than its single-variate counterpart. Our proposal allows one to use in a very simple way high-order information of the data, e.g. monotonicity or convexity by means of the functional data derivatives. The aforementioned problem is addressed with tools of Global Optimization in continuous variables: the time instants are selected to maximize the correlation between the class label and the Support Vector Machine score used for classification. The effectiveness of the proposal is shown in univariate and multivariate datasets.
On Mathematical Optimization for the visualization of frequencies and adjacencies as rectangular maps
(ELSEVIER SCIENCE BV, 2018-02-18) Carrizosa Priego, Emilio José; Guerrero Lozano, Vanesa; Romero Morales, María Dolores; Universidad de Sevilla. Departamento de Estadística e Investigación Operativa; Universidad de Sevilla. FQM329: Optimización
In this paper, we address the problem of visualizing a frequency distribution and an adjacency relation attached to a set of individuals. We represent this information using a rectangular map, i.e., a subdivision of a rectangle into rectangular portions so that each portion is associated with one individual, their areas reflect the frequencies, and the adjacencies between portions represent the adjacencies between the individuals. Due to the impossibility of satisfying both area and adjacency requirements, our aim is to fit as well as possible the areas, while representing as many adjacent individuals as adjacent rectangular portions as possible and adding as few false adjacencies, i.e., adjacencies between rectangular portions corresponding to non-adjacent individuals, as possible. We formulate this visualization problem as a Mixed Integer Linear Programming (MILP) model. We propose a matheuristic that has this MILP model at its heart. Our experimental results demonstrate that our matheuristic provides rectangular maps with a good fit in both the frequency distribution and the adjacency relation.
Optimisation of aiming strategies in Solar Power Tower plants
(PERGAMON-ELSEVIER SCIENCE LTD, 2017-10-15) Ashley, Thomas Ian; Carrizosa Priego, Emilio José; Fernández Cara, Enrique; Universidad de Sevilla. Departamento de Estadística e Investigación Operativa; Universidad de Sevilla. FQM329: Optimización
The distribution of temperature on a Solar Power Tower (SPT) plant receiver directly affects the lifespan of the structure and energy generated by the plant. Temperature peaks and uneven distributions can be caused by the aiming strategy enforced on the heliostat field. A non-optimised aiming strategy can lead to suboptimal energy generation and, more importantly, to risk of permanent damage to receiver components from thermal overloading due to sharp flux gradients. In order to reduce damage to receivers and optimise the energy generation, an aiming strategy is developed which homogenises the flux distribution on a flat plate receiver in a SPT plant. Results of a near real-time optimised aiming strategy are presented, demonstrating applicability to SPT plants of any size and shape, whilst also considering inclement weather conditions.

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