Academic literature on the topic 'Cluster approximation'

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Journal articles on the topic "Cluster approximation"

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Borisenko, O., V. Chelnokov, and V. Kushnir. "Phenomenological Renormalization Group and Cluster Approximation." Ukrainian Journal of Physics 59, no. 7 (July 2014): 655–62. http://dx.doi.org/10.15407/ujpe59.07.0655.

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Nenashev, Vadim A., Igor G. Khanykov, and Mikhail V. Kharinov. "A Model of Pixel and Superpixel Clustering for Object Detection." Journal of Imaging 8, no. 10 (October 6, 2022): 274. http://dx.doi.org/10.3390/jimaging8100274.

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The paper presents a model of structured objects in a grayscale or color image, described by means of optimal piecewise constant image approximations, which are characterized by the minimum possible approximation errors for a given number of pixel clusters, where the approximation error means the total squared error. An ambiguous image is described as a non-hierarchical structure but is represented as an ordered superposition of object hierarchies, each containing at least one optimal approximation in g0 = 1,2,..., etc., colors. For the selected hierarchy of pixel clusters, the objects-of-interest are detected as the pixel clusters of optimal approximations, or as their parts, or unions. The paper develops the known idea in cluster analysis of the joint application of Ward’s and K-means methods. At the same time, it is proposed to modernize each of these methods and supplement them with a third method of splitting/merging pixel clusters. This is useful for cluster analysis of big data described by a convex dependence of the optimal approximation error on the cluster number and also for adjustable object detection in digital image processing, using the optimal hierarchical pixel clustering, which is treated as an alternative to the modern informally defined “semantic” segmentation.
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Pizio, O. A., and Z. B. Halytch. "Structural Properties of the Ion-Dipole Model of Electrolyte Solutions in the Bulk and Near a Charged Hard Wall.Application of the Truncated Optimized Cluster Series." Zeitschrift für Naturforschung A 46, no. 1-2 (February 1, 1991): 8–18. http://dx.doi.org/10.1515/zna-1991-1-203.

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AbstractAn ion-dipole model of electrolyte solutions in the bulk case and near a charged or uncharged hard wall is considered. A method to derive the terms of optimized cluster expansions for the distribution functions of ions and dipoles which provides a set of approximations beyond the mean spherical approximation is given. The third cluster coefficient approximation is investigated
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ZIEGLER, ALFRED. "FERMION CLUSTER APPROACH TO THE HUBBARD MODEL." International Journal of Modern Physics B 07, no. 01n03 (January 1993): 601–4. http://dx.doi.org/10.1142/s0217979293001268.

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The deficiencies of the fermion cluster approximation by Caron and Pratt out-lined in a previous paper are corrected and the approximation is then applied to the one-site Hubbard model. Because the approximation in its standard form is unable to describe energy bands the boundary condition integration technique of C. Gros for free clusters is generalized to embedded clusters by averaging over the solutions to different self-consistency equations.
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Kats, Daniel, and Frederick R. Manby. "Communication: The distinguishable cluster approximation." Journal of Chemical Physics 139, no. 2 (July 14, 2013): 021102. http://dx.doi.org/10.1063/1.4813481.

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KÜMMEL, HERMANN G. "A BIOGRAPHY OF THE COUPLED CLUSTER METHOD." International Journal of Modern Physics B 17, no. 28 (November 10, 2003): 5311–25. http://dx.doi.org/10.1142/s0217979203020442.

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The origins of the coupled cluster method are described. Special attention is paid to the arguments put forward for the exponential structure of the wave functions. Various approximation schemes invented during the last 40 years are presented. The problems arising from these approximations necessarily truncating or destroying the exponential form are discussed and ways to deal with them are described.
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DESSMARK, ANDERS, JESPER JANSSON, ANDRZEJ LINGAS, EVA-MARTA LUNDELL, and MIA PERSSON. "ON THE APPROXIMABILITY OF MAXIMUM AND MINIMUM EDGE CLIQUE PARTITION PROBLEMS." International Journal of Foundations of Computer Science 18, no. 02 (April 2007): 217–26. http://dx.doi.org/10.1142/s0129054107004656.

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We consider the following clustering problems: given an undirected graph, partition its vertices into disjoint clusters such that each cluster forms a clique and the number of edges within the clusters is maximized (Max-ECP), or the number of edges between clusters is minimized (Min-ECP). These problems arise naturally in the DNA clone classification. We investigate the hardness of finding such partitions and provide approximation algorithms. Further, we show that greedy strategies yield constant factor approximations for graph classes for which maximum cliques can be found efficiently.
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Terletska, Hanna, Yi Zhang, Ka-Ming Tam, Tom Berlijn, Liviu Chioncel, N. Vidhyadhiraja, and Mark Jarrell. "Systematic Quantum Cluster Typical Medium Method for the Study of Localization in Strongly Disordered Electronic Systems." Applied Sciences 8, no. 12 (November 26, 2018): 2401. http://dx.doi.org/10.3390/app8122401.

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Great progress has been made in recent years towards understanding the properties of disordered electronic systems. In part, this is made possible by recent advances in quantum effective medium methods which enable the study of disorder and electron-electronic interactions on equal footing. They include dynamical mean-field theory and the Coherent Potential Approximation, and their cluster extension, the dynamical cluster approximation. Despite their successes, these methods do not enable the first-principles study of the strongly disordered regime, including the effects of electronic localization. The main focus of this review is the recently developed typical medium dynamical cluster approximation for disordered electronic systems. This method has been constructed to capture disorder-induced localization and is based on a mapping of a lattice onto a quantum cluster embedded in an effective typical medium, which is determined self-consistently. Unlike the average effective medium-based methods mentioned above, typical medium-based methods properly capture the states localized by disorder. The typical medium dynamical cluster approximation not only provides the proper order parameter for Anderson localized states, but it can also incorporate the full complexity of Density-Functional Theory (DFT)-derived potentials into the analysis, including the effect of multiple bands, non-local disorder, and electron-electron interactions. After a brief historical review of other numerical methods for disordered systems, we discuss coarse-graining as a unifying principle for the development of translationally invariant quantum cluster methods. Together, the Coherent Potential Approximation, the Dynamical Mean-Field Theory and the Dynamical Cluster Approximation may be viewed as a single class of approximations with a much-needed small parameter of the inverse cluster size which may be used to control the approximation. We then present an overview of various recent applications of the typical medium dynamical cluster approximation to a variety of models and systems, including single and multiband Anderson model, and models with local and off-diagonal disorder. We then present the application of the method to realistic systems in the framework of the DFT and demonstrate that the resulting method can provide a systematic first-principles method validated by experiment and capable of making experimentally relevant predictions. We also discuss the application of the typical medium dynamical cluster approximation to systems with disorder and electron-electron interactions. Most significantly, we show that in the limits of strong disorder and weak interactions treated perturbatively, that the phenomena of 3D localization, including a mobility edge, remains intact. However, the metal-insulator transition is pushed to larger disorder values by the local interactions. We also study the limits of strong disorder and strong interactions capable of producing moment formation and screening, with a non-perturbative local approximation. Here, we find that the Anderson localization quantum phase transition is accompanied by a quantum-critical fan in the energy-disorder phase diagram.
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Freericks, James K. "Operator Relationship between Conventional Coupled Cluster and Unitary Coupled Cluster." Symmetry 14, no. 3 (February 28, 2022): 494. http://dx.doi.org/10.3390/sym14030494.

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The chemistry community has long sought the exact relationship between the conventional and the unitary coupled cluster ansatz for a single-reference system, especially given the interest in performing quantum chemistry on quantum computers. In this work, we show how one can use the operator manipulations given by the exponential disentangling identity and the Hadamard lemma to relate the factorized form of the unitary coupled-cluster approximation to a factorized form of the conventional coupled cluster approximation (the factorized form is required, because some amplitudes are operator-valued and do not commute with other terms). By employing the Trotter product formula, one can then relate the factorized form to the standard form of the unitary coupled cluster ansatz. The operator dependence of the factorized form of the coupled cluster approximation can also be removed at the expense of requiring even more higher-rank operators, finally yielding the conventional coupled cluster. The algebraic manipulations of this approach are daunting to carry out by hand, but can be automated on a computer for small enough systems.
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Borgani, S., P. Coles, and L. Moscardini. "Cluster correlations in the Zel'dovich approximation." Monthly Notices of the Royal Astronomical Society 271, no. 1 (November 1, 1994): 223–32. http://dx.doi.org/10.1093/mnras/271.1.223.

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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 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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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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Books on the topic "Cluster approximation"

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Hierarchische Klassifikation einer Objektmenge: Ein globales Verfahren zur Approximation einer Distanzmatrix. Frankfurt am Main: P. Lang, 1986.

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F, Pellman Todd, Shandarin Sergei F, and United States. National Aeronautics and Space Administration., eds. Optimizing the Zel'dovich approximation. [Washington, D.C: National Aeronautics and Space Administration, 1995.

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Magnus, Ekdahl. Approximations of Bayes classifiers for statistical learning of clusters. Linköping: Linköpings universitet, 2006.

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F, Shandarin Sergei, Weinberg David Hal, and United States. National Aeronautics and Space Administration., eds. A test of the adhesion approximation for gravitational clustering. [Washington, D.C: National Aeronautics and Space Administration, 1995.

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United States. National Aeronautics and Space Administration., ed. Comparison of dynamical approximation schemes for non-linear gravitational clustering. [Washington, D.C: National Aeronautics and Space Administration, 1995.

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Horing, Norman J. Morgenstern. Non-Equilibrium Green’s Functions: Variational Relations and Approximations for Particle Interactions. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198791942.003.0009.

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Chapter 09 Nonequilibrium Green’s functions (NEGF), including coupled-correlated (C) single- and multi-particle Green’s functions, are defined as averages weighted with the time-development operator U(t0+τ,t0). Linear conductivity is exhibited as a two-particle equilibrium Green’s function (Kubo-type formulation). Admitting particle sources (S:η,η+) and non-conservation of number, the non-equilibrium multi-particle Green’s functions are constructed with numbers of creation and annihilation operators that may differ, and they may be derived as variational derivatives with respect to sources η,η+ of a generating functional eW=TrU(t0+τ,t0)CS/TrU(t0+τ,t0)C. (In the non-interacting case this yields the n-particle Green’s function as a permanent/determinant of single-particle Green’s functions.) These variational relations yield a symmetric set of multi-particle Green’s function equations. Cumulants and the Linked Cluster Theorem are discussed and the Random Phase Approximation (RPA) is derived variationally. Schwinger’s variational differential formulation of perturbation theories for the Green’s function, self-energy, vertex operator, and also shielded potential perturbation theory, are reviewed. The Langreth Algebra arises from analytic continuation of integration of products of Green’s functions in imaginary time to the real-time axis with time-ordering along the integration contour in the complex time plane. An account of the Generalized Kadanoff-Baym Ansatz is presented.
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Klingler-Vidra, Robyn. The Venture Capital State. Cornell University Press, 2018. http://dx.doi.org/10.7591/cornell/9781501723377.001.0001.

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The Venture Capital State investigates the diffusion of the globally acclaimed Silicon Valley venture capital (VC) policy model. The spread of this model has been ubiquitous, with at least 45 states across a range of countries, in terms of geography, culture, and size, attempting to build local VC markets. In contrast to the transcendent exuberance for VC, policymakers in each and every state have implemented a distinct set of policies. Even states of similar population and economic sizes that are geographically and culturally proximate, and at comparable levels of industrialization, have not implemented similar policies. This book explains why: policymakers are “contextually rational” in their learning; their context-rooted norms shape preferences, underpinning their distinct valuations of studied models. The normative context of those learning about the policy – how they see themselves and what they deem as locally appropriate – informs their design. Findings are based upon deep investigations of VC policymaking in an East Asian cluster of states: Hong Kong, Taiwan, and Singapore. These states’ VC successes reflects their ability to effectively adapt the highly-lauded model for their local context, not their policymakers’ approximation of the Silicon Valley policy model.
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Luschgy, Harald, and Siegfried Graf. Foundations of Quantization for Probability Distributions. Springer London, Limited, 2007.

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Graf, Siegfried, and Harald Luschgy. Foundations of Quantization for Probability Distributions (Lecture Notes in Mathematics). Springer, 2000.

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Billing, Gert D., ed. The Quantum Classical Theory. Oxford University Press, 2003. http://dx.doi.org/10.1093/oso/9780195146196.001.0001.

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Over a period of fifty years, the quantum-classical or semi-classical theories have been among the most popular for calculations of rates and cross sections for many dynamical processes: energy transfer, chemical reactions, photodissociation, surface dynamics, reactions in clusters and solutions, etc. These processes are important in the simulation of kinetics of processes in plasma chemistry, chemical reactors, chemical or gas lasers, atmospheric and interstellar chemistry, as well as various industrial processes. This book gives an overview of quantum-classical methods that are currently used for a theoretical description of these molecular processes. It gives the theoretical background for the derivation of the theories from first principles. Enough details are provided to allow numerical implementation of the methods. The book gives the necessary background for understanding the approximations behind the methods and the working schemes for treating energy transfer processes from diatomic to polyatomic molecules, reactions at surfaces, non-adiabatic processes, and chemical reactions.
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Book chapters on the topic "Cluster approximation"

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Fazekas, P. "Cluster Gutzwiller Approximation." In Condensed Matter Theories, 279–90. Boston, MA: Springer US, 1991. http://dx.doi.org/10.1007/978-1-4615-3686-4_23.

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Fotso, H., S. Yang, K. Chen, S. Pathak, J. Moreno, M. Jarrell, K. Mikelsons, E. Khatami, and D. Galanakis. "Dynamical Cluster Approximation." In Springer Series in Solid-State Sciences, 271–302. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-21831-6_9.

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Sinha, Shriprakash. "Online Cluster Approximation via Inequality." In IFIP Advances in Information and Communication Technology, 176–81. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-33412-2_18.

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Berger, André, Alexander Grigoriev, and Andrej Winokurow. "A PTAS for the Cluster Editing Problem on Planar Graphs." In Approximation and Online Algorithms, 27–39. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-51741-4_3.

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Schäfer, Guido, and Bernard G. Zweers. "Maximum Coverage with Cluster Constraints: An LP-Based Approximation Technique." In Approximation and Online Algorithms, 63–80. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-80879-2_5.

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Zhang, Xiaoyan, Donglei Du, Gregory Gutin, Qiaoxia Ming, and Jian Sun. "Approximation Algorithms for General Cluster Routing Problem." In Lecture Notes in Computer Science, 472–83. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-58150-3_38.

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Mohri, Tetsuo. "Glass Transition within the Cluster Variation Approximation." In Advanced Materials Research, 723–26. Stafa: Trans Tech Publications Ltd., 2007. http://dx.doi.org/10.4028/0-87849-463-4.723.

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Wada, K., H. Tsuchinaga, and T. Uchida. "The Crystal Growth Kinetics in The Cluster Approximation." In Dynamics of Ordering Processes in Condensed Matter, 29–33. Boston, MA: Springer US, 1988. http://dx.doi.org/10.1007/978-1-4613-1019-8_6.

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Guo, Longkun, Bin Xing, Peihuang Huang, and Xiaoyan Zhang. "Approximation Algorithms for the General Cluster Routing Problem." In Parallel and Distributed Computing, Applications and Technologies, 264–73. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-69244-5_23.

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Santen, R. A. "Theory of Heterogeneous Catalytic Reactivity Using the Cluster Approximation." In Chemisorption and Reactivity on Supported Clusters and Thin Films, 371–93. Dordrecht: Springer Netherlands, 1997. http://dx.doi.org/10.1007/978-94-015-8911-6_13.

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Conference papers on the topic "Cluster approximation"

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Jarrell, M., A. Macridin, K. Mikelsons, D. G. S. P. Doluweera, J. E. Gubernatis, Adolfo Avella, and Ferdinando Mancini. "The Dynamical Cluster Approximation with Quantum Monte Carlo Cluster Solvers." In LECTURES ON THE PHYSICS OF STRONGLY CORRELATED SYSTEMS XII: Twelfth Training Course in the Physics of Strongly Correlated Systems. AIP, 2008. http://dx.doi.org/10.1063/1.2940445.

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Hoshino, Tetsuya, Akihiro Ida, Toshihiro Hanawa, and Kengo Nakajima. "Load-Balancing-Aware Parallel Algorithms of H-Matrices with Adaptive Cross Approximation for GPUs." In 2018 IEEE International Conference on Cluster Computing (CLUSTER). IEEE, 2018. http://dx.doi.org/10.1109/cluster.2018.00016.

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Abdulah, Sameh, Hatem Ltaief, Ying Sun, Marc G. Genton, and David E. Keyes. "Parallel Approximation of the Maximum Likelihood Estimation for the Prediction of Large-Scale Geostatistics Simulations." In 2018 IEEE International Conference on Cluster Computing (CLUSTER). IEEE, 2018. http://dx.doi.org/10.1109/cluster.2018.00089.

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Pi, Minghong, Deren Li, Jianya Gong, and Guokuan Li. "Fractal approximation coding based on cluster of range blocks." In International Symposium on Multispectral Image Processing, edited by Ji Zhou, Anil K. Jain, Tianxu Zhang, Yaoting Zhu, Mingyue Ding, and Jianguo Liu. SPIE, 1998. http://dx.doi.org/10.1117/12.323566.

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Nabavinejad, Seyed Morteza, Lena Mashayekhy, and Sherief Reda. "ApproxDNN: Incentivizing DNN Approximation in Cloud." In 2020 20th IEEE/ACM International Symposium on Cluster, Cloud and Internet Computing (CCGRID). IEEE, 2020. http://dx.doi.org/10.1109/ccgrid49817.2020.00-29.

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Li-Chuan Chen and Hyeong-Ah Choi. "Approximation algorithms for data distribution with load balancing of web servers." In Proceedings 2001 IEEE International Conference on Cluster Computing. IEEE, 2001. http://dx.doi.org/10.1109/clustr.2001.959988.

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Miyakoshi, Shohei, and Yukinori Ohta. "Vriational-Cluster-Approximation Study of the Antiferromagnetic Topological Insulator States." In Proceedings of the International Conference on Strongly Correlated Electron Systems (SCES2013). Journal of the Physical Society of Japan, 2014. http://dx.doi.org/10.7566/jpscp.3.016011.

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Balduzzi, Giovanni, Arghya Chatterjee, Ying Wai Li, Peter W. Doak, Urs Haehner, Ed F. D'Azevedo, Thomas A. Maier, and Thomas Schulthess. "Accelerating DCA++ (Dynamical Cluster Approximation) Scientific Application on the Summit Supercomputer." In 2019 28th International Conference on Parallel Architectures and Compilation Techniques (PACT). IEEE, 2019. http://dx.doi.org/10.1109/pact.2019.00041.

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Ahmed, W. M. A., S. A. Fomenkov, and S. V. Gaevoy. "Reducing Approximation Time of Cluster Workload by Using Simplified Hypergamma Distribution." In 2018 International Conference on Industrial Engineering, Applications and Manufacturing (ICIEAM). IEEE, 2018. http://dx.doi.org/10.1109/icieam.2018.8728879.

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Sénéchal, David. "The Variational Cluster Approximation for Hubbard Models:  Practical Implementation." In 2008 22nd High performance Computing Symposium (HPCS). IEEE, 2008. http://dx.doi.org/10.1109/hpcs.2008.18.

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Reports on the topic "Cluster approximation"

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Martinez, R. F., and G. C. Osbourn. Extending applicability of cluster based pattern recognition with efficient approximation techniques. Office of Scientific and Technical Information (OSTI), March 1997. http://dx.doi.org/10.2172/464175.

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