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Orientador: Hélio Pedrini Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Computação Resumo: Malhas triangulares são representações de dados espaciais comumente utilizadas na manipulação e visualização de superfícies complexas. Este trabalho apresenta e avalia uma proposta de representação out-of-core estática de malhas de triângulos tridimensionais, a qual permite a consulta de vértices e triângulos adjacentes em tempo constante e o acesso aleatório aos vértices e triângulos da malha, requerendo pouco espaço em memória principal. A característica out-of-core da representação consiste no fato de que apenas as informações necessárias para a aplicação são carregadas em memória primária, ficando o restante armazenado em memória secundária. A representação é estática no sentido de que, ao ocorrer qualquer alteração topológica, ela deverá ser reconstruída novamente. Experimentos são realizados em vários modelos de malhas de triângulos para demonstrar a eficácia da metodologia proposta Abstract: Triangular meshes are spatial data representations commonly used in the manipulation and visualization of complex surfaces. This work proposes and evaluates a static out-of-core representation of three-dimensional triangle meshes, which allows the query of adjacent vertices and triangles in constant time and the random access to the vertices and triangles of the mesh, requiring little space in main memory. The out-of-core feature of the representation consists in the fact that only the necessary information for the application is loaded into primary memory, such that the remainder is stored in secondary memory. The representation is static in the sense that when any topological change occurs, it must be rebuilt again. Experiments are conducted on several triangle mesh models to demonstrate the efficacy of the proposed methodology Mestrado Ciência da Computação Mestre em Ciência da Computação

Huemer et al. (Discrete Mathematics, 2019) proved that for any two point sets R and B with $$|R|=|B|$$ | R | = | B | , the perfect matching that matches points of R with points of B, and maximizes the total squared Euclidean distance of the matched pairs, has the property that all the disks induced by the matching have a common point. Each pair of matched points $$p\in R$$ p ∈ R and $$q\in B$$ q ∈ B induces the disk of smallest diameter that covers p and q. Following this research line, in this paper we consider the perfect matching that maximizes the total Euclidean distance. First, we prove that this new matching for R and B does not always ensure the common intersection property of the disks. Second, we extend the study of this new matching for sets of 2n uncolored points in the plane, where a matching is just a partition of the points into n pairs. As the main result, we prove that in this case all disks of the matching do have a common point.

This abstract reports first the study of upper and lower bounds for the maximum number of all the combinatorially different (a, k)-sets of an n-point set P in the plane, 0 < a = p and 0 < 2k < n, depending on the (fixed/variable) values of a and k, relating them with the known bounds for the maximum number of k-sets: the O(nv3k) upper bound from Dey [5] and the ne¿(vlogk) lower bound from T´oth [7]; and showing also efficient algorithms for generating all of them. Second we study the depth of a point p ¿ P according to the (a, k)-set criterion (instead of the k-set criterion). We compute the depths of all the points of P for a given angle a, and also esign a data structuredfor reporting the angle-interval(s) of a given depth for a point of P in O(log n) time (if it exists). Finally, we define the (a, k)-hull of P for fixed values of a and k, and design an algorithm for computing the (a, k)-hull of P for given values of a and k. To do that, we follow the relevant ideas and techniques from Cole et al. [4]. Unfortunately, the algorithm is still no so efficient as we wish, and we believe that their complexities strong depends on the fixed values for the parameters a and k; more concretely, as a is closer to p the time complexity is close to the optimal.

Optimal viewpoint prediction is an essential task in many computer graphics applications. Unfortunately, common viewpointqualities suffer from two major drawbacks: dependency on clean surface meshes, which are not always available, and the lack ofclosed-form expressions, which requires a costly search involving rendering. To overcome these limitations we propose to sepa-rate viewpoint selection from rendering through an end-to-end learning approach, whereby we reduce the in¿uence of the meshquality by predicting viewpoints from unstructured point clouds instead of polygonal meshes. While this makes our approachinsensitive to the mesh discretization during evaluation, it only becomes possible when resolving label ambiguities that arise inthis context. Therefore, we additionally propose to incorporate the label generation into the training procedure, making the labeldecision adaptive to the current network predictions. We show how our proposed approach allows for learning viewpoint pre-dictions for models from different object categories and for different viewpoint qualities. Additionally, we show that predictiontimes are reduced from several minutes to a fraction of a second, as compared to state-of-the-art (SOTA) viewpoint quality eval-uation. Code and training data is available at https://github.com/schellmi42/viewpoint_learning, whichis to our knowledge the biggest viewpoint quality dataset available. This work was supported in part by project TIN2017-88515-C2-1-R(GEN3DLIVE), from the Spanish Ministerio de Economía yCompetitividad, by 839 FEDER (EU) funds.

Orientador: Alberto Luiz Serpa Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecânica Resumo: Neste trabalho, é formulado um método de otimização adaptativa usando as RNA (Redes Neurais Artificiais) como modelos de aproximação da função objetivo do problema de otimização. Neste caso, o domínio dos modelos é limitado de acordo com o conjunto de dados usados no treinamento das RNA. Esta limitação permite determinar a região factível do problema de otimização levando em conta o domínio do modelo, evitando desta forma que o ponto ótimo determinado seja um ponto de extrapolação por parte das RNA usadas. O método proposto permite adaptar tanto os modelos como o domínio dos modelos às novas condições operacionais que se apresentam ao sistema que se deseja otimizar. Este tipo de adaptação pode levar a obter um maior benefício do processo de otimização, conforme é mostrado nos exemplos de implementação do método apresentados nesta tese. Neste caso, são usados o algoritmo Quickhull para limitar o domínio dos modelos de RNA e o algoritmo de ângulo incremental para implementar a adaptação dos modelos e dos domínios dos modelos. Para aplicar as restrições do problema de otimização sobre o domínio dos modelos, neste trabalho, foi projetado e programado o algoritmo de intersecção. Nos resultados deste trabalho é apresentado um estudo de caso, de otimização adaptativa de um sistema de produção de petróleo e gás equipado com uma Bomba Centrífuga Submersa (BCS). Como parte desta implementação, foram desenvolvidos experimentos em uma bancada de testes de BCS trabalhando com escoamento petróleo-nitrogênio, onde foi coletado um conjunto de dados usado para o treinamento dos modelos de RNA. Nestes resultados, é mostrado que a adaptabilidade dos modelos e do domínio dos modelos pode levar ao aumento do lucro resultante da venda do petróleo e do gás produzido. Nestes resultados também é mostrado que cada um dos pontos ótimos determinados são pontos de interpolação dos modelos de RNA usados Abstract: In this work, an adaptive optimization method is formulated using the ANN (Artificial Neural Networks) to approximate the objective function of the optimization problem. In this case, the ANN model domain is limited according to the set of data used in the supervised training. This limitation allows determining the feasible region of the optimization problem, taking into account the model domain, preventing situations where the optimal point is an extrapolation of the used ANN. The proposed method allows adapting both the models and the model domain to the new operating conditions that may arise in the system that is being optimized. This type of adaptation can lead to a more significant benefit from the optimization process, as shown in the examples of method implementation presented in this thesis. In this work, the Quickhull algorithm is used to limit the model domain, and the incremental angle algorithm is used to implement the adaptations of either model and model domain. Also, the intersection algorithm was designed and programmed to apply the optimization problem constraints over the model domain. In the results of this work, a case study is presented, i.e., the adaptive optimization of an oil and gas production system equipped with an Electric Submersible Pump (ESP). As part of this implementation, experiments were carried out on a BCS test bench working with the oil-nitrogen flow, where the collected data was used to training the ANN models. These results show that the adaptability of the model and the model domain can lead to an increase in profit resulting from the sale of oil and gas produced. In these results, it is also shown that the optimal points are interpolation points of the used ANN Doutorado Mecânica de Sólidos e Projeto Mecânico Doutor em Engenharia Mecânica CNPQ 142261/2016-5

We present an edge labeling of order-$k$ Voronoi diagrams, $V_k(S)$, of point sets $S$ in the plane, and study properties of the regions defined by them. Among them, we show that $V_k(S)$ has a small orientable cycle and path double cover, and we identify configurations that cannot appear in $V_k(S)$ for small values of $k$. This paper also contains a systematic study of well-known and new properties of $V_k(S)$, all whose proofs only rely on elementary geometric arguments in the plane. The maybe most comprehensive study of structural properties of $V_k(S)$ was done by D.T. Lee (On k-nearest neighbor Voronoi diagrams in the plane) in 1982. Our work reviews and extends the list of properties of higher order Voronoi diagrams.

"Vegeu el resum a l'inici del document del fitxer adjunt".

In his pioneering research, G. K. Zipf formulated a couple of statistical laws on the relationship between the frequency of a word with its number of meanings: the law of meaning distribution, relating the frequency of a word and its frequency rank, and the meaning-frequency law, relating the frequency of a word with its number of meanings. Although these laws were formulated more than half a century ago, they have been only investigated in a few languages. Here we present the first study of these laws in Catalan. We verify these laws in Catalan via the relationship among their exponents and that of the rank-frequency law. We present a new protocol for the analysis of these Zipfian laws that can be extended to other languages. We report the first evidence of two marked regimes for these laws in written language and speech, paralleling the two regimes in Zipf's rank-frequency law in large multi-author corpora discovered in early 2000s. Finally, the implications of these two regimes will be discussed., Comment: 21 pages, 11 figures

We define a two-dimensional statistical depth function and study two important aspects of it: its robustness and computability. We begin by formally proving that the function is, indeed, a statistical depth function. To achieve this, we introduce a new notion of symmetry for distributions in Rp . We study the robustness through the concept of breakdown point. In terms of computability, we provide an implementable algorithm to calculate the depth contours with temporal complexity Θ(n²) and spatial complexity Θ(n), where n is the size of the data set. As an application of the proposed depth function, we provide a hypothesis test for the independence of two absolutely continuous variables RESUMEN: Definimos una función de profundidad estadística bi-dimensional y estudiamos dos aspectos importantes de la misma: la robustez y la computabilidad. Comenzamos probando formalmente que la función es, de hecho, una función de profundidad estadística. Para conseguirlo, introducimos una nueva noción de simetría para distribuciones en Rp . Estudiamos la robustez a través del concepto de breakdown point. En cuanto a la computabilidad, proporcionamos un algoritmo implementable para calcular los contornos de profundidad con complejidad temporal Θ(n²) y complejidad espacial Θ(n), siendo n el tamaño del conjunto de datos. Como aplicación de la función de profundidad propuesta, proporcionamos un contraste de hipótesis para la independencia de dos variables absolutamente continuas. Grado en Matemáticas

Computational modeling of porous and lattice materials is a topic that attracts the attention of ongoing research efforts. Industries such as product design, additive manufacturing, biomedicine, automotive and aerospace are environments in which porous and lattice materials are of special interest given their properties. Computer Aided Design (CAD) three-dimensional (3D) Models are nowadays ubiquitous in many engineering contexts: in the automotive industry, for instance, more than 30.000 different parts are needed for complete vehicle, and most of them have a 3D CAD representation. In this sense, the ability to inspect the topology and the geometry of a standard 3D CAD representation model (such as STEP) is of high importance. More particularly, feature recognition is a task where this model inspection is relevant for engineers and designers, since they can easily find features of interest that are related with specific tasks: optimization, planning of additional manufacturing processes, detection of design errors, etc. Gerotor pumps play an important role in the aerospace industry, specially in the processes of cooling, lubrication and fuel boost and transfer. The design process of gerotor pumps usually involves: i) a geometric modeling stage in a CAD environment, ii) a design verification stage using fluid mechanics simulations to validate the efficiency and other desired characteristics of the pump, and iii) a physical testing stage to verify the predicted characteristics of the pump in a real test bank once the design has been validated through a simulation tool. Digital Twins would allow a faster workflow for the design and testing of gerotor pumps. This work presents a compilation of different contributions to the problems stated in this introduction.

This is a work dedicated to the development of a software for creating 3D models of houses with modern design. The main goal is to generate a tool that makes use of procedural modeling techniques to generate a wide variety of models. The result is an application capable of generating realistic model renderings with an input consisting of a set of rules. The most important part of this project will be the development of grammar and of all each operation will start to be simple and basic in the form of 3D. Combinations of operations such as extrusions, subdivisions or prefabrications will then be done to increase the complexity of the whole model that makes it look like a modern house. Thispart was carried out with some tests based on a correct performance of the same algorithm, as this is the core of the whole application. Aquest és un treball dedicat al desenvolupament d'un software de creació de models 3D de cases amb disseny modern. L'objectiu principal és generar una eina que faci ús de tècniques de modelat procedural per generar una gran varietat de models. El resultat és una aplicació capaç de generar renders de models realistes amb una entrada que consisteix en un conjunt de regles. La part més important d’aquest projecte consistirà en el desenvolupament de la gramàtica i cada operació començarà a ser senzilla i bàsica en forma de 3D. A continuació, es faran combinacions d’operacions com extrusions, subdivisions o prefabricacions augmenta la complexitat de tot el model que fa que sembli una casa actual. Aquesta part es va dur a terme amb algunes proves basades en un correcte rendiment del mateix algorisme, ja que aquest és el nucli de tota l'aplicació. Este es un trabajo dedicado al desarrollo de un software de creación de modelos 3D de casas con diseño moderno. El objetivo principal es generar una herramienta que haga uso de técnicas de modelado procedural para generar una gran variedad de modelos. El resultado es una aplicación capaz de generar renders de modelos realistas con una entrada que consiste en un conjunto de reglas. La parte más importante de este proyecto consistirá en el desarrollo de la gramática y cada operación empezará a ser sencilla y básica en forma de 3D. A continuación, se harán combinaciones de operaciones como extrusiones, subdivisiones o prefabricaciones aumenta la complejidad de todo el modelo que hace que parezca una casa actual. Esta parte se llevó a cabo con algunas pruebas basadas en un correcto rendimiento del mismo algoritmo, puesto que este es el núcleo de toda la aplicación.

Unfitted (also known as embedded or immersed) finite element approximations of partial differential equations are very attractive because they have much lower geometrical requirements than standard body-fitted formulations. These schemes do not require body-fitted unstructured mesh generation. In turn, the numerical integration becomes more involved, because one has to compute integrals on portions of cells (only the interior part). In practice, these methods are restricted to level-set (implicit) geometrical representations, which drastically limit their application. Complex geometries in industrial and scientific problems are usually determined by (explicit) boundary representations. In this work, we propose an automatic computational framework for the discretisation of partial differential equations on domains defined by oriented boundary meshes. The geometrical kernel that connects functional and geometry representations generates a two-level integration mesh and a refinement of the boundary mesh that enables the straightforward numerical integration of all the terms in unfitted finite elements. The proposed framework has been applied with success on all analysis-suitable oriented boundary meshes (almost 5,000) in the Thingi10K database and combined with an unfitted finite element formulation to discretise partial differential equations on the corresponding domains. This research was partially funded by the Australian Government through the Australian Research Council (project number DP210103092), the European Commission under the FET-HPC ExaQUte project (Grant agreement ID: 800898) within the Horizon 2020 Framework Programme and the project RTI2018- 096898-B-I00 from the “FEDER/Ministerio de Ciencia e Innovación – Agencia Estatal de Investigación”. F. Verdugo acknowledges support from the Spanish Ministry of Economy and Competitiveness through the “Severo Ochoa Programme for Centers of Excellence in R&D (CEX2018-000797-S)". P.A. Martorell aknowledges the support recieved from Universitat Politècnica de Catalunya and Santander Bank through an FPI fellowship (FPI-UPC 2019). This work was also supported by computational resources provided by the Australian Government through NCI under the National Computational Merit Allocation Scheme.

[Resumen] El presente documento describe un algoritmo de generación de trayectorias para un robot móvil encargado de sanear chapas de acero. Las trayectorias generadas deben asegurar la cobertura total de las superficies poligonales que delimitan los defectos con la herramienta acoplada al robot. Además, el robot deberá resolver la tarea sin abandonar el interior de la chapa. Para resolver el problema, la chapa se divide en distintas zonas de trabajo derivadas de las orientaciones seguras que permiten al robot reparar sin abandonar la superficie de la chapa. Los defectos se recibirán en forma de polígonos que serán, en primer lugar, divididos de acuerdo con las zonas de trabajo y, a continuación, descompuestos en formas más simples teniendo en cuenta la orientación de trabajo de cada zona. El recorrido completo del defecto podrá realizarse calculando trayectorias paralelas para cada uno de los polígonos simples que lo componen. La trayectoria así calculada corresponde a la seguida por la herramienta, por lo que para calcular la trayectoria del robot bastará con aplicar una traslación. [Abstract] This paper describes a path planning algorithm to allow a mobile robot to repair surface defects of a steel sheet. The resulting trajectories ensure that the polygonal surface that encloses the defect is completely covered by the repairing tool carried by the robot. In addition, the robot should work within the surface of the metal sheet. Defects will be described as polygonal shapes. First, they will be divided according to diffierent working áreas. Then, each resulting shape will be divided again into simpler triangular and trapezoidal shapes. To guarantee that the defect is completely covered, the tool trajectory is defined as a set of rectinilear paths parallel to the axis of the sheet is generated. This trajectory is then shifted to obtain the robot trajectory.

Agência 1 A retroatividade em programação é um conceito que pode ser definido como o estudo da modificação da linha temporal em uma estrutura de dados, bem como a análise dos efeitos dessa modificação através de toda a sua existência. Em geral, essa análise e implementação tendem a serem mais custosas do ponto de vista computacional, observando-se que uma modificação no passado pode gerar um efeito cascata por toda a existência dessa estrutura. O conceito de retroatividade gera ferramentas e estruturas que otimizam as soluções para a natureza desses problemas temporais. Esse tipo de estrutura pode ser utilizada nas aplicações das mais diversas naturezas, desde em algoritmos de caminho mínimo, aplicações em segurança e até em aplicações geométricas. Nessa dissertação, tem-se os subsídios teóricos sobre essas estruturas, um material detalhado sobre a implementação das estruturas mais comuns utilizando o paradigma da retroatividade, e a implementação de alguns problemas que podem ser resolvidos utilizando técnicas de retroatividade, como, por exemplo, o algoritmo de árvore geradora mínima totalmente dinâmica. Para cada estrutura, foram executados testes práticos sobre as estruturas retroativas e seu desempenho foi comparado às outras implementações dessas mesmas estruturas. Os testes mostraram que as implementações retroativas propostas por Demaine et. al (2007) obtiveram os melhores resultados do ponto de vista temporal. Além disso, foram propostos dois algoritmos que utilizam os conceitos de retroatividade para sua construção: o algoritmo para o problema da árvore geradora mínima totalmente retroativa e o algoritmo do caminho mínimo a partir de um vértice inicial fixo em grafos dinâmicos. Seja m o tamanho da linha temporal em que a estrutura está implementada, V(G) e A(G) o conjunto de vértices e arestas de um grafo G respectivamente. Foi alcançada a complexidade de tempo amortizada de O(√m· log |V(G)|) por operação de atualização ou consulta, para o problema da árvore geradora mínima totalmente retroativa. Para o algoritmo do caminho mínimo, a partir de um vértice inicial fixo em grafos dinâmicos, por meio do algoritmo proposto por Sunita et. al [52], foi obtida a complexidade temporal de O(|A(G)| · lg |V(G)|) por modificação, utilizando filas de prioridade com retroatividade não-consistente. The retroactivity in programming is the study of a modification in a timeline for a data structure and the effects that this modification exerts throughout its existence. In general, the analysis and implementation tend to be more costly computationally, because a modification on these data structure in the past can generate a cascade effect through all the data structure timeline. The concept of retroactivity generates tools and structures that optimize the solutions facing these temporal problems. This type of data structure can be used in, for example, shortest path algorithms, security applications, and geometric problems. In this thesis, we have the theoretical subsidies about these data structures, a detailed material about the implementation of this structures, using retroactivity, and the implementation of some problems that retroactivity can be used, for example, the fully dynamic minimum spanning tree problem. For each data structure, we executed practical tests about this data retroactive data structures and a comparison between these solutions and other approaches. The tests showed that the retroactive implementations proposed by Demaine et. al (2007) [13] obtained the best results from a temporal point of view. It was proposed two algorithms which used the retroactivity concepts inside its development: the fully retroactive minimum spanning tree and the single source dynamic shortest path problem in dynamic graphs. Let m be data structure’s timeline, V(G) and A(G) the sets of vertices and edges from graph G. We reached an amortized time complexity O( √ m· lg |V(G)|) per query/update operation in the fully retroactive minimum spanning tree algorithm. The algorithm to solve the single source dynamic shortest path problem in dynamic graphs proposed by Sunita et. al [52] obtained a time complexity O(|A(G)| · lg |V(G)|) per modification using a non-oblivious retroactive priority queue.

El doblez proyectado es indisoluble de la geometría que lo hace posible. Para establecer un claro control sobre el doblez es necesario realizar un documento proyectivo, un plano. Es por eso que los asuntos ligados a la geometría y al control matemático de los patrones de doblado han sido siempre fundamentales en la construcción de este tipo de diseños. Nos acercamos aquí a uno de los principales referentes y precursores sobre el estudio y desarrollo de los patrones de doblado para fines volumétricos, Ron Resch. Se trata de un desconocido artista y científico computacional norteamericano cuyo trabajo se menciona de modo repetido cuando se habla de arquitectos contemporáneos como Greg Lynn, quien ha aplicado también el uso del ordenador como herramienta de control y desarrollo geométrico. Para situar el momento, veremos el trabajo didáctico de Josef Albers y su manera de “abrir los ojos” mediante la experiencia con la manipulación restringida de la materia. El trabajo de Ron Resch establece una manera científica de aproximarse al problema y de aplicar las por aquel entonces incipientes herramientas computacionales, como son la elaboración de modelos 3D o la utilización de maquinaria CNC para el corte o el marcado. Los sistemas topológicos de Resch son en gran medida el origen de lo que hoy es el diseño paramétrico y la arquitectura de desarrollo con ordenadores. The designed bending is inseparable of the geometry that makes it possible. To establish a clear control over the fold it is necessary to make a projective document, a plan. That is why issues related to geometry and mathematical control of bending patterns have always been fundamental in the construction of this type of design. Here we are approaching to one of the main references and pioneers on the study and development of bending patterns for volumetric purposes, Ron Resch. He is a not very well known American artist and computational scientist whose work is mentioned repeatedly when contemporary architects such as Greg Lynn are mentioned, who have also applied the use of the computer as a tool for control and geometric development. In order to situate the moment, we will look at Josef Albers’ didactic work and his way of opening the eyes through experience with the restricted manipulation of matter. Ron Resch’s work establishes a scientific way of approaching the problem and applying the incipient computational tools at that moment, such as 3d modelling or the use of CNC machines for cutting or marking. The topological systems by Resch are to a large extent the roots of what is now parametric and computer development architecture.

Roads negatively affect many vertebrate species, whereas edge effect may favor some generalist species. This study aims to: 1) present a new way to calculate "line integral effects", represented by LIE and AVLIE, through new computer software, making this concept accessible to a broad audience of researchers interested in the study of Road Ecology and Tropical Forest Ecology; and, 2) test the performance of LIE and AVLIE indices, applied to road effect (LIE_road and AVLIE_road) and to edge effect (LIE_edge and AVLIE_edge), other road effect indices and forest area, using a data set on small mammal abundance in a human modified landscape in the Brazilian Atlantic Forest. Road and edge effects were represented by new metrics: Line Integral Effect (LIE) and Average Integral Effect (AVLIE), calculated using Line Integral from Differential Calculus of Several Variables through new free software developed by the second author. LIE_road and LIE_edge measure the total sum of the effect of roads (represented by lines) and edges (polygons), respectively, in relation to the forest fragment (point). AVLIE_road and AVLIE_edge measure the average of road and edge effect, respectively, in relation to the same sampling point. We used generalized linear regression models to explore the relationships between the abundance of the two groups of small mammals (forest specialists and habitat generalists) and the independent variables representing road, edge and forest effects. For forest specialists, the best model included AVLIE_road (negatively associated with abundance) and AVLIE_edge (negatively associated), while for habitat generalists, the best model included AVLIE_road (negatively associated) and LIE_edge (positively associated). Thus, there are more small mammals where road effect is lower. Forest fragments with higher edge effect showed more habitat generalists and less forest specialists. LIE and AVLIE could be useful metrics to explore edge effect separately to road effect on wildlife in forest fragments.

El presente artículo propone una metodología (usando el modelado de datos orientado a objetos) en la utilización de entidades geométricas tales como Punto, Polilínea y Polígono de una manera abstracta con el fin de usar sus propiedades y algunas funciones para luego ser usados en los Sistemas de Información Geográfica (GIS en sus siglas en ingles) de una manera automatizada y entendible en la programación y/o automatización de algoritmos facilitando su aplicación para la representación de entidades geográficas. Al final del presente artículo se expondrán algunos ejemplos sencillos de la implementación de cada abstracción para su mejor entendimiento., This paper proposes a methodology (using Object-oriented data modeling) to use geometrical entities such as “Point” (Punto in Spanish), “Polyline” (Polilínea in Spanish) and “Polygon” (Polígono in Spanish) using an abstract way using their properties and some functions upon themselves, in order to use them in Geographic Information Systems (GIS) Programming in an easier way to represent geographical entities. The last part you can see some simple examples about performing these abstractions.

Geometric 3D scene classification is a very challenging task. Current methodologies extract the geometric information using only a depth channel provided by an RGB-D sensor. These kinds of methodologies introduce possible errors due to missing local geometric context in the depth channel. This work proposes a novel Residual Attention Graph Convolutional Network that exploits the intrinsic geometric context inside a 3D space without using any kind of point features, allowing the use of organized or unorganized 3D data. Experiments are done in NYU Depth v1 and SUN-RGBD datasets to study the different configurations and to demonstrate the effectiveness of the proposed method. Experimental results show that the proposed method outperforms current state-of-the-art in geometric 3D scene classification tasks. This research was supported by Secretary of Universities and Research of the Generalitat de Catalunya and the European Social Fund via a PhD grant (FI2019) in the framework of project TEC2016-75976-R, financed by the Ministerio de Economía, Industria y Competitividad and the European Regional Development Fund (ERDF).

Motivation Protein–protein interactions (PPIs) are usually modeled as networks. These networks have extensively been studied using graphlets, small induced subgraphs capturing the local wiring patterns around nodes in networks. They revealed that proteins involved in similar functions tend to be similarly wired. However, such simple models can only represent pairwise relationships and cannot fully capture the higher-order organization of protein interactomes, including protein complexes. Results To model the multi-scale organization of these complex biological systems, we utilize simplicial complexes from computational geometry. The question is how to mine these new representations of protein interactomes to reveal additional biological information. To address this, we define simplets, a generalization of graphlets to simplicial complexes. By using simplets, we define a sensitive measure of similarity between simplicial complex representations that allows for clustering them according to their data types better than clustering them by using other state-of-the-art measures, e.g. spectral distance, or facet distribution distance. We model human and baker’s yeast protein interactomes as simplicial complexes that capture PPIs and protein complexes as simplices. On these models, we show that our newly introduced simplet-based methods cluster proteins by function better than the clustering methods that use the standard PPI networks, uncovering the new underlying functional organization of the cell. We demonstrate the existence of the functional geometry in the protein interactome data and the superiority of our simplet-based methods to effectively mine for new biological information hidden in the complexity of the higher-order organization of protein interactomes. Availability and implementation Codes and datasets are freely available at http://www0.cs.ucl.ac.uk/staff/natasa/Simplets/. Supplementary information Supplementary data are available at Bioinformatics online.

Traditional vector field visualization has a close focus on velocity, and is typically constrained to the dynamics of massless particles. In this paper, we present a novel approach to the analysis of the force-induced dynamics of inertial particles. These forces can arise from acceleration fields such as gravitation, but also be dependent on the particle dynamics itself, as in the case of magnetism. Compared to massless particles, the velocity of an inertial particle is not determined solely by its position and time in a vector field. In contrast, its initial velocity can be arbitrary and impacts the dynamics over its entire lifetime. This leads to a four-dimensional problem for 2D setups, and a six-dimensional problem for the 3D case. Our approach avoids this increase in dimensionality and tackles the visualization by an integrated topological analysis approach. We demonstrate the utility of our approach using a synthetic time-dependent acceleration field, a system of magnetic dipoles, and N -body systems both in 2D and 3D.

The conventional wavelet transform is widely used in image and signal processing, where a signal is decomposed into a combination of known signals. By analyzing the individual contributions, the behavior of the original signal can be inferred. In this article, the authors present an introductory overview of the extension of this theory into graphs domains. They review the graph Fourier transform and graph wavelet transforms that are based on dictionaries of graph spectral filters, namely, spectral graph wavelet transforms. Then, the main features of the graph wavelet transforms are presented using real and synthetic data.

Kernel-based methods have experienced a substantial progress in the last years, tuning out an essential mechanism for data classification, clustering and pattern recognition. The effectiveness of kernel-based techniques, though, depends largely on the capability of the underlying kernel to properly embed data in the feature space associated to the kernel. However, visualizing how a kernel embeds the data in a feature space is not so straightforward, as the embedding map and the feature space are implicitly defined by the kernel. In this work, we present a novel technique to visualize the action of a kernel, that is, how the kernel embeds data into a high-dimensional feature space. The proposed methodology relies on a solid mathematical formulation to map kernelized data onto a visual space. Our approach is faster and more accurate than most existing methods while still allowing interactive manipulation of the projection layout, a game-changing trait that other kernel-based projection techniques do not have.

Let S[0,1]2 be a set of n points, randomly and uniformly selected. Let RB be a random partition, or coloring, of S in which each point of S is included in R uniformly at random with probability 1/2. We study the random variable M(n) equal to the number of points of S that are covered by the rectangles of a maximum strong matching of S with axis-aligned rectangles. The matching consists of closed rectangles that cover exactly two points of S of the same color. A matching is strong if all its rectangles are pairwise disjoint. We prove that almost surely M(n)=0.83n for n large enough. Our approach is based on modeling a deterministic greedy matching algorithm, that runs over the random point set, as a Markov chain. Research supported by projects MTM2015-63791-R MINECO/FEDER and Gen. Cat. DGR 2017SGR1640

© 2019. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/ We use the concept of production matrices to show that there exist sets of n points in the plane that admit ¿(42.11n ) crossing-free geometric graphs. This improves the previously best known bound of ¿(41.18n ) by Aichholzer et al. (2007).

Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2019, Director: Joana Cirici, [en] Over the past few years, quantum computing has become more plausible due to the great advances in technology. While quantum computers are on their birth, the underlying mathematics have evolved to the point of proving that some quantum algorithms can solve problems that were unsolvable in classic computers. In order to implement these algorithms in a real machine, it is important to develop efficient ways to do it. The Solovay-Kitaev Theorem states that is possible. This work pretends to offer a complete review of the Solovay- Kitaev Theorem giving all the necessary tools to prove it. Moreover, we offer a brief introduction to the standard mathematical model of quantum computing, based on unitary operations.

Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2019, Director: Jaume Timoneda Salat, [en] Numerical integration, also known as quadrature, belongs to the group of problems of numerical analysis. The quadrature study has been extensively developed for functions of one dimension. Although it has many applications in various areas of science, the numerical calculation of integrals in higher dimensions has not been so much worked, mainly because of the difficulties involved in the fact that there are many more integration regions than in the 1-dimensional case. In this study it is developed the quadrature in two variables, explaining with detail some of the methods that can be used, and presenting practical results to support theoretical concepts. Specifically, the quadrature product formulas are developed, using the results of dimension 1 to arrive at valid 2-dimensional methods. Mainly, Simpson’s quadrature method and the 1-dimensional Trapezoidal rule are used to extend it to integrals on rectangular regions in the plane. Finally, the concept of adaptive quadrature is introduced and worked, which aims to reduce the cost and improve the computational efficiency of the product formulas, taking into account the nature of the function in the different zones of the integration region.

Orientador: Prof. Dr. Cícero Lopes Frota Dissertação (mestrado em Matemática)--Universidade Estadual de Maringá, Dep. de Matemática, Programa de Mestrado Profissional em Matemática em Rede Nacional, 2019 Nesta dissertação apresentamos uma metodologia de ensino, alternativa, para a disciplina de Física, que pode contribuir significativamente para que os estudantes passem a enxergar a Matemática como uma ferramenta essencial para as ciências, em particular, essencial para o estudo de Física. Por meio de um estudo introdutório de mecânica, apresentamos uma proposta metodológica para o ensino do movimento retilíneo uniforme (M.R.U.) e do movimento retilíneo uniformemente variado (M.R.U.V.). Esta proposta pode ser ampliada e aplicada para todos os demais conteúdos. Evidenciamos com este trabalho que a Física é plenamente dependente da Matemática, mostrando que não é possível ter o conhecimento do M.R.U. e do M.R.U.V. sem entender os conceitos matemáticos que os mesmos exigem. In this dissertation we present a teaching methodology, alternative, a physics method, that can contribute in a significant way so that the students come to see as an essential discipline for the sciences, in particular, essential for the study of Physics. Through an introductory mechanics study, we present a methodological proposal for the teaching of uniform rectilinear movement (M.R.U.) and uniformly varied rectilinear movement (M.R.U.V.). This proposal can be extended and applied to all others. We show with this work that Physics is dependent on Mathematics, showing that it is possible to have the knowledge of M.R.U. and M.R.U.V. without the mathematical senses that they require.

Orientador: Prof. Dr. Emerson Vitor Castelani Dissertação (mestrado em Matemática)--Universidade Estadual de Maringá, Dep. de Matemática, Programa de Mestrado Profissional em Matemática em Rede Nacional, 2019 O Diagrama de Voronoi, um dos topicos mais discutidos na area da Geometria Computacional, possui grande difusao em meio a varios estudos, por ?em pouco se sabe da abordagem deste tema em atividades de ensino. Propoem-se um suporte didatico com utilização da tematica, diante das dificuldades de abstracao no campo da matematica, para metodologia mais dinamica e interativa colaborando para compreensao objetiva do aprendizado e construcao de conhecimentos. Tendo Teoria dos Jogos em evidencia, Jogos de Voronoi, diagramas condicionados, despertaram interesse para o foco da pesquisa abordando 4 jogos, a saber, Tradicional Linear, Hotelling, Tradicional No Plano e Maxima Vizinhanca, explanando suas jogabilidades e estrategias de vitoria. A sequencia da exposicao das ideias, pela revisao bibliografica, contribuiu para estabelecer a capacidade de aplicacoes da estrutura, principalmente com insercao de algoritmos e estruturas de dados, para a resolucao computacional de problemas geometricos The Voronoi Diagram, one of the most discussed topics in the area of Computational Geometry, is widely disseminated through several studies, but little is known about the approach of this topic in teaching activities. It is proposed a didactic support with the use of the thematic, faced with the difficulties of abstraction in the field of mathematics, for a more dynamic and interactive methodology collaborating for objective understanding of the learning and construction of knowledge. Having the Game Theory in evidence, Voronoi Games, conditioned diagrams, aroused interest in the research focus addressing 4 games, namely Traditional Linear, Hotelling, Traditional On A Plane and Maximum Neighborhood, explaining their gameplay and winning strategies. The sequence of the exposition of the ideas, through the bibliographic review, contributed to establish the capacity of applications of the structure, mainly with the insertion of algorithms and data structures, for the computational resolution of geometric problems

We address the problem of tracking and detecting interactions between the different groups of runners that form during a race. In athletic races control points are set to monitor the progress of athletes over the course. Intuitively, a {\it group} is a sufficiently large set of athletes that cross a control point together. After adapting an existing definition of group to our setting we go on to study two types of group evolution patterns. The primary focus of this work are {\it evolution patterns}, i.e. the transformation and interaction of groups of athletes between two consecutive control points. We provide an accurate geometric model of the following evolution patterns: survives, appears, disappears, expands, shrinks, merges, splits, coheres and disbands, and present algorithms to efficiently compute these patterns. Next, based on the algorithms introduced for identifying evolution patterns, algorithms to detect {\it long-term patterns} are introduced. These patterns track global properties over several control points: surviving, traceable forward, traceable backward and related forward and backward. Experimental evaluation of the algorithms provided is presented using real and synthetic data. Using the data currently available, our experiments show how our algorithms can provide valuable insight into how running races develop. Moreover, we also show how, even if dense (synthetic) data is considered, our algorithms are also able to process it in real time.

We present a novel methodology to generate curved high-order meshes featuring optimal mesh quality and geometric accuracy. The proposed technique combines a distortion measure and a geometric Full-size image (