On the stability of Voronoi cells

Let T be a given subset of ℝ n , whose elements are called sites, and let s∈T. The Voronoi cell of s with respect to T consists of all points closer to s than to any other site. In many real applications, the position of some elements of T is uncertain due to either random external causes or to measurement errors. In this paper we analyze the effect on the Voronoi cell of small changes in s or in a given non-empty set P⊂T\{s}. Two types of perturbations of P are considered, one of them not increasing the cardinality of T. More in detail, the paper provides conditions for the corresponding Voronoi cell mappings to be closed, lower and upper semicontinuous. All the involved conditions are expressed in terms of the data.

Voronoi cells via linear inequality systems

The theory and methods of linear algebra are a useful alternative to those of convex geometry in the framework of Voronoi cells and diagrams, which constitute basic tools of computational geometry. As shown by Voigt and Weis in 2010, the Voronoi cells of a given set of sites T, which provide a tesselation of the space called Voronoi diagram when T is finite, are solution sets of linear inequality systems indexed by T. This paper exploits systematically this fact in order to obtain geometrical information on Voronoi cells from sets associated with T (convex and conical hulls, tangent cones and the characteristic cones of their linear representations). The particular cases of T being a curve, a closed convex set and a discrete set are analyzed in detail. We also include conclusions on Voronoi diagrams of arbitrary sets.

Generalized optimal lattice covering of finite-dimensional Euclidean space

A generalization of the classical problem of optimal lattice covering of R-n is considered. Solutions to this generalized problem are found in two specific classes of lattices. The global optimal solution of the generalization is found for R-2. (C) 1998 Elsevier Science Inc. All rights reserved.

Elastic moduli of model random three-dimensional closed-cell cellular solids

Most cellular solids are random materials, while practically all theoretical structure-property results are for periodic models. To be able to generate theoretical results for random models, the finite element method (FEM) was used to study the elastic properties of solids with a closed-cell cellular structure. We have computed the density (rho) and microstructure dependence of the Young's modulus (E) and Poisson's ratio (PR) for several different isotropic random models based on Voronoi tessellations and level-cut Gaussian random fields. The effect of partially open cells is also considered. The results, which are best described by a power law E infinity rho (n) (1<n<2), show the influence of randomness and isotropy on the properties of closed-cell cellular materials, and are found to be in good agreement with experimental data. (C) 2001 Acta Materialia Inc. Published by Elsevier Science Ltd. All rights reserved.

Specialized care for people with AIDS in the state of Ceara, Brazil

OBJECTIVE To analyze if the distribution of specialized care services for HIV/AIDS is associated with AIDS rates. METHODS Ecological study, for which the distribution of 10 specialized care services in the Ceara state, Northeastern Brazil, was obtained, and the mean rates of the disease were estimated per mesoregion. We evaluated 7,896 individuals who had been diagnosed with AIDS, were aged 13 years or older, lived in Ceara, and had been informed of their condition between 2001 and 2011. Maps were constructed to verify the relationship between the distribution of AIDS cases and institutionalized support networks in the 2001-2006 and 2007-2011 periods. BoxMap and LisaMap were used for data analysis. The Voronoi diagram was applied for the distribution of the studied services. RESULTS Specialized care services concentrated in AIDS clusters in the metropolitan area. The Noroeste Cearense and west of the Sertoes Cearenses had high AIDS rates, but a low number of specialized care services over time. Two of these services were implemented where clusters of the disease exist in the second period. The application of the Voronoi diagram showed that the specialized care services located outside the metropolitan area covered a large territory. We identified one polygon that had no services. CONCLUSIONS The scenario of AIDS cases spread away from major urban areas demands the creation of social support services in areas other than the capital and the metropolitan area of the state; this can reduce access barriers to these institutions. It is necessary to create specialized care services for HIV/AIDS in the Noroeste Cearense and north of Jaguaribe.

Mapping the quality of life experience in Alfama: a case study in Lisbon, Portugal.

Dissertation submitted in partial fulfilment of the requirements for the Degree of Master of Science in Geospatial Technologies.

Linear amplification with multiple nonlinear devices

Dissertação para obtenção do Grau de Mestre em Engenharia Electrotécnica e Computadores

Modelling the influence of microstructure on elastic properties and tensile damage behaviour of Mo-base silicide alloys

Mo-Si-B alloys, Real microstructures, Voronoi structures, Microstructural characterization, Modelling and finite element simulations, Effective material properties, Damage and Crack growth, tensile strength, fracture toughness

Early white matter alterations in men predisposed to FXTAS revealed by MT imaging.

Introduction: The Fragile X - associated Tremor Ataxia Syndrome (FXTAS) is a recently described, and under-diagnosed, late onset (≈ 60y) neurodegenerative disorder affecting male carriers of a premutation in the Fragile X Mental Retardation 1 (FMR1) gene. The premutation is an CGG (Cytosine-Guanine-Guanine) expansion (55 to 200 CGG repeats) in the proximal region of the FMR1 gene. Patients with FXTAS primarily present with cerebellar ataxia and intention tremor. Neuroradiological features of FXTAS include prominent white matter disease in the periventricular, subcortical, middle cerebellar peduncles and deep white matter of the cerebellum on T2-weighted or FLAIR MR imaging (Jacquemmont 2007, Loesch 2007, Brunberg 2002, Cohen 2006). We hypothesize that a significant white matter alteration is present in younger individuals many years prior to clinical symptoms and/or the presence of visible lesions on conventional MR sequences and might be detectable by magnetization transfer (MT) imaging. Methods: Eleven asymptomatic premutation carriers (mean age = 55 years) and seven intra-familial controls participated to the study. A standardized neurological examination was performed on all participants and a neuropsychological evaluation was carried out before MR scanning performed on a 3T Siemens Trio. The protocol included a sagittal T1-weighted 3D gradient-echo sequence (MPRAGE, 160 slices, 1 mm^3 isotropic voxels) and a gradient-echo MTI (FA 30, TE 15, matrix size 256*256, pixel size 1*1 mm, 36 slices (thickness 2mm), MT pulse duration 7.68 ms, FA 500, frequency offset 1.5 kHz). MTI was performed by acquiring consecutively two set of images; first with and then without the MT saturation pulse. MT images were coregistered to the T1 acquisition. The MTR for every intracranial voxel was calculated as follows: MTR = (M0 - MS)/M0*100%, creating a MTR map for each subject. As first analysis, the whole white matter (WM) was used to mask the MTR image in order to create an histogram of the MTR distribution in the whole tissue class over the two groups examined. Then, for each subject, we performed a segmentation and parcellation of the brain by means of Freesurfer software, starting from the high resolution T1-weighted anatomical acquisition. Cortical parcellations was used to assign a label to the underlying white matter by the construction of a Voronoi diagram in the WM voxels of the MR volume based on distance to the nearest cortical parcellation label. This procedure allowed us to subdivide the cerebral WM in 78 ROIs according to the cortical parcellation (see example in Fig 1). The cerebellum, by the same procedure, was subdivided in 5 ROIs (2 per each hemisphere and one corresponding to the brainstem). For each subject, we calculated the mean value of MTR within each ROI and averaged over controls and patients. Significant differences between the two groups were tested using a two sample T-test (p<0.01). Results: Neurological examination showed that no patient met the clinical criteria of Fragile X Tremor and Ataxia Syndrome yet. Nonetheless, premutation carriers showed some subtle neurological signs of the disorder. In fact, premutation carriers showed a significant increase of tremor (CRST, T-test p=0.007) and increase of ataxia (ICARS, p=0.004) when compared to controls. The neuropsychological evaluation was normal in both groups. To obtain general characterizations of myelination for each subject and premutation carriers, we first computed the distribution of MTR values across the total white matter volume and averaged for each group. We tested the equality of the two distributions with the non parametric Kolmogorov-Smirnov test and we rejected the null-hypothesis at a p=0.03 (fig. 2). As expected, when comparing the asymptomatic permutation carriers with control subjects, the peak value and peak position of the MTR values within the whole WM were decreased and the width of the distribution curve was increased (p<0.01). These three changes point to an alteration of the global myelin status of the premutation carriers. Subsequently, to analyze the regional myelination and white matter integrity of the same group, we performed a ROI analysis of MTR data. The ROI-based analysis showed a decrease of mean MTR value in premutation carriers compared to controls in bilateral orbito-frontal and inferior frontal WM, entorhinal and cingulum regions and cerebellum (Fig 3). The detection of these differences in these regions failed with other conventional MR techniques. Conclusions: These preliminary data confirm that in premutation carriers, there are indeed alterations in "normal appearing white matter" (NAWM) and these alterations are visible with the MT technique. These results indicate that MT imaging may be a relevant approach to detect both global and local alterations within NAWM in "asymptomatic" carriers of premutations in the Fragile X Mental Retardation 1 (FMR1) gene. The sensitivity of MT in the detection of these alterations might point towards a specific physiopathological mechanism linked to an underlying myelin disorder. ROI-based analyses show that the frontal, parahippocampal and cerebellar regions are already significantly affected before the onset of symptoms. A larger sample will allow us to determine the minimum CGG expansion and age associated with these subclinical white matter alterations.

Distance Transforms on Gray-Level Surfaces

This thesis studies gray-level distance transforms, particularly the Distance Transform on Curved Space (DTOCS). The transform is produced by calculating distances on a gray-level surface. The DTOCS is improved by definingmore accurate local distances, and developing a faster transformation algorithm. The Optimal DTOCS enhances the locally Euclidean Weighted DTOCS (WDTOCS) with local distance coefficients, which minimize the maximum error from the Euclideandistance in the image plane, and produce more accurate global distance values.Convergence properties of the traditional mask operation, or sequential localtransformation, and the ordered propagation approach are analyzed, and compared to the new efficient priority pixel queue algorithm. The Route DTOCS algorithmdeveloped in this work can be used to find and visualize shortest routes between two points, or two point sets, along a varying height surface. In a digital image, there can be several paths sharing the same minimal length, and the Route DTOCS visualizes them all. A single optimal path can be extracted from the route set using a simple backtracking algorithm. A new extension of the priority pixel queue algorithm produces the nearest neighbor transform, or Voronoi or Dirichlet tessellation, simultaneously with the distance map. The transformation divides the image into regions so that each pixel belongs to the region surrounding the reference point, which is nearest according to the distance definition used. Applications and application ideas for the DTOCS and its extensions are presented, including obstacle avoidance, image compression and surface roughness evaluation.

Análise espacial de um fragmento florestal baseada no mosaico de dirichlet

A configuração espacial das árvores afeta grande número de processos fisiológicos e ecológicos em uma floresta, incluindo competição, distribuição, tamanho, crescimento e mortalidade da espécie. Métodos baseados na função K de Ripley têm sido usados com frequência para caracterizar a configuração espacial de uma floresta. Neste artigo foram propostos alguns métodos, que são baseados nas áreas do mosaico de Dirichlet (função D), para descrever a distribuição espacial de árvores. Devido à importância da Xylopia brasiliensis (pindaíba) na estrutura e dinâmica de floresta Semidecidual Montana, este trabalho avaliou as funções K e D para descrever a distribuição espacial da espécie. Os resultados indicaram que os estimadores das funções K e D, combinados com simulações Monte Carlo, levaram à rejeição da hipótese de completa aleatoriedade espacial (p < 0,10) da Xylopia brasiliensis em favor da presença de agrupamento espacial da espécie dentro do fragmento florestal.

Étude en dynamique moléculaire par approximation des liaisons fortes de l'influence des défauts ponctuels dans la relaxation du silicium amorphe

Mémoire numérisé par la Division de la gestion de documents et des archives de l'Université de Montréal

A heuristic algorithm for the Capacitated Vehicle Routing Problem with Synchronized Pick-ups and Drop-offs : a case study for medications delivery and supervision in DR Congo

Dans des contextes de post-urgence tels que le vit la partie occidentale de la République Démocratique du Congo (RDC), l’un des défis cruciaux auxquels font face les hôpitaux ruraux est de maintenir un niveau de médicaments essentiels dans la pharmacie. Sans ces médicaments pour traiter les maladies graves, l’impact sur la santé de la population est significatif. Les hôpitaux encourent également des pertes financières dues à la péremption lorsque trop de médicaments sont commandés. De plus, les coûts du transport des médicaments ainsi que du superviseur sont très élevés pour les hôpitaux isolés ; les coûts du transport peuvent à eux seuls dépasser ceux des médicaments. En utilisant la province du Bandundu, RDC pour une étude de cas, notre recherche tente de déterminer la faisabilité (en termes et de la complexité du problème et des économies potentielles) d’un problème de routage synchronisé pour la livraison de médicaments et pour les visites de supervision. Nous proposons une formulation du problème de tournées de véhicules avec capacité limitée qui gère plusieurs exigences nouvelles, soit la synchronisation des activités, la préséance et deux fréquences d’activités. Nous mettons en œuvre une heuristique « cluster first, route second » avec une base de données géospatiales qui permet de résoudre le problème. Nous présentons également un outil Internet qui permet de visualiser les solutions sur des cartes. Les résultats préliminaires de notre étude suggèrent qu’une solution synchronisée pourrait offrir la possibilité aux hôpitaux ruraux d’augmenter l’accessibilité des services médicaux aux populations rurales avec une augmentation modique du coût de transport actuel.

Face Recognition using Probabilistic Neural Networks

In this paper we address the problem of face detection and recognition of grey scale frontal view images. We propose a face recognition system based on probabilistic neural networks (PNN) architecture. The system is implemented using voronoi/ delaunay tessellations and template matching. Images are segmented successfully into homogeneous regions by virtue of voronoi diagram properties. Face verification is achieved using matching scores computed by correlating edge gradients of reference images. The advantage of classification using PNN models is its short training time. The correlation based template matching guarantees good classification results

Face Recognition using Probabilistic Neural Networks

n this paper we address the problem of face detection and recognition of grey scale frontal view images. We propose a face recognition system based on probabilistic neural networks (PNN) architecture. The system is implemented using voronoi/ delaunay tessellations and template matching. Images are segmented successfully into homogeneous regions by virtue of voronoi diagram properties. Face verification is achieved using matching scores computed by correlating edge gradients of reference images. The advantage of classification using PNN models is its short training time. The correlation based template matching guarantees good classification results.