Dissertations / Theses: 'B-spline functions'

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Grove, Olya. "Heterogeneous Modeling of Medical Image Data Using B-Spline Functions." Scholar Commons, 2011. http://scholarcommons.usf.edu/etd/3130.

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Ongoing developments in the field of medical imaging modalities have pushed the frontiers of modern medicine and biomedical engineering, prompting the need for new applications to improve diagnosis, treatment and prevention of diseases. Biomedical data visualization and modeling rely predominately on manual processing and utilization of voxel and facet based homogeneous models. Biological structures are naturally heterogeneous and in order to accurately design and biomimic biological structures, properties such as chemical composition, size and shape of biological constituents need to be incorporated in the computational biological models. Our proposed approach involves generating a density point cloud based on the intensity variations in a medical image slice, to capture tissue density variations through point cloud densities. The density point cloud is ordered and approximated with a set of cross-sectional least-squares B-Spline curves, based on which a skinned B-Spline surface is generated. The aim of this method is to capture and accurately represent density variations within the medical image data with a lofted surface function. The fitted B-Spline surface is sampled at uniformly distributed parameters, and our preliminary results indicate that the bio-CAD model preserves the density variations of the original image based point cloud. The resultant surface can thus be visualized by mapping the density in the parametric domain into color in pixel domain. The B-Spline function produced from each image slice can be used for medical visualization and heterogeneous tissue modeling. The process can be repeated for each slice in the medical dataset to produce heterogeneous B-Spline volumes. The emphasis of this research is placed on accuracy and shape fidelity needed for medical operations.

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Andriamaro, Miangaly Gaelle. "Vector refinable splines and subdivision." Thesis, Stellenbosch : Stellenbosch University, 2008. http://hdl.handle.net/10019.1/1747.

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Thesis (MSc (Mathematics))--Stellenbosch University, 2008.
In this thesis we study a standard example of refinable functions, that is, functions which can be reproduced by the integer shifts of their own dilations. Using the cardinal B-spline as an introductory example, we prove some of its properties, thereby building a basis for a later extension to the vector setting. Defining a subdivision scheme associated to the B-spline refinement mask, we then present the proof of a well-known convergence result. Subdivision is a powerful tool used in computer-aided geometric design (CAGD) for the generation of curves and surfaces. The basic step of a subdivision algorithm consists of starting with a given set of points, called the initial control points, and creating new points as a linear combination of the previous ones, thereby generating new control points. Under certain conditions, repeated applications of this procedure yields a continuous limit curve. One important goal of this thesis is to study a particular extension of scalar subdivision to matrix subdivision ...

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Santos, Tyssia Nogueira Maciel dos. "AvaliaÃÃo genÃtica da curva de lactaÃÃo de cabras saanen utilizando modelos de regressÃo aleatÃria." Universidade Federal do CearÃ, 2014. http://www.teses.ufc.br/tde_busca/arquivo.php?codArquivo=13819.

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CoordenaÃÃo de AperfeÃoamento de Pessoal de NÃvel Superior
O objetivo deste estudo foi realizar uma avaliaÃÃo genÃtico-quantitativa da curva de lactaÃÃo atÃ 305 dias de cabras da raÃa Saanen, avaliando distintos modelos de regressÃo aleatÃria para o melhor ajuste das trajetÃrias fixa e aleatÃrias desta curva, e assim estimar as covariÃncias e parÃmetros genÃticos associados a este perÃodo. Foram utilizados 11.018 controles leiteiros de 950 lactaÃÃes de cabras pertencentes a rebanhos associados ao Programa de Melhoramento GenÃtico de Caprinos Leiteiros (CaprageneÂ). Os efeitos fixos utilizados nas anÃlises foram de grupo de contemporÃneos, sexo das crias, tipo de ordenha e manejo. Foram avaliados 18 modelos, com diferentes ordens, para verificar o melhor ajuste simultÃneo das regressÃes para as trajetÃrias fixa e aleatÃrias (efeitos genÃticos aditivos diretos, de ambiente permanente e residual). Para ajuste da regressÃo fixa, foram utilizados os polinÃmios ordinÃrios e os polinÃmios ortogonais de Legendre, de segunda ordem. Para as regressÃes aleatÃrias, foram utilizados os polinÃmios ordinÃrios, os polinÃmios ortogonais de Legendre e as funÃÃes b-spline, variando da segunda a quarta ordem. O modelo com os polinÃmios ortogonais de Legendre de segunda ordem para a parte fixa e as funÃÃes b-spline de quarta ordem para a parte aleatÃria foi o mais adequado para o ajuste dos dados analisados. Na trajetÃria fixa, este modelo estimou o pico de lactaÃÃo entre 52-61 dias, com valor mÃdio de 2,378 kg de leite/dia. A curva iniciou-se com uma produÃÃo mÃdia de 2,298 kg/dia, encerrando aos 305 dias com uma produÃÃo mÃdia de 0,758 kg/dia. As estimativas de herdabilidade variaram de 0,294 Â 0,135 a 0,794 Â 0,075. Maior variabilidade genÃtica foi estimada para os controles leiteiros intermediÃrios na trajetÃria da curva de lactaÃÃo, entre 79 e 180 dias, com maiores estimativas de herdabilidade. As correlaÃÃes genÃticas entre os controles variaram entre 0,551 Â 0,125 e 0,998 Â 0,001, como maiores valores para produÃÃes de leite em dias prÃximos e subsequentes, e tornando-se menores Ã medida que os controles se distanciavam. A variabilidade genÃtica estimada indica que Ã possÃvel modificar por seleÃÃo a curva de lactaÃÃo das cabras Saanen da populaÃÃo estudada. Esta seleÃÃo deve ser realizada entre 79 e 180 dias de lactaÃÃo, perÃodo posterior ao pico de lactaÃÃo, entretanto onde se observaram as maiores herdabilidades. A seleÃÃo neste ponto permitirÃ alteraÃÃes na curva como um todo, em funÃÃo das respostas genÃticas correlacionadas.
The aim of this study was to perform a genetic-quantitative evaluation of the lactation curve up to 305 days of Saanen goats, fitting different random regression models to the best fit on the fixed and random trajectories of this curve and thus estimate the (co) variances and genetic parameters associated to this period. 11,018test-day milk yieldof 950 goats belonging to herds supported by the Dairy Goats Breeding Program (CaprageneÂ) were used. The fixed effects used in the analysis were contemporary group, sex of offspring, type of milking and management. 18 models with different orderswere evaluated, to verify the simultaneous best fit of the regressions for the fixed and random trajectories (direct additive genetic, permanent environmental and residual effects). Ordinary orthogonal polynomials and Legendre polynomials, of second order were used to fit the fixed regression. Ordinary polynomials, orthogonal Legendre polynomials and B-spline functions, ranging from second to fourth order, were used for fit the random regressions. The model with orthogonal Legendre polynomials of second order to the fixed part and the b-spline function of fourth order for the random part was the most suitable for the fitting of the data analyzed. In fixed path, this model estimated peak lactation between 52-61 days, with an average of 2.378 kg of milk / day. The curve began with an average yield of 2.298 kg / day, ending 305 days with an average yield of 0.758 kg / day. Heritability estimates ranged from 0.294 Â 0.135 to 0.794 Â 0.075. Greater genetic variability was estimated for the intermediate test-day yields in the trajectory of the lactation curve, between 79 and 180 days, with higher heritability estimates. Genetic correlations among the test-day yields ranged from 0.551 Â 0.125 and 0.998 Â 0.001, with higher values between milk yield in the next and subsequent days, and becoming smaller as the distanceamong the test-day yield increase. The estimated genetic variability indicates that it is possible to modify the lactation curve of Saanen goats of the study population. The selection should be performed between 79 and 180 days of lactation, after the peak of lactation, however where the greatest heritabilities were observed period. The selection on this point will change the curve as a whole on the basis of correlated genetic responses.

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Flores, Melvin Estuardo Murray Richard M. Murray Richard M. "Real-time trajectory generation for constrained nonlinear dynamical systems using non-uniform rational B-spline basis functions /." Diss., Pasadena, Calif. : California Institute of Technology, 2008. http://resolver.caltech.edu/CaltechETD:etd-02192008-153449.

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You, C. F. "An investigation of the use of B-spline shaped functions for the analysis of large deformations of structures." Thesis, Cranfield University, 1987. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.381051.

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Santos, Tyssia Nogueira Maciel dos. "Avaliação genética da curva de lactação de cabras saanen utilizando modelos de regressão aleatória." reponame:Repositório Institucional da UFC, 2014. http://www.repositorio.ufc.br/handle/riufc/19004.

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SANTOS, Tyssia Nogueira Maciel dos. Avaliação genética da curva de lactação de cabras saanen utilizando modelos de regressão aleatória. 2014. 51 f. : Dissertação (Mestrado) - Universidade Federal do Ceará, Centro de Ciências, Departamento de Zootecnia, Programa de Pós-Graduação em Zootecnia. Fortaleza-CE, 2014.
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The aim of this study was to perform a genetic-quantitative evaluation of the lactation curve up to 305 days of Saanen goats, fitting different random regression models to the best fit on the fixed and random trajectories of this curve and thus estimate the (co) variances and genetic parameters associated to this period. 11,018test-day milk yieldof 950 goats belonging to herds supported by the Dairy Goats Breeding Program (Capragene®) were used. The fixed effects used in the analysis were contemporary group, sex of offspring, type of milking and management. 18 models with different orderswere evaluated, to verify the simultaneous best fit of the regressions for the fixed and random trajectories (direct additive genetic, permanent environmental and residual effects). Ordinary orthogonal polynomials and Legendre polynomials, of second order were used to fit the fixed regression. Ordinary polynomials, orthogonal Legendre polynomials and B-spline functions, ranging from second to fourth order, were used for fit the random regressions. The model with orthogonal Legendre polynomials of second order to the fixed part and the b-spline function of fourth order for the random part was the most suitable for the fitting of the data analyzed. In fixed path, this model estimated peak lactation between 52-61 days, with an average of 2.378 kg of milk / day. The curve began with an average yield of 2.298 kg / day, ending 305 days with an average yield of 0.758 kg / day. Heritability estimates ranged from 0.294 ± 0.135 to 0.794 ± 0.075. Greater genetic variability was estimated for the intermediate test-day yields in the trajectory of the lactation curve, between 79 and 180 days, with higher heritability estimates. Genetic correlations among the test-day yields ranged from 0.551 ± 0.125 and 0.998 ± 0.001, with higher values between milk yield in the next and subsequent days, and becoming smaller as the distanceamong the test-day yield increase. The estimated genetic variability indicates that it is possible to modify the lactation curve of Saanen goats of the study population. The selection should be performed between 79 and 180 days of lactation, after the peak of lactation, however where the greatest heritabilities were observed period. The selection on this point will change the curve as a whole on the basis of correlated genetic responses.
O objetivo deste estudo foi realizar uma avaliação genético-quantitativa da curva de lactação até 305 dias de cabras da raça Saanen, avaliando distintos modelos de regressão aleatória para o melhor ajuste das trajetórias fixa e aleatórias desta curva, e assim estimar as covariâncias e parâmetros genéticos associados a este período. Foram utilizados 11.018 controles leiteiros de 950 lactações de cabras pertencentes a rebanhos associados ao Programa de Melhoramento Genético de Caprinos Leiteiros (Capragene®). Os efeitos fixos utilizados nas análises foram de grupo de contemporâneos, sexo das crias, tipo de ordenha e manejo. Foram avaliados 18 modelos, com diferentes ordens, para verificar o melhor ajuste simultâneo das regressões para as trajetórias fixa e aleatórias (efeitos genéticos aditivos diretos, de ambiente permanente e residual). Para ajuste da regressão fixa, foram utilizados os polinômios ordinários e os polinômios ortogonais de Legendre, de segunda ordem. Para as regressões aleatórias, foram utilizados os polinômios ordinários, os polinômios ortogonais de Legendre e as funções b-spline, variando da segunda a quarta ordem. O modelo com os polinômios ortogonais de Legendre de segunda ordem para a parte fixa e as funções b-spline de quarta ordem para a parte aleatória foi o mais adequado para o ajuste dos dados analisados. Na trajetória fixa, este modelo estimou o pico de lactação entre 52-61 dias, com valor médio de 2,378 kg de leite/dia. A curva iniciou-se com uma produção média de 2,298 kg/dia, encerrando aos 305 dias com uma produção média de 0,758 kg/dia. As estimativas de herdabilidade variaram de 0,294 ± 0,135 a 0,794 ± 0,075. Maior variabilidade genética foi estimada para os controles leiteiros intermediários na trajetória da curva de lactação, entre 79 e 180 dias, com maiores estimativas de herdabilidade. As correlações genéticas entre os controles variaram entre 0,551 ± 0,125 e 0,998 ± 0,001, como maiores valores para produções de leite em dias próximos e subsequentes, e tornando-se menores à medida que os controles se distanciavam. A variabilidade genética estimada indica que é possível modificar por seleção a curva de lactação das cabras Saanen da população estudada. Esta seleção deve ser realizada entre 79 e 180 dias de lactação, período posterior ao pico de lactação, entretanto onde se observaram as maiores herdabilidades. A seleção neste ponto permitirá alterações na curva como um todo, em função das respostas genéticas correlacionadas.

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Phan, Anh cang. "Crack removal and hole filling on composite subdivision meshes." Thesis, Aix-Marseille, 2013. http://www.theses.fr/2013AIXM4068/document.

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Construire une surface lisse d'un objet 3D est un problème important dans de nombreuses applications graphiques. En particulier, les méthodes de subdivision permettent de passer facilement d'un maillage discret à une surface continue. Un problème général résultant de la subdivision de deux maillages initialement connectés le long d'un bord est l'apparition de fissures ou de trous entre eux. Ces fissures produisent non seulement des formes indésirables, mais induisent aussi des difficultés pour les traitements ultérieurs. Il faut donc réparer ces défauts de sorte que la surface obtenue soit lisse et puisse être subdivisée ou modifiée. Nous proposons de nouvelles méthodes pour relier deux maillages avec des résolutions différentes en utilisant une transformée en ondelettes B-splines et une approximation locale ou une interpolation locale à l'aide de fonctions de base radiales (RBF). Ces procédés génèrent un maillage de connexion où la continuité est contrôlée. La résolution du maillage est ajustable pour respecter le changement de résolution entre les zones grossières et fines. En outre, nous présentons des méthodes pour combler les trous à n-côtés, et le raffinement des maillages grâce à un schéma de subdivision adaptative. Nous avons conçu, implémenté et testé les algorithmes en MatLab pour illustrer nos méthodes et montrer des résultats expérimentaux. Ces algorithmes sont mis en oeuvre sur de nombreux modèles d'objets 3D avec des formes complexes. En outre, nous avons fourni des approches différentes pour chaque problème. Ainsi, les résultats des différentes approches sont comparés et évalués afin d'exploiter les avantages et les inconvénients de ces approches
Constructing a smooth surface of a 3D object is an important problem in many graphical applications. In particular, subdivision methods permit to pass easily from a discrete mesh to a continuous surface. A generic problem arising from subdividing two meshes initially connected along a common boundary is the occurrence of cracks or holes between them. These cracks not only produce undesired shapes, but also bring serious trouble for further mesh processing. They must be removed or filled so that the produced surface is smooth and can be further subdivided or edited. In order to remove cracks, we propose new methods for joining two meshes with different resolutions using a Lifted B-spline wavelet transform and a local approximation or radial basis function (RBF) local interpolation. These methods generate a connecting mesh where continuity is controlled from one boundary to the other and the connecting mesh can change gradually in resolution between coarse and fine areas. Additionally, we introduce methods for filling n-sided holes, and refining meshes with an adaptive subdivision scheme. We have designed, implemented, and tested the algorithms in MatLab to illustrate our proposed methods and show experimental results. These algorithms are implemented on many 3D object models with complex shapes. Additionally, we have provided some different approaches for each problem. Thus, results from the different approaches are compared and evaluated to exploit the advantages and disadvantages of these approaches

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Ondroušková, Jana. "Modelování NURBS křivek a ploch v projektivním prostoru." Master's thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2009. http://www.nusl.cz/ntk/nusl-228872.

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In the first part I discuss ancestors of NURBS curves and surfaces, rather Ferguson, Beziere, Coons and B-spline curves and surfaces and furthermore B-spline functions. In the second part I devote to NURBS curves and surfaces, their description as a linear combination of B-spline functions in the projective space. I specify conical arcs more detailed, their submit in the projective space and NURBS surfasec given as tensor product of NURBS curves. Last part is devote to describtion programs for modeling conicals and NURBS surface.

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Gdhami, Asma. "Méthodes isogéométriques pour les équations aux dérivées partielles hyperboliques." Thesis, Université Côte d'Azur (ComUE), 2018. http://www.theses.fr/2018AZUR4210/document.

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L’Analyse isogéométrique (AIG) est une méthode innovante de résolution numérique des équations différentielles, proposée à l’origine par Thomas Hughes, Austin Cottrell et Yuri Bazilevs en 2005. Cette technique de discrétisation est une généralisation de l’analyse par éléments finis classiques (AEF), conçue pour intégrer la conception assistée par ordinateur (CAO), afin de combler l’écart entre la description géométrique et l’analyse des problèmes d’ingénierie. Ceci est réalisé en utilisant des B-splines ou des B-splines rationnelles non uniformes (NURBS), pour la description des géométries ainsi que pour la représentation de champs de solutions inconnus.L’objet de cette thèse est d’étudier la méthode isogéométrique dans le contexte des problèmes hyperboliques en utilisant les fonctions B-splines comme fonctions de base. Nous proposons également une méthode combinant l’AIG avec la méthode de Galerkin discontinue (GD) pour résoudre les problèmes hyperboliques. Plus précisément, la méthodologie de GD est adoptée à travers les interfaces de patches, tandis que l’AIG traditionnelle est utilisée dans chaque patch. Notre méthode tire parti de la méthode de l’AIG et la méthode de GD.Les résultats numériques sont présentés jusqu’à l’ordre polynomial p= 4 à la fois pour une méthode deGalerkin continue et discontinue. Ces résultats numériques sont comparés pour un ensemble de problèmes de complexité croissante en 1D et 2D
Isogeometric Analysis (IGA) is a modern strategy for numerical solution of partial differential equations, originally proposed by Thomas Hughes, Austin Cottrell and Yuri Bazilevs in 2005. This discretization technique is a generalization of classical finite element analysis (FEA), designed to integrate Computer Aided Design (CAD) and FEA, to close the gap between the geometrical description and the analysis of engineering problems. This is achieved by using B-splines or non-uniform rational B-splines (NURBS), for the description of geometries as well as for the representation of unknown solution fields.The purpose of this thesis is to study isogeometric methods in the context of hyperbolic problems usingB-splines as basis functions. We also propose a method that combines IGA with the discontinuous Galerkin(DG)method for solving hyperbolic problems. More precisely, DG methodology is adopted across the patchinterfaces, while the traditional IGA is employed within each patch. The proposed method takes advantageof both IGA and the DG method.Numerical results are presented up to polynomial order p= 4 both for a continuous and discontinuousGalerkin method. These numerical results are compared for a range of problems of increasing complexity,in 1D and 2D

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Bahari, Mustapha. "Transport optimal pour la génération de maillage et le r-raffinement." Electronic Thesis or Diss., Université Côte d'Azur, 2024. http://www.theses.fr/2024COAZ5032.

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Dans cette thèse, nous développons des solveurs rapides et des procédures de génération de maillage adaptatif basés sur le transport optimal dans le contexte de l'Analyse Isogéométrique, en utilisant les B-Splines comme base des éléments finis. Notre approche garantit la construction d'une bijection, abordant ainsi un défi majeur de l'Analyse Isogéométrique. Nous utilisons des éléments finis standard pour résoudre l'équation de Monge-Ampère. Cependant, une analyse de cette approche montre des limitations significatives, notamment lorsqu'elle est confrontée à des variations importantes au voisinage de la frontière. Pour surmonter ce défi, nous dérivons une nouvelle formulation utilisant une discrétisation B-Splines compatible basée sur la suite de DeRham. De plus, nous introduisons de nouveaux solveurs rapides utilisant la méthode de diagonalisation rapide pour aborder efficacement cette question.Nous proposons une variété de tests et d'applications pour illustrer la performance et l'efficacité de notre approche. Celles-ci incluent des tests utilisant des solutions construites de l'équation de Monge-Ampère ainsi que des fonctions de densité analytiques. De plus, nous appliquons notre solveur à des problèmes elliptiques et à des problèmes dépendant du temps, en relevant des défis tels que l'obtention d'une précision élevée, la capture précise des interfaces, et la réduction efficace des oscillations.Finalement, la paramétrisation B-spline de presque toutes les géométries présentées repose sur les informations donnnées par le bord, utilisant une nouvelle approche basée sur le transport optimal
In this thesis, we develop fast solvers and adaptive mesh generation procedures based on the Optimal Transport using B-Splines Finite Elements within the Isogeometric Analysis framework. Our approach ensures the construction of a bijection mapping, addressing a major challenge in Isogeometric Analysis.Initially, we employ standard B-Splines Finite Elements to solve the Monge-Ampère Equation. However, an analysis of this approach reveals significant limitations, particularly when confronted with high variations near the boundary. To overcome this challenge, we derive a new formulation utilizing compatible B-Splines discretization based on a discrete DeRham sequence. Furthermore, we introduce new fast solvers using the Fast Diagonalization method to address this issue effectively.We provide various tests and applications to demonstrate the performance and efficiency of our novel approach. These include testing our approach using manufactured solutions of the Monge-Ampère equation and employing analytical density functions. Additionally, we apply our solver to elliptic problems and time-dependent problems, addressing challenges such as achieving higher accuracy, accurately capturing sharp interfaces, and effectively reducing oscillations.Finally, the parameterization of nearly all presented geometries relies on CAD-boundary information, employing a novel approach based on optimal transport

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Hamie, Ali. "Traitement statistique du signal : applications en biologie et économie." Thesis, Université Grenoble Alpes (ComUE), 2016. http://www.theses.fr/2016GREAS012/document.

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Dans cette thèse, nous nous intéressons à développer des outils mathématiques, afin de traiter une gamme des signaux biologiques et économiques. En premier lieu, nous proposons la transformée Dynalet, considérée comme une alternative, pour des signaux de relaxation sans symétrie interne, à la transformée de Fourier et à la transformée ondelette. L'applicabilité de cette nouvelle approximation est illustrée sur des données réelles. Ensuite, nous corrigeons la ligne de base des signaux biologiques spectrométriques, à l'aide d'une régression expectile pénalisée, qui, sur les applications proposées, est plus performante qu'une régression quantile. Puis, afin d'éliminer le bruit blanc, nous adaptons aux signaux spectrométriques une nouvelle approche combinant ondelette, seuillage doux et composants PLS. Pour terminer, comme les signaux peuvent être considérés comme des données fonctionnelles, d'une part, nous développons une vraisemblance locale fonctionnelle dont le but est d'effectuer une classification supervisée des courbes, et, d'autre part, nous estimons l'opérateur de régression pour une réponse scalaire positive non nulle, par minimisation de l'erreur quadratique moyenne relative. De plus, les lois asymptotiques de notre estimateur sont établies et son efficacité est illustrée sur des données simulées et sur des données spectroscopiques et économiques
In this thesis, we focus on developing mathematical tools to treat a range of biological and economic signals. First, we propose the Dynalet transform for non-symmetrical biological relaxation signals. This transform is considered as an alternative to the Fourier transform and the wavelet transform. The applicability of the new approximation approach is illustrated on real data. Then, for spectrometric biological signals, we correct the baseline using a penalized expectile regression. Thus, the proposed applications show that our proposed regression is more efficient than the quantile regression. Then to remove random noise, we adapt to spectrometric data a new denoising method that combine wavelets, soft thresholding rule and PLS components. Finally, note that the biological signals may be often regarded as functional data. On one hand, we develop a functional local likelihood aiming to perform a supervised classification of curves. On the other hand, we estimate the regression operator with positive responses, by minimizing the mean squared relative error. Moreover, The asymptotic distributions of our estimator are established and their efficiency is illustrated on a simulation study and on a spectroscopic and economic data set

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Xu, Bo. "A new method using B-splines as shape functions and the knot insertion algorithm for shape optimization." Thesis, Cranfield University, 2007. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.444808.

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Hadrich, Ben Arab Atizez. "Étude des fonctions B-splines pour la fusion d'images segmentées par approche bayésienne." Thesis, Littoral, 2015. http://www.theses.fr/2015DUNK0385/document.

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Dans cette thèse nous avons traité le problème de l'estimation non paramétrique des lois de probabilités. Dans un premier temps, nous avons supposé que la densité inconnue f a été approchée par un mélange de base B-spline quadratique. Puis, nous avons proposé un nouvel estimateur de la densité inconnue f basé sur les fonctions B-splines quadratiques, avec deux méthodes d'estimation. La première est base sur la méthode du maximum de vraisemblance et la deuxième est basée sur la méthode d'estimation Bayésienne MAP. Ensuite, nous avons généralisé notre étude d'estimation dans le cadre du mélange et nous avons proposé un nouvel estimateur du mélange de lois inconnues basé sur les deux méthodes d'estimation adaptées. Dans un deuxième temps, nous avons traité le problème de la segmentation statistique semi supervisée des images en se basant sur le modèle de Markov caché et les fonctions B-splines. Nous avons montré l'apport de l'hybridation du modèle de Markov caché et les fonctions B-splines en segmentation statistique bayésienne semi supervisée des images. Dans un troisième temps, nous avons présenté une approche de fusion basée sur la méthode de maximum de vraisemblance, à travers l'estimation non paramétrique des probabilités, pour chaque pixel de l'image. Nous avons ensuite appliqué cette approche sur des images multi-spectrales et multi-temporelles segmentées par notre algorithme non paramétrique et non supervisé
In this thesis we are treated the problem of nonparametric estimation probability distributions. At first, we assumed that the unknown density f was approximated by a basic mixture quadratic B-spline. Then, we proposed a new estimate of the unknown density function f based on quadratic B-splines, with two methods estimation. The first is based on the maximum likelihood method and the second is based on the Bayesian MAP estimation method. Then we have generalized our estimation study as part of the mixture and we have proposed a new estimator mixture of unknown distributions based on the adapted estimation of two methods. In a second time, we treated the problem of semi supervised statistical segmentation of images based on the hidden Markov model and the B-sline functions. We have shown the contribution of hybridization of the hidden Markov model and B-spline functions in unsupervised Bayesian statistical image segmentation. Thirdly, we presented a fusion approach based on the maximum likelihood method, through the nonparametric estimation of probabilities, for each pixel of the image. We then applied this approach to multi-spectral and multi-temporal images segmented by our nonparametric and unsupervised algorithm

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14

Barbosa, Daniel. "Automated assessment of cardiac morphology and function : An integrated B-spline framework for real-time segmentation and tracking of the left ventricle." Thesis, Lyon, INSA, 2013. http://www.theses.fr/2013ISAL0111.

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L’objectif principal de cette thèse est le développement de techniques de segmentation et de suivi totalement automatisées du ventricule gauche (VG) en RT3DE. Du fait de la nature difficile et complexe des données RT3DE, l’application directe des algorithmes classiques de vision par ordinateur est le plus souvent impossible. Les solutions proposées ont donc été formalisées et implémentées de sorte à satisfaire les contraintes suivantes : elles doivent permettre une analyse complètement automatique (ou presque) et le temps de calcul nécessaire doit être faible afin de pouvoir fonctionner en temps réel pour une utilisation clinique optimale. Dans ce contexte, nous avons donc proposé un nouveau cadre ou les derniers développements en segmentation d’images par ensembles de niveaux peuvent être aisément intégrés, tout en évitant les temps de calcul importants associés à ce type d’algorithmes. La validation clinique de cette approche a été effectuée en deux temps. Tout d’abord, les performances des outils développés ont été évaluées dans un contexte global se focalisant sur l’utilisation en routine clinique. Dans un second temps, la précision de la position estimée du contour du ventricule gauche a été mesurée. Enfin, les méthodes proposées ont été intégrées dans une suite logicielle utilisée à des fins de recherche. Afin de permettre une utilisation quotidienne efficace, des solutions conviviales ont été proposées incluant notamment un outil interactif pour corriger la segmentation du VG
The fundamental goal of the present thesis was the development of automatic strategies for left ventricular (LV) segmentation and tracking in RT3DE data. Given the challenging nature of RT3DE data, classical computer vision algorithms often face complications when applied to ultrasound. Furthermore, the proposed solutions were formalized and built to respect the following requirements: they should allow (nearly) fully automatic analysis and their computational burden should be low, thus enabling real-time processing for optimal online clinical use. With this in mind, we have proposed a novel segmentation framework where the latest developments in level-set-based image segmentation algorithms could be straightforwardly integrated, while avoiding the heavy computational burden often associated with level-set algorithms. Furthermore, a strong validation component was included in order to assess the performance of the proposed algorithms in realistic scenarios comprising clinical data. First, the performance of the developed tools was evaluated from a global perspective, focusing on its use in clinical daily practice. Secondly, also the spatial accuracy of the estimated left ventricular boundaries was assessed. As a final step, we aimed at the integration of the developed methods in an in-house developed software suite used for research purposes. This included user-friendly solutions for efficient daily use, namely user interactive tools to adjust the segmented left ventricular boundaries

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DI, TOMMASO DEVIS. "APPLICATION AND DEVELOPMENT OF THE LINEAR COMBINATION OF ATOMIC ORBITALS B-SPLINE DENSITY FUNCTIONAL THEORY METHOD FOR THE MOLECULAR ELECTRONIC CONTINUUM." Doctoral thesis, Università degli studi di Trieste, 2006. http://thesis2.sba.units.it/store/handle/item/13234.

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2004/2005
Lo scopo della presente tesi è l'applicazione e lo sviluppo del metodo LCAO B-spline DFT, basato sulla Combinazione Lineare degli Orbitali Atomici (LCAO), sulla Teoria del Funzionale Densità (DFT) e sull'impiego delle funzioni di base Bspline, per lo studio della fotoionizzazione molecolare. Nel Capitolo 1 viene considerata una breve introduzione al processo di fotoionizzazione e alla teoria della fotoionizzazione molecolare. Nel Capitolo 2 vengono presentati i metodi computazionali utilizzati durante il presente lavoro di tesi. I risultati ottenuti sono presentati nei successivi Capitoli della tesi. Il lavoro è suddiviso in tre parti. Nella prima parte (Capitoli 3-6) il metodo LCAO B-spline DFT è applicato allo studio del Dicroismo Circolare nella Distribuzione Angolare (CDAD) dei fotoelettroni emessi da molecole chirali, ionizzate da luce circolarmente polarizzata di definita elicità. Un primo studio computazionale sull'effetto CDAD è focalizzato su una serie di derivati chirali dell'ossirano, con lo scopo di identificare tendenze lungo la serie molecolare. I risultati evidenziano una inaspettata sensibilità da parte del dicroismo circolare verso cambiamenti nella struttura elettronica molecolare. Inoltre i valori calcolati sottolineano come lintensità dell'effetto CD AD è da attribuire non tanto alla chiralità dello stato iniziale, ma bensì alla capacità della funzione d'onda del fotoelettrone (completamente delocalizzata su tutta la molecola) di sondare l'asimmetria nel potenziale molecolare effettivo. Il metodo LCAO B-spline DFT è quindi applicato allo studio del dicroismo circolare nella distribuzione angolare dei fotoelettroni emessi dai livelli di core e di valenza degli enantiomeri della canfora. I risultati sono confrontati con i valori calcolati attraverso l'approccio Continuum Multiple Scattering: i due metodi teorici mostrano un sostanziale accordo nei risultati. Inoltre, un confronto dei risultati calcolati con i dati sperimentali disponibili mostra un accordo sostanziale se non addirittura quantitativo. E' inoltre presentato uno studio teorico e sperimentale sul dicroismo circolare nella distribuzione angolare dei fotoelettroni emessi dai livelli di valenza del 3- idrossitetraidrofurano, il quale è una molecola relativamente flessibile. Questo lavoro mette luce su nuove caratteristiche del dicroismo in fotoemissione, il quale appare molto sensibile a fattori di tipo conformazionale. L'influenza degli effetti conformazionali sui parametri dinamici di fotoionizzazione, con particolare attenzione all'effetto CDAD, è quindi investigata in dettaglio. Il metodo LCAO E-spline DFf è applicato ai conformeri della molecola (1R,2R)-1,2-dibromo-1,2-dicloro-1,2-difluoroetano. Il parametro dicroico mostra una significativa sensibilità verso il conformero della molecola. Ciò suggerisce che il profilo energetico del parametro dicroico potrebbe essere utilizzato come un fingerprint dei conformeri di una molecola chirale. Il metodo computazionale è anche applicato alla rotazione del metile nella molecola (S)-ossirano, in modo da verificare l'assunzione che la rotazione del metile non influisca in maniera significativa sui valori calcolati dell'effetto CDAD. Si verifica invece come la rotazione del gruppo metile provochi variazioni inaspettate e drammatiche sul profilo del parametro dicroico. La seconda parte del lavoro (Capitolo 7) riguarda l'investigazione teorica sulla correttezza dell'assunzione che il Eranching Ratio nella ionizzazione dei livelli di core di siti atomici chimicamente diversi dello stesso elemento, segua il rapporto statistico. Il metodo LCAO E-spline DFT è stato impiegato per calcolare in maniera accurata le sezioni d'urto associate alla ionizzazione degli orbitali ls dei carboni per un set di molecole organiche scelte. I risultati mostrano che deviazioni nella sezione d'urto inducono forti andamenti non statistici da parte dei Eranching Ratios relativi alla ionizzazione dei livelli core, fino a diversi e V sopra la soglia di ionizzazione. La parte finale della tesi (Capitolo 8) riguarda il problema delle shape resonances. La razionalizzazione delle strutture risonanti, spesso presenti nello spettro molecolare del continuo, è un problema ampiamente discusso. Nel presente lavoro una nuova metodologia per localizzare e caratterizzare in termini molecolari le shape resonances viene proposta. Partendo da un sistema modello, è stato sviluppato un metodo per caratterizzare le risonanze in termini di contributo da parte degli orbitali virtuali di valenza. Il metodo sviluppato è quindi esteso al caso molecolare ed applicato alla localizzazione e caratterizzazione delle shape resonances che appaiono nella fotoionizzazione dei livelli crg di core e di valenza di N1.
XVIII Ciclo
1977
Versione digitalizzata della tesi di dottorato cartacea.

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Bezchlebová, Daniela. "Analýza funkčních dat a modelování specifické míry úmrtnosti a plodnosti." Master's thesis, Vysoká škola ekonomická v Praze, 2014. http://www.nusl.cz/ntk/nusl-193581.

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The aim of this thesis is to analyze two major indicators representing the processes of natural changes in population, which are not influenced by age structure -- age specific fertility rate and age specific mortality rate and to introduce functional data analysis, which has recently become increasingly applied in many scientific fields. The functional data analysis is introduced on the Czech demographic data set for more than last sixty years. The thesis briefly describes historical development of mortality and fertility and also describes selected methods of functional data analysis by using statistical program R. Functional data analysis provides a wide variety of graphics tools to explore the data which we called functional and help us to explore all typical and atypical features, identify outliers etc.

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Guedes, Silva Ronaldo Rouvher. "Nonparametric Models for Dependent Functional Data." Doctoral thesis, Università degli studi di Padova, 2016. http://hdl.handle.net/11577/3427133.

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In the framework of functional data analysis we propose two Bayesian Nonparametric models. In the first model, motivated by an application in neuroimaging, functions are assumed to be spatially correlated and clustered together by an underlying Functional Dependent Dirichlet process which encodes a conditional autoregressive dependence structure to guide the spatial selection. Spatial symmetries of the functional responses in the brain can be appropriately accounted for in our framework. Motivated by the Italian natural gas balancing platform, in the second model time dependence are induced in the weights of the underlying Functional Dependent Dirichlet process through a dynamic linear model defined over a partitioned function space. Typical shape characteristics of the functions are modeled by flexible spline-based curve estimates as atoms of the process. In both applications Bayesian variable selection techniques are used to select significant sets of bases coefficients in each cluster. Gibbs sampling algorithms are developed for posterior computation, simulation studies and application to real data assess the performance of our approaches.
Nel contesto dell'analisi di dati funzionali, in questa tesi, vengono presentati due modelli Bayesiani non parametrici. Il primo modello è motivato da un problema di analisi di neuroimmagini, e considera funzioni correlate spazialmente e raggruppate seguendo un processo di Dirichlet dipendente funzionale (Functional Dependent Dirichlet process) che include una struttura di dipendenza autoregressiva condizionata per modellare la selezione spaziale. Un tale modello permette di considerare in maniera appropriata simmetrie spaziali delle risposte funzionali nel cervello. Il secondo modello è invece motivato dalla piattaforma italiana di bilanciamento del mercato del gas naturale e include una dipendenza temporale tra funzioni attraverso i pesi di un processo di Dirichlet dipendente funzionale basato su un modello lineare dinamico definito su una partizione dello spazio funzionale. Forme caratteristiche tipiche delle funzioni vengono modellate da curve flessibili basate su splines che formano gli atomi del processo di Dirichlet. In entrambe le applicazioni vengono usate tecniche bayesiane di selezione di variabili per scegliere le funzioni di base per le splines in ciascun cluster. Algoritmi di tipo Gibbs sampling sono sviluppati per il calcolo delle distribuzioni a posteriori. Vengono proposti studi di simulazione e applicazioni a dati reali per verificare l’appropriatezza degli approcci proposti.

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Laureano, Monyka Marianna Massolini [UNESP]. "Estudo genético quantitativo do fluxo lácteo em bovinos da raça Holandesa." Universidade Estadual Paulista (UNESP), 2008. http://hdl.handle.net/11449/102782.

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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)
Parâmetros genéticos para o fluxo lácteo medido no dia do controle (FLDC) de primeiras lactações de vacas da raça Holandesa foram estimados utilizando modelos de dimensão finita (TDM) e modelos de regressão aleatória. Para os TDM foram analisadas 10 características por meio de modelos uni e bi e multi-características e de repetibilidade, que continham como aleatórios, o efeito genético aditivo e o efeito residual e, como efeitos fixos, o grupo de contemporâneos e as covariáveis idade da vaca ao parto. A variável número de dias em lactação foi incluída somente no modelo de repetibilidade. Para os MRA, foram considerados os efeitos aleatórios genético aditivo direto, de ambiente permanente e o residual. Foram considerados como efeitos fixos, o grupo de contemporâneos, os efeitos linear e quadrático da covariável idade da vaca ao parto e a curva média de lactação da população, modelada por meio de polinômios ortogonais de Legendre de quarta ordem. Os efeitos aleatórios genético aditivo e de ambiente permanente foram modelados por meio de regressão aleatória sobre polinômios ortogonais de Legendre e por meio de funções b-splines. Diferentes estruturas de variâncias residuais foram testadas, por meio de classes contendo 1, 7, 10, 20 e 43 variâncias residuais, para os MRA modelados por meio de polinômios de Legendre. Já, para os MRA modelados por funções b-splines, a estrutura residual foi considerada heterogênea, contendo 7 classes de variâncias. Os MRA foram comparados usando o teste de razão de verossimilhança, o critério de informação de Akaike e o critério de informação de Bayesiano de Schwarz. As estimativas de herdabilidade (h2) para os FLDC variaram de 0,23 a 0,32 nas análises unicaracterísticas, de 0,24 a 0,32 nas bi-características e de 0,28 a 0,37 nas multicaracterísticas. Os valores de h2 estimados variaram no decorrer da...
Flow milk genetic parameters to the first lactation test-day milk yields of Holstein cattle were estimated using Test-day models (TDM) and Random regression models (RRM). Ten TDM differents traits were analyzed using uni, bi and multi-trait and repeatability animal models, that included the additive genetic as random effect and the fixed effects of contemporary group, age of cow (linear and quadratic) as covariables. The days in milk (linear) variable was included only at repeatability model. To RRM were included the additive genetic, permanent environmental and residual as random effects, the fixed effects of contemporary group, age of cow as covariable (linear and quadratic effects) and a 4th-order Legendre orthogonal polynomials of days in milk, to model the mean trend. The additive genetic and permanent environmental effects were fitted by Legendre orthogonal polynomials and b-splines functions. Different structures of residual variances were used, through the variances classes containing 1, 7, 10, 20, and e 43 residual variances, to the models fitted by Legendre orthogonal polynomials. Moreover, for the RRM fitted by b-splines-functions, the residual estructure was considered heterogeneous, having 7 variance classes. The RRM were compared by Likelihood ratio test, Bayesian and Akaike´s information criteria. The heritability estimated ranged from 0.23 to 0.32 by uni-trait analyses, from 0.24 to 0.32 by bi-traits analyses and from 0.28 to 0.37 by multi-trait analyses. The h2 estimates varied during the lactation being the highest estimate at the fourth month. The estimate obtained by the repeatability model was 0.27, and a repeatability estimate of 0.66. For the MRA fitted by Legendre orthogonal polynomials, related to the residual variance, the best model the one that deemed 7 residual classes. For the additive and permanent environmental effects, the having 3th-order... (Complete abstract click electronic access below)

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19

Zhang, Han. "Detecting Rare Haplotype-Environmental Interaction and Nonlinear Effects of Rare Haplotypes using Bayesian LASSO on Quantitative Traits." The Ohio State University, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=osu149969433115895.

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20

Chen, Chen. "Evaluating Time-varying Effect in Single-type and Multi-type Semi-parametric Recurrent Event Models." Diss., Virginia Tech, 2015. http://hdl.handle.net/10919/64371.

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This dissertation aims to develop statistical methodologies for estimating the effects of time-fixed and time-varying factors in recurrent events modeling context. The research is motivated by the traffic safety research question of evaluating the influence of crash on driving risk and driver behavior. The methodologies developed, however, are general and can be applied to other fields. Four alternative approaches based on various data settings are elaborated and applied to 100-Car Naturalistic Driving Study in the following Chapters. Chapter 1 provides a general introduction and background of each method, with a sketch of 100-Car Naturalistic Driving Study. In Chapter 2, I assessed the impact of crash on driving behavior by comparing the frequency of distraction events in per-defined windows. A count-based approach based on mixed-effect binomial regression models was used. In Chapter 3, I introduced intensity-based recurrent event models by treating number of Safety Critical Incidents and Near Crash over time as a counting process. Recurrent event models fit the natural generation scheme of the data in this study. Four semi-parametric models are explored: Andersen-Gill model, Andersen-Gill model with stratified baseline functions, frailty model, and frailty model with stratified baseline functions. I derived model estimation procedure and and conducted model comparison via simulation and application. The recurrent event models in Chapter 3 are all based on proportional assumption, where effects are constant. However, the change of effects over time is often of primary interest. In Chapter 4, I developed time-varying coefficient model using penalized B-spline function to approximate varying coefficients. Shared frailty terms was used to incorporate correlation within subjects. Inference and statistical test are also provided. Frailty representation was proposed to link time-varying coefficient model with regular frailty model. In Chapter 5, I further extended framework to accommodate multi-type recurrent events with time-varying coefficient. Two types of recurrent-event models were developed. These models incorporate correlation among intensity functions from different type of events by correlated frailty terms. Chapter 6 gives a general review on the contributions of this dissertation and discussion of future research directions.
Ph. D.

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Zapata, Abellán Felipe. "Electron dynamics induced by single and multiphoton processes in atoms and molecules." Thesis, Sorbonne université, 2019. http://www.theses.fr/2019SORUS431.

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Cette thèse contribue aux développements de méthodes numériques utilisées pour reproduire la dynamique électronique induite par des processus à un et plusieurs photons dans les atomes et molécules. Dans le domaine perturbatif, la photoexcitation et la photoionisation ont été étudiées à l'aide de la théorie de la fonctionnelle de la densité à séparation de portée, dans le but de prendre en compte les effets d'interaction électron-électron. De plus, dans le domaine non-perturbatif, les spectres au-delà du seuil d'ionisation et les spectres de génération d'harmoniques d'ordres élevés ont été simulés en utilisant différentes représentations de la fonction d'onde dépendante du temps du système étudié. Cette étude ouvre la possibilité d'explorer des processus matière-rayonnement dans des systèmes plus complexes
The present PhD thesis contributes to the development of numerical methods used to reproduce the electron dynamics induced by single and multiphoton processes in atoms and molecules. In the perturbative regime, photoexcitation and photoionization have been studied in atoms with range-separated density-functional theory, in order to take into account the electron-electron interaction effects. Moreover, in the non-perturbative regime, above-threshold ionization and high-harmonic generation spectra have been simulated using different representations for the time-dependent wave function for the purpose of describing the continuum states of the irradiated system. Our studies open the possibility of exploring matter-radiation processes in more complex systems

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Estecahandy, Elodie. "Contribution à l'analyse mathématique et à la résolution numérique d'un problème inverse de scattering élasto-acoustique." Phd thesis, Université de Pau et des Pays de l'Adour, 2013. http://tel.archives-ouvertes.fr/tel-00880628.

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La détermination de la forme d'un obstacle élastique immergé dans un milieu fluide à partir de mesures du champ d'onde diffracté est un problème d'un vif intérêt dans de nombreux domaines tels que le sonar, l'exploration géophysique et l'imagerie médicale. A cause de son caractère non-linéaire et mal posé, ce problème inverse de l'obstacle (IOP) est très difficile à résoudre, particulièrement d'un point de vue numérique. De plus, son étude requiert la compréhension de la théorie du problème de diffraction direct (DP) associé, et la maîtrise des méthodes de résolution correspondantes. Le travail accompli ici se rapporte à l'analyse mathématique et numérique du DP élasto-acoustique et de l'IOP. En particulier, nous avons développé un code de simulation numérique performant pour la propagation des ondes associée à ce type de milieux, basé sur une méthode de type DG qui emploie des éléments finis d'ordre supérieur et des éléments courbes à l'interface afin de mieux représenter l'interaction fluide-structure, et nous l'appliquons à la reconstruction d'objets par la mise en oeuvre d'une méthode de Newton régularisée.

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Liu, Jia-Hong, and 劉家紘. "Identification of Nonlinear Wiener Model Using B-spline Functions." Thesis, 2011. http://ndltd.ncl.edu.tw/handle/8j4jj9.

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碩士
國立臺北科技大學
化學工程研究所
99
Model identification is very important for control system design. The identification of nonlinear model is of particular interest because most chemical processes are nonlinear in nature. The block-oriented nonlinear models, which involve a cascade combination of a linear dynamic subsystem and a nonlinear static function, are related very closely to linear ones and can be easily adapted to linear control techniques. One of the most frequently studied classes of block-oriented nonlinear models is the Wiener model, in which the nonlinear static element is preceded by the linear dynamic element. This study investigates the identification method of Wiener model. In the literature, most of the identification methods for Wiener model use polynomial to represent the nonlinearity. The polynomial representations become more complicated and cannot give good approximation for systems with highly nonlinear behavior or for multivariable systems. This study proposes a new identification method that represents the linear dynamics as finite impulse response (FIR) models and approximates the static nonlinearity by expansions of B-spline functions. Linear regression equations for the model parameters are formulated and the unknown parameters are identified using the least-squares estimation. Furthermore, various nonlinear functions can be compactly approximated by properly selecting the knots sequence of B-spline functions. In the proposed method, iterative and/or nonlinear optimization procedures are avoided and special design of the test input signal is not required, which enhance the practical applicability of the proposed method. Simulation examples demonstrate that the proposed identification method is valid.

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劉火炎. "Pipeline computations of B-spline functions and its applications." Thesis, 1989. http://ndltd.ncl.edu.tw/handle/26696226490511553579.

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Shan, Tse-Fen, and 山澤棻. "Lagrange,Divided Difference Polynomials and B-spline Functions and Their Applications." Thesis, 2011. http://ndltd.ncl.edu.tw/handle/26888109000126820096.

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碩士
中興大學
應用數學系所
99
In this thesis, we will recall the definition of polynomial interpolation to study the properties of B-splines and use collocation method with B-splines as basis functions for the numerical solutions of boundary value problems. We discuss the functions of B-splines in detail starting from the recursion formula of B-splines. We provide the procedure of reducing numbers of basis functions by boundary conditions. Third order and fifth order boundary value problems are employed for applications. Then we give s numerical experiment in last section and in two points singular perturbed problems we find the relationship between the solutions and the ratio of h

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Chu, Kuan-Hua, and 朱冠華. "Numerical Methods for the Monge-Amp`ere Equation by B-spline Functions." Thesis, 2017. http://ndltd.ncl.edu.tw/handle/91568229314163523398.

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碩士
國立中興大學
應用數學系所
105
In this thesis, we used the collection method with B-splines as basis functions for the numerical solutions of the partial differential equation au_{xx} (x,y) + bu_{xy}(x,y) +cu_{yy}(x,y) =f(x,y), in $Omega$. u(x,y)=g(x,y), on partialOmega. If a=c and b=0 then the equation in (0.1) is the well-known Poisson equation. In order to consider the approximations of the Monge-Amp`ere equation, the purpose of this research is considering approximationsof solutions of (0.1). For instant, let lambda_1(u) and lambda_2(u) be the eigenvalues of D^2u where u satisfies det D^2 u = f(u) in Omega and u= g on partial Omega. Then u satisfies riangle u = sqrt{lambda_1^2(u) + lambda_2^2(u) +2 f(u) }. Thus, one can carry out the following iterations: 1. Choose the first guess u^0. 2. Solve u^1 from riangle u^1 = sqrt{2f(u^0)}. 3. Solve u^{n+1} from riangle u^{n+1} = sqrt{2f(u^n) + lambda _1^2(u^n) + lambda^2_2(u^n);}. We consider the Dirichlet problem in dimension two. In this research, a new basis is provided which reduces the number of basis functions and coincides with that of the knots. The reducing process is using the boundary conditions to redefine the basis. The approximation solutions are solved by the argument of the tensor product of matrices.

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洪宗瑾. "Constrained minimum-time path planning for robot manipulatorsvia virtual knots of the cubic B-spline functions." Thesis, 1988. http://ndltd.ncl.edu.tw/handle/41342635606597348774.

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Flores, Contreras Melvin Estuardo. "Real-Time Trajectory Generation for Constrained Nonlinear Dynamical Systems Using Non-Uniform Rational B-Spline Basis Functions." Thesis, 2008. https://thesis.library.caltech.edu/682/2/mflores_cds_thesis.pdf.

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The thesis describes a new method for obtaining minimizers for optimal control problems whose minima serve as control policies for guiding nonlinear dynamical systems to achieve prescribed goals under imposed trajectory and actuator constraints. One of the major contributions of the present work resides in the approximation of such minimizers by piecewise polynomial functions expressed in terms of a linear combination of non-uniform rational B-spline (NURBS) basis functions and the judicious exploitation of the properties of the resulting NURBS curves to improve the computational effort often associated with solving optimal control problems for constrained dynamical systems.

In particular, by exploiting the two structures combined in a NURBS curve, NURBS basis functions and an associated union of overlapping polytopes constructed from the coefficients of the linear combination, we are able to separate an optimal control problem into two subproblems | guidance and obstacle avoidance, making the original problem tractable. This is accomplished by laying out the union of overlapping polytopes in such a way that they delineate a section of space that avoids all obstacles and then manipulating the NURBS basis functions to obtain trajectories that are guaranteed to remain bounded by this section of space without explicitly including the conjunction of disjunctions naturally induced from obstacles into the guidance problem.

In addition, we show how one can construct systematically a feasible region that corresponds to a NURBS parameterization starting from an ordered union of pairwise adjacently overlapping nonempty compact convex sets. Specifically, we show how to setup a nonlinear programming problem to solve for the feasible region in terms of an ordered union of pairwise adjacently overlapping polytopes with nonempty interiors by maximizing the sum of their volumes and starting from a feasible region described by an ordered union of pairwise adjacently overlapping nonempty convex compact simi-algebraic sets. Finally, we show how this strategy can be implemented practically for an autonomous system traversing an urban environment.

Finally, this work culminated in the filing of patent US20070179685 on behalf of Northrop Grumman for the Space Technology sector and in the development of the NURBS-based OTG software package. This C++ package contains the theoretical results of this thesis in the form of an object-oriented implementation optimized for real-time trajectory generation.

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29

Sheng, Chen Shun, and 陳舜生. "The Design of FIR Digital Filter by Using B-spline Function." Thesis, 1995. http://ndltd.ncl.edu.tw/handle/89321104238483539098.

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30

Feng, Po-Wei. "Functional representation and manipulation of shapes with applications in surface and solid modeling." Thesis, 2013. http://hdl.handle.net/1911/71952.

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Real-valued functions have wide applications in various areas within computer graphics. In this work, we examine three representation of shapes using functions. In particular, we study the classical B-spline representation of piece-wise polynomials in the univariate domain. We provide a generalization of B-spline to the bivariate domain using intuition gained from the univariate construction. We also study the popular scheme of representing 3D density distribution using a uniform, rectilinear grid, where we provide a novel contouring scheme that culls occluded inner geometries. Lastly, we examine a ray-based representation for 3D indicator functions called ray-rep, for which we present a novel meshing scheme with multi-material extensions.

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31

Guo, Zhi-Chang, and 郭志昌. "A high order panel method using B-splines blending function." Thesis, 1993. http://ndltd.ncl.edu.tw/handle/75272585006751036969.

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32

Jhy-Chang, Guo, and 郭志昌. "A High Order Panel Mehtod Using B-splines Blending Function." Thesis, 1993. http://ndltd.ncl.edu.tw/handle/32930218901279465544.

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33

Kuo, Chung-Yu, and 郭重佑. "Nonlinear Function Approximation using B-spline Neural Networks and Reduced-Form Genetic Algorithms." Thesis, 2004. http://ndltd.ncl.edu.tw/handle/83653240194501929485.

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碩士
輔仁大學
電子工程學系
92
In this thesis, a novel method for gene boundary adjustment of reduced-form genetic algorithms (GBARGA) is proposed to tune the control points of B-spline neural networks. GBARGA is developed not only to search for the optimal control points but also to adaptively tune the boundaries of the control points (genes) of the B-spline neural networks by way of enlarging the search space of the control points (genes). To reduce the iteration of learning of the reduced-form genetic algorithm, GBARGA is derived, such that preferable boundaries of the control points (genes) of B-spline neural networks are determined and paralleled with the optimal control points searched. It is shown that better efficiency can be obtained if the boundaries of the control points (genes) are adjusted properly for the RGA-based B-spline neural networks. In other way, we also proposed a gradational B-spline neural network (GBNN) to approximate an unknown system. The GBNN scheme not only can approximate the overall systems but also reduce the number of the control points to enhauce the approximation performance and reduce the searching iterations. Finally, several examples are illustrated to show the effectiveness of the GBARGA and GBNN.

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34

Yen, Chin-Tien, and 顏金田. "A Study of Structural Shape Design by Topology Optimization and B-spline Function." Thesis, 2007. http://ndltd.ncl.edu.tw/handle/86308111479096685335.

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碩士
淡江大學
航空太空工程學系碩士班
95
A Methodology of structural shape design by topology optimization and B-spline function was developed in this study. The finite element analysis software ANSYS was used for structural analysis. The optimum shape design was obtained by the concept of material distribution borrowed from density method with sequential linear programming. In addition to using the element growth-removal combined method (EGRCM) simultaneously to grow and remove the essential element and the non-essential element, the concept of B-spline curve was used to smooth the design shape.Three stages topology design was employed in this study. After three stages design strategy , the primitive optimum design can be improved to more practical design. Six examples were discussed in the numerical examples. The results of final design were better than the traditional topology design. We hope the results of this study can provide the convenience of manufacturing to the industry of structural design.

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35

YANG, CHING-WEN, and 楊景雯. "Self-Updating Process with B-splines on Functional Data Clustering." Thesis, 2018. http://ndltd.ncl.edu.tw/handle/23uyn2.

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碩士
國立臺北大學
統計學系
106
The self-updating process (SUP) is competitive in clustering data with noise, data with a large number of clusters, and unbalanced data. This paper presents an extension of SUP to functional data clustering by the use of B-spline basis functions. The curves in data are first represented by B-spline functions, then the updating process is to perform clustering in the B-spline space. This paper provides comparison results between the proposed extension of SUP and other existing methods for functional data clustering.

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36

Lin, Jia-Syun, and 林佳勳. "Application of Density Functional Theory with B-splines to Atomic System : The PBE Functional." Thesis, 2017. http://ndltd.ncl.edu.tw/handle/8639c4.

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碩士
國立高雄師範大學
物理學系
105
Density functional theory (DFT) is one of the methods to calculate many-electron systems. Calculated the DFT, only need to deal with a single variable; thus, the calculation is very convenient and fast, along with the development of theory, results of the DFT calculation more and more accurate. Therefore, the DFT is widely used for the calculation of many-electronic systems in recent years. And the choice of the basis will affect the computational efficiency of the theory. This paper will use B-splines as a basis function, Applications in simple hydrogen atom system and processing of many-electron systems by density functional theory. The density functional theory is use the PW92 and PBE of exchange-correlation energy approximate method, calculate atomic number 1 to 18 of the atomic system. By a quick and accurate calculate of the result with well-description of orbital wave function, the B-spline is suited for applied to the calculation of atomic systems.

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37

Lin, Sang-Jung, and 林三榮. "Application of B-splines Basis in Density Functional Theory for Diatomic Molecules." Thesis, 1998. http://ndltd.ncl.edu.tw/handle/51104598870955799820.

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碩士
國立清華大學
物理學系
86
The B-spline basis is used to calculate for diatomic molecules in DFT. We construct orbital wave functions and density functions by the B-spline. Matrixs constructed by nonrelativistic KS equations and Poisson equations in B-spline are solved as eigenvalue problems, self-consistent iteration. These self-consistent-field calculations with local-densityapproximation(LDA), local-spin-density (LSD) approximation, and generalized gradient expansion(GGA) approximation can obtain good results by using appropriate exchange-correlation approaches. Gunnarsson-Lundqvist(GL) and Ceperley-Alder(CA) exchange-correlation potentials of homogenous electron gases are used for solving KS equation. The generalized gradient expansion(GGA) approximation which considers the gradient expansion of density also be calculated. In this work, calculations within LDA, LSD, and GGA formalism constructed by prolate spheroidal coordinate and B-spline basis are run by programs in C language. The homonuclear diatomic molecule of lithum is calculated, and we attain excellent results. Effects of relativistic and reduced mass do not consider in this work.

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38

鄭弘泰. "Applications of finite B-splines basis in density functional theories for atoms from H(Z." Thesis, 1996. http://ndltd.ncl.edu.tw/handle/62169523941285880345.

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39

Narayan, Shashi. "Smooth Finite Element Methods with Polynomial Reproducing Shape Functions." Thesis, 2013. http://etd.iisc.ac.in/handle/2005/3332.

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A couple of discretization schemes, based on an FE-like tessellation of the domain and polynomial reproducing, globally smooth shape functions, are considered and numerically explored to a limited extent. The first one among these is an existing scheme, the smooth DMS-FEM, that employs Delaunay triangulation or tetrahedralization (as approximate) towards discretizing the domain geometry employs triangular (tetrahedral) B-splines as kernel functions en route to the construction of polynomial reproducing functional approximations. In order to verify the numerical accuracy of the smooth DMS-FEM vis-à-vis the conventional FEM, a Mindlin-Reissner plate bending problem is numerically solved. Thanks to the higher order continuity in the functional approximant and the consequent removal of the jump terms in the weak form across inter-triangular boundaries, the numerical accuracy via the DMS-FEM approximation is observed to be higher than that corresponding to the conventional FEM. This advantage notwithstanding, evaluations of DMS-FEM based shape functions encounter singularity issues on the triangle vertices as well as over the element edges. This shortcoming is presently overcome through a new proposal that replaces the triangular B-splines by simplex splines, constructed over polygonal domains, as the kernel functions in the polynomial reproduction scheme. Following a detailed presentation of the issues related to its computational implementation, the new method is numerically explored with the results attesting to a higher attainable numerical accuracy in comparison with the DMS-FEM.

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40

Narayan, Shashi. "Smooth Finite Element Methods with Polynomial Reproducing Shape Functions." Thesis, 2013. http://etd.iisc.ernet.in/2005/3332.

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A couple of discretization schemes, based on an FE-like tessellation of the domain and polynomial reproducing, globally smooth shape functions, are considered and numerically explored to a limited extent. The first one among these is an existing scheme, the smooth DMS-FEM, that employs Delaunay triangulation or tetrahedralization (as approximate) towards discretizing the domain geometry employs triangular (tetrahedral) B-splines as kernel functions en route to the construction of polynomial reproducing functional approximations. In order to verify the numerical accuracy of the smooth DMS-FEM vis-à-vis the conventional FEM, a Mindlin-Reissner plate bending problem is numerically solved. Thanks to the higher order continuity in the functional approximant and the consequent removal of the jump terms in the weak form across inter-triangular boundaries, the numerical accuracy via the DMS-FEM approximation is observed to be higher than that corresponding to the conventional FEM. This advantage notwithstanding, evaluations of DMS-FEM based shape functions encounter singularity issues on the triangle vertices as well as over the element edges. This shortcoming is presently overcome through a new proposal that replaces the triangular B-splines by simplex splines, constructed over polygonal domains, as the kernel functions in the polynomial reproduction scheme. Following a detailed presentation of the issues related to its computational implementation, the new method is numerically explored with the results attesting to a higher attainable numerical accuracy in comparison with the DMS-FEM.

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41

Wischerhoff, Marius. "Reconstruction of Structured Functions From Sparse Fourier Data." Doctoral thesis, 2015. http://hdl.handle.net/11858/00-1735-0000-001C-7131-B.

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42

"A Mesh-Free Finite Element Solution for Unilateral Contact Problems." Doctoral diss., 2010. http://hdl.handle.net/2286/R.I.8783.

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abstract: Current trends in the Computer Aided Engineering (CAE) involve the integration of legacy mesh-based finite element software with newer solid-modeling kernels or full CAD systems in order to simplify laborious or highly specialized tasks in engineering analysis. In particular, mesh generation is becoming increasingly automated. In addition, emphasis is increasingly placed on full assembly (multi-part) models, which in turn necessitates an automated approach to contact analysis. This task is challenging due to increases in algebraic system size, as well as increases in the number of distorted elements - both of which necessitate manual intervention to maintain accuracy and conserve computer resources. In this investigation, it is demonstrated that the use of a mesh-free B-Spline finite element basis for structural contact problems results in significantly smaller algebraic systems than mesh-based approaches for similar grid spacings. The relative error in calculated contact pressure is evaluated for simple two dimensional smooth domains at discrete points within the contact zone and compared to the analytical Hertz solution, as well as traditional mesh-based finite element solutions for similar grid spacings. For smooth curved domains, the relative error in contact pressure is shown to be less than for bi-quadratic Serendipity elements. The finite element formulation draws on some recent innovations, in which the domain to be analyzed is integrated with the use of transformed Gauss points within the domain, and boundary conditions are applied via distance functions (R-functions). However, the basis is stabilized through a novel selective normalization procedure. In addition, a novel contact algorithm is presented in which the B-Spline support grid is re-used for contact detection. The algorithm is demonstrated for two simple 2-dimensional assemblies. Finally, a modified Penalty Method is demonstrated for connecting elements with incompatible bases.
Dissertation/Thesis
Ph.D. Mechanical Engineering 2010

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43

Paul, Alexandre. "Application des méthodes de partitionnement de données fonctionnelles aux trajectoires de voiture." Thesis, 2020. http://hdl.handle.net/1866/25430.

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La classification et le regroupement des données fonctionnelles longitudinales ont fait beaucoup de progrès dans les dernières années. Plusieurs méthodes ont été proposées et ont démontré des résultats prometteurs. Pour ce mémoire, on a comparé le comportement des algorithmes de partitionnement sur un ensemble de données décrivant les trajectoires de voitures dans une intersection de Montréal. La motivation est qu’il est coûteux et long de faire la classification manuellement et on démontre dans cet ouvrage qu’il est possible d’obtenir des prédictions adéquates avec les différents algorithmes. Parmi les méthodes utilisées, la méthode distclust utilise l’approche des K-moyennes avec une notion de distance entre les courbes fonctionnelles. On utilise aussi une classification par mélange de densité gaussienne, mclust. Ces deux approches n’étant pas conçues uniquement pour le problème de classification fonctionnelle, on a donc également appliqué des méthodes fonctionnelles spécifiques au problème : fitfclust, funmbclust, funclust et funHDDC. On démontre que les résultats du partitionnement et de la prédiction obtenus par ces approches sont comparables à ceux obtenus par ceux basés sur la distance. Les méthodes fonctionnelles sont préférables, car elles permettent d’utiliser des critères de sélection objectifs comme le AIC et le BIC. On peut donc éviter d’utiliser une partition préétablie pour valider la qualité des algorithmes, et ainsi laisser les données parler d’elles-mêmes. Finalement, on obtient des estimations détaillées de la structure fonctionnelle des courbes, comme sur l’impact de la réduction de données avec une analyse en composantes principales fonctionnelles multivariées.
The study of the clustering of functional data has made a lot of progress in the last couple of years. Multiple methods have been proposed and the respective analysis has shown their eÿciency with some benchmark studies. The objective of this Master’s thesis is to compare those clustering algorithms with datasets from traÿc at an intersection of Montreal. The idea behind this is that the manual classification of these data sets is time-consuming. We show that it is possible to obtain adequate clustering and prediction results with several algorithms. One of the methods that we discussed is distclust : a distance-based algorithm that uses a K-means approach. We will also use a Gaussian mixture density clustering method known as mclust. Although those two techniques are quite e˙ective, they are multi-purpose clustering methods, therefore not tailored to the functional case. With that in mind, we apply four functional clustering methods : fitfclust, funmbclust, funclust, and funHDDC. Our results show that there is no loss in the quality of the clustering between the afore-mentioned functional methods and the multi-purpose ones. We prefer to use the functional ones because they provide a detailed estimation of the functional structure of the trajectory curves. One notable detail is the impact of a dimension reduction done with multivari-ate functional principal components analysis. Furthermore, we can use objective selection criteria such as the AIC and the BIC, and avoid using cluster quality indices that use a pre-existing classification of the data.

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Dissertations / Theses on the topic 'B-spline functions'

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