Dissertations / Theses on the topic 'Cluster approximation'
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Zhang, Kai. "Kernel-based clustering and low rank approximation /." View abstract or full-text, 2008. http://library.ust.hk/cgi/db/thesis.pl?CSED%202008%20ZHANG.
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Benedikt, Udo. "Low-Rank Tensor Approximation in post Hartree-Fock Methods." Doctoral thesis, Universitätsbibliothek Chemnitz, 2014. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-qucosa-133194.
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In this thesis the application of novel tensor decomposition and tensor representation techniques in highly accurate post Hartree-Fock methods is evaluated. These representation techniques can help to overcome the steep scaling behaviour of high level ab-initio calculations with increasing system size and therefore break the "curse of dimensionality". After a comparison of various tensor formats the application of the "canonical polyadic" format (CP) is described in detail. There, especially the casting of a normal, index based tensor into the CP format (tensor decomposition) and a method for a low rank approximation (rank reduction) of the two-electron integrals in the AO basis are investigated. The decisive quantity for the applicability of the CP format is the scaling of the rank with increasing system and basis set size. The memory requirements and the computational effort for tensor manipulations in the CP format are only linear in the number of dimensions but still depend on the expansion length (rank) of the approximation. Furthermore, the AO-MO transformation and a MP2 algorithm with decomposed tensors in the CP format is evaluated and the scaling with increasing system and basis set size is investigated. Finally, a Coupled-Cluster algorithm based only on low-rank CP representation of the MO integrals is developed. There, especially the successive tensor contraction during the iterative solution of the amplitude equations and the error propagation upon multiple application of the reduction procedure are discussed. In conclusion the overall complexity of a Coupled-Cluster procedure with tensors in CP format is evaluated and some possibilities for improvements of the rank reduction procedure tailored to the needs in electronic structure calculations are shownDie vorliegende Arbeit beschäftigt sich mit der Anwendung neuartiger Tensorzerlegungs- und Tensorrepesentationstechniken in hochgenauen post Hartree-Fock Methoden um das hohe Skalierungsverhalten dieser Verfahren mit steigender Systemgröße zu verringern und somit den "Fluch der Dimensionen" zu brechen. Nach einer vergleichenden Betrachtung verschiedener Representationsformate wird auf die Anwendung des "canonical polyadic" Formates (CP) detailliert eingegangen. Dabei stehen zunächst die Umwandlung eines normalen, indexbasierten Tensors in das CP Format (Tensorzerlegung) und eine Methode der Niedrigrang Approximation (Rangreduktion) für Zweielektronenintegrale in der AO Basis im Vordergrund. Die entscheidende Größe für die Anwendbarkeit ist dabei das Skalierungsverhalten das Ranges mit steigender System- und Basissatzgröße, da der Speicheraufwand und die Berechnungskosten für Tensormanipulationen im CP Format zwar nur noch linear von der Anzahl der Dimensionen des Tensors abhängen, allerdings auch mit der Expansionslänge (Rang) skalieren. Im Anschluss wird die AO-MO Transformation und der MP2 Algorithmus mit zerlegten Tensoren im CP Format diskutiert und erneut das Skalierungsverhalten mit steigender System- und Basissatzgröße untersucht. Abschließend wird ein Coupled-Cluster Algorithmus vorgestellt, welcher ausschließlich mit Tensoren in einer Niedrigrang CP Darstellung arbeitet. Dabei wird vor allem auf die sukzessive Tensorkontraktion während der iterativen Bestimmung der Amplituden eingegangen und die Fehlerfortpanzung durch Anwendung des Rangreduktions-Algorithmus analysiert. Abschließend wird die Komplexität des gesamten Verfahrens bewertet und Verbesserungsmöglichkeiten der Reduktionsprozedur aufgezeigt
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Scherrer, Alexander. "Adaptive approximation of nonlinear minimization problems : the adaptive clustering method in inverse radiation therapy planning /." Aachen : Shaker, 2006. http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&doc_number=015733837&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA.
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Filor, Stephan [Verfasser], Stefan [Akademischer Betreuer] [Gutachter] Kehrein, and Andreas [Gutachter] Honecker. "A Variational Cluster Approximation for the Heisenberg Model / Stephan Filor ; Gutachter: Stefan Kehrein, Andreas Honecker ; Betreuer: Stefan Kehrein." Göttingen : Niedersächsische Staats- und Universitätsbibliothek Göttingen, 2017. http://d-nb.info/1129956415/34.
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Filor, Stephan Verfasser], Stefan [Akademischer Betreuer] [Gutachter] [Kehrein, and Andreas [Gutachter] Honecker. "A Variational Cluster Approximation for the Heisenberg Model / Stephan Filor ; Gutachter: Stefan Kehrein, Andreas Honecker ; Betreuer: Stefan Kehrein." Göttingen : Niedersächsische Staats- und Universitätsbibliothek Göttingen, 2017. http://d-nb.info/1129956415/34.
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Sen, Asok Kumar. "Part I, traveling cluster approximation for uncorrelated amorphous systems ; Part II, influence of long-range forces on the wetting transition /." The Ohio State University, 1985. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487260859496667.
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Heinen, Milton Roberto. "A connectionist approach for incremental function approximation and on-line tasks." reponame:Biblioteca Digital de Teses e Dissertações da UFRGS, 2011. http://hdl.handle.net/10183/29015.
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Este trabalho propõe uma nova abordagem conexionista, chamada de IGMN (do inglês Incremental Gaussian Mixture Network), para aproximação incremental de funções e tarefas de tempo real. Ela é inspirada em recentes teorias do cérebro, especialmente o MPF (do inglês Memory-Prediction Framework) e a Inteligência Artificial Construtivista, que fazem com que o modelo proposto possua características especiais que não estão presentes na maioria dos modelos de redes neurais existentes. Além disso, IGMN é baseado em sólidos princípios estatísticos (modelos de mistura gaussianos) e assintoticamente converge para a superfície de regressão ótima a medida que os dados de treinamento chegam. As principais vantagens do IGMN em relação a outros modelos de redes neurais são: (i) IGMN aprende instantaneamente analisando cada padrão de treinamento apenas uma vez (cada dado pode ser imediatamente utilizado e descartado); (ii) o modelo proposto produz estimativas razoáveis baseado em poucos dados de treinamento; (iii) IGMN aprende de forma contínua e perpétua a medida que novos dados de treinamento chegam (não existem fases separadas de treinamento e utilização); (iv) o modelo proposto resolve o dilema da estabilidade-plasticidade e não sofre de interferência catastrófica; (v) a topologia da rede neural é definida automaticamente e de forma incremental (novas unidades são adicionadas sempre que necessário); (vi) IGMN não é sensível às condições de inicialização (de fato IGMN não utiliza nenhuma decisão e/ou inicialização aleatória); (vii) a mesma rede neural IGMN pode ser utilizada em problemas diretos e inversos (o fluxo de informações é bidirecional) mesmo em regiões onde a função alvo tem múltiplas soluções; e (viii) IGMN fornece o nível de confiança de suas estimativas. Outra contribuição relevante desta tese é o uso do IGMN em importantes tarefas nas áreas de robótica e aprendizado de máquina, como por exemplo a identificação de modelos, a formação incremental de conceitos, o aprendizado por reforço, o mapeamento robótico e previsão de séries temporais. De fato, o poder de representação e a eficiência e do modelo proposto permitem expandir o conjunto de tarefas nas quais as redes neurais podem ser utilizadas, abrindo assim novas direções nos quais importantes contribuições do estado da arte podem ser feitas. Através de diversos experimentos, realizados utilizando o modelo proposto, é demonstrado que o IGMN é bastante robusto ao problema de overfitting, não requer um ajuste fino dos parâmetros de configuração e possui uma boa performance computacional que permite o seu uso em aplicações de controle em tempo real. Portanto pode-se afirmar que o IGMN é uma ferramenta de aprendizado de máquina bastante útil em tarefas de aprendizado incremental de funções e predição em tempo real.This work proposes IGMN (standing for Incremental Gaussian Mixture Network), a new connectionist approach for incremental function approximation and real time tasks. It is inspired on recent theories about the brain, specially the Memory-Prediction Framework and the Constructivist Artificial Intelligence, which endows it with some unique features that are not present in most ANN models such as MLP, RBF and GRNN. Moreover, IGMN is based on strong statistical principles (Gaussian mixture models) and asymptotically converges to the optimal regression surface as more training data arrive. The main advantages of IGMN over other ANN models are: (i) IGMN learns incrementally using a single scan over the training data (each training pattern can be immediately used and discarded); (ii) it can produce reasonable estimates based on few training data; (iii) the learning process can proceed perpetually as new training data arrive (there is no separate phases for leaning and recalling); (iv) IGMN can handle the stability-plasticity dilemma and does not suffer from catastrophic interference; (v) the neural network topology is defined automatically and incrementally (new units added whenever is necessary); (vi) IGMN is not sensible to initialization conditions (in fact there is no random initialization/ decision in IGMN); (vii) the same neural network can be used to solve both forward and inverse problems (the information flow is bidirectional) even in regions where the target data are multi-valued; and (viii) IGMN can provide the confidence levels of its estimates. Another relevant contribution of this thesis is the use of IGMN in some important state-of-the-art machine learning and robotic tasks such as model identification, incremental concept formation, reinforcement learning, robotic mapping and time series prediction. In fact, the efficiency of IGMN and its representational power expand the set of potential tasks in which the neural networks can be applied, thus opening new research directions in which important contributions can be made. Through several experiments using the proposed model it is demonstrated that IGMN is also robust to overfitting, does not require fine-tunning of its configuration parameters and has a very good computational performance, thus allowing its use in real time control applications. Therefore, IGMN is a very useful machine learning tool for incremental function approximation and on-line prediction.
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Choudhury, Salimur Rashid, and University of Lethbridge Faculty of Arts and Science. "Approximation algorithms for a graph-cut problem with applications to a clustering problem in bioinformatics." Thesis, Lethbridge, Alta. : University of Lethbridge, Deptartment of Mathematics and Computer Science, 2008, 2008. http://hdl.handle.net/10133/774.
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Clusters in protein interaction networks can potentially help identify functional relationships
among proteins. We study the clustering problem by modeling it as graph cut problems.
Given an edge weighted graph, the goal is to partition the graph into a prescribed
number of subsets obeying some capacity constraints, so as to maximize the total weight
of the edges that are within a subset. Identification of a dense subset might shed some light
on the biological function of all the proteins in the subset.
We study integer programming formulations and exhibit large integrality gaps for various
formulations. This is indicative of the difficulty in obtaining constant factor approximation
algorithms using the primal-dual schema. We propose three approximation algorithms for
the problem. We evaluate the algorithms on the database of interacting proteins and on
randomly generated graphs. Our experiments show that the algorithms are fast and have
good performance ratio in practice.xiii, 71 leaves : ill. ; 29 cm.
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Nachaoui, Mourad. "Étude théorique et approximation numérique d'un problème inverse de transfert de la chaleur." Phd thesis, Université de Nantes, 2011. http://tel.archives-ouvertes.fr/tel-00678032.
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Nous nous intéressons à l'étude d'un problème d'analyse des transferts de chaleur qui modélise une opération de soudage. L'approche que nous considérons ne s'occupe que de la partie solide de la plaque. Elle consiste à résoudre un problème à frontière libre. Pour cela, nous proposons une formulation en optimisation de forme. Le problème d'état est gouverné par un opérateur qui, pour certaines données, n'est pas coercif. Cela complique l'étude de la continuité du problème d'état. Nous surmontons cette difficulté en utilisant le degré topologique de Leray-Shauder, ainsi nous montrons l'existence d'un domaine optimal. Ensuite, nous considérons une discrétisation de ce problème basée sur les éléments finis linéaires. Nous prouvons alors que le problème discret admet une solution et nous montrons qu'une sous-suite des solutions de ce problème convergence vers la solution du problème continu. Enfin, nous présentons des résultats numériques réalisés par deux méthodes : la méthode déterministe basée sur le calcul du gradient de forme, et les algorithmes génétiques combinés avec la logique floue et le calcul parallèle. Ainsi une étude comparative de ces deux méthodes aux niveaux qualitatif et quantitatif a été présentée.
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Madjet, Mohamed El-Amine. "Etude théorique des propriétés électroniques et dynamiques des agrégats métalliques simples dans le modèle du jellium." Université Joseph Fourier (Grenoble), 1994. http://www.theses.fr/1994GRE10094.
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Nous avons etudie les proprietes electroniques des agregats d alcalins dans diverses approximations theoriques et dans le cadre du modele du jellium spherique. Pour l'etat fondamental de ces agregats nous avons decrit les electrons delocalises dans l'approximation de hf (hartree fock) et dans la lda (approximation de la densite locale). Nous avons compare les calculs de la lda aux calculs hf obtenus pour la densite et les energies electroniques totales. C'est ce qui nous a permis de confirmer la validite de la theorie de la fonctionnelle densite pour la description de l'etat fondamental d'un systeme fini de fermions. Pour l'etude des modes dipolaires collectives, nous avons considere une excitation electromagnetique. Nous avons aborde la description de ces modes avec les approximations suivantes: l'approximation des phases aleatoires (rpa), l'approximation de la densite locale dependant du temps (tdl-da) et l'approche des regles de somme. En comparant les resultats obtenus par les deux premieres methodes pour les proprietes statiques et dynamiques nous avons pu montrer la validite de la discretisation du continuum dans la rpa. L'etude comparative, que nous avons menee sur l'effet de l'echange et des correlations sur les proprietes electroniques et optiques, a montre que le desaccord observe entre experience et theorie est du essentiellement a l'approximation du jellium faite pour le fond ionique
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BOTTO, DAVIDE. "Dynamical transitions in driven diffusive models." Doctoral thesis, Politecnico di Torino, 2020. http://hdl.handle.net/11583/2790160.
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Ekdahl, Magnus. "Approximations of Bayes Classifiers for Statistical Learning of Clusters." Licentiate thesis, Linköping : Linköpings universitet, 2006. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-5856.
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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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Vimont, Guillaume. "Approximation dynamique de clusters dans un graphe social : méthodes et applications." Thesis, Paris 2, 2019. http://www.theses.fr/2019PA020007.
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Nous étudions comment détecter des clusters dans un graphe défini par un flux d’arêtes, sans stocker l'ensemble du graphe. Nous montrons comment détecter de gros clusters de l'ordre de √n dans des graphes qui ont m = O(n log(n)) arêtes, tout en stockant √n.log(n) arêtes. Les graphes sociaux suivent le régime où m satisfait cette condition. Nous étendons notre approche aux graphes dynamiques définis par les arêtes les plus récentes du flux et à plusieurs flux. Nous proposons des méthodes simples et robustes afin de détecter ces clusters de manière approchée.Nous définissons la corrélation de contenu de deux flux ρ(t) par la similarité de Jaccard de leurs clusters, dans les fenêtres au temps t. Nous proposons une méthode simple et efficace pour approcher cette corrélation en ligne et montrons que pour les graphes aléatoires dynamiques qui suivent une loi de puissance, nous pouvons garantir une bonne approximation.Une des applications est l’analyse des flux Twitter. Nous calculons les corrélations de contenu de ces flux en ligne. Nous proposons ensuite une recherche par corrélation où les réponses aux ensembles de mots-clés sont entièrement basées sur les petites corrélations des flux. Les réponses sont ordonnées par les corrélations, et les explications peuvent être tracées avec les clusters stockésWe study how to detect clusters in a graph defined by a stream of edges, without storing the entire graph. We show how to detect large clusters in the order of √n in graphs that have m = O(n log(n)) edges, while storing √n.log(n) edges. Social graphs satisfy this condition m. We extend our approach to dynamic graphs defined by the most recent stream of edges and multiple streams. We propose simple and robust methods based on the approximation to detect these clusters.We define the content correlation of two streams ρ(t) is the Jaccard similarity of their clusters in the windows before time t. We propose a simple and efficient method to approach this online correlation and show that for dynamic random graphs that follow a power law, we can guarantee a good approximation.As an applications we follow Twitter streams and compute their content correlations online. We then propose a search by correlation where answers to sets of keywords are entirely based on the small correlations of the streams. Answers are ordered by the correlations, and explanations can be traced with the stored clusters
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Gutlé, Claudine. "Espaces orbitalaires et théorie de la fonctionnelle de la densité : éléments pour le développement d' une approche de la chimie quantique basée sur le théorème de Hohenberg et Kohn ainsi que sur l' équation de Schrödinger, et qui conduit à des résultats exacts en suivant une systématique gouvernée par l' espace orbitalaire." Paris 7, 2003. http://www.theses.fr/2003PA077160.
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Gibson, Matthew Richard. "Clusters and covers: geometric set cover algorithms." Diss., University of Iowa, 2010. https://ir.uiowa.edu/etd/502.
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The set cover problem is a well studied problem in computer science. The problem cannot be approximated to better than an log n-factor in polynomial time unless P = NP and has an O(log n)-factor approximation algorithm. We consider several special cases of the set cover problem in which geometry plays a key role. With geometric structure introduced to the problem, it may be possible to construct approximation algorithms with approximation ratios asymptotically better than log n.
The first problem we consider is the decomposing coverings problem. Here, we consider a combinatorial problem: given a collection of points in the plane and a collection of objects in the plane such that each point is contained in at least k objects, partition the objects into as many sets as possible so that each set covers all of the points. We show that if the objects are translates of a convex polygon, then it is possible to partition the translates into Ω(k) covers.
The second problem we consider is the planar sensor cover problem. This problem is a generalization of the decomposing coverings problem. We are given a collection of points in the plane and a collection of objects in the plane. Each of the objects can be thought of as a sensor. The sensors have a duration which can be thought of as the battery life of the sensor. The planar sensor cover problem is to schedule a start time to each of the sensors so that the points are covered by a sensor for as long as possible. We give a constant factor approximation for this problem. The key contribution to this result is a constant factor approximation to a one-dimensional version of the problem called the restricted strip cover (RSC) problem. Our result for RSC improves upon the previous best O(log log log n)-approximation, and our result for the planar sensor cover problem improves upon the previous best O(log n)-approximation.
The next problem we consider is the metric clustering to minimize the sum of radii problem. Here, we are given an n-point metric (P,d) and an integer k > 0. We are interested in covering the points in P with at most k balls so that the sum of the radii of the balls is minimized. We give a randomized algorithm which solves the problem exactly in nO(log n log Δ) time, where Δ is the ratio of the maximum interpoint distance to the minimum interpoint distance. We also show that the problem is NP-hard, even in metrics induced by weighted planar graphs and when the metric has constant doubling dimension.
The last problem we consider is the minimum dominating set problem for disk graphs. In this problem, we are given a set of disks in the plane, and we want to choose a minimum-cardinality subset of disks such that every disk is either in the set or intersects a disk in the set. For any ε > 0, we show that a simple local search algorithm is a (1+ ε)-approximation for the problem which improves upon the previous best O(log n)-approximation algorithm.
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Kubát, Milan. "Borcení časové osy v oblasti biosignálů." Master's thesis, Vysoké učení technické v Brně. Fakulta elektrotechniky a komunikačních technologií, 2014. http://www.nusl.cz/ntk/nusl-220845.
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This work is dedicated to dynamic time warping in biosignal processing, especially it´s application for ECG signals. On the beginning the theoretical notes about cardiography are summarized. Then, the DTW analysis follows along with conditions and demands assessments for it’s successful application. Next, several variants and application possibilities are described. The practical part covers the design of this method, the outputs comprehension, settings optimization and realization of methods related with DTW
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Jacobson, Leif David. "Approximating Many-Body Induction to Efficiently Describe Molecular Liquids and Clusters With Improved Accuracy." The Ohio State University, 2011. http://rave.ohiolink.edu/etdc/view?acc_num=osu1312480919.
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Christlmaier, Evelin Martine. "CC2 response method using local correlation and density fitting approximations for the calculation of the electronic g-tensor of extended open-shell molecules." Doctoral thesis, Humboldt-Universität zu Berlin, 2021. http://dx.doi.org/10.18452/22835.
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In dieser Arbeit wird eine unrestricted Coupled-Cluster CC2 Response-Methode für die Berechnung von Eigenschaften erster und zweiter Ordnung, mit dem elektronischen g-Tensor als Schwerpunkt, präsentiert. Lokale Korrelations- und Dichtefittingnäherungen wurden verwendet. Die fundamentalen Konzepte notwendig für das Verständnis von Coupled-Cluster-Theorie, Dichtefitting, lokaler Korrelation, allgemeinen Coupled-Cluster Eigenschaften
und dem elektronischen g-Tensor werden diskutiert. Die berechneten g-Tensoren werden mit denen durch Coupled-Cluster Singles and Doubles, Dichtefunktionaltheorie und Experiment erhaltenen verglichen. Effizienz und Genauigkeit der Näherung wird untersucht. Ein detailierter Anhang beschreibt die diagrammatische Coupled-Cluster-Theorie sowie ihre Anwendung zur Herleitung der verwendeten Arbeitsgleichungen. Die in dieser Arbeit entwickelte Methode ermöglicht es, den elektronischen g-Tensor von ausgedehnten Systemen mit einer Methode, die nicht auf Dichtefunktionaltheorie basiert, quantitativ vorherzusagen.
Damit ist sie ein wichtiger Schritt hin zur Entwicklung von niedrig skalierenden Coupled-Cluster-Methoden höherer Ordnung für diese Art von Problem.This work presents an unrestricted coupled-cluster CC2 response method using local correlation and density fitting approximations for the calculation of first and second order properties with particular focus on the electronic g-tensor. The fundamental concepts related to coupled-cluster theory, density fitting, local correlation, general coupled-cluster properties and the electronic g-tensor are discussed. The calculated g-tensors are benchmarked against those obtained from coupled-cluster singles and doubles, density functional theory and experiment. Efficiency and accuracy of the approximations is investigated. A detailed appendix covers the fundamentals of diagrammatic coupled-cluster and its application to the derivation of the working equations. The method presented in this thesis enables the quantitative prediction of the electronic g-tensor of extended systems with a method other than density functional theory. It represents an important step towards the development of low-scaling higher order coupled-cluster methods for this type of problem.
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Ndoye, Chérif A. A. "Electronic spectroscopy of small organic and organometallic molecules : electronic correlation, vibronic and spin-orbit couplings." Université Louis Pasteur (Strasbourg) (1971-2008), 2008. https://publication-theses.unistra.fr/public/theses_doctorat/2008/NDOYE_Cherif_AA_2008.pdf.
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La prédiction de propriétés spectroscopiques moléculaires et l’interprétation de spectres expérimentaux nécessitent de faire appel à la théorie. Une première étape consiste à se limiter à la spectroscopie électronique dans l’approximation de Born-Oppenheimer ce qui consiste à considérer les noyaux de la molécule comme étant fixes et les états électroniques indépendants les uns des autres. L’objectif de cette thèse est d’étudier la structure électronique de petites molécules organiques et organométalliques dans l’approximation de Born-Oppenheimer dans un premier temps avant d’aller au delà en prenant en compte des effets tels que le couplage vibronique ou le couplage spin-orbite entre les états électroniques. Le premier chapitre est consacré aux méthodes ab initio utilisées pour obtenir les résultats présentés dans les chapitres ultérieurs. Une première partie est consacrée aux méthodes de structure électronique dans l’approximation de Born-Oppenheimer, elle est suivie d’une partie qui traite des effets de couplage vibronique et spin-orbite. Le second chapitre présente une étude de la structure électronique et des courbes d’énergie potentielle des carbènes de métaux de transition MCH+2 (M=Fe, Co, Ni). Le troisième chapitre rapporte les spectres vibroniques des fluoroéthylènes obtenus par simulation et comparés aux spectres expérimentaux afin d’identifier l’origine de différentes contributions spectroscopiques. Enfin le dernier chapitre traite des effets spin-orbite dans l’eau et ses homologues lourds (H2X avec X=O, Te, Po)Theory is sometime necessary to predict molecular spectroscopic properties and interpret experimental spectra. A first step study can be limited to the electronic spectroscopy in Born-Oppenheimer approximation which consists in considering nuclei fixed and electronic states independent from each other. The scope of this thesis is to first study the electronic structure of small organic and orgnometallic molecules in the Born-Oppenheimer approximation and ultimatly go beyond by taking into account effects such as vibronic or spin-orbit couplings between electronic states. The first chapter is dedicated to the ab initio methods used to obtain the results presented in the following chapters. Electronic structure methods in the Born-Oppenheimer approximation are first presented followed by the methods that treat vibronic and spin-orbit couplings. The second chapter is a study of the electronic structure and potential energy curves of MCH+2 (M=Fe, Co, Ni) transition metal carbenes. Chapter three reports simulated vibronic spectra of fluoroethylenes, they are compared to experimental spectra to indentify the origin of the different spectroscopic contributions. A last chapter deals with the spin-orbit effects in water and its heavy homologous (H2X with X=O, Te, Po)
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Plagne, Laurent. "Equation de Vlasov appliquée à la dynamique électronique des agrégats de sodium lors de collisions avec des ions." Université Joseph Fourier (Grenoble), 1998. http://www.theses.fr/1998GRE10272.
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L'objet de ce travail est l'etude theorique de la reponse non-lineaire des electrons d'un agregat de sodium lors de collisions avec des ions. Dans ce but, nous utilisons une approximation semi-classique qui substitue a la fonction d'onde a n corps quantique representant les electrons de valence de l'agregat, une densite d'espace de phase. L'evolution de cette densite est regie par l'equation de vlasov qui est resolue numeriquement. Grace a la realisation d'un programme parallele de resolution de l'equation de vlasov, la dynamique semi-classique conserve le caractere fermionique de la distribution pour des durees superieures a 100 fs. Cette propriete de l'equation de vlasov est pour la premiere fois verifiee par l'experience numerique pour des systemes tridimensionnels de fermions en interaction coulombienne. L'etude des collisions peripheriques ion multicharge-agregat montre qu'il n'existe pas de difference significative entre les resultats quantiques (tdlda) et leurs correspondants semi-classiques (vlasov), relatifs a la charge et a l'energie d'excitation finale des agregats. L'approche semi-classique est donc un modele particulierement adapte pour traiter de gros systemes. L'analyse de l'energie d'excitation des agregats confirme que les collisions ion multi-charge-agregat constituent un outil unique pour produire des agregats fortement charges et faiblement excites. Cela rend possible la determination de leur charge critique. Une etude des collisions centrales montre que pour des vitesses inferieures a la vitesse de fermi, la perte d'energie cinetique des protons dans les agregats est identique a celle qu'ils subissent en traversant la matiere infinie. Pour des vitesses superieures, des effets de taille finie apparaissent. Dans ce cas, l'extension spatiale de la deformation de la densite, induite par le passage de l'ion, est comparable a la taille des agregats.
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Miti, Filippo. "Mathematical models for cellular aggregation: the chemotactic instability and clustering formation." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2016. http://amslaurea.unibo.it/12020/.
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In this thesis we present a mathematical formulation of the interaction between microorganisms such as bacteria or amoebae and chemicals, often produced by the organisms themselves. This interaction is called chemotaxis and leads to cellular aggregation. We derive some models to describe chemotaxis. The first is the pioneristic Keller-Segel parabolic-parabolic model and it is derived by two different frameworks: a macroscopic perspective and a microscopic perspective, in which we start with a stochastic differential equation and we perform a mean-field approximation. This parabolic model may be generalized by the introduction of a degenerate diffusion parameter, which depends on the density itself via a power law. Then we derive a model for chemotaxis based on Cattaneo's law of heat propagation with finite speed, which is a hyperbolic model. The last model proposed here is a hydrodynamic model, which takes into account the inertia of the system by a friction force. In the limit of strong friction, the model reduces to the parabolic model, whereas in the limit of weak friction, we recover a hyperbolic model. Finally, we analyze the instability condition, which is the condition that leads to aggregation, and we describe the different kinds of aggregates we may obtain: the parabolic models lead to clusters or peaks whereas the hyperbolic models lead to the formation of network patterns or filaments. Moreover, we discuss the analogy between bacterial colonies and self gravitating systems by comparing the chemotactic collapse and the gravitational collapse (Jeans instability).
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Pham, The Anh. "Détection robuste de jonctions et points d'intérêt dans les images et indexation rapide de caractéristiques dans un espace de grande dimension." Thesis, Tours, 2013. http://www.theses.fr/2013TOUR4023/document.
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Les caractéristiques locales sont essentielles dans de nombreux domaines de l’analyse d’images comme la détection et la reconnaissance d’objets, la recherche d’images, etc. Ces dernières années, plusieurs détecteurs dits locaux ont été proposés pour extraire de telles caractéristiques. Ces détecteurs locaux fonctionnent généralement bien pour certaines applications, mais pas pour toutes. Prenons, par exemple, une application de recherche dans une large base d’images. Dans ce cas, un détecteur à base de caractéristiques binaires pourrait être préféré à un autre exploitant des valeurs réelles. En effet, la précision des résultats de recherche pourrait être moins bonne tout en restant raisonnable, mais probablement avec un temps de réponse beaucoup plus court. En général, les détecteurs locaux sont utilisés en combinaison avec une méthode d’indexation. En effet, une méthode d’indexation devient nécessaire dans le cas où les ensembles de points traités sont composés de milliards de points, où chaque point est représenté par un vecteur de caractéristiques de grande dimensionLocal features are of central importance to deal with many different problems in image analysis and understanding including image registration, object detection and recognition, image retrieval, etc. Over the years, many local detectors have been presented to detect such features. Such a local detector usually works well for some particular applications but not all. Taking an application of image retrieval in large database as an example, an efficient method for detecting binary features should be preferred to other real-valued feature detection methods. The reason is easily seen: it is expected to have a reasonable precision of retrieval results but the time response must be as fast as possible. Generally, local features are used in combination with an indexing scheme. This is highly needed for the case where the dataset is composed of billions of data points, each of which is in a high-dimensional feature vector space
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Filor, Stephan. "A Variational Cluster Approximation for the Heisenberg Model." Doctoral thesis, 2016. http://hdl.handle.net/11858/00-1735-0000-0023-3E15-1.
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Martin, Lee C. "The Kondo Lattice Model: a Dynamical Cluster Approximation Approach." Doctoral thesis, 2010. https://nbn-resolving.org/urn:nbn:de:bvb:20-opus-49446.
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We apply an antiferromagnetic symmetry breaking implementation of the dynamical cluster approximation (DCA) to investigate the two-dimensional hole-doped Kondo lattice model (KLM) with hopping $t$ and coupling $J$. The DCA is an approximation at the level of the self-energy. Short range correlations on a small cluster, which is self-consistently embedded in the remaining bath electrons of the system, are handled exactly whereas longer ranged spacial correlations are incorporated on a mean-field level. The dynamics of the system, however, are retained in full. The strong temporal nature of correlations in the KLM make the model particularly suitable to investigation with the DCA. Our precise DCA calculations of single particle spectral functions compare well with exact lattice QMC results at the particle-hole symmetric point. However, our DCA version, combined with a QMC cluster solver, also allows simulations away from particle-hole symmetry and has enabled us to map out the magnetic phase diagram of the model as a function of doping and coupling $J/t$. At half-filling, our results show that the linear behaviour of the quasi-particle gap at small values of $J/t$ is a direct consequence of particle-hole symmetry, which leads to nesting of the Fermi surface. Breaking the symmetry, by inclusion of a diagonal hopping term, results in a greatly reduced gap which appears to follow a Kondo scale. Upon doping, the magnetic phase observed at half-filling survives and ultimately gives way to a paramagnetic phase. Across this magnetic order-disorder transition, we track the topology of the Fermi surface. The phase diagram is composed of three distinct regions: Paramagnetic with {\it large} Fermi surface, in which the magnetic moments are included in the Luttinger sum rule, lightly antiferromagnetic with large Fermi surface topology, and strongly antiferromagnetic with {\it small} Fermi surface, where the magnetic moments drop out of the Luttinger volume. We draw on a mean-field Hamiltonian with order parameters for both magnetisation and Kondo screening as a tool for interpretation of our DCA results. Initial results for fixed coupling and doping but varying temperature are also presented, where the aim is look for signals of the energy scales in the system: the Kondo temperature $T_{K}$ for initial Kondo screening of the magnetic moments, the Neel temperature $T_{N}$ for antiferromagnetic ordering, a possible $T^{*}$ at which a reordering of the Fermi surface is observed, and finally, the formation of the coherent heavy fermion state at $T_{coh}$Wir setzen eine Implementierung der dynamischen Cluster Näherung (DCA) mit gebrochener Symmetrie ein um das zweidimensionale lochdotierte Kondo Gitter Model (KLM) mit dem Hüpfmatrixelement $t$ und der Kopplung $J$ zu untersuchen. Die DCA beruht auf einer Näherung der Selbstenergie. Kurzreichweitige Korrelationen auf einem kleinen Cluster, der selbstkonsistent in ein Bad der übrigen Systemelektronen eingebettet ist, werden exakt behandelt, während langreichweitige Korrelationen auf Mean-Field Basis berücksichtigt werden. Dabei wird jedoch die Dynamik des Systems voll beibehalten. Auf Grund starker dynamischer Korrelationen zeigt sich das KLM als besonders geeignet für Untersuchungen im Rahmen der DCA. Präzise Berechnungen der Einteilchen Spektralfunktion geben gute Übereinstimmung mit exakten Gitter-QMC Resultaten am Teilchen-Loch symmetrischen Punkt. Unsere DCA Version, kombiniert mit einem QMC Cluster Solver, erlaubt es, Simulationen fern vom Teilchen-Loch symmetrischen Punkt durchzuführen und hat es uns ermöglicht das magnetische Phasendiagram des Models als Funktion der Dotierung und der Kopplung $J/t$ abzutasten. Bei halber Füllung zeigen unsere Resultate, dass das lineare Verhalten der Quasiteilchenlücke bei kleinem $J/t$ direkt aus der vorliegenden Teilchen-Loch Symmetrie, die ihrerseits zu Nesting führt, hervorgeht. Brechung dieser Symmetrie durch das Einführen eines diagonalen Hüpfmatrixelements, hat eine an die Kondo Skala gekoppelte, stark reduzierte Quasiteilchenlücke zur Folge. Im dotiertem System setzt sich die bei Halbfüllung beobachtete magnetische Phase fort bis sie letztendlich der paramagnetischen Phase weicht. Wir verfolgen die Entwicklung der Topologie der Fermifläche beim Durchstoßen dieses magnetischen Übergangs vom Ordnungs- zum Unordnungregime. Das Phasendiagram unterteilt sich in drei verschiedenen Regionen: Den Paramagnetischen Bereich mit {\it großer} Fermifläche, in dem die magnetische Momente zum Luttinger Volumen beitragen, den schwachen Antiferromagneten, mit großer Fermiflächetopologie, und den starken Antiferromagneten mit {\it kleiner} Fermifläche, bei dem die magnetischen Momente nicht am Luttinger Volumen beteiligt sind. Wir beziehen uns zur weiteren Interpretation unserer DCA Resultate auf einen Mean-Field Hamiltonian mit Ordnungsparametern sowohl für die Magnetisierung als auch für die Kondo-Abschirmung. Erste Resultate bei fester Kopplung und Dotierung, jedoch bei unterschiedlichen Temperaturen, zwecks der Ermittlung der verschiedene Energieskalen des Systems, werden dargestellt. Wir suchen Signale der Kondo Temperatur $T_{K}$ bei der die Kondo-Abschirmung der magnetische Momente einsetzt, der Neel Temperatur $T_{N}$ der antiferromagnetischem Ordnung, das eventuelle Auftreten einer durch $T^{*}$ gekennzeichnete Änderung der Fermiflächen Topologie, und letztendlich die Ausbildung eines kohärenten schwerfermionischen Zustandes bei $T_{coh}$
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Benedikt, Udo. "Low-Rank Tensor Approximation in post Hartree-Fock Methods." Doctoral thesis, 2013. https://monarch.qucosa.de/id/qucosa%3A19999.
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In this thesis the application of novel tensor decomposition and tensor representation techniques in highly accurate post Hartree-Fock methods is evaluated. These representation techniques can help to overcome the steep scaling behaviour of high level ab-initio calculations with increasing system size and therefore break the "curse of dimensionality". After a comparison of various tensor formats the application of the "canonical polyadic" format (CP) is described in detail. There, especially the casting of a normal, index based tensor into the CP format (tensor decomposition) and a method for a low rank approximation (rank reduction) of the two-electron integrals in the AO basis are investigated. The decisive quantity for the applicability of the CP format is the scaling of the rank with increasing system and basis set size. The memory requirements and the computational effort for tensor manipulations in the CP format are only linear in the number of dimensions but still depend on the expansion length (rank) of the approximation. Furthermore, the AO-MO transformation and a MP2 algorithm with decomposed tensors in the CP format is evaluated and the scaling with increasing system and basis set size is investigated. Finally, a Coupled-Cluster algorithm based only on low-rank CP representation of the MO integrals is developed. There, especially the successive tensor contraction during the iterative solution of the amplitude equations and the error propagation upon multiple application of the reduction procedure are discussed. In conclusion the overall complexity of a Coupled-Cluster procedure with tensors in CP format is evaluated and some possibilities for improvements of the rank reduction procedure tailored to the needs in electronic structure calculations are shown.Die vorliegende Arbeit beschäftigt sich mit der Anwendung neuartiger Tensorzerlegungs- und Tensorrepesentationstechniken in hochgenauen post Hartree-Fock Methoden um das hohe Skalierungsverhalten dieser Verfahren mit steigender Systemgröße zu verringern und somit den "Fluch der Dimensionen" zu brechen. Nach einer vergleichenden Betrachtung verschiedener Representationsformate wird auf die Anwendung des "canonical polyadic" Formates (CP) detailliert eingegangen. Dabei stehen zunächst die Umwandlung eines normalen, indexbasierten Tensors in das CP Format (Tensorzerlegung) und eine Methode der Niedrigrang Approximation (Rangreduktion) für Zweielektronenintegrale in der AO Basis im Vordergrund. Die entscheidende Größe für die Anwendbarkeit ist dabei das Skalierungsverhalten das Ranges mit steigender System- und Basissatzgröße, da der Speicheraufwand und die Berechnungskosten für Tensormanipulationen im CP Format zwar nur noch linear von der Anzahl der Dimensionen des Tensors abhängen, allerdings auch mit der Expansionslänge (Rang) skalieren. Im Anschluss wird die AO-MO Transformation und der MP2 Algorithmus mit zerlegten Tensoren im CP Format diskutiert und erneut das Skalierungsverhalten mit steigender System- und Basissatzgröße untersucht. Abschließend wird ein Coupled-Cluster Algorithmus vorgestellt, welcher ausschließlich mit Tensoren in einer Niedrigrang CP Darstellung arbeitet. Dabei wird vor allem auf die sukzessive Tensorkontraktion während der iterativen Bestimmung der Amplituden eingegangen und die Fehlerfortpanzung durch Anwendung des Rangreduktions-Algorithmus analysiert. Abschließend wird die Komplexität des gesamten Verfahrens bewertet und Verbesserungsmöglichkeiten der Reduktionsprozedur aufgezeigt.
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Martin, Lee C. [Verfasser]. "The Kondo lattice model : a dynamical cluster approximation approach / vorgelegt von Lee C. Martin." 2009. http://d-nb.info/1005117349/34.
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Aoki, Yasunori. "Study of Singular Capillary Surfaces and Development of the Cluster Newton Method." Thesis, 2012. http://hdl.handle.net/10012/6908.
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In this thesis, we explore two important aspects of study of differential equations: analytical and computational aspects. We first consider a partial differential equation model for a static liquid surface (capillary surface). We prove through mathematical analyses that the solution of this mathematical model (the Laplace-Young equation) in a cusp domain can be bounded or unbounded depending on the boundary conditions. By utilizing the knowledge we have obtained about the singular behaviour of the solution through mathematical analysis, we then construct a numerical methodology to accurately approximate unbounded solutions of the Laplace-Young equation. Using this accurate numerical methodology, we explore some remaining open problems on singular solutions of the Laplace-Young equation. Lastly, we consider ordinary differential equation models used in the pharmaceutical industry and develop a numerical method for estimating model parameters from incomplete experimental data. With our numerical method, the parameter estimation can be done significantly faster and more robustly than with conventional methods.
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Cao, Weisheng. "Application of the cluster/site approximation to calculation of multicomponent alloy phase diagrams and coherent interphase energies." 2006. http://www.library.wisc.edu/databases/connect/dissertations.html.
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Lenz, Benjamin. "Unconventional Phases in Two-Dimensional Hubbard and Kondo-Lattice Models by Variational Cluster Approaches." Doctoral thesis, 2016. http://hdl.handle.net/11858/00-1735-0000-0023-3DFC-1.
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Guo, Yi-Heng, and 郭奕亨. "An Approximation Algorithm for Broadcast Scheduling in Heterogeneous Clusters." Thesis, 2002. http://ndltd.ncl.edu.tw/handle/36355502244581982459.
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碩士國立中正大學
資訊工程研究所
90
Network of workstation (NOW) is a cost-effective alternative to massively parallel supercomputers. As commercially available off-the-shelf processors become cheaper and faster, it is now possible to build a PC or workstation cluster that provides high computing power within a limited budget. However, a cluster may consist of different types of processors and this heterogeneity within a cluster complicates the design of efficient collective communication protocols. This paper shows that a simple heuristic called fastest-node-first(FNF))[M.Banikazemi, V.Moorthy, and D.K. Panda]is very effective in reducing broadcast time for heterogeneous cluster systems. Despite the fact that FNF heuristic does not guarantee an optimal broadcast time for general heterogeneous network of workstation, we prove that FNF always gives near optimal broadcast time in a special case of cluster, and this finding helps us show that FNF delivers guaranteed performance for general clusters. In a previous paper we showed a similar bound on the competitive ratio in a send-only communication model. This paper extends the result to a more realistic sender-receiver model. We show that FNF gives a total broadcast of $2T + \beta$, where $T$ is the optimum time and $\beta$ is a constant. This improves over the previous bound on $2 \alpha T + \beta$ [Libeskind-Hadas and J.Hartline], where $\alpha$ is a theoretically unbounded ratio of the processor performance in the cluster.
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Hsu, KoChung, and 許克仲. "The approximation algorithm for broadcast scheduling in synchronous heterogeneous clusters." Thesis, 2003. http://ndltd.ncl.edu.tw/handle/20516305079060859107.
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碩士國立臺灣大學
資訊工程學研究所
91
Network of workstation (NOW) is a cost-effective alternative to massively parallel supercomputers. As commercially available off-the-shelf processors become cheaper and faster, it is now possible to build a PC or workstation cluster that provides high computing power within a limited budget. However, a cluster may consist of different types of processors and this heterogeneity within a cluster complicates the design of efficient collective communication protocols. This paper introduces a synchronous communication model where the communication cost is determined by both sender and receiver. In this synchronous model both sender and receiver of a message must wait until the current communication finishes. We show that a technique called SNF tree scheduling is an approximation algorithm with competitive ratio 4. We conduct experiments to demonstrate that SNF tree scheduling produces broadcast schedules that are very close to the optimal solutions without extensive computation time. We also propose a greedy broadcast algorithm that achieves near optimal solutions in our experiments.
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Dang, Sanjeena. "Variational Approximations and Other Topics in Mixture Models." Thesis, 2012. http://hdl.handle.net/10214/3876.
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Mixture model-based clustering has become an increasingly popular data analysis technique since its introduction almost fifty years ago. Families of mixture models are said to arise when the component parameters, usually the component covariance matrices, are decomposed and a number of constraints are imposed. Within the family setting, it is necessary to choose the member of the family --- i.e., the appropriate covariance structure --- in addition to the number of mixture components. To date, the Bayesian information criterion (BIC) has proved most effective for this model selection process, and the expectation-maximization (EM) algorithm has been predominantly used for parameter estimation.
We deviate from the EM-BIC rubric, using variational Bayes approximations for parameter estimation and the deviance information criterion (DIC) for model selection. The variational Bayes approach alleviates some of the computational complexities associated with the EM algorithm. We use this approach on the most famous family of Gaussian mixture models known as Gaussian parsimonious clustering models (GPCM). These models have an eigen-decomposed covariance structure.
Cluster-weighted modelling (CWM) is another flexible statistical framework for modelling local relationships in heterogeneous populations on the basis of weighted combinations of local models. In particular, we extend cluster-weighted models to include an underlying latent factor structure of the independent variable, resulting in a novel family of models known as parsimonious cluster-weighted factor analyzers. The EM-BIC rubric is utilized for parameter estimation and model selection.
Some work on a mixture of multivariate t-distributions is also presented, with a linear model for the mean and a modified Cholesky-decomposed covariance structure leading to a novel family of mixture models. In addition to model-based clustering, these models are also used for model-based classification, i.e., semi-supervised clustering. Parameters are estimated using the EM algorithm and another approach to model selection other than the BIC is also considered.NSERC PGS-D
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Lourenço, Sofia Pinheiro. "From the local density approximation to exact exchange in time-dependent density functional theory: the case of rare-gas cationic clusters." Master's thesis, 2019. http://hdl.handle.net/10316/87977.
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Dissertação de Mestrado em Física apresentada à Faculdade de Ciências e TecnologiaMediante ionização, o espectro de absorção de clusters neutras de gases raros transita da gama do ultravioleta (UV) para a gama do visível. Em time-dependent density functional theory (TDDFT) e utilizando os tradicionais funcionais para a correlação e troca (LDA, GGA), é posível fazer boas previsões para o posicionamento dos dois picos experimentais da cluster de Xe_3^+, mas a intensidade dos mesmos surge trocada, i.e. o pico experimental de maior intensidade corresponde ao pico teórico de menor intensidade e vice versa. O facto deste problema ter sido resolvido ao nível da aproximação de Hartree-Fock sugere como possível explicação para esta incapacidade preditiva da DFT a forma insatisfatória como a interação de troca é tratada nos funcionais da densidade típicos. O principal objetivo desta tese é continuar a estudar a forma como a troca exata melhora a intensidade relativa dos picos, calculando-se para tal geometrias de estado fundamental e espectros de absorção com os seguintes funcionais: LDA+ADSIC (LDA com Average Density Self-Interaction Correction), OEP-SLATER, OEP-KLI, OEP-FULL (sem aproximação ao potencial de troca). No fim, conclui-se que a aquisição das geometrias de estado fundamental corretas é necessária para a obtenção de espectros corretos, comparáveis ao experimental. Também, quanto maior a quantidade de troca incluída no funcional, melhor o espectro. Por último, não se verificou a inversão dos picos que, provavelmente, só se viria a verificar com OEP-FULL. Os espectros de absorção e as geometrias foram calculados no código open-source OCTOPUS.
Upon ionization, the optical absorption of neutral rare-gas clusters shifts from the ultraviolet range (UV) to the visible range. Within time-dependent density functional theory (TDDFT), the photoabsorption spectra of the Xe_3^+ cluster, employing traditional DFT functionals (LDA, GGA), predicts a reasonable position for the two experimental peaks, but their relative intensities appears to be inverted, i.e. the highest experimental peak correspond to the lowest theoretical peak and vice versa. The improvement on the problem reached within the Hartree-Fock approximation level suggested an explanation based on the unsatisfactory treatment of the exchange interaction in common density functionals. The main goal of this thesis project is to continue investigating on how the exact exchange improves peaks' relative height by calculating ground state geometries and absorption spectra with the following functionals: LDA+ADSIC (LDA with Average Density Self-Interaction Correction), OEP-SLATER, OEP-KLI, OEP-FULL (no approximation to the exchange-only potential). In the end, it is concluded that adequate ground state geometries are necessary for the generation of correct spectra, comparable to the experimental one. Also, the bigger the amount of exchange added, the better the spectrum, even though the peaks did not invert their intensities. At last, OEP-FULL probably is the level of theory required to invert the peaks. Absorption spectra and geometries were calculated in the open-source code OCTOPUS.