Дисертації з теми "Tensors methods"
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1
Handschuh, Stefan. "Numerical methods in Tensor Networks." Doctoral thesis, Universitätsbibliothek Leipzig, 2015. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-159672.
Анотація:
In many applications that deal with high dimensional data, it is important to not store the high dimensional object itself, but its representation in a data sparse way. This aims to reduce the storage and computational complexity.
There is a general scheme for representing tensors with the help of sums of elementary tensors, where the summation structure is defined by a graph/network. This scheme allows to generalize commonly used approaches in representing a large amount of numerical data (that can be interpreted as a high dimensional object) using sums of elementary tensors. The classification does not only distinguish between elementary tensors and non-elementary tensors, but also describes the number of terms that is needed to represent an object of the tensor space. This classification is referred to as tensor network (format).
This work uses the tensor network based approach and describes non-linear block Gauss-Seidel methods (ALS and DMRG) in the context of the general tensor network framework.
Another contribution of the thesis is the general conversion of different tensor formats. We are able to efficiently change the underlying graph topology of a given tensor representation while using the similarities (if present) of both the original and the desired structure. This is an important feature in case only minor structural changes are required.
In all approximation cases involving iterative methods, it is crucial to find and use a proper initial guess. For linear iteration schemes, a good initial guess helps to decrease the number of iteration steps that are needed to reach a certain accuracy, but it does not change the approximation result. For non-linear iteration schemes, the approximation result may depend on the initial guess. This work introduces a method to successively create an initial guess that improves some approximation results. This algorithm is based on successive rank 1 increments for the r-term format.
There are still open questions about how to find the optimal tensor format for a given general problem (e.g. storage, operations, etc.). For instance in the case where a physical background is given, it might be efficient to use this knowledge to create a good network structure. There is however, no guarantee that a better (with respect to the problem) representation structure does not exist.
2
Wu, Yanqi. "New methods for measuring CSA tensors : applications to nucleotides and nucleosides." Thesis, University of Nottingham, 2011. http://eprints.nottingham.ac.uk/11859/.
Анотація:
A novel version of the CSA (Chemical Shift Anisotropy) amplification experiment which results in large amplification factors is introduced. Large xa (up to 48) are achieved by sequences which are efficient in terms of the number of π pulses and total duration compared to a modification due to Orr et al. (2005), and greater flexibility in terms of the choice of amplification factor is possible than in our most recent version. Furthermore, the incorporation of XiX decoupling ensures the overall sensitivity of the experiment is optimal. This advantage has been proved by extracting the CSA tensors for a novel vinylphosphonate-linked nucleotide. The application of CSA amplification experiment to six nucleosides is also discussed. The measured principal tensor values are compared with those calculated using the recently developed first-principles methods. Throughout this work, the NMR parameters of all nucleosides are presented. Finally, high-resolution multi-nuclear solid-state NMR experiments are used to study some novel vinyl phosphonate-linked oligo-nucleotides.
3
Damodaran, K. "Spatially dependent interaction tensors determined through novel methods of high resolution solid state NMR." Thesis(Ph.D.), CSIR-National Chemical Laboratory, Pune, 2006. http://dspace.ncl.res.in:8080/xmlui/handle/20.500.12252/2493.
4
Lund, Kathryn. "A new block Krylov subspace framework with applications to functions of matrices acting on multiple vectors." Diss., Temple University Libraries, 2018. http://cdm16002.contentdm.oclc.org/cdm/ref/collection/p245801coll10/id/493337.
Анотація:
MathematicsPh.D.
We propose a new framework for understanding block Krylov subspace methods, which hinges on a matrix-valued inner product. We can recast the ``classical" block Krylov methods, such as O'Leary's block conjugate gradients, global methods, and loop-interchange methods, within this framework. Leveraging the generality of the framework, we develop an efficient restart procedure and error bounds for the shifted block full orthogonalization method (Sh-BFOM(m)). Regarding BFOM as the prototypical block Krylov subspace method, we propose another formalism, which we call modified BFOM, and show that block GMRES and the new block Radau-Lanczos method can be regarded as modified BFOM. In analogy to Sh-BFOM(m), we develop an efficient restart procedure for shifted BGMRES with restarts (Sh-BGMRES(m)), as well as error bounds. Using this framework and shifted block Krylov methods with restarts as a foundation, we formulate block Krylov subspace methods with restarts for matrix functions acting on multiple vectors f(A)B. We obtain convergence bounds for \bfomfom (BFOM for Functions Of Matrices) and block harmonic methods (i.e., BGMRES-like methods) for matrix functions. With various numerical examples, we illustrate our theoretical results on Sh-BFOM and Sh-BGMRES. We also analyze the matrix polynomials associated to the residuals of these methods. Through a variety of real-life applications, we demonstrate the robustness and versatility of B(FOM)^2 and block harmonic methods for matrix functions. A particularly interesting example is the tensor t-function, our proposed definition for the function of a tensor in the tensor t-product formalism. Despite the lack of convergence theory, we also show that the block Radau-Lanczos modification can reduce the number of cycles required to converge for both linear systems and matrix functions.
Temple University--Theses
5
Savas, Berkant. "Algorithms in data mining using matrix and tensor methods." Doctoral thesis, Linköpings universitet, Beräkningsvetenskap, 2008. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-11597.
Анотація:
In many fields of science, engineering, and economics large amounts of data are stored and there is a need to analyze these data in order to extract information for various purposes. Data mining is a general concept involving different tools for performing this kind of analysis. The development of mathematical models and efficient algorithms is of key importance. In this thesis we discuss algorithms for the reduced rank regression problem and algorithms for the computation of the best multilinear rank approximation of tensors. The first two papers deal with the reduced rank regression problem, which is encountered in the field of state-space subspace system identification. More specifically the problem is \[ \min_{\rank(X) = k} \det (B - X A)(B - X A)\tp, \] where $A$ and $B$ are given matrices and we want to find $X$ under a certain rank condition that minimizes the determinant. This problem is not properly stated since it involves implicit assumptions on $A$ and $B$ so that $(B - X A)(B - X A)\tp$ is never singular. This deficiency of the determinant criterion is fixed by generalizing the minimization criterion to rank reduction and volume minimization of the objective matrix. The volume of a matrix is defined as the product of its nonzero singular values. We give an algorithm that solves the generalized problem and identify properties of the input and output signals causing a singular objective matrix. Classification problems occur in many applications. The task is to determine the label or class of an unknown object. The third paper concerns with classification of handwritten digits in the context of tensors or multidimensional data arrays. Tensor and multilinear algebra is an area that attracts more and more attention because of the multidimensional structure of the collected data in various applications. Two classification algorithms are given based on the higher order singular value decomposition (HOSVD). The main algorithm makes a data reduction using HOSVD of 98--99 \% prior the construction of the class models. The models are computed as a set of orthonormal bases spanning the dominant subspaces for the different classes. An unknown digit is expressed as a linear combination of the basis vectors. The resulting algorithm achieves 5\% in classification error with fairly low amount of computations. The remaining two papers discuss computational methods for the best multilinear rank approximation problem \[ \min_{\cB} \| \cA - \cB\| \] where $\cA$ is a given tensor and we seek the best low multilinear rank approximation tensor $\cB$. This is a generalization of the best low rank matrix approximation problem. It is well known that for matrices the solution is given by truncating the singular values in the singular value decomposition (SVD) of the matrix. But for tensors in general the truncated HOSVD does not give an optimal approximation. For example, a third order tensor $\cB \in \RR^{I \x J \x K}$ with rank$(\cB) = (r_1,r_2,r_3)$ can be written as the product \[ \cB = \tml{X,Y,Z}{\cC}, \qquad b_{ijk}=\sum_{\lambda,\mu,\nu} x_{i\lambda} y_{j\mu} z_{k\nu} c_{\lambda\mu\nu}, \] where $\cC \in \RR^{r_1 \x r_2 \x r_3}$ and $X \in \RR^{I \times r_1}$, $Y \in \RR^{J \times r_2}$, and $Z \in \RR^{K \times r_3}$ are matrices of full column rank. Since it is no restriction to assume that $X$, $Y$, and $Z$ have orthonormal columns and due to these constraints, the approximation problem can be considered as a nonlinear optimization problem defined on a product of Grassmann manifolds. We introduce novel techniques for multilinear algebraic manipulations enabling means for theoretical analysis and algorithmic implementation. These techniques are used to solve the approximation problem using Newton and Quasi-Newton methods specifically adapted to operate on products of Grassmann manifolds. The presented algorithms are suited for small, large and sparse problems and, when applied on difficult problems, they clearly outperform alternating least squares methods, which are standard in the field.
6
Flores, Philippe. "Estimation of high dimensional probability density functions with low rank-tensors models : application to flow cytometry." Electronic Thesis or Diss., Université de Lorraine, 2024. http://www.theses.fr/2024LORR0021.
Анотація:
La cytométrie en flux (CMF) est une technique d'analyse de cellules biologiques largement utilisée en immunologie, par exemple dans la recherche sur les leucémies. Le principe de la CMF est de mesurer les propriétés de fluorescence individuellement dans un volume de cellules. L'analyse des données de CMF permet d'identifier et de caractériser les populations de cellules à l'intérieur d'un volume de cellules. Les analyses effectuées manuellement reposent sur la sélection de cellules sur des nuages de points bivariés. Cette opération, appelée gating, prend du temps et est subjective. Bien qu'il existe des méthodes non supervisées, ces méthodes prennent souvent beaucoup de temps et ne permettent pas de traiter de grands jeux de données. Pour analyser les jeux de données de CMF, nous avons décidé d'utiliser une approche probabiliste. Dans ce cas, le problème d'analyse de données de CMF revient à une estimation de densités de probabilité. Dans un chapitre préliminaire, nous présentons le problème d'estimation d'histogrammes multivariés. Ce problème est considéré comme impossible en pratique en raison de la malédiction de la dimension (MdD) affirmant que la complexité d'un problème augmente de façon exponentielle avec le nombre de dimensions. Pour résoudre ce problème, deux solutions sont proposées dans la littérature. Premièrement, la densité est modélisée avec un modèle Bayésien naïf (MBN) dont la complexité est linéaire avec le nombre de dimensions. Deuxièmement, les facteurs du MBN sont obtenus via un algorithme de factorisation tensorielle couplée. Cette méthode, appelée CTF3D, couple des marginales 3D qui sont faciles à calculer en CMF par exemple. Cependant, CTF3D n'a pas résolu la MdD mais l'a plutôt déplacée à un autre niveau : le nombre de marginales 3D. Nous proposons alors un algorithme résolvant le troisième niveau de MdD. Cette méthode appelée PCTF3D couple des sous-ensembles de marginales 3D. En choisissant un sous-ensemble de triplets et donc le nombre de triplets, la complexité de PCTF3D est réduite et contrôlée par l'utilisateur. Le choix des triplets est appelé une stratégie de couplage et différentes stratégies sont présentées sous la forme d'hypergraphes. Par exemple, les stratégies aléatoires consistent à choisir des triplets au hasard alors que les stratégies équilibrées consistent à choisir des triplets de telle sorte que toutes les variables soient représentées de manière égale. Un algorithme de génération de couplages équilibrés est proposé. Enfin, des expériences numériques sur des ensembles de données réelles et synthétiques sont réalisées. Notre nouvelle méthode a introduit un modèle couplé de tenseur. Dans le quatrième chapitre, nous abordons le problème d'unicité de ce nouveau modèle. Tout d'abord, la recouvrabilité est étudiée et un algorithme qui trouve la borne de recouvrabilité est présenté. Il est basé sur l'étude du rang de la jacobienne de la paramétrisation. Quand il est appliqué à des couplages aléatoires, des cas défectueux sont observés et conduisent à des baisses de bornes de recouvrabilité. Ces cas ne sont pas observés pour les couplages équilibrés, ce qui en fait une bonne alternative pour garantir l'unicité du modèle. Deuxièmement, l'identifiabilité du modèle a été examinée. Nous utilisons les preuves précédemment démontrées dans la littérature pour prouver de meilleures conditions suffisantes d'identifiabilité. Enfin, notre méthode d'estimation est utilisée pour l'analyse de données de CMF. En considérant un MBN pour la distribution des cellules, les facteurs du MBN sont interprétés comme des groupes de cellules représentés par une proportion et leurs propriétés de fluorescence. Cette méthode nommée CTFlowHD utilise PCTF3D pour obtenir les facteurs du MBN. Après cette étape, nous présentons plusieurs outils pour visualiser les termes de rang 1. Notre méthode permet d'utiliser divers outils de visualisation, en particulier des outils déjà utilisés dans la communauté FCMFlow cytometry (FCM) is one of a most popular techniques for biological cells analysis. It is widely used in immunology, where it permits to make advances in leukemia research for example. The principle of FCM is to measure fluorescence properties for each cell present in a volume of cells. FCM data analysis permit to identify and characterize cell populations. Analysis performed manually rely on selection of cells plotted with bivariate plots. This operation, called gating, is time-consuming and introduces subjectivity. Although unsupervised methods exists, they are time-consuming and does not handle large datasets. To analyze FCM datasets, we decided to use a probabilistic approach. In that sense, the problem of FCM data analysis comes to an estimation of a probability density function. In the second and preliminary chapter, we present the problem of multivariate histogram estimation. This problem is considered impossible in practice because of the Curse of Dimensionality (CoD) which states that the complexity of a problem increases exponentially with the number of dimensions. To solve this issue, two solutions are performed in the litterature. First, the density is modelled with a naive Bayes model (NBM) whose complexity remains linear with the number of dimensions. Secondly, the factors of the NBM are obtained via a coupled tensor factorization algorithm. This method called CTF3D couples 3D marginals which are easy to compute with the amount of data available in FCM. However, CTF3D did not fully solved the CoD but instead moved it to another level: the number of 3D marginals. In a third chapter, we propose a new algorithm that solves the third level of CoD. This method called Partial Coupled Tensor Factorization of 3D marginals or PCTF3D is coupling subsets of 3D marginals. By choosing a subset of triplets hence the number of triplets, PCTF3D's complexity is reduced and controlled by end-users. The choice of triplets is called a coupling strategy and different strategies are presented with the formalism of hypergraphs. For example, random strategies consists in choosing triplets randomly. Balanced strategies consists in choosing triplets such that variables are represented evenly. An algorithm for balanced coupling generation is proposed. Finally, numerical experiments on real and synthetic datasets are performed. Our new method introduced a partially coupled tensor model. In the fourth chapter, we address the problem of uniqueness of this new model. First, recoverability is studied and an algorithm that finds the recoverability bound is presented. This algorithm is based on the study of the rank of the Jacobian of the parametrization. When applied to random couplings, defective cases are observed which leads to drops in recoverability bounds. Those cases are not observed for balanced couplings, making this strategy a good alternative for uniqueness guarantees. In a second part, the identifiability of the model was examined. We use previous proofs to demonstrate new identifiability sufficient conditions that exceed the conditions of the litterature. At last, our new histogram estimation method was used for FCM data analysis. We present Coupled Tensor factorization for Flow cytometry in High Dimensions or CTFlowHD: an unsupervised workflow for FCM data analysis. By considering a NBM for the cell distribution, NBM component are interpreted as cell groups which are represented by a proportion and a set of fluorescence properties. CTFlowHD uses PCTF3D to obtain the factors of the NBM. After this step, we present several tools for visualizing the rank-one terms. The main advantage of our method is that the visualization step can be applied without having to compute the NBM factors again. This permits to use various tools for visualization, especially tools already used in the FCM community. Finally, CTFlowHD is applied to real datasets
7
Bridgeman, Jacob. "Tensor Network Methods for Quantum Phases." Thesis, The University of Sydney, 2017. http://hdl.handle.net/2123/17647.
Анотація:
The physics that emerges when large numbers of particles interact can be complex and exotic. The collective behaviour may not re ect the underlying constituents, for example fermionic quasiparticles can emerge from models of interacting bosons. Due to this emergent complexity, manybody phenomena can be very challenging to study, but also very useful. A theoretical understanding of such systems is important for robust quantum information storage and processing. The emergent, macroscopic physics can be classi ed using the idea of a quantum phase. All models within a given phase exhibit similar low-energy emergent physics, which is distinct from that displayed by models in di erent phases. In this thesis, we utilise tensor networks to study many-body systems in a range of quantum phases. These include topologically ordered phases, gapless symmetry-protected phases, and symmetry-enriched topological phases.
8
Gomes, Paulo Ricardo Barboza. "Tensor Methods for Blind Spatial Signature Estimation." Universidade Federal do CearÃ, 2014. http://www.teses.ufc.br/tde_busca/arquivo.php?codArquivo=11635.
Анотація:
FundaÃÃo Cearense de Apoio ao Desenvolvimento Cientifico e TecnolÃgicoIn this dissertation the problem of spatial signature and direction of arrival estimation in Linear 2L-Shape and Planar arrays is investigated Methods based on tensor decompositions are proposed to treat the problem of estimating blind spatial signatures disregarding the use of training sequences and knowledge of the covariance structure of the sources By assuming that the power of the sources varies between successive time blocks decompositions for tensors of third and fourth orders obtained from spatial and spatio-temporal covariance of the received data in the array are proposed from which iterative algorithms are formulated to estimate spatial signatures of the sources Then greater spatial diversity is achieved by using the Spatial Smoothing in the 2L-Shape and Planar arrays In that case the estimation of the direction of arrival of the sources can not be obtained directly from the formulated algorithms The factorization of the Khatri-Rao product is then incorporated into these algorithms making it possible extracting estimates for the azimuth and elevation angles from matrices obtained using this method A distinguishing feature of the proposed tensor methods is their efficiency to treat the cases where the covariance matrix of the sources is non-diagonal and unknown which generally happens when working with sample data covariances computed from a reduced number of snapshots
Nesta dissertaÃÃo o problema de estimaÃÃo de assinaturas espaciais e consequentemente da direÃÃo de chegada dos sinais incidentes em arranjos Linear 2L-Shape e Planar à investigado MÃtodos baseados em decomposiÃÃes tensoriais sÃo propostos para tratar o problema de estimaÃÃo cega de assinaturas espaciais desconsiderando a utilizaÃÃo de sequÃncias de treinamento e o conhecimento da estrutura de covariÃncia das fontes Ao assumir que a potÃncia das fontes varia entre blocos de tempos sucessivos decomposiÃÃes para tensores de terceira e quarta ordem obtidas a partir da covariÃncia espacial e espaÃo-temporal dos dados recebidos no arranjo de sensores sÃo propostas a partir das quais algoritmos iterativos sÃo formulados para estimar a assinatura espacial das fontes em seguida uma maior diversidade espacial à alcanÃada utilizando a tÃcnica Spatial Smoothing na recepÃÃo de sinais nos arranjos 2L-Shape e Planar Nesse caso as estimaÃÃes da direÃÃo de chegada das fontes nÃo podem ser obtidas diretamente a partir dos algoritmos formulados de forma que a fatoraÃÃo do produto de Khatri-Rao à incorporada a estes algoritmos tornando possÃvel a obtenÃÃo de estimaÃÃes para os Ãngulos de azimute e elevaÃÃo a partir das matrizes obtidas utilizando este mÃtodo Uma caracterÃstica marcante dos mÃtodos tensoriais propostos està presente na eficiÃncia obtida no tratamento de casos em que a matriz de covariÃncia das fontes à nÃo-diagonal e desconhecida o que geralmente ocorre quando se trabalha com covariÃncias de amostras reais calculadas a partir de um nÃmero reduzido de snapshots
9
Hibraj, Feliks <1995>. "Efficient tensor kernel methods for sparse regression." Master's Degree Thesis, Università Ca' Foscari Venezia, 2020. http://hdl.handle.net/10579/16921.
Анотація:
Recently, classical kernel methods have been extended by the introduction of suitable tensor kernels so to promote sparsity in the solution of the underlying regression problem. Indeed, they solve an lp-norm regularization problem, with p=m/(m-1) and m even integer, which happens to be close to a lasso problem. However, a major drawback of the method is that storing tensors requires a considerable amount of memory, ultimately limiting its applicability. In this work we address this problem by proposing two advances. First, we directly reduce the memory requirement, by introducing a new and more efficient layout for storing the data. Second, we use a Nyström-type subsampling approach, which allows for a training phase with a smaller number of data points, so to reduce the computational cost. Experiments, both on synthetic and real datasets, show the effectiveness of the proposed improvements. Finally, we take care of implementing the code in C++ so to further speed-up the computation.
10
Rabusseau, Guillaume. "A tensor perspective on weighted automata, low-rank regression and algebraic mixtures." Thesis, Aix-Marseille, 2016. http://www.theses.fr/2016AIXM4062.
Анотація:
Ce manuscrit regroupe différents travaux explorant les interactions entre les tenseurs et l'apprentissage automatique. Le premier chapitre est consacré à l'extension des modèles de séries reconnaissables de chaînes et d'arbres aux graphes. Nous y montrons que les modèles d'automates pondérés de chaînes et d'arbres peuvent être interprétés d'une manière simple et unifiée à l'aide de réseaux de tenseurs, et que cette interprétation s'étend naturellement aux graphes ; nous étudions certaines propriétés de ce modèle et présentons des résultats préliminaires sur leur apprentissage. Le second chapitre porte sur la minimisation approximée d'automates pondérés d'arbres et propose une approche théoriquement fondée à la problématique suivante : étant donné un automate pondéré d'arbres à n états, comment trouver un automate à mThis thesis tackles several problems exploring connections between tensors and machine learning. In the first chapter, we propose an extension of the classical notion of recognizable function on strings and trees to graphs. We first show that the computations of weighted automata on strings and trees can be interpreted in a natural and unifying way using tensor networks, which naturally leads us to define a computational model on graphs: graph weighted models; we then study fundamental properties of this model and present preliminary learning results. The second chapter tackles a model reduction problem for weighted tree automata. We propose a principled approach to the following problem: given a weighted tree automaton with n states, how can we find an automaton with m
11
Liu, Dong Dong. "Analysis of numerical methods for some tensor equations." Thesis, University of Macau, 2018. http://umaclib3.umac.mo/record=b3952476.
12
Kim, Junkyoung. "Complex seismic sources and time-dependent moment tensor inversion." Diss., The University of Arizona, 1989. http://hdl.handle.net/10150/184841.
Анотація:
There are many examples of earthquakes whose surface expressions are much more complicated than the seismologically derived faulting models. Seismologists also have found seismic source complexity and improved seismicity data have shown that rupture may occur on irregular or multiple shear surfaces. To simultaneously map both geometrical and temporal variation of the seismic sources for a complex rupture history from observed seismograms, it is possible to use a time dependent moment tensor (TDMT) inversion. The TDMT inversion algorithm has been tested with three synthetic data examples with varying degrees of complexity. The first example demonstrates that a multiple source with no focal depth change can be recovered, and the source parameters of each of the subevents can be accurately determined. In the second case we allowed the depth to vary for subevents (9-km and 13-km source depth, respectively). The two subevents can be identified on the basis of simultaneous shape-change of the moment tensor elements along with non-causality and the size of the CLVD component. The third example introduced source complexity by having two subevents which overlapped in time. The overlapped period could be seen in the moment tensor elements as unusually abrupt changes in the time function shape. The TDMT inversion was also performed on long-period body waves for three earthquakes: the 1982 Yemen earthquake, the 1971 San Fernando earthquake, and the 1952 Kern County earthquake. The Yemen earthquake was mapped as two simple, normal-slip subevents (with onset timing of the second subevent 5 seconds after the first) without a significant component of left- or right-lateral displacement or source depth change. The San Fernando earthquake is interpreted as two shear dislocation sources with changing source depths, possibly indicating upward rupture propagation (from 13-km to 7-km). The interpretation of the TDMT inversion for the Kern County earthquake was also a double point source which propagates upward from 20-km to 5-km. The resultant moment tensor functions from inversion of the synthetic waveforms, a combination of isotropic and tectonic release, demonstrated that the tectonic release associated with underground nuclear explosion can be separated and identified if the source depth between the explosions and tectonic release are different.
13
Zander, Elmar K. [Verfasser]. "Tensor Approximation Methods for Stochastic Problems / Elmar K. Zander." Aachen : Shaker, 2013. http://d-nb.info/1051573688/34.
14
Milsted, Ashley [Verfasser]. "Tensor network methods for quantum lattice systems / Ashley Milsted." Hannover : Technische Informationsbibliothek (TIB), 2016. http://d-nb.info/1097229254/34.
15
Zander, Elmar K. [Verfasser]. "Tensor approximation methods for stochastic problems / Elmar Klaus Zander." Braunschweig : Technische Universität Braunschweig, 2017. http://d-nb.info/1231992832/34.
16
Teng, Peiyuan. "Tensor network and neural network methods in physical systems." The Ohio State University, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=osu1524836522115804.
17
Lenglet, Christophe. "Geometric and variational methods for diffusion tensor MRI processing." Nice, 2006. http://www.theses.fr/2006NICE4083.
Анотація:
Cette thèse est consacrée au développement d'outils de traitement pour l'Imagerie par Résonance Magnétique du Tenseur de Diffusion (IRM-TD). Cette technique d'IRM récente est d'une grande importance pour comprendre le fonctionnement du cerveau ou pour améliorer le diagnostic de pathologies neurologiques. Nous proposons des méthodes de traitement basées sur la géométrie Riemannienne, les équations aux dérivées partielles et les techniques de propagation de front. La première partie de ce travail est théorique. Après des rappels sur le système nerveux humain, l'IRM et la géométrie différentielle, nous étudions l'espace des lois normales multivariées. L'introduction d'une structure Riemannienne sur cet espace nous permet de définir des statistiques et des schémas numériques intrinsèques qui sont à la base des algorithmes proposés dans la seconde partie. Les propriétés de cet espace sont importantes pour l'IRM-TD car les tenseurs de diffusion sont les matrices de covariance de lois normales modélisant la diffusion des molécules d'eau en chaque voxel du milieu imagé. La seconde partie est méthodologique. Nous y introduisons des approches originales pour l'estimation et la régularisation d'IRM-TD. Puis nous montrons comment évaluer le degré de connectivité entre aires corticales et introduisons un modèle statistique d'évolution de surface permettant de segmenter ces images. Finalement, nous proposons une méthode de recalage non-rigide. La dernière partie de cette thèse est consacrée à l'analyse des connexions entre le cortex cérébral et les noyaux gris centraux, impliquées dans des tâches motrices, et à l'étude du réseau anatomo-fonctionnel du cortex visuel humainThis thesis deals with the development of new processing tools for Diffusion Tensor Magnetic Resonance Imaging (DT-MRI). This recent MRI technique is of utmost importance to acquire a better understanding of the brain mechanisms and to improve the diagnosis of neurological disorders. We introduce new algorithms relying on Riemannian geometry, partial differential equations and front propagation techniques. The first part of this work is theoretical. After a few reminders about the human nervous system, MRI and differential geometry, we study the space of multivariate normal distributions. The introduction of a Riemannian structure on that space allows us to define statistics and intrinsic numerical schemes that will constitute the core of the algorithms proposed in the second part. The properties of that space are important for DT-MRI since diffusion tensors are the covariance matrices of normal laws modeling the diffusion of water molecules at each voxel of the acquired volume. The second part of this thesis is methodological. We start with the introduction of original approaches for the estimation and regularization of DT-MRI. We then show how to evaluate the degree of connectivity between cortical areas. Next, we introduce a statistical surface evolution framework for the segmentation of those images. Finally, we propose a non-rigid registration method. The last part of this thesis is dedicated to the application of our tools to two important neuroscience problems: the analysis of the connections between the cerebral cortex and the basal ganglia, implicated in motor tasks, and the study of the anatomo-functional network of the human visual cortex
18
Chen, Tianhong. "New methods for accurate upscaling with full-tensor effects /." May be available electronically:, 2009. http://proquest.umi.com/login?COPT=REJTPTU1MTUmSU5UPTAmVkVSPTI=&clientId=12498.
19
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.
Анотація:
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
20
Zou, Haiyuan. "Tensor renormalization group methods for spin and gauge models." Diss., University of Iowa, 2014. https://ir.uiowa.edu/etd/1420.
Анотація:
The analysis of the error of perturbative series by comparing it to the exact solution is an important tool to understand the non-perturbative physics of statistical models. For some toy models, a new method can be used to calculate higher order weak coupling expansion and modified perturbation theory can be constructed. However, it is nontrivial to generalize the new method to understand the critical behavior of high dimensional spin and gauge models. Actually, it is a big challenge in both high energy physics and condensed matter physics to develop accurate and efficient numerical algorithms to solve these problems. In this thesis, one systematic way named tensor renormalization group method is discussed. The applications of the method to several spin and gauge models on a lattice are investigated. theoretically, the new method allows one to write an exact representation of the partition function of models with local interactions. E.g. O(N) models, Z2 gauge models and U(1) gauge models. Practically, by using controllable approximations, results in both finite volume and the thermodynamic limit can be obtained. Another advantage of the new method is that it is insensitive to sign problems for models with complex coupling and chemical potential. Through the new approach, the Fisher's zeros of the 2D O(2) model in the complex coupling plane can be calculated and the finite size scaling of the results agrees well with the Kosterlitz-Thouless assumption. Applying the method to the O(2) model with a chemical potential, new phase diagram of the models can be obtained. The structure of the tensor language may provide a new tool to understand phase transition properties in general.
21
BRANDI, GIUSEPPE. "Decompose et Impera: tensor methods in high-dimensional data." Doctoral thesis, Luiss Guido Carli, 2018. http://hdl.handle.net/11385/201174.
Анотація:
This thesis is written with the scope of exploring multiway data. Multiway
data, also referred to as tensor data, is a collection of data points in multidimensional matrices. At a first glance one may think that these objects
are only a convenient representation of a datasets. They are not just a col-
lection of data, they have their own structure. For this reason, multiway
data need specific models to be correctly analysed. In this spirit, I developed
my personal idea on data analysis which can be represented by following
statement:
\It is not the data that should fit models, but models that should fit the data"
However, this should not be taken literary I do think that models are im-
portant: giving a structure to our techniques is necessary. Nevertheless, I do
think that data should be the main driver.This means that instead of trimming data at our necessity to fit existing models, researchers should develop
new models to re
ect the complexity of the data.
The purpose of this work is to provide an overview of tensor methods applied
to Economics and Finance. Yet, the most important aspect of this thesis are
ideas and applications rather than the mathematical content. New models
are proposed and fitted to data in order to test their performance and get
insights from the datasets analysed.
The description of the tensor methods provided in this thesis is not intended
to be complete but rather restricted to the model applicable to the analysed
data.
22
De, Lazzari Claudia. "Algebraic, geometric and numerical methods for Tensor Network Varieties." Doctoral thesis, Università degli studi di Trento, 2022. https://hdl.handle.net/11572/361027.
Анотація:
In this thesis, we study tensor network varieties, which are varieties of tensors described by the combinatorial structure of a given graph and two sets of integer weights, called bond and local dimensions, respectively. Tensor network varieties are geometric objects studied in the field of Algebraic Geometry, and they have received much attention in the recent years due to their usefulness in the field of Quantum Physics and other application areas. In the first part of the thesis, we study the dimension of tensor network varieties. We provide a completely general upper bound on their dimension and we give the exact value of the dimension in a particular range of parameters. We refine the upper bound in cases relevant for applications, such as matrix product states and projected entangled pairs states. We then focus on the study of the linear span of uniform matrix product states, which are translation invariant tensor network varieties associated to the cyclic graph. We provide nontrivial linear trace relations which prove the strict containment of the linear span in the ambient space as long as the number of sites is at least quadratic in the bond dimension, improving the state of the art. Finally, based on dimensional considerations, we propose a variation of the nonlinear conjugate gradient method used to approximate the ground states of a given Hamiltonian on the variety of matrix product states.
23
Friedrich, Ulrich [Verfasser], and Stephan [Akademischer Betreuer] Dahlke. "Adaptive Wavelet Methods for Inverse Problems: Acceleration Strategies, Adaptive Rothe Method and Generalized Tensor Wavelets / Ulrich Friedrich. Betreuer: Stephan Dahlke." Marburg : Philipps-Universität Marburg, 2015. http://d-nb.info/1076865518/34.
24
Gerster, Matthias [Verfasser]. "Tensor network methods for quantum many-body simulations / Matthias Gerster." Ulm : Universität Ulm, 2021. http://d-nb.info/1233737406/34.
25
Dinckal, Cigdem. "Decomposition Of Elastic Constant Tensor Into Orthogonal Parts." Phd thesis, METU, 2010. http://etd.lib.metu.edu.tr/upload/12612226/index.pdf.
Анотація:
All procedures in the literature for decomposing symmetric second rank (stress) tensor and symmetric fourth rank (elastic constant) tensor are elaborated and compared which have many engineering and scientific applications
for anisotropic materials. The decomposition methods for symmetric second rank tensors are orthonormal tensor basis method, complex variable representation and spectral method. For symmetric fourth rank (elastic constant)
tensor, there are four mainly decomposition methods namely as, orthonormal tensor basis, irreducible, harmonic decomposition and spectral. Those are
applied to anisotropic materials possessing various symmetry classes which are isotropic, cubic, transversely isotropic, tetragonal, trigonal and orthorhombic.
For isotropic materials, an expression for the elastic constant tensor different than the traditionally known form is given. Some misprints found in the literature are corrected.
For comparison purposes, numerical examples of each decomposition process are presented for the materials possessing different symmetry classes. Some
applications of these decomposition methods are given. Besides, norm and norm ratio concepts are introduced to measure and compare the anisotropy degree for
various materials with the same or di¤erent symmetries. For these materials,norm and norm ratios are calculated. It is suggested that the norm of a tensor may be used as a criterion for comparing the overall e¤
ect of the properties of anisotropic materials and the norm ratios may be used as a criterion to represent the anisotropy degree of the properties of materials. Finally, comparison of all methods are done in order to determine similarities and differences between them. As a result of this comparison process, it is proposed that the spectral method is a non-linear decomposition method which yields non-linear orthogonal decomposed parts. For symmetric second rank and fourth rank tensors, this case is a significant innovation in decomposition procedures in the literature.
26
Cheung, Charlton. "Diffusion tensor imaging pre-processing methods and application in autism research." Click to view the E-thesis via HKUTO, 2008. http://sunzi.lib.hku.hk/hkuto/record/B39793916.
27
Dolgov, Sergey. "Tensor product methods in numerical simulation of high-dimensional dynamical problems." Doctoral thesis, Universitätsbibliothek Leipzig, 2014. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-151129.
Анотація:
Quantification of stochastic or quantum systems by a joint probability density or wave function is a notoriously difficult computational problem, since the solution depends on all possible states (or realizations) of the system.
Due to this combinatorial flavor, even a system containing as few as ten particles may yield as many as $10^{10}$ discretized states.
None of even modern supercomputers are capable to cope with this curse of dimensionality straightforwardly, when the amount of quantum particles, for example, grows up to more or less interesting order of hundreds.
A traditional approach for a long time was to avoid models formulated in terms of probabilistic functions,
and simulate particular system realizations in a randomized process.
Since different times in different communities, data-sparse methods came into play.
Generally, they aim to define all data points indirectly, by a map from a low amount of representers,
and recast all operations (e.g. linear system solution) from the initial data to the effective parameters.
The most advanced techniques can be applied (at least, tried) to any given array, and do not rely explicitly on its origin.
The current work contributes further progress to this area in the particular direction: tensor product methods for separation of variables.
The separation of variables has a long history, and is based on the following elementary concept: a function of many variables may be expanded as a product of univariate functions.
On the discrete level, a function is encoded by an array of its values, or a tensor.
Therefore, instead of a huge initial array, the separation of variables allows to work with univariate factors with much less efforts.
The dissertation contains a short overview of existing tensor representations: canonical PARAFAC, Hierarchical Tucker, Tensor Train (TT) formats, as well as the artificial tensorisation, resulting in the Quantized Tensor Train (QTT) approximation method.
The contribution of the dissertation consists in both theoretical constructions and practical numerical algorithms for high-dimensional models, illustrated on the examples of the Fokker-Planck and the chemical master equations.
Both arise from stochastic dynamical processes in multiconfigurational systems, and govern the evolution of the probability function in time.
A special focus is put on time propagation schemes and their properties related to tensor product methods.
We show that these applications yield large-scale systems of linear equations,
and prove analytical separable representations of the involved functions and operators.
We propose a new combined tensor format (QTT-Tucker), which descends from the TT format (hence TT algorithms may be generalized smoothly), but provides complexity reduction by an order of magnitude.
We develop a robust iterative solution algorithm, constituting most advantageous properties of the classical iterative methods from numerical analysis and alternating density matrix renormalization group (DMRG) techniques from quantum physics.
Numerical experiments confirm that the new method is preferable to DMRG algorithms.
It is as fast as the simplest alternating schemes, but as reliable and accurate as the Krylov methods in linear algebra.
28
MacDonald, C. S. "Efficient moving mesh methods for Q-tensor models of liquid crystals." Thesis, University of Strathclyde, 2018. http://digitool.lib.strath.ac.uk:80/R/?func=dbin-jump-full&object_id=29525.
Анотація:
As devices using liquid crystals become ever smaller and increasingly complex, there is a commensurate increase in the need for more effective numerical modelling tools in the area. In this thesis, an adaptive finite element method is used to solve a non-linear singularly perturbed boundary value problem which arises from a one dimensional Q-tensor model of liquid crystals. The adaptive non-uniform mesh is generated by equidistribution of a selection of strictly positive monitor functions. By an appropriate selection of the monitor function parameters, it is shown that the computed numerical solution converges at an optimal rate with respect to the mesh density and that the solution accuracy is robust to the size of the singular perturbation parameter. A robust and efficient numerical scheme is then used to solve the system of six coupled partial differential equations which arises from Q-tensor theory. The key novel feature is the use of a full moving mesh partial differential equation (MMPDE) approach to generate an adaptive mesh which accurately resolves important solution features. This includes the use of a new monitor function based on a local measure of biaxiality. The behaviour of the method is illustrated on a one-dimensional time-dependent problem in a π-cell geometry with an applied electric field. The numerical results show that, as well as achieving optimal rates of convergence in space and time, higher levels of solution accuracy and a considerable improvement in computational efficiency are obtained compared to other moving mesh methods used by previous authors on similar problems. The numerical scheme is then extended to tackle a two-dimensional π-cell problem. It is shown that the adaptive moving mesh method copes well with the presence of moving defects, with the mesh adapting and relaxing to capture the motion, growth and annihilation of the defects.
29
Huang, Furong. "Discovery of Latent Factors in High-dimensional Data Using Tensor Methods." Thesis, University of California, Irvine, 2016. http://pqdtopen.proquest.com/#viewpdf?dispub=10125323.
Анотація:
Unsupervised learning aims at the discovery of hidden structure that drives the observations in the real world. It is essential for success in modern machine learning and artificial intelligence. Latent variable models are versatile in unsupervised learning and have applications in almost every domain, e.g., social network analysis, natural language processing, computer vision and computational biology. Training latent variable models is challenging due to the non-convexity of the likelihood objective function. An alternative method is based on the spectral decomposition of low order moment matrices and tensors. This versatile framework is guaranteed to estimate the correct model consistently. My thesis spans both theoretical analysis of tensor decomposition framework and practical implementation of various applications.
This thesis presents theoretical results on convergence to globally optimal solution of tensor decomposition using the stochastic gradient descent, despite non-convexity of the objective. This is the first work that gives global convergence guarantees for the stochastic gradient descent on non-convex functions with exponentially many local minima and saddle points.
This thesis also presents large-scale deployment of spectral methods (matrix and tensor decomposition) carried out on CPU, GPU and Spark platforms. Dimensionality reduction techniques such as random projection are incorporated for a highly parallel and scalable tensor decomposition algorithm. We obtain a gain in both accuracies and in running times by several orders of magnitude compared to the state-of-art variational methods.
To solve real world problems, more advanced models and learning algorithms are proposed. After introducing tensor decomposition framework under latent Dirichlet allocation (LDA) model, this thesis discusses generalization of LDA model to mixed membership stochastic block model for learning hidden user commonalities or communities in social network, convolutional dictionary model for learning phrase templates and word-sequence embeddings, hierarchical tensor decomposition and latent tree structure model for learning disease hierarchy in healthcare analytics, and spatial point process mixture model for detecting cell types in neuroscience.
30
Unmuth-Yockey, Judah Francis. "Duality methods and the tensor renormalization group: applications to quantum simulation." Diss., University of Iowa, 2017. https://ir.uiowa.edu/etd/5869.
Анотація:
This thesis describes the duality methods used in the tensor renormalization group method and their application to quantum simulation with cold atoms in optical lattices. Here we consider specifically the O(2) and O(3) nonlinear sigma models in two dimensions, as well as the Abelian Higgs model in two dimensions. We give numerical results from the tensor renormalization group and comparisons with other numerical methods for all three models. We give proposals for possible experimental methods with which these models could be simulated using cold atoms trapped in optical lattices as is done in ongoing experiments.
31
Aggarwal, Shalini. "Comparison of Cylindrical Boundary Pasting Methods." Thesis, University of Waterloo, 2004. http://hdl.handle.net/10012/1177.
Анотація:
Surface pasting is an interactive hierarchical modelling technique used to construct surfaces with varying levels of local detail. The concept is similar to that of the physical process of modelling with clay, where features are placed on to a base surface and attached by a smooth join obtained by adjusting the feature. Cylindrical surface pasting extends this modelling paradigm by allowing for two base surfaces to be joined smoothly via a blending cylinder, as in attaching a clay head to the body using a neck.
Unfortunately, computer-based pasting involves approximations that can cause cracks to appear in the composite surface. In particular this occurs when the pasted feature boundary does not lie exactly over the user-specified pasting region on the base surface. Determining pasted locations for the feature boundary control points that give a close to exact join is non-trivial, especially in the case of cylinders as their control points can not be defined to lie on their closed curve boundary. I propose and compare six simple methods for positioning a feature cylinder's control points such that the join boundary discontinuities are minimized. The methods considered are all algorithmically simple alternatives having low computational costs. While the results demonstrate an order of magnitude quality improvement for some methods on a convex-only curved base, as the complexity of the base surface increases, all the methods show similar performance. Although unexpected, it turns out that a simple mapping of the control points directly onto the pasting closed curve given on the base surface offers a reasonable cylindrical boundary pasting technique.
32
Cordeiro, Ana Lúcia Meyer. "Metodismo e educação no Brasil: as tensões com o catolicismo na primeira república." Universidade Federal de Juiz de Fora (UFJF), 2008. https://repositorio.ufjf.br/jspui/handle/ufjf/3363.
Анотація:
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CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior
Este estudo tem por objetivo analisar, no contexto da Primeira República brasileira, o desenvolvimento do projeto educacional da Igreja Metodista Episcopal do Sul dos Estados Unidos na região Sudeste, enfocando, sobretudo, as tensões com o catolicismo. O momento de implantação das instituições de ensino metodistas no setor educacional brasileiro coincide com dois importantes períodos da história da Igreja Católica Apostólica Romana no Brasil: o da romanização e o da neocristandade. Em ambos os períodos as autoridades eclesiásticas católicas, visando manter a hegemonia do catolicismo na sociedade brasileira, procuraram se contrapor à difusão de correntes políticas e ideológicas consideradas heterodoxas, entre elas, o protestantismo. Sendo o metodismo uma confissão religiosa protestante que se estabeleceu no Brasil sobretudo pela influência do seu projeto educacional junto às elites liberais e progressistas brasileiras, os colégios metodistas não foram poupados da oposição da Igreja romana, seja por meio da fundação de colégios católicos, seja através dos documentos oficiais e de artigos veiculados na imprensa ultramontana. Uma vez que os metodistas pretendiam difundir no Brasil, por meio do seu projeto educacional, os valores religiosos protestantes e os valores culturais norte-americanos, visando assegurar a hegemonia ideológico-cultural da sociedade, eles reagiram à ofensiva católica, ora respondendo aos ataques sofridos, ora denunciando o não cumprimento da legislação republicana, tanto por parte das autoridades católicas como por parte das autoridades governamentais.
This study aims to analyze, in the Brazilian First Republic context, the development of the educational project of the Methodist Episcopal Church South of the United States in the southeast region, focusing, above all, the tensions towards the Catholicism. The implantation moment of the Methodist Teaching Institutions in the Brazilian educational sector coincides with two important periods in the history of the Roman Apostolic Catholic Church in Brazil: the one of Romanization and the one of Neochristianity. In both periods the Catholic ecclesiastic authorities, trying to keeps the Catholicism hegemony in the Brazilian society, sought to pit against the spread of ideological and political groups considered heterodox, among them, the Protestantism. Being the Methodism a Protestant religious confession that was established in Brazil mainly by the influence of its education project on Brazilian liberal and progressive elites, the Methodist schools were not spared by the Roman Church opposition, either through Catholic school foundation, or through the official documents and articles conveyed in the ultramountain press. Since the Methodists wanted to spread in Brazil, through its educational project, the Protestant religious values and the North American cultural values, aiming to guarantee the society ideological-cultural hegemony, they reacted against the Catholic offensive, both responding to attacks that were suffered, and denouncing the not-fulfilment of the republican legislation, not only by the Catholic authorities but also by the governmental authorities.
33
UGWU, UGOCHUKWU OBINNA. "Iterative tensor factorization based on Krylov subspace-type methods with applications to image processing." Kent State University / OhioLINK, 2021. http://rave.ohiolink.edu/etdc/view?acc_num=kent1633531487559183.
34
Telyatnyk, Lyudmyla. "Magnetic Resonance Parameters of Radicals Studied by Density Functional Theory Methods." Licentiate thesis, KTH, Biotechnology, 2004. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-1727.
Анотація:
The recent state of art in the magnetic resonance area putsforward the electron paramagnetic resonance, EPR, and nuclearmagnetic resonance, NMR, experiments on prominent positions forinvestigations of molecular and electronic structure. A mostdifficult aspect of such experiments is usually the properinterpretation of data obtained from high-resolution spectra,that, however, at the same time opens a great challenge forpure theoretical methods to interpret the spectral features.This thesis constitutes an effort in this respect, as itpresents and discusses calculations of EPR and NMR parametersof paramagnetic molecules. The calculations are based on newmethodology for determination of properties of paramagneticmolecules in the framework of the density functional theory,which has been developed in our laboratory.
Paramagnetic molecules are, in some sense, very special. Thepresence of unpaired electrons essentially modifies theirspectra. The experimental determination of the magneticresonance parameters of such molecules is, especially in theNMR case, quite complicated and requires special techniques ofspectral detection. The significant efforts put into suchexperiments are completely justi fied though by the importantroles of paramagnetic species playing in many areas, such as,for example, molecular magnets, active centers in biologicalsystems, and defects in inorganic conductive materials.
The first two papers of this thesis deal with thetheoretical determination of NMR parameters, such as thenuclear shielding tensors and the chemical shifts, inparamagnetic nitroxides that form core units in molecularmagnets. The developed methodology aimed to realize highaccuracy in the calculations in order to achieve successfulapplications for the mentioned systems. Theeffects of hydrogenbonding are also described in that context. Our theory forevaluation of nuclear shielding tensors in paramagneticmolecules is consistent up to the second order in the finestructure constant and considers orbital, fully isotropicdipolar, and isotropic contact contributions to the shieldingtensor.
The next three projects concern electron paramagneticresonance. The wellknown EPR parameters, such as the g-tensorsand the hyperfine coupling constants are explored. Calculationsof electronic g-tensors were carried out in the framework of aspin-restricted open-shell Kohn-Sham method combined with thelinear response theory recently developed in our laboratory.The spincontamination problem is then automatically avoided.The solvent effects, described by the polarizable continuummodel, are also considered. For calculations of the hyperfinecoupling constants a so-called restricted-unrestricted approachhas been developed in the context of density functional theory.Comparison of experimentally and theoretically determinedparameters shows that qualitative mutual agreement of the twosets of data can be easily achieved by employing the proposedformalisms.
35
Sokolović, Sonja [Verfasser]. "Multigrid methods for highdimensional, tensor structured continuous time Markov chains / Sonja Sokolović." Wuppertal : Universitätsbibliothek Wuppertal, 2017. http://d-nb.info/1135623945/34.
36
Jacot, Benjamin (Benjamin Paul Emmanuel). "A strain tensor method for three-dimensional optimal Michell structures." Thesis, Massachusetts Institute of Technology, 2016. http://hdl.handle.net/1721.1/104125.
Анотація:
Thesis: M. Eng., Massachusetts Institute of Technology, Department of Civil and Environmental Engineering, 2016.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.
Cataloged from student-submitted PDF version of thesis.
Includes bibliographical references (pages 94-95).
In the design of discrete structures such as trusses and frames, important quantitative goals such as minimal weight or minimal compliance often dominate. Many numerical techniques exist to address these needs. However, an analytical approach exists to meet similar goals, which was initiated by A.G.M. Michell (1904) and has been mostly used for two-dimensional structures so far. This thesis develops a method to extend the existing mainly two-dimensional approach to apply to three-dimensional structures. It will be referred as the Michell strain tensor method (MSTM). First, the proof that MSTM is consistent with the existing theory in two dimensions is provided. Second, two-dimensional known solutions will be replicated based on MSTM. Finally, MSTM will be used to solve new three- dimensional cases.
by Benjamin Jacot.
M. Eng.
37
Parrish, Robert M. "Rank reduction methods in electronic structure theory." Diss., Georgia Institute of Technology, 2015. http://hdl.handle.net/1853/53850.
Анотація:
Quantum chemistry is plagued by the presence of high-rank quantities, stemming from the N-body nature of the electronic Schrödinger equation. These high-rank quantities present a significant mathematical and computational barrier to the computation of chemical observables, and also drastically complicate the pedagogical understanding of important interactions between particles in a molecular system. The application of physically-motivated rank reduction approaches can help address these to problems. This thesis details recent efforts to apply rank reduction techniques in both of these arenas.
With regards to computational tractability, the representation of the 1/r Coulomb repulsion between electrons is a critical stage in the solution of the electronic Schrödinger equation. Typically, this interaction is encapsulated via the order-4 electron repulsion integral (ERI) tensor, which is a major bottleneck in terms of generation, manipulation, and storage. Many rank reduction techniques for the ERI tensor have been proposed to ameliorate this bottleneck, most notably including the order-3 density fitting (DF) and pseudospectral (PS) representations. Here we detail a new and uniquely powerful factorization - tensor hypercontraction (THC). THC decomposes the ERI tensor as a product of five order-2 matrices (the first wholly order-2 compression proposed for the ERI) and offers great flexibility for low-scaling algorithms for the manipulations of the ERI tensor underlying electronic structure theory. THC is shown to be physically-motivated, markedly accurate, and uniquely efficient for some of the most difficult operations encountered in modern quantum chemistry.
On the front of chemical understanding of electronic structure theory, we present our recent work in developing robust two-body partitions for ab initio computations of intermolecular interactions. Noncovalent interactions are the critical and delicate forces which govern such important processes as drug-protein docking, enzyme function, crystal packing, and zeolite adsorption. These forces arise as weak residual interactions leftover after the binding of electrons and nuclei into molecule, and, as such, are extremely difficult to accurately quantify or systematically understand. Symmetry-adapted perturbation theory (SAPT) provides an excellent approach to rigorously compute the interaction energy in terms of the physically-motivated components of electrostatics, exchange, induction, and dispersion. For small intermolecular dimers, this breakdown provides great insight into the nature of noncovalent interactions. However, SAPT abstracts away considerable details about the N-body interactions between particles on the two monomers which give rise to the interaction energy components. In the work presented herein, we step back slightly and extract an effective 2-body interaction for each of the N-body SAPT terms, rather than immediately tracing all the way down to the order-0 interaction energy. This effective order-2 representation of the order-N SAPT interaction allows for the robust assignment of interaction energy contributions to pairs of atoms or functional groups (the A-SAPT or F-SAPT partitions), allowing one to discuss the interaction in terms of atom- or functional-group-pairwise interactions. These A-SAPT and F-SAPT partitions can provide deep insight into the origins of complicated noncovalent interactions, e.g., by clearly shedding light on the long-contested question of the nature of the substituent effect in substituted sandwich benzene dimers.
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Molnar, Andras [Verfasser], and Jan von [Akademischer Betreuer] Delft. "Tensor Network methods in many-body physics / Andras Molnar ; Betreuer: Jan von Delft." München : Universitätsbibliothek der Ludwig-Maximilians-Universität, 2019. http://d-nb.info/1185979328/34.
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Paula, Geyverson Teixeira de. "Cálculo da força contra eletromotriz em máquinas síncronas com ímãs na superfície do rotor." Universidade de São Paulo, 2016. http://www.teses.usp.br/teses/disponiveis/18/18153/tde-14062016-113636/.
Анотація:
O presente trabalho trata do cálculo da força contra eletromotriz em carga de uma máquina síncrona com ímãs na superfície do rotor (cuja forma de onda de força contra eletromotriz é não senoidal) sendo esta alimentada por correntes de fase cujas forma de onda são quadradas. Para conduzir esta investigação e calcular a força contra eletromotriz da máquina em estudo, faz-se uma revisão sobre o Método da Permeabilidade Fixa, método este que permite a linearização do ponto de operação da máquina. Dessa forma, as simulações são conduzidas por meio do método dos elementos finitos e do Método da Permeabilidade Fixa, levando-se em conta a forma de onda da corrente de alimentação. Atenção especial é dada ao modo que se analisa o fluxo concatenado e a forma de obtenção da força contra eletromotriz uma vez que as formas de onda do fluxo concatenado sofrem variações abruptas a cada 60º elétricos. Além destes parâmetros, analisa-se também cada uma das parcelas do torque eletromagnético, i.e., torque mútuo, torque de relutância e torque de borda, sendo realizado ao final do trabalho, uma comparação entre a soma da estimativa de cada parâmetro com o valor do torque eletromagnético obtido por meio de uma simulação não linear.This work deals with the assessment of a surface mounted magnet synchronous machine\'s parameters (whose back-EMF is approximately trapezoidal) and that is fed by an ideal square current waveform. In order to investigate and describe each machine\'s parameter, a review on Frozen Permeability Method is presented. Some simulation by means of finite element method with the aid of Frozen Permeability Method are carried out taking into account that the machine is fed by an ideal square current waveform. The results for flux-linkage wave-form and back-EMF waveform are shown and analyzed. A special attention is given to back-EMF calculation since the linkage flux of each phase has an abrupt change every sixty electrical degrees due to the phase commutation. In addition, an attention is given to each torque component on load condition, i.e., mutual torque, reluctance torque, cogging torque and a comparison between the electromagnetic torque and the summation of these components.
40
Zhu, Lierong. "Topological visualization of tensor fields using a generalized Helmholtz decomposition." Morgantown, W. Va. : [West Virginia University Libraries], 2010. http://hdl.handle.net/10450/10962.
Анотація:
Thesis (M.S.)--West Virginia University, 2010.Title from document title page. Document formatted into pages; contains viii, 75 p. : ill. (some col.). Includes abstract. Includes bibliographical references (p. 72-75).
41
Böhm, Karl-Heinz. "Anwendung von Tensorapproximationen auf die Full Configuration Interaction Methode." Doctoral thesis, Universitätsbibliothek Chemnitz, 2016. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-qucosa-209065.
Анотація:
In dieser Arbeit werden verschiedene Ansätze untersucht, um Tensorzerlegungsmethoden auf die Full-Configuration-Interaction-Methode (FCI) anzuwenden. Das Ziel dieser Ansätze ist es, zuverlässig konvergierende Algorithmen zu erstellen, welche es erlauben, die Wellenfunktion effizient im Canonical-Product-Tensorformat (CP) zu approximieren. Hierzu werden drei Ansätze vorgestellt, um die FCI-Wellenfunktion zu repräsentieren und darauf basierend die benötigten Koeffizienten zu bestimmen. Der erste Ansatz beruht auf einer Entwicklung der Wellenfunktion als Linearkombination von Slaterdeterminanten, bei welcher in einer Hierarchie ausgehend von der Hartree-Fock-Slaterdeterminante sukzessive besetzte Orbitale durch virtuelle Orbitale ersetzt werden. Unter Nutzung von Tensorrepräsentationen im CP wird ein lineares Gleichungssystem gelöst, um die FCI-Koeffizienten zu bestimmen. Im darauf folgenden Ansatz, welcher an Direct-CI angelehnt ist, werden Tensorrepräsentationen der Hamiltonmatrix und des Koeffizientenvektors aufgestellt, welche zur Lösung des FCI-Eigenwertproblems erforderlich sind. Hier wird ein Algorithmus vorgestellt, mit welchem das Eigenwertproblem im CP gelöst wird. In einem weiteren Ansatz wird die Repräsentation der Hamiltonmatrix und des Koeffizientenvektors im Fockraum formuliert. Dieser Ansatz erlaubt die Lösung des FCI-Eigenwertproblems mit Hilfe verschiedener Algorithmen. Diese orientieren sich an den Rayleighquotienteniterationen oder dem Davidsonalgorithmus, wobei für den ersten Algorithmus eine zweite Version entwickelt wurde, wo die Rangreduktion teilweise durch Projektionen ersetzt wurde. Für den Davidsonalgorithmus ist ein breiteres Spektrum von Molekülen behandelbar und somit können erste Untersuchungen zur Skalierung und zu den zu erwartenden Fehlern vorgestellt werden. Schließlich wird ein Ausblick auf mögliche Weiterentwicklungen gegeben, welche eine effizientere Berechnung ermöglichen und somit FCI im CP auch für größere Moleküle zugänglich machtIn this thesis, various approaches are investigated to apply tensor decomposition methods to the Full Configuration Interaction method (FCI). The aim of these approaches is the development of algorithms, which converge reliably and which permit to approximate the wave function efficiently in the Canonical Product format (CP). Three approaches are introduced to represent the FCI wave function and to obtain the corresponding coefficients. The first approach ist based on an expansion of the wave function as a linear combination of slater determinants. In this hierarchical expansion, starting from the Hartree Fock slater determinant, the occupied orbitals are substituted by virtual orbitals. Using tensor representations in the CP, a linear system of equations is solved to obtain the FCI coefficients. In a further approach, tensor representations of the Hamiltonian matrix and the coefficient vectors are set up, which are required to solve the FCI eigenvalue problem. The tensor contractions and an algorithm to solve the eigenvalue problem in the CP are explained her in detail. In the next approach, tensor representations of the Hamiltonian matrix and the coefficient vector are constructed in the Fock space. This approach allows the application of various algorithms. They are based on the Rayleight Quotient Algorithm and the Davidson algorithm and for the first one, there exists a second version, where the rank reduction algorithm is replaced by projections. The Davidson algorithm allows to treat a broader spectrum of molecules. First investigations regarding the scaling behaviour and the expectable errors can be shown for this approach. Finally, an outlook on the further development is given, that allows for more efficient calculations and makes FCI in the CP accessible for larger molecules
42
Fan, Li 1958. "Solution of the ill-conditioned load flow problem by the tensor method." Thesis, McGill University, 1989. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=62002.
43
Taliotis, Anastasios Socrates. "Geometrical Methods in Heavy Ion Collisions." The Ohio State University, 2010. http://rave.ohiolink.edu/etdc/view?acc_num=osu1285088429.
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Handschuh, Stefan [Verfasser], Wolfgang [Akademischer Betreuer] Hackbusch, Wolfgang [Gutachter] Hackbusch, and Daniel [Gutachter] Kressner. "Numerical methods in Tensor Networks / Stefan Handschuh ; Gutachter: Wolfgang Hackbusch, Daniel Kressner ; Betreuer: Wolfgang Hackbusch." Leipzig : Universitätsbibliothek Leipzig, 2015. http://d-nb.info/123942308X/34.
45
Ervin, Jason. "On O-basis groups and generalizations." Auburn, Ala., 2007. http://repo.lib.auburn.edu/07M%20Dissertations/ERVIN_JASON_11.pdf.
46
Ballani, Jonas. "Fast Evaluation of Near-Field Boundary Integrals using Tensor Approximations." Doctoral thesis, Universitätsbibliothek Leipzig, 2012. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-97317.
Анотація:
In this dissertation, we introduce and analyse a scheme for the fast evaluation of integrals stemming from boundary element methods including discretisations of the classical single and double layer potential operators. Our method is based on the parametrisation of boundary elements in terms of a d-dimensional parameter tuple. We interpret the integral as a real-valued function f depending on d parameters and show that f is smooth in a d-dimensional box. A standard interpolation of f by polynomials leads to a d-dimensional tensor which is given by the values of f at the interpolation points. This tensor may be approximated in a low rank tensor format like the canonical format or the hierarchical format. The tensor approximation has to be done only once and allows us to evaluate interpolants in O(dr(m+1)) operations in the canonical format, or O(dk³ + dk(m + 1)) operations in the hierarchical format, where m denotes the interpolation order and the ranks r, k are small integers. In particular, we apply an efficient black box scheme in the hierarchical tensor format in order to adaptively approximate tensors even in high dimensions d with a prescribed (but heuristic) target accuracy. By means of detailed numerical experiments, we demonstrate that highly accurate integral values can be obtained at very moderate costs.
47
Furuhashi, Takeshi, Tomohiro Yoshikawa, and Hiroaki Masai. "A visualization method of third-order tensor for knowledge extraction from questionnaire data." IEEE, 2013. http://hdl.handle.net/2237/20712.
48
Spencer, Timothy J. "Lattice Boltzmann method for Q-tensor nemato-dynamics in liquid crystal display devices." Thesis, Sheffield Hallam University, 2005. http://shura.shu.ac.uk/20393/.
Анотація:
Nematic liquid crystals are fluids whose anisometric molecules show long range orientational order but no positional order. The orientational order gives rise to anisotropic properties that have widely been exploited as the basis for liquid crystal display devices. The Ericksen-Leslie director theory has successfully been used to describe many dynamic properties of liquid crystals however there are situations in which a more complete description may be given in terms of the second rank traceless symmetric Q-tensor. The development of a liquid crystal device solver is described. The solver calculates the flow, director and order parameter fields in three-dimensions through the Q-tensor equations of nemato-dynamics. The solver includes elastic, electric, magnetic, thermotropic, flexoelectric, dielectric and surface anchoring effects. Coupled lattice Boltzmann algorithms are used with anisotropic forcing terms included in order to reproduce the governing equations. A Chapman-Enskog analysis demonstrates that the algorithm recovers the target macroscopic equations. The method is successfully validated against analytical results for the effect of temperature, external electric fields, flow alignment and Miesowicz viscosities. Further validation is given against numerical solutions of a one-dimensional model of a liquid crystal display device proposed by Davidson. The switching behaviour of a Zenithal Bistable Display is then investigated. It is shown how flexoelectric properties of nematics produce bistability within this device. Defect creation and annihilation processes are shown during device switching for which it is necessary to use a method with variable order parameter. An approach to determine the flexoelectric coefficients is discussed. Results are presented for the preliminary characterisation and operation of this display that may enable optimisation for use in the display industry.
49
QUINAN, MARCO A. D. "Uma metodologia para determinação do fator de intensidade de tensões causado por tensões térmicas utilizando a fotoelasticidade." reponame:Repositório Institucional do IPEN, 2005. http://repositorio.ipen.br:8080/xmlui/handle/123456789/11270.
Анотація:
Made available in DSpace on 2014-10-09T12:50:08Z (GMT). No. of bitstreams: 0Made available in DSpace on 2014-10-09T13:58:46Z (GMT). No. of bitstreams: 1 10458.pdf: 6292161 bytes, checksum: 035d670a36d319ca420fee75d85f96a6 (MD5)
Tese (Doutoramento)
IPEN/T
Instituto de Pesquisas Energeticas e Nucleares - IPEN/CNEN-SP
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Li, Bowei. "Implementation of full permeability tensor representation in a dual porosity reservoir simulator." Access restricted to users with UT Austin EID Full text (PDF) from UMI/Dissertation Abstracts International, 2001. http://wwwlib.umi.com/cr/utexas/fullcit?p3034930.