Ponencias (Matemática Aplicada I)

URI permanente para esta colecciónhttps://hdl.handle.net/11441/10896

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Topological Data Analysis for Self-organization of Biological Tissues
(Springer, 2017) Jiménez Rodríguez, María José; Rucco, Matteo; Vicente Munuera, Pablo; Gómez Gálvez, Pedro; Escudero Cuadrado, Luis María; Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII); Ministerio de Economía y Competitividad (MINECO). España; Programa Ramón y Cajal; Fundación Asociación Española contra el cáncer; Universidad de Sevilla
In this paper we propose a method to topologically analyze segmented images of cells in a biological tissue. This is a mainly exper- imental paper in which we present initial results of applying persistent homology computation to characterize cell organization. For that aim, a graph is constructed to model the cell organization and a simplicial complex is derived from such a graph. Then a filter function is designed, on the simplicial complex, that reflects neighbouring relations on cells as well as their size. Finally, persistent homology and persistent entropy are computed and the results are analyzed.
Topological Analysis of Simple Segmentation Maps
(Springer, 2022) Jiménez Rodríguez, María José; Medrano Garfia, Belén; Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII); Ministerio de Ciencia e Innovación; Agencia Estatal de Investigación. España; Agencia Andaluza del Conocimiento
In this paper, we propose a geometry-aware topological anal- ysis of a segmentation of an image into regions which might correspond, for example, to a geographical map or to segmented cells in a micro- scopic image of a biological packed tissue. The regions must satisfy that the centroid of each one lies inside the region itself. We propose a novel simplicial complex modeling such data, for persistent homology compu- tation, that better respects the geometry of the regions than existing techniques. More specifically, our approach joins benefits from previous models by encoding both neighbouring relations between the regions, as well as spatial distribution of the set of centroids. In addition, we intro- duce geometric information regarding distances between centroids and boundaries delimiting each region.
On topological analysis of cells organization in biological images
(Springer, 2021-05-16) Jiménez Rodríguez, María José; Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII); Ministerio de Ciencia e Innovación
There are many problems inside the field of biomedical image analysis that can be dealt from a topological (and geometric) point of view. One of them refers to the way in which cells are self-organised inside a tissue, mainly motivated by the changes that may occur in such an organization in case of disease. This problem can be faced from differ ent perspectives in terms, first, of how to model the cells and their ‘con nections’ and second, how to computationally characterise their organi zation. We will discuss some topological approaches to this topic as well as future lines of research.
On the Computation of A∞-Maps
(Springer, 2007) Berciano, Ainhoa; Jiménez Rodríguez, María José; Real Jurado, Pedro; Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII)
Starting from a chain contraction (a special chain homotopy equivalence) connecting a differential graded algebra A with a differen tial graded module M, the so-called homological perturbation technique “tensor trick” [8] provides a family of maps, {mi}i≥1, describing an A∞- algebra structure on M derived from the one of algebra on A. In this paper, taking advantage of some annihilation properties of the compo nent morphisms of the chain contraction, we obtain a simplified version of the existing formulas of the mentioned A∞-maps, reducing the com putational cost of computing mn from O(n! 2) to O(n!).
Finding Multiple Solutions in Nonlinear Integer Programming with Algebraic Test-Sets
(Springer, 2018-08-23) Hartillo Hermoso, Isabel; Jiménez Cobano, José Manuel; Ucha Enríquez, José María; Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII)
We explain how to compute all the solutions of a nonlinear integer problem using the algebraic test-sets associated to a suitable linear subproblem. These test-sets are obtained using Gr¨obner bases. The main advantage of this method, compared to other available alternatives, is its exactness within a quite good efficiency.
Numerical Simulation of an Induction-Conduction Model Arising in Steel Hardening
(Int Assoc. Engineers-Iaeng NT, 2009) Díaz Moreno, J.M.; García Vazquez, C.; González Montesinos, María Teresa; Ortegón Gallego, F.; Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII)
We study a mathematical model for the description of the heating-cooling industrial process of a steel workpiece. The complete thermomechanical model is governed by a nonlinear coupled partial differential system of equations involving the electric potential, the magnetic vector potential, the temperature, the stress tensor and the displacement field together with a system of ordinary differential equations for the steel phase fractions. In this situation, the electric conductivity on the workpiece depends strongly on the temperature b = b(x, theta), theta being the temperature. Usually one has b(x, s) -> 0 when s -> infinity uniformly on the workpiece, leading to degenerate parabolic/elliptic equations. Our analysis considers the case 0 < C-1/(1 + vertical bar s vertical bar) b(x, s) C-2, C-1 and C-2 being constant values. Also we have performed some 2D numerical simulations of the heating-cooling process in a simplified version of the model.
Numerical Simulation of Potential Maxwell's Equations in the Harmonic Regime
(Springer Nature, 2015) González Montesinos, María Teresa; Ortegón Gallego, Francisco; Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII)
The aim of this work is to perform some numerical experiments for the resolution of a strongly coupled parabolic–elliptic system that describes the heating induction–conduction industrial process of a steel workpiece, whose unknowns are the electric potential, the magnetic vector potential, and the temperature. In order to make the numerical simulations lighter, and taking into account the different time scales between the potentials and the temperature, a new system of nonlinear partial differential equations (PDEs) has been constructed that describes the heating process in the harmonic regime.
Desarrollo de una práctica de eficiencia energética en Arquitectura mediante simulación numérica
(REDINE, Red de Investigación e Innovación Educativa, 2021) Domínguez Torres, Carlos Antonio; Domínguez Delgado, Antonio; Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII); Universidad de Sevilla. Departamento de Estructuras de Edificación e Ingeniería del Terreno
En este trabajo se presenta el desarrollo de una práctica de eficiencia energética en Arquitectura efectuada mediante técnicas de simulación numérica. El objetivo de la práctica es doble: por un lado concienciar al alumnado de la necesidad de implementar medidas de eficiencia energética conducentes a reducir el consumo energético necesario para conseguir condiciones de habilitad adecuadas en las viviendas y por otro lado, introducir al alumnado en el manejo de técnicas de simulación numérica cada día más usadas en el ámbito técnico, y específicamente en Arquitectura, tanto en la fase de diseño previo de un proyecto arquitectónico nuevo como de la implementación de medidas de rehabilitación sobre viviendas ya construidas, con el objetivo de reducir el consumo energético de los edificios y por ende, contribuir a la reducción de la pobreza energética y del impacto ambiental y climático del consumo de energía en el parque de viviendas.
El tamaño de un grafo con cintura inferiormente acotada
(Servicio de Publicaciones de la Universidad de Cádiz, 2007) Abajo Casado, María Encarnación; Diánez Martínez, Ana Rosa; Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII)
Automorphisms, derivations and gradings of the split quartic Cayley algebra
(Springer, 2023) Blasco Jiménez, Víctor; Daza García, Alberto; Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII); Agencia Estatal de Investigación. España; European Commission (EC). Fondo Europeo de Desarrollo Regional (FEDER)
The split quartic Cayley algebra is a structurable algebra which has been used to give constructions of Lie algebras of type D4. Here, we calculate it’s group of automorphisms, it’s algebra of derivations and it’s gradings.
Measuring the error of linear separators on linearly inseparable data
(Prensas Universitarias de Zaragoza, 2009-06) Aronov, Boris; Garijo Royo, Delia; Núñez Rodríguez, Yurai; Rappaport, David; Seara Ojea, Carlos; Urrutia, Jorge; Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII); Ministerio de Educación y Ciencia (MEC). España; Junta de Andalucía
Given linearly inseparable sets R of red points and B of blue points, we consider several measures of how far they are from being separable. Intuitively, given a potential separator ("classifier"), we measure its quality ("error") according to how much work it would take to move the misclassified points across the classifier to yield separated sets. We consider several measures of work and provide algorithms to find linear classifiers that minimize the error under these diferent measures.
Breaking symmetries of graphs with resolving sets
(2014) Garijo Royo, Delia; González Herrera, Antonio; Márquez Pérez, Alberto; Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII); Junta de Andalucía; Ministerio de Ciencia, Innovación y Universidades (MICINN). España
We undertake a study on the maximum value of the difference between the metric dimension and the determining number of a graph as a function of its order. Our results include lower and upper bounds on that maximum, and exact computations when restricting to some specific families of graphs. Although our technique is mainly based on locating-dominating sets, it also requires very diverse tools and relationships with well-known objects in graph theory; among them: a classical result in graph domination by Ore, a Ramsey-type result by ErdHos and Szekeres, a polynomial time algorithm to compute distinguishing sets and dominating sets of twin-free graphs, k-dominating sets, and matchings.
Shortcut sets for Euclidean graphs
(2015-07) Cáceres, José; Garijo Royo, Delia; González Herrera, Antonio; Márquez Pérez, Alberto; Puertas, María Luz; Universidad de Sevilla. Departamento de Matemática Aplicada I; Universidad de Sevilla. Departamento de Didáctica de las Matemáticas
A Euclidean graph G is the locus of a rectilinear embedding of a planar graph in the Euclidean plane. A shortcut set S is a collection of segments with end points on G such that the Euclidean graph obtained from G byadding the segments in S has smaller diameter than G. The minimum cardinality of a shortcut set is the shortcut number scn(G). In this work, we first provide a tight upper bound on scn(G). We then show that it is possible, in polynomial time, to determine if scn(G) = 1 and, in that case, to construct a shortcut set that minimizes the diameter among all possible shortcut sets. Finally, we compute the shortcut number in some families of Euclidean graphs.
Weighted graph homomorphisms and the Tutte polynomial
(Universidad de Cádiz, 2007) Garijo Royo, Delia; Nesetril, Jaroslav; Revuelta Marchena, María Pastora; Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII)
This work studies the connection between weighted graph parameters re lated to homomorphisms and the Tutte polynomial. In terms of statistical physics, we prove that there exists a strong relationship between some partition functions of vertex models and the Tutte polynomial.
The metric-aware kernel-width choice for LIME
(CEUR-WS, 2023) Barrera Vicent, Aurelio; Paluzo Hidalgo, Eduardo; Gutiérrez Naranjo, Miguel Ángel; Universidad de Sevilla. Departamento de Ciencias de la Computación e Inteligencia Artificial
Local Interpretable Model-Agnostic Explanations (LIME) are a well-known approach to provide local interpretability to Machine Learning models. LIME uses an exponential smoothing kernel based on the kernel width value, which defines the width of the local neighbourhood. In this paper, we study the influence of the distances for these local explanations, and we explore the choice of kernel width to guarantee a fair performance comparison between the distances.
Algorithm for planning faster routes in urban networks with time-dependant arcs and the possibility of introducing waiting periods at nodes
(WIT Press, 2022) Ortega Riejos, Francisco Alonso; Marseglia, Guido; Mesa López-Colmenar, Juan Antonio; Piedra de la Cuadra, Ramón; Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII); Universidad de Sevilla. Departamento de Matemática Aplicada II (ETSI); Passerini, Giorgio; Ricci, Stefano; Ministerio de Ciencia e Innovación (MICIN). España; European Commission (EC). Fondo Europeo de Desarrollo Regional (FEDER); Universidad de Sevilla. FQM241: Grupo de Investigación en Localización
Navigation systems implemented in mobile devices allow users to search for the shortest routes between pairs of points. Many of the existing commercial products assume in a simplified way that the travel time to cross each arc of a road network is fixed, once a starting time has been established. However, the real travel time along a road section within cities depends on many factors that are related to traffic congestion, weather conditions, possible incidents, etc., and consequently, it depends on the time. As can easily be shown, determining the shortest itineraries in a network whose arcs are time-dependent can result in a diversity of optimal routes for a same origin–destination pair based on different departure times. Assuming the availability of the estimated data of the time required to travel along each section of the street network, once the departure time has been previously set, we propose in this work an efficient algorithm for obtaining faster routes on time-dependent arcs, in such a way that the sum of driving times is minimized, which in parallel allows improving fuel consumption and reducing associated polluting emissions. The possibility of introducing waiting periods in the nodes to optimize the total time spent on the trip has also been considered in the design of the proposed procedure. An experimental evaluation is carried out to show the effectiveness of the provided algorithm.
A Step Towards Learning Contraction Kernels for Irregular Image Pyramid
(SciTePress, 2022-02) Batavia, Darshan; González Díaz, María del Rocío; Kropatsch, Walter G.; Universidad de Sevilla. Departamento de Matemática Aplicada I
A structure preserving irregular image pyramid can be computed by applying basic graph operations (contraction and removal of edges) on the 4 adjacent neighbourhood graph of an image. In this paper, we derive an objective function that classifies the edges as contractible or removable for building an irregular graph pyramid. The objective function is based on the cost of the edges in the contraction kernel (sub-graph selected for contraction) together with the size of the contraction kernel. Based on the objective function, we also provide an algorithm that decomposes a 2D image into monotonically connected regions of the image surface, called slope regions. We proved that the proposed algorithm results in a graph-based irregular image pyramid that preserves the structure and the topology of the critical points (the local maxima, the local minima, and the saddles). Later we introduce the concept of the dictionary for the connected components of the contraction kernel, consisting of sub-graphs that can be combined together to form a set of contraction kernels. A favorable contraction kernel can be selected that best satisfies the objective function. Lastly, we show the experimental verification for the claims related to the objective function and the cost of the contraction kernel. The outcome of this paper can be envisioned as a step towards learning the contraction kernel for the construction of an irregular image pyramid
Energy and economic efficiency analysis of the use of cold roofs for social housing retrofitting in Southern Spain
(2021) Domínguez Torres, Carlos Antonio; Domínguez Delgado, Antonio; Domínguez Torres, Helena; Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII); Universidad de Sevilla. Departamento de Análisis Económico y Economía Política; Mercader-Moyano, Pilar; Pellicer, Homero; Universidad de Sevilla. HUM965: Transhumancias : Hábitat, Salud, Patrimonio, Tecnología y Arte
Energy retrofitting of the housing stock is needed in order to reduce the consumption of the energy used to achieve comfort conditions and, this way, meet the objectives aimed at reducing the impact of energy consumption on climate change. In particular, the social housing stock built in Spain in the middle of the last century have poor conditions in terms of energy efficiency and its obsolete energy conditions make some type of retrofitting necessary in order to avoid indoor thermal discomfort and energy poverty situations. This study focuses on perform an energy and economic analysis, throughout the life cycle, of the use of cool roofs to retrofit the roofs of buildings belonging to the social park. The analysis is carried out on three cities, Seville, Malaga and Jaen, in the region of Andalusia, Southern Spain, representative of a wide range of the climatic conditions of this region. The findings of this work show noticeable energy and economic costs savings, which endorse the efficiency of the use of cold roofs to retrofit the roofs customary in social housing built in the central decades of the last century under the analyzed climatic framework.
On the Topological Disparity Characterization of Square-Pixel Binary Image Data by a Labeled Bipartite Graph
(Springer, 2022) Sánchez Cuevas, Pablo; Real Jurado, Pedro; Díaz del Río, Fernando; Molina Abril, Helena; Morón Fernández, María José; Universidad de Sevilla. Departamento de Arquitectura y Tecnología de Computadores; Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII); Ministerio de Economia, Industria y Competitividad (MINECO). España; Junta de Andalucía; Universidad de Sevilla. TEP108 : Robotica y Tecnología de Computadores; Universidad de Sevilla. TIC245: Topological Pattern Analysis, Recognition and Learning
Given an nD digital image I based on cubical n-xel, to fully characterize the degree of internal topological dissimilarity existing in I when using different adjacency relations (mainly, comparing 2n or 2n −1 adjacency relations) is a relevant issue in current problems of digital image processing relative to shape detection or identification. In this paper, we design and implement a new self-dual representation for a binary 2D image I, called {4, 8}-region adjacency forest of I ({4, 8}-RAF, for short), that allows a thorough analysis of the differences between the topology of the 4-regions and that of the 8-regions of I. This model can be straightforwardly obtained from the classical region adjacency tree of I and its binary complement image Ic, by a suitable region label identification. With these two labeled rooted trees, it is possible: (a) to compute Euler number of the set of foreground (resp. background) pixels with regard to 4-adjacency or 8-adjacency; (b) to identify new local and global measures and descriptors of topological dissimilarity not only for one image but also between two or more images. The parallelization of the algorithms to extract and manipulate these structures is complete, thus producing efficient and unsophisticated codes with a theoretical computing time near the logarithm of the width plus the height of an image. Some toy examples serve to explain the representation and some experiments with gray real images shows the influence of the topological dissimilarity when detecting feature regions, like those returned by the MSER (maximally stable extremal regions) method.
Building Hierarchical Tree Representations Using Homological-Based Tools
(Springer, 2021) Díaz del Río, Fernando; Sánchez Cuevas, Pablo; Molina Abril, Helena; Real Jurado, Pedro; Morón Fernández, María José; Universidad de Sevilla. Departamento de Arquitectura y Tecnología de Computadores; Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII); Ministerio de Ciencia e Innovación (MICIN). España; Universidad de Sevilla. TEP108 : Robotica y Tecnología de Computadores; Universidad de Sevilla. TIC245: Topological Pattern Analysis, Recognition and Learning
A new algorithm for computing the α-tree hierarchical repre sentation of a grey-scale digital image is presented here. The technique is based on an efficient simplified version of the Homological Spanning For est (HSF) for encoding homological and homotopy-based information of binary digital images. We create one Adjacency Tree (AdjT) for each intensity contrast in a fully parallel manner. These trees, which define a Contrast Adjacency Forest (CAdjF), are in turn transversely intercon nected by another couple of trees: the classical α-tree, and a new one complementing it, called here the α∗-tree. They convey the information of the contours and the flat regions of the original color image, plus the relations between them. Using both the α and α∗-trees, this new topolog ical representation prevents some classical drawbacks that appear when working with a single tree. An implementation in OCTAVE/MATLAB validates the correctness of our algorithm.

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