Ponencias (Matemática Aplicada I)

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

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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.
On the vulnerability of some families of graphs
(Iniciativa Digital Politècnica, 2010) Moreno Casablanca, Rocío; Diánez Martínez, Ana Rosa; García Vázquez, Pedro; Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII); Ministerio de Educación y Ciencia (MEC). España; Junta de Andalucía
The toughness of a noncomplete graph G is defined as τ (G) = min{|S|/ω(G − S)}, where the minimum is taken over all cutsets S of vertices of G and ω(G − S) denotes the number of components of the resultant graph G − S by deletion of S. In this paper, we investigate the toughness of the corona of two connected graphs and obtain the exact value for the corona of two graphs belonging to some families as paths, cycles, wheels or complete graphs. We also get an upper and a lower bounds for the toughness of the cartesian product of the complete graph K2 with a predetermined graph G.
Image = Structure + Few Colors
(Springer, 2021) Batavia, Darshan; González Díaz, Rocío; Kropatsch, Walter G.; Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII)
Topology plays an important role in computer vision by capturing the structure of the objects. Nevertheless, its potential applications have not been sufficiently developed yet. In this paper, we combine the topological properties of an image with hierarchical approaches to build a topology preserving irregular image pyramid (TIIP). The TIIP algorithm uses combinatorial maps as data structure which implicitly capture the structure of the image in terms of the critical points. Thus, we can achieve a compact representation of an image, preserving the structure and topology of its critical points (maxima, the minima and the saddles). The parallel algorithmic complexity of building the pyramid is O(log d) where d is the diameter of the largest object.We achieve promising results for image reconstruction using only a few color values and the structure of the image, although preserving fine details including the texture of the image.
Persistent homology-based gait recognition robust to upper body variations
(IEEE Computer Society, 2016) Lamar León, Javier; Alonso Baryolo, Raúl; García Reyes, Edel; González Díaz, Rocío; Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII); Ministerio de Economía y Competitividad (MINECO). España
Gait recognition is nowadays an important biometric technique for video surveillance tasks, due to the advantage of using it at distance. However, when the upper body movements are unrelated to the natural dynamic of the gait, caused for example by carrying a bag or wearing a coat, the reported results show low accuracy. With the goal of solving this problem, we apply persistent homology to extract topological features from the lowest fourth part of the body silhouettes. To obtain the features, we modify our previous algorithm for gait recognition, to improve its efficacy and robustness to variations in the amount of simplices of the gait complex. We evaluate our approach using the CASIA-B dataset, obtaining a considerable accuracy improvement of 93:8%, achieving at the same time invariance to upper body movements unrelated with the dynamic of the gait.
Persistent Homology Computation Using Combinatorial Map Simplification
(Springer, 2019) Damiand, Guillaume; González Díaz, Rocío; Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII); Ministerio de Economía y Competitividad (MINECO). España
We propose an algorithm for persistence homology computation of orientable 2-dimensional (2D) manifolds with or without boundary (meshes) represented by 2D combinatorial maps. Having as an input a real function h on the vertices of the mesh, we first compute persistent homology of filtrations obtained by adding cells incident to each vertex of the mesh, The cells to add are controlled by both the function h and a parameter δ . The parameter δ is used to control the number of cells added to each level of the filtration. Bigger δ produces less levels in the filtration and consequently more cells in each level. We then simplify each level (cluster) by merging faces of the same cluster. Our experiments demonstrate that our method allows fast computation of persistent homology of big meshes and it is persistent-homology aware in the sense that persistent homology does not change in the simplification process when fixing δ .
Parallel Homology Computation of Meshes
(Springer, 2016) Damiand, Guillaume; González Díaz, Rocío; Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII); Ministerio de Economía y Competitividad (MINECO). España; Agence Nationale de la Recherche. France
In this paper, we propose a method to compute, in parallel, the homology groups of closed meshes (i.e., orientable 2D manifolds without boundary) represented by combinatorial maps. Our experiments illustrate the interest of our approach which is really fast on big meshes and which obtains good speed-up when increasing the number of threads.
One More Step Towards Well-Composedness of Cell Complexes over nD Pictures
(Springer, 2019) Boutry, Nicolas; González Díaz, Rocío; Jiménez Rodríguez, María José; Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII); Ministerio de Economía y Competitividad (MINECO). España
An nD pure regular cell complex K is weakly well-composed (wWC) if, for each vertex v of K, the set of n-cells incident to v is face-connected. In previous work we proved that if an nD picture I is digitally well composed (DWC) then the cubical complex Q(I) associated to I is wWC. If I is not DWC, we proposed a combinatorial algorithm to “locally repair” Q(I) obtaining an nD pure simplicial complex PS(I) homotopy equivalent to Q(I) which is always wWC. In this paper we give a combinatorial procedure to compute a simplicial complex PS(¯I) which decomposes the complement space of |PS(I)| and prove that PS(¯I) is also wWC. This paper means one more step on the way to our ultimate goal: to prove that the nD repaired complex is continuously well-composed (CWC), that is, the boundary of its continuous analog is an (n − 1)- manifold.
On the Space Between Critical Points
(Springer, 2019) Kropatsch, Walter G.; Moreno Casablanca, Rocío; Batavia, Darshan; González Díaz, Rocío; Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII)
The vertices of the neighborhood graph of a digital picture P can be interpolated to form a 2-manifold M with critical points (maxima, minima, saddles), slopes and plateaus being the ones recognized by local binary patterns (LBPs). Neighborhood graph produces a cell decomposition of M: each 0-cell is a vertex in the neighborhood graph, each 1-cell is an edge in the neighborhood graph and, if P is well-composed, each 2-cell is a slope region in M in the sense that every pair of s in the region can be connected by a monotonically increasing or decreasing path. In our previous research, we produced superpixel hierarchies (combinatorial graph pyramids) that are multiresolution segmentations of the given picture. Critical points of P are preserved along the pyramid. Each level of the pyramid produces a slope complex which is a cell decomposition of M preserving critical points of P and such that each 2-cell is a slope region. Slope complexes in different levels of the pyramid are always homeomorphic. Our aim in this research is to explore the configuration at the top level of the pyramid which consists of a slope complex with vertices being only the critical points of P. We also study the number of slope regions on the top.

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