Collection of abstracts of the 24th European Workshop on Computational Geometry

International audienceThe 24th European Workshop on Computational Geomety (EuroCG'08) was held at INRIA Nancy - Grand Est & LORIA on March 18-20, 2008. The present collection of abstracts contains the 63 scientific contributions as well as three invited talks presented at the workshop

Algorithm Engineering for Realistic Journey Planning in Transportation Networks

Diese Dissertation beschäftigt sich mit der Routenplanung in Transportnetzen. Es werden neue, effiziente algorithmische Ansätze zur Berechnung optimaler Verbindungen in öffentlichen Verkehrsnetzen, Straßennetzen und multimodalen Netzen, die verschiedene Transportmodi miteinander verknüpfen, eingeführt. Im Fokus der Arbeit steht dabei die Praktikabilität der Ansätze, was durch eine ausführliche experimentelle Evaluation belegt wird

Visual recognition of objects : behavioral, computational, and neurobiological aspects

I surveyed work on visual object recognition and perception. In animals, vision has been studied mainly on the behavioral and neurobiological levels. Behavioral data typically show what the visual system, by itself or together with the rest of the organism, is capable of. They show, for example, that humans can recognie objects regardless of size and position, but that rotated objects pose problems. Important insights into the organization of behavior have also been provided by people who suffered localized brain damage. We have learned that the brain is divided into areas subserving different and relatively well-defined behaviors. The visual system itself is also organized in different subsystems; the visual cortex alone contains nearly twenty maps of the visual field. And individual neurons respond selectively to visual stimuli, e.g., the orientation of line segments, color, direction of motion, and, most intriguingly, faces. The question is how the actions of all these neurons produce the behavior we observe. How do neurons represent the shape of objects such that they can be recognized? Before we can answer the question, we have to understand the computational aspect of shape representation, the nature of the problem as it were. Many methods for representing shape have been explored, mainly by computer scientists, but so far no satisfactory answers have been found

Large bichromatic point sets admit empty monochromatic 4-gons

We consider a variation of a problem stated by Erd˝os and Szekeres in 1935 about the existence of a number fES(k) such that any set S of at least fES(k) points in general position in the plane has a subset of k points that are the vertices of a convex k-gon. In our setting the points of S are colored, and we say that a (not necessarily convex) spanned polygon is monochromatic if all its vertices have the same color. Moreover, a polygon is called empty if it does not contain any points of S in its interior. We show that any bichromatic set of n ≥ 5044 points in R2 in general position determines at least one empty, monochromatic quadrilateral (and thus linearly many).Postprint (published version

LIPIcs, Volume 244, ESA 2022, Complete Volume

LIPIcs, Volume 244, ESA 2022, Complete Volum

Network based data oriented methods for application driven problems

Networks are amazing. If you think about it, some of them can be found in almost every single aspect of our life from sociological, financial and biological processes to the human body. Even considering entities that are not necessarily connected to each other in a natural sense, can be connected based on real life properties, creating a whole new aspect to express knowledge. A network as a structure implies not only interesting and complex mathematical questions, but the possibility to extract hidden and additional information from real life data. The data that is one of the most valuable resources of this century. The different activities of the society and the underlying processes produces a huge amount of data, which can be available for us due to the technological knowledge and tools we have nowadays. Nevertheless, the data without the contained knowledge does not represent value, thus the main focus in the last decade is to generate or extract information and knowledge from the data. Consequently, data analytics and science, as well as data-driven methodologies have become leading research fields both in scientific and industrial areas. In this dissertation, the author introduces efficient algorithms to solve application oriented optimization and data analysis tasks built on network science based models. The main idea is to connect these problems along graph based approaches, from virus modelling on an existing system through understanding the spreading mechanism of an infection/influence and maximize or minimize the effect, to financial applications, such as fraud detection or cost optimization in a case of employee rostering

Feature network models for proximity data : statistical inference, model selection, network representations and links with related models

Feature Network Models (FNM) are graphical structures that represent proximity data in a discrete space with the use of features. A statistical inference theory is introduced, based on the additivity properties of networks and the linear regression framework. Considering features as predictor variables leads in a natural way to a univariate multiple regression problem with positivity restrictions on the parameters, which represent edge lengths in the network representation. Theoretical standard errors and confidence intervals are obtained for the parameters and their performance is evaluated by Monte Carlo simulation. When the feature structure is not known in advance, a strategy is proposed to select an adequate subset of features that takes into account a good compromise between model fit and model complexity using Gray codes and the positive lasso. The same statistical inference theory also holds for additive trees that are special cases of FNM. Standard errors and confidence intervals, model tests and prediction error are obtained for the estimates of the branch lengths of additive trees. The dissertation concludes by demonstrating that there exists a universal network representation of city-block models based on key elements of the network representation consisting of betweenness, metric segmental additivity and internal nodes.LEI Universiteit LeidenMultivariate analysis of psychological data - ou

Medical image enhancement

Each image acquired from a medical imaging system is often part of a two-dimensional (2-D) image set whose total presents a three-dimensional (3-D) object for diagnosis. Unfortunately, sometimes these images are of poor quality. These distortions cause an inadequate object-of-interest presentation, which can result in inaccurate image analysis. Blurring is considered a serious problem. Therefore, “deblurring” an image to obtain better quality is an important issue in medical image processing. In our research, the image is initially decomposed. Contrast improvement is achieved by modifying the coefficients obtained from the decomposed image. Small coefficient values represent subtle details and are amplified to improve the visibility of the corresponding details. The stronger image density variations make a major contribution to the overall dynamic range, and have large coefficient values. These values can be reduced without much information loss

Adaptive Space-Time Finite Element Method in High Temperature Superconductivity

RÉSUMÉ : Cette thèse porte sur le développement d’une méthode d’éléments finis adaptative pour discrétiser un modèle électromagnétique issu du domaine de la supraconductivité à haute température critique. Dans les faits, ce modèle consiste en une version non-linéaire du problème de courants de Foucault classique en électromagnétisme, dans lequel la non-linéarité engendre un état mixte de régions supraconductrices et de régions normales. La méthode développée dans cette thèse peut être appliquée directement à la conception et à l’optimisation de dispositifs supraconducteurs à haute température critique, sans s’y limiter. Le problème mathématique correspondant à ce modèle, que l’on appelle p-rotationnel (p-curl en anglais), est une équation différentielle aux dérivées partielles de type évolutionnaire monotone dont les solutions de la forme faible appartiennent à un espace fonctionnel de Sobolev de type L^p. Étant donnée la présence de singularités dans les solutions, les méthodes numériques développées à ce jour pour résoudre ce probléme se généralisent mal aux domaines 2D et 3D. La principale difficulté provient de l’absence d’estimateur d’erreur qui permettrait un contrôle adaptatif de la finesse du maillage et du pas de temps. Cette thèse présente deux contributions principales. Premièrement, nous avons développé et implémenté une méthode d’éléments finis adaptative basée sur une formulation espace-temps. Afin de faciliter l’adaptivité, nous avons conçu une structure arborescente espace-temps, qui se construit de façon récursive en fonction du raffinement tout en préservant l’irrégularité de premier niveau (1-irregularity) du maillage espace-temps. De plus, nous avons développé un opérateur d’interpolation qui permet de préserver la continuité des degrés de liberté sur les arêtes “sans voisins” (hanging edges). La seconde contribution principale de la thèse est le développement d’un estimateur d’erreur a posteriori basé sur le résidu, et nous avons prouvé mathématiquement sa fiabilité dans le cas semi-discret. Un élément clé de cette preuve fut d’utiliser une nouvelle version de la décomposition d’Helmholtz pour l’espace 〖W_0〗^p (curl;Ω), requis pour démonter une variante de l’orthogonalité de Galerkin. La fiabilité d’une grandeur physique d’intérêt, appelée pertes AC, a aussi été démontrée. Des résultats numériques en 1D et 2D sont aussi présentés dans les cas uniformes et adaptatifs. En bref, cette recherche se distingue des travaux précédents sur le p-rotationnel parce qu’elle se base sur une analyse mathématique théorique rigoureuse pour guider le développement et l’analyse des nouvelles techniques proposées.---------- ABSTRACT : This thesis is on the development of an adaptive finite element method to discretize a model from high temperature superconductivity. In essence, this model is a nonlinear version of the classical eddy current problem from electromagnetics, where the nonlinear resistivity gives rise to the behaviour of mixed states between normal and superconducting regions. An application for this method is in the design optimization of high temperature superconducting devices. This mathematical problem, which we called the p-curl problem, is an evolutionary monotone-type partial differential equation with weak solutions belonging to a L^p-type Sobolev function space. Due to singularities which arise in the solutions, numerical methods developed for this problem so far have been inefficient to general 2D or 3D domains. The main difficulty has been the lack of error estimator in order to adaptively control the mesh refinement and time-stepping schemes. The primary contributions of this work are two-fold. First, we develop and implement the adaptive finite element method based on a continuous space-time formulation. To facilitate adaptivity, we introduce the space-time simplex tree structure, a recursive refinement procedure to preserve 1-irregularity of the space-time mesh and a local interpolation operator for preserving the continuity of degrees of freedom on hanging edges. Second, we derived residual-based a posteriori error estimators and showed its reliability in the semi-discretization setting. A key ingredient in proving reliability was a new version of the Helmholtz decomposition for 〖W_0〗^p (curl;Ω) necessary in showing a variant of the Galerkin orthogonality. Reliability for a quantity of interest, AC loss, was also proved. Numerical results are shown for the uniform and adaptive discretization in 1D/2D. This research distinguishes itself from previous numerical studies of the p-curl problem because it relies on rigorous mathematical theory to guide the development and analysis of these new techniques