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Dissertations / Theses on the topic 'Local approximation of a function'
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Jochym, Dominik Bogdan. "Development of non-local density functional methods." Thesis, Durham University, 2008. http://etheses.dur.ac.uk/2174/.
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Density functional theory (DFT) is a popular approach to solving the many-electron Schrödinger equation, in order to investigate the properties of matter from first principles. While DFT can give the exact ground state electronic density of a system, in practice, an approximation is required for the many-body effects contained in the exchange-correlation functional. The accuracy of calculations performed using DFT is strongly related to the choice of approximation. In this thesis we will investigate and build upon a fully non-local approach to modeling exchange-correlation in the form of the weighted density approximation (WDA). Central to the WDA is the model function chosen for the coupling-constant averaged pair-correlation function (PCF). We show that a model PCF can be selected from a set to give excellent bulk properties for a particular system. However, this model is not necessarily transferable to other systems and there is no method of selecting an appropriate model from this set a priori. We suggest that the model PCF can be improved systematically by satisfying known physical constraints. One such constraint is the Kimball cusp condition, which we include in our model and implement. We demonstrate that surfaces are systems that require a non-local treatment of exchange-correlation by applying the WDA to metal surfaces and investigate the dissociative adsorption of H2 on the Cu(100) surface. A new framework for a model PCF with spin resolution is developed, providing a route for more physical constraints to be satisfied within a weighted spin density approximation (WSDA). A simple model is suggested and implemented and comparisons are made to the coupling-constant averaged PCF in the homogeneous electron gas. We then apply a selection of our new models to a number of materials and show that our model for the WSDA gives improved band gaps over the local density approximation. Application of the WSDA to spin polarised materials reveals shortcomings in our simple model. We then suggest further refinements to our implementation of the WSDA. It is expected that the inclusion of additional physical constraints will systematically improve results given in a weighted-density based approximation to exchange-correlation.
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Générau, François. "Sur une approximation variationnelle stable du cut locus, et un problème isopérimetrique non local." Thesis, Université Grenoble Alpes, 2020. http://www.theses.fr/2020GRALM014.
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Cette thèse comporte deux parties. Dans la première partie, nous étudions une généralisation du problème variationnel de torsion élastique-plastique à des variétés. Nous montrons que dans le cas des variétés, le problème n'est pas équivalent à un problème d'obstacle, contrairement au cas euclidien, mais nous établissons l'équivalence lorsque le paramètre du problème tend vers l'infini. Nous montrons, comme dans le cas euclidien, que l'ensemble de non contact contient le cut locus de la variété, et converge vers ce dernier au sens de Hausforff. Nous montrons de plus que les miniseurs du problème sont uniformément semiconcaves. Nous en déduisons une approximation stable de cut locus, dans l'esprit du lambda axe médian de Chazal et Lieutier. Nous utilisons ensuite ce résultat pour calculer numériquement le cut locus de surfaces de géométries variées.Dans la seconde partie, nous étudions une extension d'un problème isopérimétrique non local. Précisément, on adjoint un potentiel de confinement au modèle de goutte liquide du noyau de Gamow. Nous étudions alors les minimiseurs de grand volume. Nous montrons que pour certains jeux de paramètres, les minimiseurs de grand volume convergent vers des boules, voire sont exactement des boules. Nous développons ensuite une méthode numérique pour ce problème variationnel. Cela permet de confirmer numériquement une conjecture de Choksi et Peletier en dimension 2 : dans ce cas les minimiseurs du modèle de Gamow semble être des boules si ils existentThis thesis is composed of two parts. In the first part, we study a generalization of the variational problem of elastic-plastic torsion problem to manifolds. We show that in the case of manifolds, the problem is not equivalent to an obstacle type problem, contrary to the euclidean case, but we establish the equivalence when the parameter of the problem goes to infinity. We show, as in the euclidean case, that the non contact set contains the cut locus of the manifold, and converges to the latter in the Hausdorff sense. What is more, we show that the minimizers of the problem are uniformly semiconcave. We deduce a stable approximation of the cut locus, in the spirit of the lambda medial axis of Chazal and Lieutier. We then use this result to compute numerically the cut locus of some surfaces of varied geometries.In the second part, we study an extension of a nonlocal isoperimetric problem. More precisely, we add a confinement potential to Gamow's liquid drop model for the nucleus. We then study large volume minimizers. We show that for certain sets of parameters, large volume minimizers converge to the ball, or may even exactly be the ball. Moreover, we develop a numerical method for this variational problem. Our results confirm numerically a conjecture of Choksi and Peletier, in dimension 2: it seems that minimizers of Gamow'sliquid drop model are balls as long as they exist
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Yasuda, Koji. "Local Approximation of the Correlation Energy Functional in the Density Matrix Functional Theory." American Physical Society, 2002. http://hdl.handle.net/2237/8743.
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Mancini, Lorenzo. "Adiabatic and local approximations for the kohn-sham potential in the hubbard model." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2013. http://amslaurea.unibo.it/5935/.
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We obtain the exact time-dependent Kohn-Sham potentials Vks for 1D Hubbard chains, driven by a d.c. external field, using the time-dependent electron density and current density obtained from exact many-body time-evolution. The exact Vxc is compared to the adiabatically-exact Vad-xc and the “instantaneous ground state” Vigs-xc. The effectiveness of these two approximations is analyzed. Approximations for the exchange-correlation potential Vxc and its gradient, based on the local density and on the local current density, are also considered and both physical quantities are observed to be far outside the reach of any possible local approximation. Insight into the respective roles of ground-state and excited-state correlation in the time-dependent system, as reflected in the potentials, is provided by the pair correlation function.
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Izquierdo, Diego. "Dualité et principe local-global sur les corps de fonctions." Thesis, Université Paris-Saclay (ComUE), 2016. http://www.theses.fr/2016SACLS345/document.
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Dans cette thèse, nous nous intéressons à l'arithmétique de certains corps de fonctions. Nous cherchons à établir dans un premier temps des théorèmes de dualité arithmétique sur ces corps, pour les appliquer ensuite à l'étude des points rationnels sur certaines variétés algébriques. Dans les trois premiers chapitres, nous travaillons sur le corps des fonctions d'une courbe sur un corps local supérieur (comme Qp, Qp((t)), C((t)) ou C((t))((u))). Dans le premier chapitre, nous établissons sur un tel corps des théorèmes de dualité arithmétique « à la Poitou-Tate » pour les modules finis, les tores, et même pour certains complexes de tores. Nous montrons aussi l'existence, sous certaines hypothèses, de certaines portions des suites exactes de Poitou-Tate correspondantes. Ces résultats sont appliqués dans le deuxième chapitre à l'étude du principe local-global pour les algèbres simples centrales, de l'approximation faible pour les tores, et des obstructions au principe local-global pour les torseurs sous des groupes linéaires connexes. Dans le troisième chapitre, nous nous penchons sur les variétés abéliennes et établissons des théorèmes de dualité arithmétique « à la Cassels-Tate ». Cela demande aussi de mener une étude fine des variétés abéliennes sur les corps locaux supérieurs. Dans le quatrième et dernier chapitre, nous travaillons sur les corps des fractions de certaines algèbres locales normales de dimension 2 (typiquement C((x, y)) ou Fp((x, y))). Nous établissons d'abord un théorème de dualité en cohomologie étale « à la Artin-Verdier » dans ce contexte. Cela nous permet ensuite de montrer des théorèmes de dualité arithmétique en cohomologie galoisienne « à la Poitou-Tate » pour les modules finis et les tores. Nous appliquons finalement ces résultats à l'étude de l'approximation faible pour les tores et des obstructions au principe local-global pour les torseurs sous des groupes linéaires connexesIn this thesis, we are interested in the arithmetic of some function fields. We first want to establish arithmetic duality theorems over those fields, in order to apply them afterwards to the study of rational points on algebraic varieties. In the first three chapters, we work on the function field of a curve defined over a higher-dimensional local field (such as Qp, Qp((t)), C((t)) or C((t))((u))). In the first chapter, we establish "Poitou-Tate type" arithmetic duality theorems over such fields for finite modules, tori and even some complexes of tori. We also prove the existence, under some hypothesis, of parts of the corresponding Poitou-Tate exact sequences. These results are applied in the second chapter to the study of the local-global principle for central simple algebras, of weak approximation for tori, and of obstructions to local-global principle for torsors under connected linear algebraic groups. In the third chapter, we are interested in abelian varieties and we establish "Cassels-Tate type" arithmetic duality theorems. To do so, we also need to carry out a precise study of abelian varieties over higher-dimensional local fields. In the fourth and last chapter, we work on the field of fractions of some 2-dimensional normal local algebras (such as C((x, y)) or Fp((x, y))). We first establish in this context an "Artin-Verdier type" duality theorem in étale cohomology. This allows us to prove "Poitou-Tate type" arithmetic duality theorems in Galois cohomology for finite modules and tori. In the end, we apply these results to the study of weak approximation for tori and of obstructions to local-global principle for torsors under connected linear algebraic groups
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Belhaj, Amor Fatma. "Enseignement et apprentissage des approximations locales des fonctions au début du cursus dans le Supérieur - Cas des classes préparatoires aux études d'ingénieurs." Electronic Thesis or Diss., Pau, 2022. https://theses.hal.science/tel-04051033.
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Au début du cycle des classes préparatoires aux études d'ingénieurs, les concepts de la relation de comparaison des fonctions, la formule de Taylor-Young et développements limités ont pour caractéristique fondamentale celle de résoudre des problèmes d'approximations locales des fonctions et de modélisations physique, mécanique, optique, etc. Une revue de lecture des travaux liés au domaine de didactique de l'Analyse nous a conduit à émettre l'hypothèse que l'identification et la caractérisation des obstacles liés à l'appropriation et à l'usage raisonné des notions d'approximation locale d'une fonction, contribuent significativement à étudier la nature et l'origine des difficultés rencontrées par les étudiants concernant la conceptualisation de ces objets en première année de section Physique-Chimie (PC). Ces obstacles résultent a priori en grande partie de l'absence des situations mathématiques dévolues aux étudiants nécessitant l'utilisation des représentations graphiques. Afin de surmonter ces obstacles de natures épistémologique, didactique et culturelle et de permettre aux étudiants de donner du sens au concept d'approximation locale d'une fonction, nous avons élaboré et mis en œuvre, en collaboration avec l'enseignante de la classe de première année (PC), une ingénierie didactique de développement par l'intégration de deux situations à dimension adidactique dans l'enseignement du chapitre « Analyse asymptotique ». Cette ingénierie, construite dans le cadre de la théorie des situations didactiques, vise à introduire ce concept par l'articulation des dimensions sémantique et syntaxique et la mobilisation de ses différentes représentations en utilisant un logiciel dynamique de géométrie Geogebra pour des constructions graphiques. L'analyse didactique des raisonnements, qui sous-tendent les procédures de résolution des étudiants, nous renseigne très précisément sur les connaissances et les savoirs mobilisés par confrontation aux différentes situations, sur la nature et le type de raisonnements ainsi que sur les dimensions sémantique et/ou syntaxique inhérentes à ses différentes étapes. Dans notre travail, l'expérimentation combinant la visualisation des représentations graphiques « dynamiques » et les raisonnements mathématiques, produits par les étudiants par la mobilisation de leurs connaissances antérieures sur l'étude d'une fonction, ont contribué à une approche analytique permettant l'introduction de la définition formelle du développement limité avec toute la complexité du travail dans le paradigme [Analyse Infinitésimale] qui couple la topologie et l'Analyse fonctionnelle. L'ingénierie a également permis, au sein des groupes et en classe entière, de générer des discussions, d'amener des échanges et de faire percevoir aux étudiants la richesse de l'articulation des différentes représentations du concept d'approximation locale d'une fonction pour poser des raisonnements articulant les dimensions sémantique et syntaxique. De ce fait, au lieu de se concentrer initialement sur le processus formel de la conceptualisation du développement limité d'ordre n d'une fonction au voisinage d'un réel, il devient possible de cibler précisément les représentations graphiques d'une fonction et de ses approximations polynômiales successives (d'ordre 1, 2, 3 et 4) en tant qu'objet pour visualiser l'amélioration de l'approximation polynômiale lorsque l'ordre augmente ; ainsi l'erreur d'approximation diminue et elle sera « meilleure » au voisinage de ce réel. L'ingénierie a permis l'adaptation des situations produites aux conditions ordinaires d'enseignement et aux besoins des enseignants. Cette étude pourra ainsi jouer un rôle dans la formation des enseignants du point de vue de la construction des connaissances, de l'importance de contrat didactique et de l'ouverture sur leur formation par l'usage du cadre graphique par un travail dans l'environnement de la technologie lors de l'enseignement des nouvelles notions au niveau SupérieurAt the beginning of the preparatory classes for engineering studies, the concepts of the comparison relation of functions, the Taylor-Young formula and limited developments have as a fundamental characteristic that of solving problems of local approximations of functions and of physical, mechanical, optical modelling, etc. A review of works related to the didactical field of Analysis led us to the hypothesis that the identification and the characterization of the obstacles related to the appropriation and the reasoned use of the notions of local approximation of a function, contribute significantly to the study of the nature and the origin of the difficulties encountered by the students concerning the conceptualization of these objects in the first year of the Physics-Chemistry section (PC). These obstacles result a priori in large part from the absence of mathematical situations devolved to the students requiring the use of graphical representations. In order to overcome these epistemological, didactical and cultural obstacles and to allow the students to give meaning to the concept of local approximation of a function, we have elaborated and implemented, in collaboration with the teacher of the first year class (PC), a didactical engineering of development by the integration of two situations with an adidactical dimension in the teaching of the chapter "Asymptotic analysis". This engineering, built within the framework of the theory of didactical situations, aims at introducing this concept by the articulation of the semantic and syntactic dimensions and the mobilization of its various representations by using a dynamic software of geometry Geogebra for graphic constructions. The didactical analysis of the reasoning, which underlie the resolution procedures of the students, informs us very precisely on the knowledge and the knowledges mobilized by confrontation with the various situations, on the nature and the type of reasonings as well as on the semantic and/or syntactic dimensions inherent to its various stages. In our work, the experimentation combining the visualization of "dynamic" graphical representations and the mathematical reasoning, produced by the students by mobilizing their previous knowledge on the study of a function, contributed to an analytical approach allowing the introduction of the formal definition of the limited development with all the complexity of the work in the paradigm [Infinitesimal Analysis] which couples topology and Functional Analysis. Engineering also allowed, within the groups and in the whole class, to generate discussions, to bring exchanges and to make the students perceive the richness of the articulation of the various representations of the concept of local approximation of a function to pose reasoning articulating the semantic and syntactic dimensions. Thus, instead of focusing initially on the formal process of conceptualizing the limited development of order n of a function in the neighborhood of a real, it becomes possible to precisely target the graphical representations of a function and its successive polynomial approximations (of order 1, 2, 3 and 4) as an object to visualize the improvement of the polynomial approximation when the order increases; thus the approximation error decreases and it will be "better" in the neighborhood of this real. The engineering allowed the adaptation of the situations produced to the ordinary conditions of teaching and to the needs of the teachers. This study will thus be able to play a role in the training of teachers from the point of view of the construction of knowledge, the importance of didactical contract and the opening on their training by the use of the graphic framework by a work in the environment of technology at the time of the teaching of the new concepts at the Higher level
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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 approchesConstructing 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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Tas, Murat. "Dielectric Formulation Of The One Dimensional Electron Gas." Phd thesis, METU, 2004. http://etd.lib.metu.edu.tr/upload/12604981/index.pdf.
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The charge and spin density correlations in a one dimensional electron gas (1DEG) confined in a semiconductor quantum wire structure at zero temperature are studied. The dielectric formulation of the many--body problem is employed and the longitudinal dielectric function, local-field correction, static structure factor, pair correlation function, ground state energy, compressibility, spin-dependent effective interaction potentials, paramagnon dispersion and static spin response function of the 1DEG are computed within the self-consistent field approximations of Singwi et al., known as the STLS and SSTL. The results are compared with those of other groups,
and those obtained for two-dimensional electron gas systems whenever it is possible.
It is observed that the SSTL satisfies the compressibility sum rule better than the STLS. Calculating the ground state energy of the 1DEG in unpolarized and fully polarized states, it is shown that both STLS and SSTL predict a Bloch transition for 1DEG systems at low electron densities.
Finally, the coupled plasmon-phonon modes in semiconductor quantum wires are calculated within the Fermi and Luttinger liquid theories. The coupling of electrons to bulk longitudinal optical phonons without dispersion and to acoustic phonons via deformation potential with a linear dispersion are considered. Using the dielectric formalism, a unified picture of the collective coupled plasmon-phonon modes is presented. Considerable differences between the predictions of the Fermi and Luttinger liquid approaches at large wave vector values,
which may be observed experimentally, are found.
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De, Silva Shalutha. "Force controlled hexapod walking." Thesis, Queensland University of Technology, 2014. https://eprints.qut.edu.au/78978/1/Karunakalage_De%20Silva_Thesis.pdf.
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This thesis is a study on controlling methods for six-legged robots. The study is based on mathematical modeling and simulation. A new joint controller is proposed and tested in simulation that uses joint angles and leg reaction force as inputs to generate a torque, and a method to optimise this controller is formulated and validated. Simulation shows that hexapod can walk on flat ground based on PID controllers with just four target configurations and a set of leg coordination rules, which provided the basis for the design of the new controller.
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Madani, Soffana. "Contributions à l’estimation à noyau de fonctionnelles de la fonction de répartition avec applications en sciences économiques et de gestion." Thesis, Lyon, 2017. http://www.theses.fr/2017LYSE1183/document.
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La répartition des revenus d'une population, la distribution des instants de défaillance d'un matériel et l'évolution des bénéfices des contrats d'assurance vie - étudiées en sciences économiques et de gestion – sont liées a des fonctions continues appartenant à la classe des fonctionnelles de la fonction de répartition. Notre thèse porte sur l'estimation à noyau de fonctionnelles de la fonction de répartition avec applications en sciences économiques et de gestion. Dans le premier chapitre, nous proposons des estimateurs polynomiaux locaux dans le cadre i.i.d. de deux fonctionnelles de la fonction de répartition, notées LF et TF , utiles pour produire des estimateurs lisses de la courbe de Lorenz et du temps total de test normalisé (scaled total time on test transform). La méthode d'estimation est décrite dans Abdous, Berlinet et Hengartner (2003) et nous prouvons le bon comportement asymptotique des estimateurs polynomiaux locaux. Jusqu'alors, Gastwirth (1972) et Barlow et Campo (1975) avaient défini des estimateurs continus par morceaux de la courbe de Lorenz et du temps total de test normalisé, ce qui ne respectait pas la propriété de continuité des courbes initiales. Des illustrations sur données simulées et réelles sont proposées. Le second chapitre a pour but de fournir des estimateurs polynomiaux locaux dans le cadre i.i.d. des dérivées successives des fonctionnelles de la fonction de répartition explorées dans le chapitre précédent. A part l'estimation de la dérivée première de la fonction TF qui se traite à l'aide de l'estimation lisse de la fonction de répartition, la méthode d'estimation employée est l'approximation polynomiale locale des fonctionnelles de la fonction de répartition détaillée dans Berlinet et Thomas-Agnan (2004). Divers types de convergence ainsi que la normalité asymptotique sont obtenus, y compris pour la densité et ses dérivées successives. Des simulations apparaissent et sont commentées. Le point de départ du troisième chapitre est l'estimateur de Parzen-Rosenblatt (Rosenblatt (1956), Parzen (1964)) de la densité. Nous améliorons dans un premier temps le biais de l'estimateur de Parzen-Rosenblatt et de ses dérivées successives à l'aide de noyaux d'ordre supérieur (Berlinet (1993)). Nous démontrons ensuite les nouvelles conditions de normalité asymptotique de ces estimateurs. Enfin, nous construisons une méthode de correction des effets de bord pour les estimateurs des dérivées de la densité, grâce aux dérivées d'ordre supérieur. Le dernier chapitre s'intéresse au taux de hasard, qui contrairement aux deux fonctionnelles de la fonction de répartition traitées dans le premier chapitre, n'est pas un rapport de deux fonctionnelles linéaires de la fonction de répartition. Dans le cadre i.i.d., les estimateurs à noyau du taux de hasard et de ses dérivées successives sont construits à partir des estimateurs à noyau de la densité et ses dérivées successives. La normalité asymptotique des premiers estimateurs est logiquement obtenue à partir de celle des seconds. Nous nous plaçons ensuite dans le modèle à intensité multiplicative, un cadre plus général englobant des données censurées et dépendantes. Nous menons la procédure à terme de Ramlau-Hansen (1983) afin d'obtenir les bonnes propriétés asymptotiques des estimateurs du taux de hasard et de ses dérivées successives puis nous tentons d'appliquer l'approximation polynomiale locale dans ce contexte. Le taux d'accumulation du surplus dans le domaine de la participation aux bénéfices pourra alors être estimé non parametriquement puisqu'il dépend des taux de transition (taux de hasard d'un état vers un autre) d'une chaine de Markov (Ramlau-Hansen (1991), Norberg (1999))The income distribution of a population, the distribution of failure times of a system and the evolution of the surplus in with-profit policies - studied in economics and management - are related to continuous functions belonging to the class of functionals of the distribution function. Our thesis covers the kernel estimation of some functionals of the distribution function with applications in economics and management. In the first chapter, we offer local polynomial estimators in the i.i.d. case of two functionals of the distribution function, written LF and TF , which are useful to produce the smooth estimators of the Lorenz curve and the scaled total time on test transform. The estimation method is described in Abdous, Berlinet and Hengartner (2003) and we prove the good asymptotic behavior of the local polynomial estimators. Until now, Gastwirth (1972) and Barlow and Campo (1975) have defined continuous piecewise estimators of the Lorenz curve and the scaled total time on test transform, which do not respect the continuity of the original curves. Illustrations on simulated and real data are given. The second chapter is intended to provide smooth estimators in the i.i.d. case of the derivatives of the two functionals of the distribution function presented in the last chapter. Apart from the estimation of the first derivative of the function TF with a smooth estimation of the distribution function, the estimation method is the local polynomial approximation of functionals of the distribution function detailed in Berlinet and Thomas-Agnan (2004). Various types of convergence and asymptotic normality are obtained, including the probability density function and its derivatives. Simulations appear and are discussed. The starting point of the third chapter is the Parzen-Rosenblatt estimator (Rosenblatt (1956), Parzen (1964)) of the probability density function. We first improve the bias of this estimator and its derivatives by using higher order kernels (Berlinet (1993)). Then we find the modified conditions for the asymptotic normality of these estimators. Finally, we build a method to remove boundary effects of the estimators of the probability density function and its derivatives, thanks to higher order derivatives. We are interested, in this final chapter, in the hazard rate function which, unlike the two functionals of the distribution function explored in the first chapter, is not a fraction of two linear functionals of the distribution function. In the i.i.d. case, kernel estimators of the hazard rate and its derivatives are produced from the kernel estimators of the probability density function and its derivatives. The asymptotic normality of the first estimators is logically obtained from the second ones. Then, we are placed in the multiplicative intensity model, a more general framework including censored and dependent data. We complete the described method in Ramlau-Hansen (1983) to obtain good asymptotic properties of the estimators of the hazard rate and its derivatives and we try to adopt the local polynomial approximation in this context. The surplus rate in with-profit policies will be nonparametrically estimated as its mathematical expression depends on transition rates (hazard rates from one state to another) in a Markov chain (Ramlau-Hansen (1991), Norberg (1999))
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Marten, Tobias. "Ab-initio study of disorder broadening of core photoemission spectra in random metallic alloys." Thesis, Linköping University, The Department of Physics, Chemistry and Biology, 2004. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-2580.
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Ab-initio results of the core-level shift and the distribution about the average for the 3d5/2 electrons of Ag, Pd and 2p3/2 of Cu are presented for the face-centered-cubic AgPd and CuPd random alloys. The complete screening model, which includes both initial and final states effects in the same scheme, has been used in the investigations.
The alloys have been modeled with a supercell containing 256 atoms. Density-functional theory calculations are carried out using the locally self consistent Green's function approach.
Results from the calculations clearly shows that the core-level shift distributions characteristic is Gaussian, but the components reveals a substantial difference in the FWHM (Full-Width at Half-Maximum). Comparison between the experimental and the calculated broadening shows a remarkable agreement.
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楊文聰 and Man-chung Yeung. "Korovkin approximation in function spaces." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1990. http://hub.hku.hk/bib/B31209531.
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Gebresilassie, Abel Gebreegziabher. "Atomic scale simulations in zirconia : Effect of yttria doping and environment on stability of phases." Thesis, Lyon, 2016. http://www.theses.fr/2016LYSEI038/document.
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Ce travail de thèse est une étude par des méthodes de simulation de structure électronique du phénomène de dégradation en milieu aqueux de la zircone yttriée. La zircone yttriée est notamment utilisée pour la fabrication de prothèses dont la durée de vie dépend du matériau et de son environnement. Pour ces applications, la zircone yttriée est de structure tétragone, mais en fonction du dopage en yttrium et de l'environnement, cette phase est en compétition avec des structures monoclinique et cubique. Cette compétition est cruciale dans ce travail car elle peut à la fois, augmenter la résistance, ou favoriser la détérioration de ce matériau. L'étude réalisée se concentre sur des taux de dopage inférieurs à 20% mol. en oxyde d'yttrium Y2O3.Dans un premier temps, les structures atomiques d'équilibre à basse température ont été déterminées dans les trois phases en utilisant une méthode de calcul basée sur la Théorie de la Fonctionnelle de la Densité, dans l'approximation de la densité locale. Les résultats incluent de nouvelles structures qui n'ont jusqu'alors pas été discutées dans la littérature et qui sont cohérentes avec le diagramme de phase de la zircone yttriée à basse température. Une analyse plus détaillée suggère que le mécanisme de stabilisation de la zircone yttriée tetragonale est un effet du dépistage ionocovalent particulièrement efficace dans cette phase et dont la signature dans la structure s'exprime par la présence d'ions zirconium en coordination 7. Ceci représente un point important permettant de lier stabilité et structure dans ces systèmes. Une deuxième partie de ce travail est consacrée à l’effet de l'eau dans la zircone yttriée en volume. Pour conclure, ce manuscrit représente une contribution originale à la compréhension de mécanismes à l'échelle atomique qui sont à l'origine des propriétés de la zircone yttriée et de ses applications.yttriée et de ses applicationsThis PhD thesis is an electronic structure simulation work to study the stabilization mechanism of yttria stabilized zirconia (YSZ) and the phenomena of the degradation of YSZ due to the presence of an aqueous media. YSZ is used especially in dental and orthopedics application sbut its service depends on the environment. For these biomedical applications a crystallographic tetragonal YSZ (t-YSZ) structure is used, but depending on the concentration of yttria (Y2O3) and the environment, this tetragonal structure is thermodynamically in competition with a monoclinic and cubic phases. This competition is crucial in this work, because it has both effects : increase the resistance or promote the degradation of this material. The study is conducted for Y2O3 concentrations less than 20% mol. First, atomic structures of the three phases at low temperature were determined using density functional theory (DFT)with the local density approximations (LDA). The results include new structures that were not discussed in the literature and which are consistent with the phase diagram of YSZ at low temperature. A more detailed analysis suggests that the stabilization mechanism in YSZ is due to an effective ionocovalent screening : particularly in t-YSZ phase, its signature is expressed in Zr-ions with a coordination number of 7. This represents an important point for linking stability and structure in these systems. A second part of this work is devoted to the effect of water on YSZ bulk systems which leads to low temperature degradation (LTD) of YSZ based bioceramics materials. In conclusion, this PhD thesis represents an original contribution to the understanding of the mechanism and properties of YSZ and its applications at the atomic scale
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Berzin, Corinne. "Surfaces aléatoires : approximation du temps local." Paris 11, 1989. http://www.theses.fr/1989PA112337.
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Soit { X(t,ω), t ∈ Rd, ω ∈ Ω }, d ≥2 un processus gaussien stationnaire, à valeurs réelles sur un espace de probabilité ( Ω, Around, P ). Nous étudions le comportement asymptotique d'une intégrale stochastique particulière, par rapport à la mesure géométrique de l'ensemble de niveau u, u ∈ R, du champ régularisé, obtenu par la composition d'une convoluée de X, soit Xɛ, et d'une normalisation matricielle contenant une partie de l'information de la matrice des moments spectraux d'ordre deux de Xɛ. Sous l'hypothèse que la fonction de covariance de X est deux fois continûment différentiable en dehors d'un ensemble de mesure de Lebesgue nulle dans Rd, cette intégrale converge dans L²(Ω ) vers le temps local de X, évalué en u. En outre, une majoration de la vitesse de convergence est proposée, à une constante prèsLet { X(t,ω), t ∈ Rd, ω ∈ Ω }, d ≥2, be a real stationary gaussian field, defined on a probability space ( Ω, Around, P ). We look at the asymptotic behavior of a particular stochastic integral, with respect to the geometric measure of the u-level sets, u ∈ R, of the regularized field, obtained by composition of a convolution of X, say Xɛ, with a matrix normalization which contains part of the information contained in the spectral moments matrix of second order of Xɛ. Under the condition that the covariance function is twice continuously differentiable out of a set of zero Lebesgue's measure, this functional converges in L² (Ω ) to the local time of X at the level u. Furthermore, we give a bound for the speed of convergence
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Yorke, Rory. "Chaos control using local polynomial approximation." Master's thesis, University of Cape Town, 2001. http://hdl.handle.net/11427/5075.
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Includes bibliographical references.Chaotic systems may be defined as those whose behaviour is sensitively dependent on initial conditions. Such systems may be made periodic using small input perturbations, as proposed in [OGY90]; this is called Ott-Grebogi-Yorke (OGY) chaos control. The original method used a linear model for controller design; a later development of chaos control was [CCdF99], in which a polynomial model is used. This dissertation proposes using local Taylor polynomial models as a basis for chaos control.
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伍卓仁 and Cheuk-yan Ng. "Pointwise Korovkin approximation in function spaces." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1993. http://hub.hku.hk/bib/B31210934.
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吳家樂 and Ka-lok Ng. "Relative korovkin approximation in function spaces." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1995. http://hub.hku.hk/bib/B31213479.
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Miranda, Brando M. Eng Massachusetts Institute of Technology. "Training hierarchical networks for function approximation." Thesis, Massachusetts Institute of Technology, 2016. http://hdl.handle.net/1721.1/113159.
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Thesis: M. Eng., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2016.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.
Cataloged from student-submitted PDF version of thesis.
Includes bibliographical references (pages 59-60).
In this work we investigate function approximation using Hierarchical Networks. We start of by investigating the theory proposed by Poggio et al [2] that Deep Learning Convolutional Neural Networks (DCN) can be equivalent to hierarchical kernel machines with the Radial Basis Functions (RBF).We investigate the difficulty of training RBF networks with stochastic gradient descent (SGD) and hierarchical RBF. We discovered that training singled layered RBF networks can be quite simple with a good initialization and good choice of standard deviation for the Gaussian. Training hierarchical RBFs remains as an open question, however, we clearly identified the issue surrounding training hierarchical RBFs and potential methods to resolve this. We also compare standard DCN networks to hierarchical Radial Basis Functions in tasks that has not been explored yet; the role of depth in learning compositional functions.
by Brando Miranda.
M. Eng.
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Ng, Ka-lok. "Relative korovkin approximation in function spaces /." Hong Kong : University of Hong Kong, 1995. http://sunzi.lib.hku.hk/hkuto/record.jsp?B17506074.
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Ng, Cheuk-yan. "Pointwise Korovkin approximation in function spaces /." [Hong Kong : University of Hong Kong], 1993. http://sunzi.lib.hku.hk/hkuto/record.jsp?B13474522.
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Stankovski, Martin. "Local and non-local vertex corrections beyond the GW approximation." Thesis, University of York, 2008. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.490311.
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In order to increase the predictive pmver of electronic structure calculations on atomic and condensed matter systems, this work explores vertex corrections within the framework of many-body perturbation theory. Hedin's GW approximation has, during the last decades, emerged as a powerful technique to calculate single-particle energy excitation levels in both extended and isolated systems, where other current methods usually fail to account properly for screening. GW calculations should in principle be performed in a self-consistent manner, i.e. be taken by several iterations to their solution, starting from a Hartree zeroth-order calculation. If the initial Green's function is constructed from single-particle orbitals with a zeroth-order approximation to the self-energy like DFT, there is in principle a vertex given by the first iteration. This is routinely ignored in standard calculations today, which are typically perfomed with only a single iteration. vVe have investigated the effects of the vertex correction derived from the DFT starting point in single iterations on two systems, the homogenous electron gas, and closed shell atoms. vVe ~nd that a local potential, i.e. depending on the density at one point only, gives a pathological subsequent vertex correction, if it is consistently applied. To'cure these pathologies, we propose nonlocal initial approximations to the starting self-energy. The vertices subsequently derived from these are well-behaved and can capture many physical effects beyond the one-shot G(O)W(O) approach. Finally, we investigate the interplay of these vertices with self-consistency in GW calculations.
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Webber, Nicholas Jon. "Local tangent space approximation in canonical quantization." Thesis, Imperial College London, 1986. http://hdl.handle.net/10044/1/38183.
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Cheung, Ho Yin. "Function approximation with higher-order fuzzy systems /." View abstract or full-text, 2006. http://library.ust.hk/cgi/db/thesis.pl?ELEC%202006%20CHEUNG.
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Ong, Wen Eng. "Some Basis Function Methods for Surface Approximation." Thesis, University of Canterbury. Mathematics and Statistics, 2012. http://hdl.handle.net/10092/7776.
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This thesis considers issues in surface reconstruction such as identifying approximation methods that work well for certain applications and developing efficient methods to compute and manipulate these approximations.
The first part of the thesis illustrates a new fast evaluation scheme to efficiently calculate thin-plate splines in two dimensions. In the fast multipole method scheme, exponential expansions/approximations are used as an intermediate step in converting far field series to local polynomial approximations. The contributions here are extending the scheme to the thin-plate spline and a new error analysis. The error analysis covers the practically important case where truncated series are used throughout, and through off line computation of error constants gives sharp error bounds.
In the second part of this thesis, we investigates fitting a surface to an object using blobby models as a coarse level approximation. The aim is to achieve a given quality of approximation with relatively few parameters. This process involves an optimization procedure where a number of blobs (ellipses or ellipsoids) are separately fitted to a cloud of points. Then the optimized blobs are combined to yield an implicit surface approximating the cloud of points. The results for our test cases in 2 and 3 dimensions are very encouraging. For many applications, the coarse level blobby model itself will be sufficient. For example adding texture on top of the blobby surface can give a surprisingly realistic image.
The last part of the thesis describes a method to reconstruct surfaces with known discontinuities. We fit a surface to the data points by performing a scattered data interpolation using compactly supported RBFs with respect to a geodesic distance. Techniques from computational geometry such as the visibility graph are used to compute the shortest Euclidean distance between two points, avoiding any obstacles. Results have shown that discontinuities on the surface were clearly reconstructed, and the
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Strand, Filip. "Latent Task Embeddings forFew-Shot Function Approximation." Thesis, KTH, Optimeringslära och systemteori, 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-243832.
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Approximating a function from a few data points is of great importance in fields where data is scarce, like, for example, in robotics applications. Recently, scalable and expressive parametric models like deep neural networks have demonstrated superior performance on a wide variety of function approximation tasks when plenty of data is available –however, these methods tend to perform considerably worse in low-data regimes which calls for alternative approaches. One way to address such limitations is by leveraging prior information about the function class to be estimated when such data is available. Sometimes this prior may be known in closed mathematical form but in general it is not. This the-sis is concerned with the more general case where the prior can only be sampled from, such as a black-box forward simulator. To this end, we propose a simple and scalable approach to learning a prior over functions by training a neural network on data from a distribution of related functions. This steps amounts to building a so called latent task embedding where all related functions (tasks) reside and which later can be efficiently searched at task-inference time - a process called fine-tuning. The pro-posed method can be seen as a special type of auto-encoder and employs the same idea of encoding individual data points during training as the recently proposed Conditional Neural Processes. We extend this work by also incorporating an auxiliary task and by providing additional latent space search methods for increased performance after the initial training step. The task-embedding framework makes finding the right function from a family of related function quick and generally requires only a few informative data points from that function. We evaluate the method by regressing onto the harmonic family of curves and also by applying it to two robotic systems with the aim of quickly identifying and controlling those systems.Att snabbt kunna approximera en funktion baserat på ett fåtal data-punkter är ett viktigt problem, speciellt inom områden där tillgängliga datamängder är relativt små, till exempel inom delar av robotikområdet. Under de senaste åren har flexibla och skalbara inlärningsmetoder, såsom exempelvis neurala nätverk, uppvisat framstående egenskaper i scenarion där en stor mängd data finns att tillgå. Dessa metoder tenderar dock att prestera betydligt sämre i låg-data regimer vilket motiverar sökandet efter alternativa metoder. Ett sätt att adressera denna begränsning är genom att utnyttja tidigare erfarenheter och antaganden (eng. prior information) om funktionsklassen som skall approximeras när sådan information finns tillgänglig. Ibland kan denna typ av information uttryckas i sluten matematisk form, men mer generellt är så inte fallet. Denna uppsats är fokuserad på det mer generella fallet där vi endast antar att vi kan sampla datapunkter från en databas av tidigare erfarenheter - exempelvis från en simulator där vi inte känner till de interna detaljerna. För detta ändamål föreslår vi en metod för att lära från dessa tidigare erfarenheter genom att i förväg träna på en större datamängd som utgör en familj av relaterade funktioner. I detta steg bygger vi upp ett så kallat latent funktionsrum (eng. latent task embeddings) som innesluter alla variationer av funktioner från träningsdatan och som sedan effektivt kan genomsökas i syfte av att hitta en specifik funktion - en process som vi kallar för finjustering (eng. fine-tuning). Den föreslagna metoden kan betraktas som ett specialfall av en auto-encoder och använder sig av samma ide som den nyligen publicerade Conditional Neural Processes metoden där individuella datapunkter enskilt kodas och grupperas. Vi utökar denna metod genom att inkorporera en sidofunktion (eng. auxiliary function) och genom att föreslå ytterligare metoder för att genomsöka det latenta funktionsrummet efter den initiala träningen. Den föreslagna metoden möjliggör att sökandet efter en specifik funktion typiskt kan göras med endast ett fåtal datapunkter. Vi utvärderar metoden genom att studera kurvanpassningsförmågan på sinuskurvor och genom att applicera den på två robotikproblem med syfte att snabbt kunna identifiera och styra dessa dynamiska system.
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Hou, Jun. "Function Approximation and Classification with Perturbed Data." The Ohio State University, 2021. http://rave.ohiolink.edu/etdc/view?acc_num=osu1618266875924225.
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Jackson, Ian Robert Hart. "Radial basis function methods for multivariable approximation." Thesis, University of Cambridge, 1988. https://www.repository.cam.ac.uk/handle/1810/270416.
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Berard, Bergery Blandine. "Approximation du temps local et intégration par régularisation." Phd thesis, Université Henri Poincaré - Nancy I, 2007. http://tel.archives-ouvertes.fr/tel-00181777.
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Cette thèse s'inscrit dans la théorie de l'intégration par régularisation de Russo et Vallois. La première partie est consacrée à l'approximation du temps local des semi-martingales continues. On montre que, si $X$ est une diffusion réversible, alors $ \frac{1}{\epsilon}\int_0^t \left( \indi_{\{ y < X_{s+\epsilon}\}} - \indi_{\{ y < X_{s}\}} \right) \left( X_{s+\epsilon}-X_{s} \right)ds$ converge vers $L_t^y(X)$, en probabilité uniformément sur les compacts, quand $\epsilon \to 0$. De ce premier schéma, on tire deux autres schémas d'approximation du temps local, l'un valable pour les semi-martingales continues, l'autre pour le mouvement Brownien standard. Dans le cas du mouvement Brownien, une vitesse de convergence dans $L^2(\Omega)$ et un résultat de convergence presque sûre sont établis. La deuxième partie de la thèse est consacrée à l'intégrale "forward" et à la variation quadratique généralisée, définies par des limites en probabilité de famille d'intégrales. Dans le cas Höldérien, la convergence presque sûre est établie. Enfin, on montre la convergence au second ordre pour une série de processus particuliers.
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Harvey-Fros, Christopher Simon Francis. "The local potential approximation of the renormalization group." Thesis, University of Southampton, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.285624.
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Bérard, Bergery Blandine. "Approximation du temps local et intégration par régularisation." Thesis, Nancy 1, 2007. http://www.theses.fr/2007NAN10058/document.
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Cette thèse s'inscrit dans la théorie de l'intégration par régularisation de Russo et Vallois. La première partie est consacrée à l'approximation du temps local des semi-martingales continues. Si X est une diffusion réversible, on montre la convergence d'un premier schéma d'approximation vers le temps local de X, en probabilité uniformément sur les compacts. De ce premier schéma, on tire deux autres schémas d'approximation du temps local, l'un valable pour les semi-martingales continues, l'autre pour le mouvement Brownien standard. Dans le cas du mouvement Brownien, une vitesse de convergence dans L^2(Omega) et un résultat de convergence presque sûre sont établis. La deuxième partie de la thèse est consacrée à l'intégrale "forward" et à la variation quadratique généralisée, définies par des limites en probabilité de famille d'intégrales. Dans le cas Höldérien, la convergence presque sûre est établie. Enfin, on montre la convergence au second ordre pour une série de processus particuliersThe setting of this work is the integration by regularization of Russo and Vallois. The first part studies schemes of approximation of the local time of continuous semimartingales. If X is a reversible diffusion, the convergence of a first schema of approximation to the local time of X is proven, in probability uniformly on the compact sets. From this first schema, two other schemas of approximation for the local time are found. One converges in the semi-martingale case, the other in the Brownian case. Moreover, in the Brownian case, we estimate the rate of convergence in L^2(Omega) and a result of almost sure convergence is proven. The second part study the forward integral and the generalized quadratic variation, which have been defined by convergence of families of integrals, in probability uniformly on the compacts sets. In the case of Hölder processes, the almost sure convergence is proven. Finally, the second order convergence is studied in many cases
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Bérard, Bergery Blandine Vallois Pierre. "Approximation du temps local et intégration par régularisation." S. l. : S. n, 2007. http://www.scd.uhp-nancy.fr/docnum/SCD_T_2007_0058_BERARD-BERGERY.pdf.
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Hales, Stephen. "Approximation by translates of a radial basis function." Thesis, University of Leicester, 2000. http://hdl.handle.net/2381/30513.
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The aim of this work is to investigate the properties of approximations obtained by translates of radial basis functions. A natural progression in the discussion starts with an iterative refinement scheme using a strictly positive definite inverse multiquadric. Error estimates for this method are greatly simplified if the inverse multiquadric is replaced by a strictly conditionally positive definite polyharmonic spline. Such error analysis is conducted in a native space generated by the Fourier transform of the basis function. This space can be restrictive when using very smooth basis functions. Some instances are discussed where the native space of can be enlarged by creating a strictly positive definite basis function with comparable approximating properties to , but with a significantly different Fourier transform to . Before such a construction is possible however, strictly positive definite functions in d for d < with compact support must be examined in some detail. It is demonstrated that the dimension in which a function is positive definite can be determined from its univariate Fourier transform. This work is biased towards the computational aspects of interpolation, and the theory is always given with a view to explaining observable phenomena.
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Steuding, Rasa, Jörn Steuding, Kohji Matsumoto, Antanas Laurinčikas, and Ramūnas Garunkštis. "Effective uniform approximation by the Riemann zeta-function." Department of Mathematics of the Universitat Autònoma de Barcelona, 2010. http://hdl.handle.net/2237/20429.
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Manganas, Spyridon. "A Novel Methodology for Timely Brain Formations of 3D Spatial Information with Application to Visually Impaired Navigation." Wright State University / OhioLINK, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=wright1567452284983244.
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Van, Gysen Hermanus Gerhardus. "Splines and local approximation of the earth's gravity field." Doctoral thesis, University of Cape Town, 1988. http://hdl.handle.net/11427/15821.
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Bibliography: pages 214-220.The Hilbert space spline theory of Delvos and Schempp, and the reproducing kernel theory of L. Schwartz, provide the conceptual foundation and the construction procedure for rotation-invariant splines on Euclidean spaces, splines on the circle, and splines on the sphere and harmonic outside the sphere. Spherical splines and surface splines such as multi-conic functions, Hardy's multiquadric functions, pseudo-cubic splines, and thin-plate splines, are shown to be largely as effective as least squares collocation in representing geoid heights or gravity anomalies. A pseudo-cubic spline geoid for southern Africa is given, interpolating Doppler-derived geoid heights and astro-geodetic deflections of the vertical. Quadrature rules are derived for the thin-plate spline approximation (over a circular disk, and to a planar approximation) of Stokes's formula, the formulae of Vening Meinesz, and the L₁ vertical gradient operator in the analytical continuation series solution of Molodensky's problem.
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Lu, Zhi Wei. "Local density approximation study of transition andf-electron materials." W&M ScholarWorks, 1989. https://scholarworks.wm.edu/etd/1539623781.
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The local density approximation (LDA) has been proved to be a powerful starting point for calculating electronic and structural properties for many real materials. We have studied the effects of particular forms of exchange-correlation potentials (the X{dollar}\alpha{dollar} and Hedin-Lundqvist form) upon the structural properties for the 3d Ti and 4d Zr using a highly accurate linearized augmented plane wave (LAPW) method. The calculated equilibrium volumes differ by 6-8% for these two forms (with X{dollar}\alpha{dollar} results in better agreement with experiment) with proportional differences in other structural properties, which we take to be an indication of the intrinsic reliability of the LDA. Considerable sensitivity in the calculated structural properties to the particular exchange-correlation potential (the X{dollar}\alpha{dollar}, Wigner, and Hedin-Lundqvist) was also found for the fcc and the high temperature bcc La. The calculation on SmS reveals that the LDA is inadequate for this very localized 4f electron system, while the LDA works fairly well for the chemically similar material LaS. For HgTe and HgSe, the fully occupied 5d electrons in Hg has been found to be important in determining the structural properties through the Hg d - chalcogen p interactions, however this p-d hybridization appears to be relatively unchanged through the various pressure induced phase transitions. We calculated the total energy of the seven layer slabs of Pd(111) surface as a function of the top layer spacing, the relaxation is found to be very small ({dollar}<{dollar}1%).
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Zhang, Qi. "Multilevel adaptive radial basis function approximation using error indicators." Thesis, University of Leicester, 2016. http://hdl.handle.net/2381/38284.
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In some approximation problems, sampling from the target function can be both expensive and time-consuming. It would be convenient to have a method for indicating where the approximation quality is poor, so that generation of new data provides the user with greater accuracy where needed. In this thesis, the author describes a new adaptive algorithm for Radial Basis Function (RBF) interpolation which aims to assess the local approximation quality and adds or removes points as required to improve the error in the specified region. For a multiquadric and Gaussian approximation, one has the flexibility of a shape parameter which one can use to keep the condition number of the interpolation matrix to a moderate size. In this adaptive error indicator (AEI) method, an adaptive shape parameter is applied. Numerical results for test functions which appear in the literature are given for one, two, and three dimensions, to show that this method performs well. A turbine blade design problem form GE Power (Rugby, UK) is considered and the AEI method is applied to this problem. Moreover, a new multilevel approximation scheme is introduced in this thesis by coupling it with the adaptive error indicator. Preliminary numerical results from this Multilevel Adaptive Error Indicator (MAEI) approximation method are shown. These indicate that the MAEI is able to express the target function well. Moreover, it provides a highly efficient sampling.
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Mahadevan, Swaminathan. "Probabilistic linear function approximation for value-based reinforcement learning." Thesis, McGill University, 2005. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=98759.
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Reinforcement learning (RL) is a computational framework for learning sequential decision strategies from the interaction of an agent with an unknown dynamic environment. This thesis focuses on value-based reinforcement learning methods, which rely on computing utility values for different behavior strategies that can be adopted by the agent. Real-world complex problems involve very large discrete or continuous state spaces where the use of approximate methods is required. It has been observed that subtle differences in the approximate methods result in very different theoretical properties and empirical behavior. In this thesis, we propose a new framework for discussing many popular function approximation methods, called Probabilistic Linear Function Approximation. This allows us to highlight the key differences of several approximation algorithms used in RL.
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Van, Roy Benjamin. "Learning and value function approximation in complex decision processes." Thesis, Massachusetts Institute of Technology, 1998. http://hdl.handle.net/1721.1/9960.
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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1998.Includes bibliographical references (p. 127-133).
by Benjamin Van Roy.
Ph.D.
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Swingler, Kevin. "Mixed order hyper-networks for function approximation and optimisation." Thesis, University of Stirling, 2016. http://hdl.handle.net/1893/25349.
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Many systems take inputs, which can be measured and sometimes controlled, and outputs, which can also be measured and which depend on the inputs. Taking numerous measurements from such systems produces data, which may be used to either model the system with the goal of predicting the output associated with a given input (function approximation, or regression) or of finding the input settings required to produce a desired output (optimisation, or search). Approximating or optimising a function is central to the field of computational intelligence. There are many existing methods for performing regression and optimisation based on samples of data but they all have limitations. Multi layer perceptrons (MLPs) are universal approximators, but they suffer from the black box problem, which means their structure and the function they implement is opaque to the user. They also suffer from a propensity to become trapped in local minima or large plateaux in the error function during learning. A regression method with a structure that allows models to be compared, human knowledge to be extracted, optimisation searches to be guided and model complexity to be controlled is desirable. This thesis presents such as method. This thesis presents a single framework for both regression and optimisation: the mixed order hyper network (MOHN). A MOHN implements a function f:{-1,1}^n →R to arbitrary precision. The structure of a MOHN makes the ways in which input variables interact to determine the function output explicit, which allows human insights and complexity control that are very difficult in neural networks with hidden units. The explicit structure representation also allows efficient algorithms for searching for an input pattern that leads to a desired output. A number of learning rules for estimating the weights based on a sample of data are presented along with a heuristic method for choosing which connections to include in a model. Several methods for searching a MOHN for inputs that lead to a desired output are compared. Experiments compare a MOHN to an MLP on regression tasks. The MOHN is found to achieve a comparable level of accuracy to an MLP but suffers less from local minima in the error function and shows less variance across multiple training trials. It is also easier to interpret and combine from an ensemble. The trade-off between the fit of a model to its training data and that to an independent set of test data is shown to be easier to control in a MOHN than an MLP. A MOHN is also compared to a number of existing optimisation methods including those using estimation of distribution algorithms, genetic algorithms and simulated annealing. The MOHN is able to find optimal solutions in far fewer function evaluations than these methods on tasks selected from the literature.
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Skelly, Margaret Mary. "Hierarchical Reinforcement Learning with Function Approximation for Adaptive Control." Case Western Reserve University School of Graduate Studies / OhioLINK, 2004. http://rave.ohiolink.edu/etdc/view?acc_num=case1081357818.
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Bridle, Ismail Hamzaan. "Non-polynomial scalar field potentials in the local potential approximation." Thesis, University of Southampton, 2017. https://eprints.soton.ac.uk/410270/.
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We present the renormalisation group analysis of O(N) invariant scalar field theory in the local potential approximation. Linearising around the Gaussian fixed point, we find the same eigenoperators solutions exist for both the Wilsonian and the Legendre effective actions, given by solutions to Kummer’s equations. We find the usual polynomial eigenoperators and the Hilbert space they define are a natural subset of these solutions given by a specific set of quantised eigenvalues. Allowing for continuous eigenvalues, we find non-polynomial eigenoperator solutions, the so called Halpern-Huang directions, that exist outside of the polynomial Hilbert space due to the exponential field dependence. Carefully analysing the large field behaviour shows that the exponential dependence implies the Legendre effective action does not have a well defined continuum limit. In comparison, flowing towards the infrared we find that the non-polynomial eigenoperators flow into the polynomial Hilbert space. These conclusions are based off RG flow initiated at an arbitrary scale, implying non-polynomial eigenoperators are dependent upon a scale other than k. Therefore, the asymptotic field behaviour forbids self-similar scaling. These results hold when generalised from the Halpern-Huang directions around the Gaussian fixed point to a general fixed point with a general non-polynomial eigenoperator. Legendre transforming to results of the Polchinski equation, we find the flow of the Wilsonian effective action is much better regulated and always fall into the polynomial Hilbert space. For large Wilsonian effective actions, we find that the non-linear terms of the Polchinski equation forbid any non-polynomial field scaling, regardless of the fixed point. These observations lead to the conclusion that only polynomial eigenoperators show the correct, self-similar, scaling behaviour to construct a non-perturbatively renormalisable scalar QFT.
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Rama, Ritesh Rao. "Local maximum entropy approximation-based modelling of the canine heart." Master's thesis, University of Cape Town, 2012. http://hdl.handle.net/11427/16963.
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Local Maximum Entropy (LME) method is an approximation technique which has been known to have good approximation characteristics. This is due to its non-negative shape functions and the weak Kronecker delta property which allow the solutions to be continuous and smooth as compared to the Moving Least Square method (MLS) which is used in the Element Free Galerkin method (EFG). The method is based on a convex optimisation scheme where a non-linear equation is solved with the help of a Newton algorithm, implemented in an in-house code called SESKA. In this study, the aim is to compare LME and MLS and highlight the differences. Preliminary benchmark tests of LME are found to be very conclusive. The method is able to approximate deformation of a cantilever beam with higher accuracy as compared to MLS. Moreover, its rapid convergence rate, based on a Cook's membrane problem, demonstrated that it requires a relatively coarser mesh to reach the exact solution. With those encouraging results, LME is then applied to a larger non-linear cardiac mechanics problem. That is simulating a healthy and a myocardial infarcted canine left ventricle (LV) during one heart beat. The LV is idealised by a prolate spheroidal ellipsoid. It undergoes expansion during the diastolic phase, addressed by a non-linear passive stress model which incorporates the transversely isotropic properties of the material. The contraction, during the systolic phase, is simulated by Guccione's active stress model. The infarct region is considered to be non-contractile and twice as stiff as the healthy tissue. The material loss, especially during the necrotic phase, is incorporated by the use of a homogenisation approach. Firstly, the loss of the contraction ability of the infarct region counteracts the overall contraction behaviour by a bulging deformation where the occurrence of high stresses are noted. Secondly, with regards to the behaviour of LME, it is found to feature high convergence rate and a decrease in computation time with respect to MLS. However, it is also observed that LME is quite sensitive to the nodal spacing in particular for an unstructured nodal distribution where it produces results that are completely unreliable.
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Burniston, J. D. "A neural network/rule-based architecture for continuous function approximation." Thesis, University of Nottingham, 1994. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.387198.
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Tham, Chen Khong. "Modular on-line function approximation for scaling up reinforcement learning." Thesis, University of Cambridge, 1994. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.309702.
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Fischer, Manfred M. "Neural networks. A general framework for non-linear function approximation." Wiley-Blackwell, 2006. http://epub.wu.ac.at/5493/1/NeuralNetworks.pdf.
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The focus of this paper is on the neural network modelling approach that has gained increasing recognition in GIScience in recent years. The novelty about neural networks lies in their ability to model non-linear processes with few, if any, a priori assumptions about the nature of the data-generating process. The paper discusses some important issues that are central for successful application development. The scope is limited to feedforward neural networks, the leading example of neural networks. It is argued that failures in applications can usually be attributed to inadequate learning and/or inadequate complexity of the network model. Parameter estimation and a suitably chosen number of hidden units are, thus, of crucial importance for the success of real world neural network applications. The paper views network learning as an optimization problem, reviews two alternative approaches to network learning, and provides insights into current best practice to optimize complexity so to perform well on generalization tasks.
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Burton, Christina Marie. "Quadratic Spline Approximation of the Newsvendor Problem Optimal Cost Function." BYU ScholarsArchive, 2012. https://scholarsarchive.byu.edu/etd/3087.
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We consider a single-product dynamic inventory problem where the demand distributions in each period are known and independent but with density. We assume the lead time and the fixed cost for ordering are zero and that there are no capacity constraints. There is a holding cost and a backorder cost for unfulfilled demand, which is backlogged until it is filled by another order. The problem may be nonstationary, and in fact our approximation of the optimal cost function using splines is most advantageous when demand falls suddenly. In this case the myopic policy, which is most often used in practice to calculate optimal inventory level, would be very costly. Our algorithm uses quadratic splines to approximate the optimal cost function for this dynamic inventory problem and calculates the optimal inventory level and optimal cost.
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Geva, Shlomo. "Exponential response artificial neurons for pattern classification and function approximation." Thesis, Queensland University of Technology, 1992.
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Valenzuela, Zaldy M. "Constant and power-of-2 segmentation algorithms for a high speed numerical function generator." Thesis, Monterey, Calif. : Springfield, Va. : Naval Postgraduate School ; Available from National Technical Information Service, 2005. http://library.nps.navy.mil/uhtbin/hyperion/05Jun%5FValenzuela.pdf.
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Huang, Guo Qin 1973. "Application of the Flexible Local Approximation Method to photonic crystal cavities." Thesis, McGill University, 2006. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=99413.
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This thesis investigates the application of a recently developed numerical technique, the Flexible Local Approximation Method (FLAME) to compute the resonances of 2D photonic crystal (PC) cavities, formed by a defect in a regular array of dielectric rods. FLAME is a finite-difference-like method which is ideally suited to problems consisting of large numbers of identical structures.The anisotropic perfectly matched layer (PML) is used as an artificial absorbing layer to truncate the computational domain. The parameters of the PML are chosen carefully to provide adequate absorption without a large computational cost.
FLAME method and PML boundaries are applied to cavities with 3x3, 5x5 and 7x7 arrays of rods. The resonant modes, field distribution, and quality factor are computed and compared with previously-published results. Good agreement is obtained. However, the matrix eigenproblem generated by FLAME is of a kind for which sparse-matrix algorithms are not available and dense-matrix software had to be used. This limitation will have to be overcome if FLAME is to be widely used for PC cavities.