Tensor analysis for physicists
Schouten, J A
1989-01-01
This brilliant study by a famed mathematical scholar and former professor of mathematics at the University of Amsterdam integrates a concise exposition of the mathematical basis of tensor analysis with admirably chosen physical examples of the theory. The first five chapters incisively set out the mathematical theory underlying the use of tensors. The tensor algebra in EN and RN is developed in Chapters I and II. Chapter II introduces a sub-group of the affine group, then deals with the identification of quantities in EN. The tensor analysis in XN is developed in Chapter IV. In chapters VI through IX, Professor Schouten presents applications of the theory that are both intrinsically interesting and good examples of the use and advantages of the calculus. Chapter VI, intimately connected with Chapter III, shows that the dimensions of physical quantities depend upon the choice of the underlying group, and that tensor calculus is the best instrument for dealing with the properties of anisotropic media. In Chapte...
Sparse tensor discriminant analysis.
Lai, Zhihui; Xu, Yong; Yang, Jian; Tang, Jinhui; Zhang, David
2013-10-01
The classical linear discriminant analysis has undergone great development and has recently been extended to different cases. In this paper, a novel discriminant subspace learning method called sparse tensor discriminant analysis (STDA) is proposed, which further extends the recently presented multilinear discriminant analysis to a sparse case. Through introducing the L1 and L2 norms into the objective function of STDA, we can obtain multiple interrelated sparse discriminant subspaces for feature extraction. As there are no closed-form solutions, k-mode optimization technique and the L1 norm sparse regression are combined to iteratively learn the optimal sparse discriminant subspace along different modes of the tensors. Moreover, each non-zero element in each subspace is selected from the most important variables/factors, and thus STDA has the potential to perform better than other discriminant subspace methods. Extensive experiments on face databases (Yale, FERET, and CMU PIE face databases) and the Weizmann action database show that the proposed STDA algorithm demonstrates the most competitive performance against the compared tensor-based methods, particularly in small sample sizes.
Application of tensor analysis
McConnell, Albert Joseph
1957-01-01
Standard work applies tensorial methods to subjects within realm of advanced college mathematics. Text explains fundamental ideas and notation of tensor theory; covers geometrical treatment of tensor algebra; introduces theory of differentiation of tensors; and applies mathematics to dynamics, electricity, elasticity and hydrodynamics. 685 exercises, most with answers.
Tensor SOM and tensor GTM: Nonlinear tensor analysis by topographic mappings.
Iwasaki, Tohru; Furukawa, Tetsuo
2016-05-01
In this paper, we propose nonlinear tensor analysis methods: the tensor self-organizing map (TSOM) and the tensor generative topographic mapping (TGTM). TSOM is a straightforward extension of the self-organizing map from high-dimensional data to tensorial data, and TGTM is an extension of the generative topographic map, which provides a theoretical background for TSOM using a probabilistic generative model. These methods are useful tools for analyzing and visualizing tensorial data, especially multimodal relational data. For given n-mode relational data, TSOM and TGTM can simultaneously organize a set of n-topographic maps. Furthermore, they can be used to explore the tensorial data space by interactively visualizing the relationships between modes. We present the TSOM algorithm and a theoretical description from the viewpoint of TGTM. Various TSOM variations and visualization techniques are also described, along with some applications to real relational datasets. Additionally, we attempt to build a comprehensive description of the TSOM family by adapting various data structures. Copyright © 2016 Elsevier Ltd. All rights reserved.
Tensor Fusion Network for Multimodal Sentiment Analysis
Zadeh, Amir; Chen, Minghai; Poria, Soujanya; Cambria, Erik; Morency, Louis-Philippe
2017-01-01
Multimodal sentiment analysis is an increasingly popular research area, which extends the conventional language-based definition of sentiment analysis to a multimodal setup where other relevant modalities accompany language. In this paper, we pose the problem of multimodal sentiment analysis as modeling intra-modality and inter-modality dynamics. We introduce a novel model, termed Tensor Fusion Network, which learns both such dynamics end-to-end. The proposed approach is tailored for the vola...
Vector and tensor analysis with applications
Borisenko, A I; Silverman, Richard A
1979-01-01
Concise and readable, this text ranges from definition of vectors and discussion of algebraic operations on vectors to the concept of tensor and algebraic operations on tensors. It also includes a systematic study of the differential and integral calculus of vector and tensor functions of space and time. Worked-out problems and solutions. 1968 edition.
Complete stress tensor determination by microearthquake analysis
Slunga, R.
2010-12-01
the depth based on the assumptions of a fractured crust, widely vary ing stress field, and a general closeness to instability as found by stress measurements (Jamison and Cook 1976). Wheather this approach is working or not is best answered by applying it to real data. This was provided by the IMO network in Iceland. Along Southern Iceland Seismic Zone (SISZ) more than 200,000 microearthquakes and a few M 5 EQs and 2 M=6.6 EQs have been recorded. The results will be presented it is obvious that the use of the stresses determined from the microearthquake recordings may significa ntly improve earthquake warnings and will make it possible to use the absolute C FS method for more deterministic predictions. Note that the microearthquake meth od only shows the part of the stress field that has caused slip. Volumes with st able stress will not show up. However stress measurements (Brown and Hoek 1978, Slunga 1988) have shown that the crustal stresses in general are close to instabi lity and microearthquake source analysis has shown that a large number of differ ent fractures become unstable within longer time windows. This may explain the e xcellent results given by the Icelandic tests of the absolute stress tensor fiel d as given by the microearthquakes. However I prefer to call this stress apparen t.
Spectral analysis of the full gravity tensor
Rummel, R.; van Gelderen, M.
1992-10-01
It is shown that, when the five independent components of the gravity tensor are grouped into (Gamma-zz), (Gamma-xz, Gamma-yz), and (Gamma-xx - Gamma-yy, 2Gamma-xy) sets and expanded into an infinite series of pure-spin spherical harmonic tensors, it is possible to derive simple eigenvalue connections between these three sets and the spherical harmonic expansion of the gravity potential. The three eigenvalues are (n + 1)(n + 2), -(n + 2) sq rt of n(n + 1), and sq rt of (n - 1)n(n + 1)(n + 2). The joint ESA and NASA Aristoteles mission is designed to measure with high precision the tensor components Gamma-zz, Gamma-yz, and Gamma-yy, which will make it possible to determine the global gravity field in six months time with a high precision.
Magnetotelluric impedance tensor analysis for identification of ...
Indian Academy of Sciences (India)
We present the results of magnetotelluric (MT) impedance tensors analyses of 18 sites located along a profile cutting various faults in the uplifted Wagad block of the Kachchh basin. The MT time series of 4–5 days recording duration have been processed and the earth response functions are estimated in broad frequency ...
Introduction to vector and tensor analysis
Wrede, Robert C
1972-01-01
A broad introductory treatment, this volume examines general Cartesian coordinates, the cross product, Einstein's special theory of relativity, bases in general coordinate systems, maxima and minima of functions of two variables, line integrals, integral theorems, fundamental notions in n-space, Riemannian geometry, algebraic properties of the curvature tensor, and more. 1963 edition.
Multidimensional seismic data reconstruction using tensor analysis
Kreimer, Nadia
Exploration seismology utilizes the seismic wavefield for prospecting oil and gas. The seismic reflection experiment consists on deploying sources and receivers in the surface of an area of interest. When the sources are activated, the receivers measure the wavefield that is reflected from different subsurface interfaces and store the information as time-series called traces or seismograms. The seismic data depend on two source coordinates, two receiver coordinates and time (a 5D volume). Obstacles in the field, logistical and economical factors constrain seismic data acquisition. Therefore, the wavefield sampling is incomplete in the four spatial dimensions. Seismic data undergoes different processes. In particular, the reconstruction process is responsible for correcting sampling irregularities of the seismic wavefield. This thesis focuses on the development of new methodologies for the reconstruction of multidimensional seismic data. This thesis examines techniques based on tensor algebra and proposes three methods that exploit the tensor nature of the seismic data. The fully sampled volume is low-rank in the frequency-space domain. The rank increases when we have missing traces and/or noise. The methods proposed perform rank reduction on frequency slices of the 4D spatial volume. The first method employs the Higher-Order Singular Value Decomposition (HOSVD) immersed in an iterative algorithm that reinserts weighted observations. The second method uses a sequential truncated SVD on the unfoldings of the tensor slices (SEQ-SVD). The third method formulates the rank reduction problem as a convex optimization problem. The measure of the rank is replaced by the nuclear norm of the tensor and the alternating direction method of multipliers (ADMM) minimizes the cost function. All three methods have the interesting property that they are robust to curvature of the reflections, unlike many reconstruction methods. Finally, we present a comparison between the methods
Tensor analysis and elementary differential geometry for physicists and engineers
Nguyen-Schäfer, Hung
2017-01-01
This book comprehensively presents topics, such as Dirac notation, tensor analysis, elementary differential geometry of moving surfaces, and k-differential forms. Additionally, two new chapters of Cartan differential forms and Dirac and tensor notations in quantum mechanics are added to this second edition. The reader is provided with hands-on calculations and worked-out examples at which he will learn how to handle the bra-ket notation, tensors, differential geometry, and differential forms; and to apply them to the physical and engineering world. Many methods and applications are given in CFD, continuum mechanics, electrodynamics in special relativity, cosmology in the Minkowski four-dimensional spacetime, and relativistic and non-relativistic quantum mechanics. Tensors, differential geometry, differential forms, and Dirac notation are very useful advanced mathematical tools in many fields of modern physics and computational engineering. They are involved in special and general relativity physics, quantum m...
Tensor and vector analysis with applications to differential geometry
Springer, C E
2012-01-01
Concise and user-friendly, this college-level text assumes only a knowledge of basic calculus in its elementary and gradual development of tensor theory. The introductory approach bridges the gap between mere manipulation and a genuine understanding of an important aspect of both pure and applied mathematics.Beginning with a consideration of coordinate transformations and mappings, the treatment examines loci in three-space, transformation of coordinates in space and differentiation, tensor algebra and analysis, and vector analysis and algebra. Additional topics include differentiation of vect
Tucker Tensor analysis of Matern functions in spatial statistics
Litvinenko, Alexander
2017-11-18
In this work, we describe advanced numerical tools for working with multivariate functions and for the analysis of large data sets. These tools will drastically reduce the required computing time and the storage cost, and, therefore, will allow us to consider much larger data sets or finer meshes. Covariance matrices are crucial in spatio-temporal statistical tasks, but are often very expensive to compute and store, especially in 3D. Therefore, we approximate covariance functions by cheap surrogates in a low-rank tensor format. We apply the Tucker and canonical tensor decompositions to a family of Matern- and Slater-type functions with varying parameters and demonstrate numerically that their approximations exhibit exponentially fast convergence. We prove the exponential convergence of the Tucker and canonical approximations in tensor rank parameters. Several statistical operations are performed in this low-rank tensor format, including evaluating the conditional covariance matrix, spatially averaged estimation variance, computing a quadratic form, determinant, trace, loglikelihood, inverse, and Cholesky decomposition of a large covariance matrix. Low-rank tensor approximations reduce the computing and storage costs essentially. For example, the storage cost is reduced from an exponential O(n^d) to a linear scaling O(drn), where d is the spatial dimension, n is the number of mesh points in one direction, and r is the tensor rank. Prerequisites for applicability of the proposed techniques are the assumptions that the data, locations, and measurements lie on a tensor (axes-parallel) grid and that the covariance function depends on a distance, ||x-y||.
Tensor analysis and elementary differential geometry for physicists and engineers
Nguyen-Schäfer, Hung
2014-01-01
Tensors and methods of differential geometry are very useful mathematical tools in many fields of modern physics and computational engineering including relativity physics, electrodynamics, computational fluid dynamics (CFD), continuum mechanics, aero and vibroacoustics, and cybernetics. This book comprehensively presents topics, such as bra-ket notation, tensor analysis, and elementary differential geometry of a moving surface. Moreover, authors intentionally abstain from giving mathematically rigorous definitions and derivations that are however dealt with as precisely as possible. The reader is provided with hands-on calculations and worked-out examples at which he will learn how to handle the bra-ket notation, tensors and differential geometry and to use them in the physical and engineering world. The target audience primarily comprises graduate students in physics and engineering, research scientists, and practicing engineers.
Multilinear Discriminant Analysis for Higher-Order Tensor Data Classification.
Li, Qun; Schonfeld, Dan
2014-12-01
In the past decade, great efforts have been made to extend linear discriminant analysis for higher-order data classification, generally referred to as multilinear discriminant analysis (MDA). Existing examples include general tensor discriminant analysis (GTDA) and discriminant analysis with tensor representation (DATER). Both the two methods attempt to resolve the problem of tensor mode dependency by iterative approximation. GTDA is known to be the first MDA method that converges over iterations. However, its performance relies highly on the tuning of the parameter in the scatter difference criterion. Although DATER usually results in better classification performance, it does not converge, yet the number of iterations executed has a direct impact on DATER's performance. In this paper, we propose a closed-form solution to the scatter difference objective in GTDA, namely, direct GTDA (DGTDA) which also gets rid of parameter tuning. We demonstrate that DGTDA outperforms GTDA in terms of both efficiency and accuracy. In addition, we propose constrained multilinear discriminant analysis (CMDA) that learns the optimal tensor subspace by iteratively maximizing the scatter ratio criterion. We prove both theoretically and experimentally that the value of the scatter ratio criterion in CMDA approaches its extreme value, if it exists, with bounded error, leading to superior and more stable performance in comparison to DATER.
The tensor product in Wadler's analysis of lists
DEFF Research Database (Denmark)
Nielson, Flemming; Nielson, Hanne Riis
1994-01-01
We consider abstract interpretation (in particular strictness analysis) for pairs and lists. We begin by reviewing the well-known fact that the best known description of a pair of elements is obtained using the tensor product rather than the cartesian product. We next present a generalisation of ...
Tensor-Dictionary Learning with Deep Kruskal-Factor Analysis
Energy Technology Data Exchange (ETDEWEB)
Stevens, Andrew J.; Pu, Yunchen; Sun, Yannan; Spell, Gregory; Carin, Lawrence
2017-04-20
We introduce new dictionary learning methods for tensor-variate data of any order. We represent each data item as a sum of Kruskal decomposed dictionary atoms within the framework of beta-process factor analysis (BPFA). Our model is nonparametric and can infer the tensor-rank of each dictionary atom. This Kruskal-Factor Analysis (KFA) is a natural generalization of BPFA. We also extend KFA to a deep convolutional setting and develop online learning methods. We test our approach on image processing and classification tasks achieving state of the art results for 2D & 3D inpainting and Caltech 101. The experiments also show that atom-rank impacts both overcompleteness and sparsity.
Simultaneous analysis and quality assurance for diffusion tensor imaging.
Directory of Open Access Journals (Sweden)
Carolyn B Lauzon
Full Text Available Diffusion tensor imaging (DTI enables non-invasive, cyto-architectural mapping of in vivo tissue microarchitecture through voxel-wise mathematical modeling of multiple magnetic resonance imaging (MRI acquisitions, each differently sensitized to water diffusion. DTI computations are fundamentally estimation processes and are sensitive to noise and artifacts. Despite widespread adoption in the neuroimaging community, maintaining consistent DTI data quality remains challenging given the propensity for patient motion, artifacts associated with fast imaging techniques, and the possibility of hardware changes/failures. Furthermore, the quantity of data acquired per voxel, the non-linear estimation process, and numerous potential use cases complicate traditional visual data inspection approaches. Currently, quality inspection of DTI data has relied on visual inspection and individual processing in DTI analysis software programs (e.g. DTIPrep, DTI-studio. However, recent advances in applied statistical methods have yielded several different metrics to assess noise level, artifact propensity, quality of tensor fit, variance of estimated measures, and bias in estimated measures. To date, these metrics have been largely studied in isolation. Herein, we select complementary metrics for integration into an automatic DTI analysis and quality assurance pipeline. The pipeline completes in 24 hours, stores statistical outputs, and produces a graphical summary quality analysis (QA report. We assess the utility of this streamlined approach for empirical quality assessment on 608 DTI datasets from pediatric neuroimaging studies. The efficiency and accuracy of quality analysis using the proposed pipeline is compared with quality analysis based on visual inspection. The unified pipeline is found to save a statistically significant amount of time (over 70% while improving the consistency of QA between a DTI expert and a pool of research associates. Projection of QA
Simultaneous analysis and quality assurance for diffusion tensor imaging.
Lauzon, Carolyn B; Asman, Andrew J; Esparza, Michael L; Burns, Scott S; Fan, Qiuyun; Gao, Yurui; Anderson, Adam W; Davis, Nicole; Cutting, Laurie E; Landman, Bennett A
2013-01-01
Diffusion tensor imaging (DTI) enables non-invasive, cyto-architectural mapping of in vivo tissue microarchitecture through voxel-wise mathematical modeling of multiple magnetic resonance imaging (MRI) acquisitions, each differently sensitized to water diffusion. DTI computations are fundamentally estimation processes and are sensitive to noise and artifacts. Despite widespread adoption in the neuroimaging community, maintaining consistent DTI data quality remains challenging given the propensity for patient motion, artifacts associated with fast imaging techniques, and the possibility of hardware changes/failures. Furthermore, the quantity of data acquired per voxel, the non-linear estimation process, and numerous potential use cases complicate traditional visual data inspection approaches. Currently, quality inspection of DTI data has relied on visual inspection and individual processing in DTI analysis software programs (e.g. DTIPrep, DTI-studio). However, recent advances in applied statistical methods have yielded several different metrics to assess noise level, artifact propensity, quality of tensor fit, variance of estimated measures, and bias in estimated measures. To date, these metrics have been largely studied in isolation. Herein, we select complementary metrics for integration into an automatic DTI analysis and quality assurance pipeline. The pipeline completes in 24 hours, stores statistical outputs, and produces a graphical summary quality analysis (QA) report. We assess the utility of this streamlined approach for empirical quality assessment on 608 DTI datasets from pediatric neuroimaging studies. The efficiency and accuracy of quality analysis using the proposed pipeline is compared with quality analysis based on visual inspection. The unified pipeline is found to save a statistically significant amount of time (over 70%) while improving the consistency of QA between a DTI expert and a pool of research associates. Projection of QA metrics to a low
Tensor Algebra and Tensor Analysis for Engineers With Applications to Continuum Mechanics
Itskov, Mikhail
2013-01-01
There is a large gap between the engineering course in tensor algebra on the one hand and the treatment of linear transformations within classical linear algebra on the other hand. The aim of this modern textbook is to bridge this gap by means of the consequent and fundamental exposition. The book primarily addresses engineering students with some initial knowledge of matrix algebra. Thereby the mathematical formalism is applied as far as it is absolutely necessary. Numerous exercises are provided in the book and are accompanied by solutions, enabling self-study. The last chapters of the book deal with modern developments in the theory of isotropic and anisotropic tensor functions and their applications to continuum mechanics and are therefore of high interest for PhD-students and scientists working in this area. This third edition is completed by a number of additional figures, examples and exercises. The text and formulae have been revised and improved where necessary.
Diffusion tensor analysis of corpus callosum in progressive supranuclear palsy
Energy Technology Data Exchange (ETDEWEB)
Ito, Shoichi; Makino, Takahiro; Shirai, Wakako; Hattori, Takamichi [Department of Neurology, Graduate School of Medicine, Chiba University (Japan)
2008-11-15
Progressive supranuclear palsy (PSP) is a neurodegenerative disease featuring parkinsonism, supranuclear ophthalmoplegia, dysphagia, and frontal lobe dysfunction. The corpus callosum which consists of many commissure fibers probably reflects cerebral cortical function. Several previous reports showed atrophy or diffusion abnormalities of anterior corpus callosum in PSP patients, but partitioning method used in these studies was based on data obtained in nonhuman primates. In this study, we performed a diffusion tensor analysis using a new partitioning method for the human corpus callosum. Seven consecutive patients with PSP were compared with 29 age-matched patients with Parkinson's Disease (PD) and 19 age-matched healthy control subjects. All subjects underwent diffusion tensor magnetic resonance imaging, and the corpus callosum was partitioned into five areas on the mid-sagittal plane according to a recently established topography of human corpus callosum (CC1-prefrontal area, CC2-premotor and supplementary motor area, CC3-motor area, CC4-sensory area, CC5-parietal, temporal, and occipital area). Fractional anisotropy (FA) and apparent diffusion coefficient (ADC) were measured in each area and differences between groups were analyzed. In the PSP group, FA values were significantly decreased in CC1 and CC2, and ADC values were significantly increased in CC1 and CC2. Receiver operating characteristic analysis showed excellent reliability of FA and ADC analyses of CC1 for differentiating PSP from PD. The anterior corpus callosum corresponding to the prefrontal, premotor, and supplementary motor cortices is affected in PSP patients. This analysis can be an additional test for further confirmation of the diagnosis of PSP.
Polarizable vacuum analysis of the gravitational metric tensor
Ye, Xing-Hao
2009-01-01
The gravitational metric tensor implies a variable dielectric tensor of vacuum around gravitational matter. The curved spacetime in general relativity is then associated with a polarizable vacuum. It is found that the number density of the virtual dipoles in vacuum decreases with the distance from the gravitational centre. This result offers a polarizable vacuum interpretation of the gravitational force. Also, the anisotropy of vacuum polarization is briefly discussed, which appeals for obser...
TensorLy: Tensor Learning in Python
Kossaifi, Jean; Panagakis, Yannis; Pantic, Maja
2016-01-01
Tensor methods are gaining increasing traction in machine learning. However, there are scant to no resources available to perform tensor learning and decomposition in Python. To answer this need we developed TensorLy. TensorLy is a state of the art general purpose library for tensor learning.
DEFF Research Database (Denmark)
Escudero, Javier; Evrim, Acar Ataman; Fernández, Alberto
2015-01-01
Tensor factorisations have proven useful to model amplitude and spectral information of brain recordings. Here, we assess the usefulness of tensor factorisations in the multiway analysis of other brain signal features in the context of complexity measures recently proposed to inspect multiscale......'s disease and 26 control subjects. Instead of traditional simple visual examinations, we organise the entropy profiles as a three-way tensor to inspect relationships across temporal and spatial scales and subjects with multiway data analysis techniques based on PARAFAC and PARAFAC2 factorisations. A PARAFAC...
Site symmetry and crystal symmetry: a spherical tensor analysis
Energy Technology Data Exchange (ETDEWEB)
Brouder, Christian; Juhin, Amelie; Bordage, Amelie; Arrio, Marie-Anne [Institut de Mineralogie et de Physique des Milieux Condenses, CNRS UMR 7590, Universites Paris 6 et 7, IPGP, 140 rue de Lourmel, 75015 Paris (France)], E-mail: christian.brouder@impmc.jussieu.fr
2008-11-12
The relation between the properties of a specific crystallographic site and the properties of the full crystal is discussed by using spherical tensors. The concept of spherical tensors is introduced and the way it transforms under the symmetry operations of the site and from site to site is described in detail. The law of spherical tensor coupling is given and illustrated with the example of the electric dipole and quadrupole transitions in x-ray absorption spectroscopy. The main application of the formalism is the reduction of computation time in the calculation of the properties of crystals by band-structure methods. The general approach is illustrated by the examples of substitutional chromium in spinel and substitutional vanadium in garnet.
Tensor renormalization group analysis of CP(N-1) model
Kawauchi, Hikaru
2016-01-01
We apply the higher order tensor renormalization group to lattice CP($N-1$) model in two dimensions. A tensor network representation of the CP($N-1$) model in the presence of the $\\theta$-term is derived. We confirm that the numerical results of the CP(1) model without the $\\theta$-term using this method are consistent with that of the O(3) model which is analyzed by the same method in the region $\\beta \\gg 1$ and that obtained by Monte Carlo simulation in a wider range of $\\beta$. The numerical computation including the $\\theta$-term is left for future challenges.
Uncertainty analysis and visualization of diffusion tensor images
Jiao, Fangxiang
Diffusion magnetic resonance imaging (dMRI) has become a popular technique to detect brain white matter structure. However, imaging noise, imaging artifacts, and modeling techniques, etc., create many uncertainties, which may generate misleading information for further analysis or applications, such as surgical planning. Therefore, how to analyze, effectively visualize, and reduce these uncertainties become very important research questions. In this dissertation, we present both rank-k decomposition and direct decomposition approaches based on spherical deconvolution to decompose the fiber directions more accurately for high angular resolution diffusion imaging (HARDI) data, which will reduce the uncertainties of the fiber directions. By applying volume rendering techniques to an ensemble of 3D orientation distribution function (ODF) glyphs, which we call SIP functions of diffusion shapes, one can elucidate the complex heteroscedastic structural variation in these local diffusion shapes. Furthermore, we quantify the extent of this variation by measuring the fraction of the volume of these shapes, which is consistent across all noise levels, the certain volume ratio . To better understand the uncertainties in white matter fiber tracks, we propose three metrics to quantify the differences between the results of diffusion tensor magnetic resonance imaging (DT-MRI) fiber tracking algorithms: the area between corresponding fibers of each bundle, the Earth Mover's Distance (EMD) between two fiber bundle volumes, and the current distance between two fiber bundle volumes. Based on these metrics, we discuss an interactive fiber track comparison visualization toolkit we have developed to visualize these uncertainties more efficiently. Physical phantoms, with high repeatability and reproducibility, are also designed with the hope of validating the dMRI techniques. In summary, this dissertation provides a better understanding about uncertainties in diffusion magnetic resonance
Kinetics of Fluid Demixing in Complex Plasmas: Domain Growth Analysis using Minkowski Tensors
Böbel, Alexander
2016-01-01
A molecular dynamics simulation of the demixing process of a binary complex plasma is analysed and the role of distinct interaction potentials is discussed by using morphological Minkowski tensor analysis of the minority phase domain growth in a demixing simulated binary complex plasma. These Minkowski tensor methods are compared with previous results that utilized a power spectrum method based on the time-dependent average structure factor. It is shown that the Minkowski tensor methods are superior to the previously used power spectrum method in the sense of higher sensitivity to changes in domain size. By analysis of the slope of the temporal evolution of Minkowski tensor measures qualitative differences between the case of particle interaction with a single length scale compared to particle interactions with two different length scales (dominating long range interaction) are revealed. After proper scaling the graphs for the two length scale scenario coincide, pointing towards universal behaviour. The quali...
Hess, Siegfried
2015-01-01
This book presents the science of tensors in a didactic way. The various types and ranks of tensors and the physical basis is presented. Cartesian Tensors are needed for the description of directional phenomena in many branches of physics and for the characterization the anisotropy of material properties. The first sections of the book provide an introduction to the vector and tensor algebra and analysis, with applications to physics, at undergraduate level. Second rank tensors, in particular their symmetries, are discussed in detail. Differentiation and integration of fields, including generalizations of the Stokes law and the Gauss theorem, are treated. The physics relevant for the applications in mechanics, quantum mechanics, electrodynamics and hydrodynamics is presented. The second part of the book is devoted to tensors of any rank, at graduate level. Special topics are irreducible, i.e. symmetric traceless tensors, isotropic tensors, multipole potential tensors, spin tensors, integration and spin-...
Tensor analysis methods for activity characterization in spatiotemporal data
Energy Technology Data Exchange (ETDEWEB)
Haass, Michael Joseph; Van Benthem, Mark Hilary; Ochoa, Edward M
2014-03-01
Tensor (multiway array) factorization and decomposition offers unique advantages for activity characterization in spatio-temporal datasets because these methods are compatible with sparse matrices and maintain multiway structure that is otherwise lost in collapsing for regular matrix factorization. This report describes our research as part of the PANTHER LDRD Grand Challenge to develop a foundational basis of mathematical techniques and visualizations that enable unsophisticated users (e.g. users who are not steeped in the mathematical details of matrix algebra and mulitway computations) to discover hidden patterns in large spatiotemporal data sets.
Klatt, Michael A; Schröder-Turk, Gerd E; Mecke, Klaus
2017-07-01
Structure-property relations, which relate the shape of the microstructure to physical properties such as transport or mechanical properties, need sensitive measures of structure. What are suitable fabric tensors to quantify the shape of anisotropic heterogeneous materials? The mean intercept length is among the most commonly used characteristics of anisotropy in porous media, e.g., of trabecular bone in medical physics. Yet, in this series of two papers we demonstrate that it has conceptual shortcomings that limit the validity of its results. We test the validity of general assumptions regarding the properties of the mean-intercept length tensor using analytical formulas for the mean-intercept lengths in anisotropic Boolean models (derived in part I of this series), augmented by numerical simulations. We discuss in detail the functional form of the mean intercept length as a function of the test line orientations. As the most prominent result, we find that, at least for the example of overlapping grains modeling porous media, the polar plot of the mean intercept length is in general not an ellipse and hence not represented by a second-rank tensor. This is in stark contrast to the common understanding that for a large collection of grains the mean intercept length figure averages to an ellipse. The standard mean intercept length tensor defined by a least-square fit of an ellipse is based on a model mismatch, which causes an intrinsic lack of accuracy. Our analysis reveals several shortcomings of the mean intercept length tensor analysis that pose conceptual problems and limitations on the information content of this commonly used analysis method. We suggest the Minkowski tensors from integral geometry as alternative sensitive measures of anisotropy. The Minkowski tensors allow for a robust, comprehensive, and systematic approach to quantify various aspects of structural anisotropy. We show the Minkowski tensors to be more sensitive, in the sense, that they can
Multi-template tensor-based morphometry: application to analysis of Alzheimer's disease
DEFF Research Database (Denmark)
Koikkalainen, Juha; Lötjönen, Jyrki; Thurfjell, Lennart
2011-01-01
In this paper methods for using multiple templates in tensor-based morphometry (TBM) are presented and compared to the conventional single-template approach. TBM analysis requires non-rigid registrations which are often subject to registration errors. When using multiple templates and, therefore,...
Generalized Tensor Analysis Model for Multi-Subcarrier Analog Optical Systems
DEFF Research Database (Denmark)
Zhao, Ying; Yu, Xianbin; Zheng, Xiaoping
2011-01-01
We propose and develop a general tensor analysis framework for a subcarrier multiplex analog optical fiber link for applications in microwave photonics. The goal of this work is to construct an uniform method to address nonlinear distortions of a discrete frequency transmission system. We employ...
Erdtman, Elias; Jönsson, Carl
2012-01-01
This master's thesis addresses numerical methods of computing the typical ranks of tensors over the real numbers and explores some properties of tensors over finite fields. We present three numerical methods to compute typical tensor rank. Two of these have already been published and can be used to calculate the lowest typical ranks of tensors and an approximate percentage of how many tensors have the lowest typical ranks (for some tensor formats), respectively. The third method was developed...
Energy Technology Data Exchange (ETDEWEB)
Sato, Kanako; Masutani, Yoshitaka; Watadani, Takeyuki; Nakata, Yasuhiro; Yoshida, Mariko; Abe, Osamu; Ohtomo, Kuni [University of Tokyo, Department of Radiology, Graduate School of Medicine, Bunkyo, Tokyo (Japan); Aoki, Shigeki [Juntendo University, Department of Radiology, Bunkyo, Tokyo (Japan); Iwata, Nobue K.; Terao, Yasuo; Tsuji, Shoji [University of Tokyo, Department of Neurology, Graduate School of Medicine, Bunkyo, Tokyo (Japan)
2010-08-15
The uncinate fasciculus (UF) consists of core fibers connecting the frontal and temporal lobes and is considered to be related to cognitive/behavioral function. Using diffusion tensor tractography, we quantitatively evaluated changes in fractional anisotropy (FA) and the apparent diffusion coefficient (ADC) of the UF by tract-specific analysis to evaluate the damage of the UF in patients with amyotrophic lateral sclerosis (ALS). We obtained diffusion tensor images of 15 patients with ALS and 9 age-matched volunteers. Patients with ALS showed significantly lower mean FA (P = 0.029) compared with controls. No significant difference was seen in mean ADC. The results suggest that damage of the UF in patients with ALS can be quantitatively evaluated with FA. (orig.)
Vector-Tensor and Vector-Vector Decay Amplitude Analysis of B0->phi K*0
Aubert, B; Abrams, G S; Adye, T; Ahmed, S; Alam, M S; Albert, J; Aleksan, R; Allen, M T; Allison, J; Altenburg, D D; Andreotti, M; Angelini, C; Anulli, F; Arnaud, N; Asgeirsson, D J; Aston, D; Azzolini, V; Baak, M A; Back, J J; Baldini-Ferroli, R; Band, H R; Banerjee, Sw; Bard, D J; Barlow, N R; Barlow, R J; Barrett, M; Bartoldus, R; Batignani, G; Battaglia, M; Bauer, J M; Bechtle, P; Beck, T W; Behera, P K; Bellini, F; Benayoun, M; Benelli, G; Berger, N; Bernard, D; Berryhill, J W; Best, D S; Bettarini, S; Bettoni, D; Bevan, A J; Bhimji, W; Bhuyan, B; Bianchi, F; Biasini, M; Biesiada, J; Blanc, F; Blaylock, G; Blinov, V E; Bloom, P C; Blount, N L; Bomben, M; Bondioli, M; Bonneaud, G R; Bosisio, L; Boutigny, D; Bowerman, D A; Boyd, J T; Bozzi, C; Brandenburg, G; Brandt, T; Brau, J E; Briand, H; Brown, C M; Brown, D N; Bruinsma, M; Brunet, S; Bucci, F; Buchanan, C; Bugg, W; Bukin, A D; Bula, R; Burchat, P R; Burke, J P; Button-Shafer, J; Buzzo, A; Bóna, M; Cahn, R N; Calabrese, R; Calcaterra, A; Calderini, G; Campagnari, C; Carpinelli, M; Cartaro, C; Cavallo, N; Cavoto, G; Cenci, R; Chai, X; Chaisanguanthum, K S; Chao, M; Charles, E; Charles, M J; Chauveau, J; Chavez, C A; Chen, A; Chen, C; Chen, E; Chen, J C; Chen, S; Chen, X; Chen, X R; Cheng, B; Cheng, C H; Chia, Y M; Cibinetto, G; Clark, P J; Clarke, C K; Claus, R; Cochran, J; Coleman, J P; Contri, R; Convery, M R; Corwin, L A; Cossutti, F; Cottingham, W N; Couderc, F; Covarelli, R; Cowan, G; Cowan, R; Crawley, H B; Cremaldi, L; Cunha, A; Curry, S; Côté, D; D'Orazio, A; Dahmes, B; Dallapiccola, C; Danielson, N; Dasu, S; Datta, M; Dauncey, P D; David, P; Davier, M; Davis, C L; De Nardo, Gallieno; De Sangro, R; Del Amo-Sánchez, P; Del Buono, L; Del Re, D; Della Ricca, G; Denig, A G; Di Lodovico, F; Di Marco, E; Dingfelder, J C; Dittongo, S; Dong, L; Dorfan, J; Druzhinin, V P; Dubitzky, R S; Dubois-Felsmann, G P; Dujmic, D; Dunwoodie, W M; Dvoretskii, A; Ebert, M; Eckhart, E A; Eckmann, R; Edgar, C L; Edwards, A J; Egede, U; Eigen, G; Eisner, A M; Elmer, P; Emery, S; Ernst, J A; Eschenburg, V; Eschrich, I; Eyges, V; Fabozzi, F; Faccini, R; Fang, F; Feltresi, E; Ferrarotto, F; Ferroni, F; Field, R C; Finocchiaro, G; Flacco, C J; Flack, R L; Flächer, H U; Flood, K T; Ford, K E; Ford, W T; Forster, I J; Forti, F; Fortin, D; Foulkes, S D; Franek, B; Frey, R; Fritsch, M; Fry, J R; Fulsom, B G; Gabathuler, E; Gaidot, A; Gallo, F; Gamba, D; Gamet, R; Gan, K K; Ganzhur, S F; Gao, Y; Gary, J W; Gaspero, M; Gatto, C; Gaz, A; George, K A; Gill, M S; Giorgi, M A; Gladney, L; Glanzman, T; Godang, R; Golubev, V B; Gowdy, S J; Gradl, W; Graham, M T; Graugès-Pous, E; Grenier, P; Gritsan, A V; Grosdidier, G; Groysman, Y; Guo, Z J; Hadavand, H K; Haire, M; Halyo, V; Hamano, K; Hamel de Monchenault, G; Hamon, O; Harrison, P F; Harrison, T J; Hart, A J; Hartfiel, B L; Hast, C; Hauke, A; Hawkes, C M; Hearty, C; Held, T; Hertzbach, S S; Heusch, C A; Hill, E J; Hirschauer, J F; Hitlin, D G; Hollar, J J; Hong, T M; Honscheid, K; Hopkins, D A; Hrynóva, T; Hufnagel, D; Hulsbergen, W D; Hutchcroft, D E; Höcker, A; Igonkina, O; Innes, W R; Izen, J M; Jackson, P D; Jackson, P S; Jacobsen, R G; Jain, V; Jasper, H; Jawahery, A; Jessop, C P; Judd, D; Kadyk, J A; Kagan, H; Karyotakis, Yu; Kass, R; Kelsey, M H; Kerth, L T; Khan, A; Kim, H; Kim, P; Kirkby, D; Klose, V; Knecht, N S; Koch, H; Kolb, J A; Kolomensky, Yu G; Kovalskyi, D; Kowalewski, R V; Kozanecki, Witold; Kreisel, A; Krishnamurthy, M; Kroeger, R; Kroseberg, J; Kukartsev, G; Kutter, P E; Kyberd, P; La Vaissière, C de; Lacker, H M; Lae, C K; Lafferty, G D; Lanceri, L; Lange, D J; Lankford, A J; Latham, T E; Latour, E; Lau, Y P; Lazzaro, A; Le Diberder, F R; Lee, C L; Lees, J P; Legendre, M; Leith, D W G S; Lepeltier, V; Leruste, P; Lewandowski, B; Li Gioi, L; Li, S; Li, X; Lista, L; Liu, H; Lo Vetere, M; LoSecco, J M; Lockman, W S; Lombardo, V; Long, O; Lopes-Pegna, D; Lopez-March, N; Lou, X C; Lu, M; Luitz, S; Lund, P; Luppi, E; Lusiani, A; Lutz, A M; Lynch, G; Lynch, H L; Lü, C; Lüth, V; MacFarlane, D B; Macri, M M; Mader, W F; Majewski, S A; Malcles, J; Mallik, U; Mancinelli, G; Mandelkern, M A; Marchiori, G; Margoni, M; Marks, J; Marsiske, H; Martínez-Vidal, F; Mattison, T S; Mazur, M A; Mazzoni, M A; McKenna, J A; McMahon, T R; Mclachlin, S E; Meadows, B T; Mellado, B; Menges, W; Merkel, J; Messner, R; Meyer, N T; Meyer, W T; Mihályi, A; Mir, L M; Mishra, K; Mohanty, G B; Monge, M R; Monorchio, D; Moore, T B; Morandin, M; Morganti, M; Morganti, S; Morii, M; Muheim, F; Müller, D R; Nagel, M; Naisbit, M T; Narsky, I; Nash, J A; Nauenberg, U; Neal, H; Negrini, M; Neri, N; Nesom, G; Nicholson, H; Nikolich, M B; Nogowski, R; Nugent, I M; O'Grady, C P; Ocariz, J; Ofte, I; Olaiya, E O; Olivas, A; Olsen, J; Onuchin, A P; Orimoto, T J; Oyanguren, A; Ozcan, V E; Paar, H P; Pacetti, S; Palano, A; Palombo, F; Pan, B; Pan, Y; Panduro, W; Paoloni, E; Paolucci, P; Pappagallo, M; Park, W; Passaggio, S; Patel, P M; Patrignani, C; Patteri, P; Payne, D J; Pelizaeus, M; Perazzo, A; Perl, M; Peruzzi, I M; Peters, K; Petersen, B A; Petrella, A; Petzold, A; Piatenko, T; Piccolo, D; Piccolo, M; Piemontese, L; Pierini, M; Piredda, G; Playfer, S; Poireau, V; Polci, F; Pompili, A; Porter, F C; Posocco, M; Potter, C T; Prell, S; Prencipe, E; Prepost, R; Pripstein, M; Pruvot, S; Pulliam, T; Purohit, M V; Qi, N D; Rahatlou, S; Rahimi, A M; Rahmat, R; Rama, M; Ratcliff, B N; Raven, G; Regensburger, J J; Ricciardi, S; Richman, J D; Ritchie, J L; Rizzo, G; Roberts, D A; Robertson, A I; Robertson, S H; Robutti, E; Rodier, S; Roe, N A; Ronan, M T; Roney, J M; Rong, G; Roodman, A; Roos, L; Rosenberg, E I; Rotondo, M; Roudeau, P; Rubin, A E; Ruddick, W O; Röthel, W; Sacco, R; Saeed, M A; Safai-Tehrani, F; Saleem, M; Salnikov, A A; Salvatore, F; Sanders, D A; Santroni, A; Saremi, S; Satpathy, A; Schalk, T; Schenk, S; Schilling, C J; Schindler, R H; Schofield, K C; Schott, G; Schröder, T; Schröder, H; Schubert, J; Schubert, K R; Schumm, B A; Schune, M H; Schwiening, J; Schwierz, R; Schwitters, R F; Sciacca, C; Sciolla, G; Seiden, A; Sekula, S J; Serednyakov, S I; Serrano, J; Sharma, V; Shen, B C; Sherwood, D J; Simard, M; Simi, G; Simonetto, F; Sinev, N B; Skovpen, Yu I; Smith, A J S; Smith, J G; Snoek, H L; Snyder, A; Sobie, R J; Soffer, A; Sokoloff, M D; Solodov, E P; Spaan, B; Spanier, S M; Spitznagel, M; Spradlin, P; Steinke, M; Stelzer, J; Stocchi, A; Stoker, D P; Stroili, R; Strom, D; Strube, J; Stugu, B; Stängle, H; Su, D; Sullivan, M K; Summers, D J; Sundermann, J E; Suzuki, K; Swain, S K; Taras, P; Taylor, F; Telnov, A V; Teodorescu, L; Ter-Antonian, R; Therin, G; Thiebaux, C; Thompson, J M; Tisserand, V; Todyshev, Y K; Toki, W H; Torrence, E; Tosi, S; Touramanis, C; Ulmer, K A; Uwer, U; Van Bakel, N; Vasseur, G; Vavra, J; Vazquez, A; Verderi, M; Viaud, F B; Vitale, L; Voci, C; Voena, C; Volk, A; Wagner, A P; Wagner, S R; Wagoner, D E; Waldi, R; Walker, D; Walsh, J J; Wang, K; Wang, P; Wang, W F; Wappler, F R; Watson, A T; Weaver, M; Weinstein, A J R; Wenzel, W A; Wilden, L; Williams, D C; Williams, J C; Wilson, F F; Wilson, J R; Wilson, M G; Wilson, R J; Winklmeier, F; Wisniewski, W J; Wittgen, M; Wong, Q K; Wormser, G; Wren, A C; Wright, D H; Wright, D M; Wu, J; Wu, S L; Wulsin, H W; Xie, Y; Yamamoto, R K; Yarritu, A K; Ye, S; Yi, J I; Yi, K; Young, C C; Yu, Z; Yéche, C; Zain, S B; Zallo, A; Zeng, Q; Zghiche, A; Zhang, J; Zhang, L; Zhao, H W; Zhu, Y S; Ziegler, V; Zito, M; Çuhadar-Dönszelmann, T; al, et
2007-01-01
We perform an amplitude analysis of the decays B0->phi K^*_2(1430)0, phi K^*(892)0, and phi(K pi)^0_S-wave with a sample of about 384 million BBbar pairs recorded with the BABAR detector. The fractions of longitudinal polarization f_L of the vector-tensor and vector-vector decay modes are measured to be 0.853 +0.061-0.069 +-0.036 and 0.506 +-0.040 +-0.015, respectively. Overall, twelve parameters are measured for the vector-vector decay and seven parameters for the vector-tensor decay, including the branching fractions and parameters sensitive to CP-violation.
Cartesian tensors an introduction
Temple, G
2004-01-01
This undergraduate text provides an introduction to the theory of Cartesian tensors, defining tensors as multilinear functions of direction, and simplifying many theorems in a manner that lends unity to the subject. The author notes the importance of the analysis of the structure of tensors in terms of spectral sets of projection operators as part of the very substance of quantum theory. He therefore provides an elementary discussion of the subject, in addition to a view of isotropic tensors and spinor analysis within the confines of Euclidean space. The text concludes with an examination of t
Zuo, Boxin; Wang, Lizhe; Chen, Weitao
2017-01-01
The detection of dipole-like sources, such as unexploded ordnances (UXO) and other metallic objects, based on a magnetic gradiometer system, has been increasingly applied in recent years. In this paper, a novel dipole-like source detection algorithm, based on eigenvector analysis with magnetic gradient tensor data interpretation is presented. Firstly, the theoretical basis of the eigenvector decomposition of magnetic gradient tensor is analyzed. Then, a detection algorithm is proposed by usin...
Noel, Jean; Prieto, Juan C.; Styner, Martin
2017-03-01
Functional Analysis of Diffusion Tensor Tract Statistics (FADTTS) is a toolbox for analysis of white matter (WM) fiber tracts. It allows associating diffusion properties along major WM bundles with a set of covariates of interest, such as age, diagnostic status and gender, and the structure of the variability of these WM tract properties. However, to use this toolbox, a user must have an intermediate knowledge in scripting languages (MATLAB). FADTTSter was created to overcome this issue and make the statistical analysis accessible to any non-technical researcher. FADTTSter is actively being used by researchers at the University of North Carolina. FADTTSter guides non-technical users through a series of steps including quality control of subjects and fibers in order to setup the necessary parameters to run FADTTS. Additionally, FADTTSter implements interactive charts for FADTTS' outputs. This interactive chart enhances the researcher experience and facilitates the analysis of the results. FADTTSter's motivation is to improve usability and provide a new analysis tool to the community that complements FADTTS. Ultimately, by enabling FADTTS to a broader audience, FADTTSter seeks to accelerate hypothesis testing in neuroimaging studies involving heterogeneous clinical data and diffusion tensor imaging. This work is submitted to the Biomedical Applications in Molecular, Structural, and Functional Imaging conference. The source code of this application is available in NITRC.
Vo, An; Eidelberg, David; Uluǧ, Aziz M
2013-01-01
To determine brain tissue affected by dystonia by making group comparison of parameter-based diffusion tensor imaging (DTI) distributions of patients with control subjects. A 2D distribution analysis of mean diffusivity and fractional anisotropy index was used for modeling brain tissues according to the inherent diffusion characteristics. Seven affected carriers of the DYT1 dystonia mutation and eight healthy control subjects were imaged for a previous study. We employed a 2D distribution analysis of all the diffusion voxels and a four compartmental brain model for group comparison of the dystonia subjects and controls. Our analysis showed disease involvement in the white matter of the patients. Excellent tissue characterization was achieved automatically using the 2D distribution analysis based on a physical brain model. This 2D analysis implicated white matter in dystonia and could be useful as a screening tool in diseases with unknown pathologies. Copyright © 2012 Wiley Periodicals, Inc.
Global QCD Analysis of the Nucleon Tensor Charge with Lattice QCD Constraints
Shows, Harvey, III; Melnitchouk, Wally; Sato, Nobuo
2017-09-01
By studying the parton distribution functions (PDFs) of a nucleon, we probe the partonic scale of nature, exploring what it means to be a nucleon. In this study, we are interested in the transversity PDF-the least studied of the three collinear PDFs. By conducting a global analysis on experimental data from semi-inclusive deep inelastic scattering (SIDIS), as well as single-inclusive e+e- annihilation (SIA), we extract the fit parameters needed to describe the transverse moment dependent (TMD) transversity PDF, as well as the Collins fragmentation function. Once the collinear transversity PDF is obtained by integrating the extracted TMD PDF, we wish to resolve discrepancies between lattice QCD calculations and phenomenological extractions of the tensor charge from data. Here we show our results for the transversity distribution and tensor charge. Using our method of iterative Monte Carlo, we now have a more robust understanding of the transversity PDF. With these results we are able to progress in our understanding of TMD PDFs, as well as testify to the efficacy of current lattice QCD calculations. This work is made possible through support from NSF award 1659177 to Old Dominion University.
Roldan-Valadez, Ernesto; Rios, Camilo; Cortez-Conradis, David; Favila, Rafael; Moreno-Jimenez, Sergio
2014-01-01
Background Histological behavior of glioblastoma multiforme suggests it would benefit more from a global rather than regional evaluation. A global (whole-brain) calculation of diffusion tensor imaging (DTI) derived tensor metrics offers a valid method to detect the integrity of white matter structures without missing infiltrated brain areas not seen in conventional sequences. In this study we calculated a predictive model of brain infiltration in patients with glioblastoma using global tensor metrics. Methods Retrospective, case and control study; 11 global DTI-derived tensor metrics were calculated in 27 patients with glioblastoma multiforme and 34 controls: mean diffusivity, fractional anisotropy, pure isotropic diffusion, pure anisotropic diffusion, the total magnitude of the diffusion tensor, linear tensor, planar tensor, spherical tensor, relative anisotropy, axial diffusivity and radial diffusivity. The multivariate discriminant analysis of these variables (including age) with a diagnostic test evaluation was performed. Results The simultaneous analysis of 732 measures from 12 continuous variables in 61 subjects revealed one discriminant model that significantly differentiated normal brains and brains with glioblastoma: Wilks’ λ = 0.324, χ2 (3) = 38.907, p < .001. The overall predictive accuracy was 92.7%. Conclusions We present a phase II study introducing a novel global approach using DTI-derived biomarkers of brain impairment. The final predictive model selected only three metrics: axial diffusivity, spherical tensor and linear tensor. These metrics might be clinically applied for diagnosis, follow-up, and the study of other neurological diseases. PMID:24991202
Quantitative and visual analysis of white matter integrity using diffusion tensor imaging
Liang, Xuwei; Zhuang, Qi; Cao, Ning; Zhang, Jun
2009-02-01
A new fiber tract-oriented quantitative and visual analysis scheme using diffusion tensor imaging (DTI) is developed to study the regional micro structural white matter changes along major fiber bundles which may not be effectively revealed by existing methods due to the curved spatial nature of neuronal paths. Our technique is based on DTI tractography and geodesic path mapping, which establishes correspondences to allow cross-subject evaluation of diffusion properties by parameterizing the fiber pathways as a function of geodesic distance. A novel isonodes visualization scheme is proposed to render regional statistical features along the fiber pathways. Assessment of the technique reveals specific anatomical locations along the genu of the corpus callosum paths with significant diffusion property changes in the amnestic mild cognitive impairment subjects. The experimental results show that this approach is promising and may provide a sensitive technique to study the integrity of neuronal connectivity in human brain.
The dynamics of the 2001 Etna eruption as seen by full moment tensor analysis
Saraò, A.; Cocina, O.; Privitera, E.; Panza, G. F.
2010-05-01
The Mt. Etna eruption of July 2001 was announced by severe seismic activity and by the opening of a 7-km-long zone of densely distributed fractures. The large amount of data collected gave a unique opportunity to study the magma migration process and to infer the position and geometry of the uprising dyke. Results from multidisciplinary approaches suggest that the observed phenomenology was the result of the rapid intrusion of a vertical dyke, oriented roughly N-S and located a few km south of the summit region. To add new constraints to the dynamics of the eruption process, in this study we determine the full seismic moment tensors of 61 earthquakes, selected among those occurring between July 12 and July 18 (Md >= 2.2), located in a depth ranging from 1 km above sea level (a.s.l.) to 3 km below sea level (b.s.l.). At the beginning of the seismic swarm, the dominant component of the seismic source tensor is double-couple percentage (around 65 per cent on average) statistical significant at 95 per cent confidence level and in the following hours the non-double-couple components increase at the expenses of the double-couple. Such observations are related well with the system of fractures formed just before the eruption, whereas the increasing non-double-couple components can be explained as the response of the confining rocks to the rising magma and degassing processes. The type of focal mechanisms retrieved are predominantly of normal fault type (44 per cent), strike slip (30 per cent) and thrust mechanisms (9 per cent), and outline a scenario that concurs with the stress regime induced by a dyke injection. The space-time analysis of seismic source locations and source moment tensors (1) confirms the evidence of a vertical dyke emplacement that fed the 2001 lateral eruption and (2) adds new insights to support the hypothesis of the injection of a second aborted dyke, 2 km SE from the fractures zone.
Kolecki, Joseph C.
2005-01-01
Tensor analysis is one of the more abstruse, even if one of the more useful, higher math subjects enjoined by students of physics and engineering. It is abstruse because of the intellectual gap that exists between where most physics and engineering mathematics leave off and where tensor analysis traditionally begins. It is useful because of its great generality, computational power, and compact, easy to use, notation. This paper bridges the intellectual gap. It is divided into three parts: algebra, calculus, and relativity. Algebra: In tensor analysis, coordinate independent quantities are sought for applications in physics and engineering. Coordinate independence means that the quantities have such coordinate transformations as to leave them invariant relative to a particular observer s coordinate system. Calculus: Non-zero base vector derivatives contribute terms to dynamical equations that correspond to pseudoaccelerations in accelerated coordinate systems and to curvature or gravity in relativity. These derivatives have a specific general form in tensor analysis. Relativity: Spacetime has an intrinsic geometry. Light is the tool for investigating that geometry. Since the observed geometry of spacetime cannot be made to match the classical geometry of Euclid, Einstein applied another more general geometry differential geometry. The merger of differential geometry and cosmology was accomplished in the theory of relativity. In relativity, gravity is equivalent to curvature.
Kim, Jee-Eun; Oh, Jungsu S; Sung, Jung-Joon; Lee, Kwang-Woo; Song, In Chan; Hong, Yoon-Ho
2014-07-01
Involvement of the corpus callosum (CC) is reported to be a consistent feature of amyotrophic lateral sclerosis (ALS). We examined the CC pathology using diffusion tensor tractography analysis to identify precisely which fiber bundles are involved in ALS. Diffusion tensor imaging was performed in 14 sporadic ALS patients and 16 age-matched healthy controls. Whole brain tractography was performed using the multiple-region of interest (ROI) approach, and CC fiber bundles were extracted in two ways based on functional and structural relevance: (i) cortical ROI selection based on Brodmann areas (BAs), and (ii) the sulcal-gyral pattern of cortical gray matter using FreeSurfer software, respectively. The mean fractional anisotropy (FA) values of the CC fibers interconnecting the primary motor (BA4), supplementary motor (BA6), and dorsolateral prefrontal cortex (BA9/46) were significantly lower in ALS patients than in controls, whereas those of the primary sensory cortex (BA1, BA2, BA3), Broca's area (BA44/45), and the orbitofrontal cortex (BA11/47) did not differ significantly between the two groups. The FreeSurfer ROI approach revealed a very similar pattern of abnormalities. In addition, a significant correlation was found between the mean FA value of the CC fibers interconnecting the primary motor area and disease severity, as assessed using the revised Amyotrophic Lateral Sclerosis Functional Rating Scale, and the clinical extent of upper motor neuron signs. Our findings suggest that there is some degree of selectivity or a gradient in the CC pathology in ALS. The CC fibers interconnecting the primary motor and dorsolateral prefrontal cortices may be preferentially involved in ALS.
Domino, Krzysztof
2017-02-01
The cumulant analysis plays an important role in non Gaussian distributed data analysis. The shares' prices returns are good example of such data. The purpose of this research is to develop the cumulant based algorithm and use it to determine eigenvectors that represent investment portfolios with low variability. Such algorithm is based on the Alternating Least Square method and involves the simultaneous minimisation 2'nd- 6'th cumulants of the multidimensional random variable (percentage shares' returns of many companies). Then the algorithm was tested during the recent crash on the Warsaw Stock Exchange. To determine incoming crash and provide enter and exit signal for the investment strategy the Hurst exponent was calculated using the local DFA. It was shown that introduced algorithm is on average better that benchmark and other portfolio determination methods, but only within examination window determined by low values of the Hurst exponent. Remark that the algorithm is based on cumulant tensors up to the 6'th order calculated for a multidimensional random variable, what is the novel idea. It can be expected that the algorithm would be useful in the financial data analysis on the world wide scale as well as in the analysis of other types of non Gaussian distributed data.
The effect of template selection on diffusion tensor voxel-based analysis results.
Van Hecke, Wim; Leemans, Alexander; Sage, Caroline A; Emsell, Louise; Veraart, Jelle; Sijbers, Jan; Sunaert, Stefan; Parizel, Paul M
2011-03-15
Diffusion tensor imaging (DTI) is increasingly being used to study white matter (WM) degeneration in patients with psychiatric and neurological disorders. In order to compare diffusion measures across subjects in an automated way, voxel-based analysis (VBA) methods were introduced. In VBA, all DTI data are transformed to a template, after which the diffusion measures of control subjects and patients are compared quantitatively in each voxel. Although VBA has many advantages compared to other post-processing approaches, such as region of interest analysis or tractography, VBA results need to be interpreted cautiously, since it has been demonstrated that they depend on the different parameter settings that are applied in the VBA processing pipeline. In this paper, we examine the effect of the template selection on the VBA results of DTI data. We hypothesized that the choice of template to which all data are transformed would also affect the VBA results. To this end, simulated DTI data sets as well as DTI data from control subjects and multiple sclerosis patients were aligned to (i) a population-specific DTI template, (ii) a subject-based DTI atlas in MNI space, and (iii) the ICBM-81 DTI atlas. Our results suggest that the highest sensitivity and specificity to detect WM abnormalities in a VBA setting was achieved using the population-specific DTI atlas, presumably due to the better spatial image alignment to this template. Copyright © 2010 Elsevier Inc. All rights reserved.
Lee, Jae-Seung; Im, In-Chul; Kang, Su-Man; Goo, Eun-Hoe; Kwak, Byung-Joon
2013-07-01
This study aimed to quantitatively analyze data from diffusion tensor imaging (DTI) using statistical parametric mapping (SPM) in patients with brain disorders and to assess its potential utility for analyzing brain function. DTI was obtained by performing 3.0-T magnetic resonance imaging for patients with Alzheimer's disease (AD) and vascular dementia (VD), and the data were analyzed using Matlab-based SPM software. The two-sample t-test was used for error analysis of the location of the activated pixels. We compared regions of white matter where the fractional anisotropy (FA) values were low and the apparent diffusion coefficients (ADCs) were increased. In the AD group, the FA values were low in the right superior temporal gyrus, right inferior temporal gyrus, right sub-lobar insula, and right occipital lingual gyrus whereas the ADCs were significantly increased in the right inferior frontal gyrus and right middle frontal gyrus. In the VD group, the FA values were low in the right superior temporal gyrus, right inferior temporal gyrus, right limbic cingulate gyrus, and right sub-lobar caudate tail whereas the ADCs were significantly increased in the left lateral globus pallidus and left medial globus pallidus. In conclusion by using DTI and SPM analysis, we were able to not only determine the structural state of the regions affected by brain disorders but also quantitatively analyze and assess brain function.
Etingof, Pavel; Nikshych, Dmitri; Ostrik, Victor
2015-01-01
Is there a vector space whose dimension is the golden ratio? Of course not-the golden ratio is not an integer! But this can happen for generalizations of vector spaces-objects of a tensor category. The theory of tensor categories is a relatively new field of mathematics that generalizes the theory of group representations. It has deep connections with many other fields, including representation theory, Hopf algebras, operator algebras, low-dimensional topology (in particular, knot theory), homotopy theory, quantum mechanics and field theory, quantum computation, theory of motives, etc. This bo
Schulz, Simone; Koos, Bernd; Duske, Kathrin; Stahl, Franka
2016-11-01
The purpose of this work was to employ both cephalometric and tensor analysis in characterizing the skeletal changes experienced by patients with Angle Class II/1 malocclusion during functional orthodontic treatment with the functional regulator type II. A total of 23 patients with Class II/1 malocclusion based on lateral cephalograms obtained before and after treatment with the functional regulator type II were analyzed. Another 23 patients with Angle Class II/1 malocclusion who had not undergone treatment were included as controls. Our cephalometric data attest to significant therapeutic effects of the functional regulator type II on the skeletal mandibular system, including significant advancement of the mandible, increases in effective mandibular length with enhancement of the chin profile, and reduction of growth-related bite deepening. No treatment-related effects were observed at the cranial-base and midface levels. In addition, tensor analysis revealed significant stimulation of mandibular growth in sagittal directions, without indications of growth effects on the maxilla. Its growth-pattern findings differed from those of cephalometric analysis by indicating that the appliance did promote horizontal development, which supports the functional orthodontic treatment effect in Angle Class II/1 cases. Tensor analysis yielded additional insights into sagittal and vertical growth changes not identifiable by strictly cephalometric means. The functional regulator type II was an effective treatment modality for Angle Class II/1 malocclusion and influenced the skeletal development of these patients in favorable ways.
Directory of Open Access Journals (Sweden)
Antonio Carlos da Silva Senra Filho
2017-08-01
Full Text Available Abstract Introduction: The search for human brain templates has been progressing in the past decades and in order to understand disease patterns a need for a standard diffusion tensor imaging (DTI dataset was raised. For this purposes, some DTI templates were developed which assist group analysis studies. In this study, complementary information to the most commonly used DTI template is proposed in order to offer a patient-specific statistical analysis on diffusion-weighted data. Methods 131 normal subjects were used to reconstruct a population-averaged template. After image pre processing, reconstruction and diagonalization, the eigenvalues and eigenvectors were used to reconstruct the quantitative DTI maps, namely fractional anisotropy (FA, mean diffusivity (MD, relative anisotropy (RA, and radial diffusivity (RD. The mean absolute error (MAE was calculated using a voxel-wise procedure, which informs the global error regarding the mean intensity value for each quantitative map. Results the MAE values presented a low MAE estimate (max(MAE = 0.112, showing a reasonable error measure between our DTI-USP-131 template and the classical DTI-JHU-81 approach, which also shows a statistical equivalence (p<0.05 with the classical DTI template. Hence, the complementary standard deviation (SD maps for each quantitative DTI map can be added to the classical DTI-JHU-81 template. Conclusion In this study, variability DTI maps (SD maps were reconstructed providing the possibility of a voxel-wise statistical analysis in patient-specific approach. Finally, the brain template (DTI-USP-131 described here was made available for research purposes on the web site (http://dx.doi.org/10.17632/br7bhs4h7m.1, being valuable to research and clinical applications.
Tensor norms and operator ideals
Defant, A; Floret, K
1992-01-01
The three chapters of this book are entitled Basic Concepts, Tensor Norms, and Special Topics. The first may serve as part of an introductory course in Functional Analysis since it shows the powerful use of the projective and injective tensor norms, as well as the basics of the theory of operator ideals. The second chapter is the main part of the book: it presents the theory of tensor norms as designed by Grothendieck in the Resumé and deals with the relation between tensor norms and operator ideals. The last chapter deals with special questions. Each section is accompanied by a series of exer
Martí, A.; Queralt, P.; Ledo, J.
2009-12-01
In the magnetotelluric (MT) method, the analysis of geoelectric dimensionality has acquired special importance in the last years, because numerical codes have made it possible to model and invert data using either one-dimensional (1D), two-dimensional (2D) or three-dimensional (3D) approaches. We present a FORTRAN code termed WALDIM to perform the dimensionality analysis of a set of MT data, according to the WAL rotational invariants criteria. These criteria are based on the possible annulment of the invariants of the MT tensor, which allow retrieval of as much information as possible from this tensor, without taking any a priori dimensionality assumption. When determining the dimensionality of real and therefore noisy data, two problems arise. The first is due to the data errors, which propagate into the invariants values, and therefore, to the determination of the dimensionality. The second is the fact that the invariants are rarely precisely zero, and the definition of a threshold is necessary. To solve these problems, WALDIM takes into account the data errors. Additionally, the dimensionality results can be grouped into frequency bands. Thus, we provide a software utility that allows providing a robust description of the dimensionality, and the parameters necessary for data correction prior to modeling. Given its completeness at analyzing the MT tensor for both individual and bands of frequencies, this code is meant to be a practical tool for MT data analysis.
Directory of Open Access Journals (Sweden)
Wenchao Qiu
2016-09-01
Full Text Available Purpose: Childhood absence epilepsy (CAE is a common syndrome of idiopathic generalized epilepsy. However, little is known about the brain structural changes in this type of epilepsy, especially in the default mode network (DMN regions. This study aims at using the diffusion tensor imaging (DTI technique to quantify structural abnormalities of DMN nodes in CAE patients. Method: DTI data were acquired in 14 CAE patients (aged 8.64±2.59 years, 7 females and 7 males and 16 age- and sex-matched healthy controls. The data were analyzed using voxel-based analysis (VBA and statistically compared between patients and controls. Pearson correlation was explored between altered DTI metrics and clinical parameters. The difference of brain volumes between patients and controls were also tested using unpaired t-test. Results: Patients showed significant increase of mean diffusivity (MD and radial diffusivity (RD in left medial prefrontal cortex, and decrease of fractional anisotropy (FA in left precuneus and axial diffusivity (AD in both left medial prefrontal cortex and precuneus. In correlation analysis, MD value from left medial prefrontal cortex was positively associated with duration of epilepsy. Neither the disease duration nor the seizure frequency showed significant correlation with FA values. Between-group comparison of brain volumes got no significant difference. Conclusion: The findings indicate that structural impairments exist in DMN regions in children suffering from absence epilepsy and MD values positively correlate with epilepsy duration. This may contribute to understanding the pathological mechanisms of chronic neurological deficits and promote the development of new therapies for this disorder.
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Yang, Xu [Chongqing Medical University, Department of Medical Imaging, Second Affiliated Hospital, Chongqing (China); Fifth People' s Hospital of Chongqing, Department of Medical Imaging, Chongqing (China); Cao, Ding [Chongqing Medical University, Department of Hepatobiliary Surgery, Second Affiliated Hospital, Chongqing (China); Liang, Xiumei [Fifth People' s Hospital of Chongqing, Department of Medical Imaging, Chongqing (China); Zhao, Jiannong [Chongqing Medical University, Department of Medical Imaging, Second Affiliated Hospital, Chongqing (China)
2017-07-15
Several studies have examined the relationships between diffusion tensor imaging (DTI)-measured fractional anisotropy (FA) and the symptoms of schizophrenia, but results vary across the studies. The aim of this study was to carry out a meta-analysis of correlation coefficients reported by relevant studies to evaluate the correlative relationships between FA of various parts of the brain and schizophrenia symptomatic assessments. Literature was searched in several electronic databases, and study selection was based on precised eligibility criteria. Correlation coefficients between FA of a part of the brain and schizophrenia symptom were first converted into Fisher's z-scores for meta-analyses, and then overall effect sizes were back transformed to correlation coefficients. Thirty-three studies (1121 schizophrenia patients; age 32.66 years [95% confidence interval (CI) 30.19, 35.13]; 65.95 % [57.63, 74.28] males) were included in this meta-analysis. Age was inversely associated with brain FA (z-scores [95% CI] -0.23 [-0.14, -0.32]; p %<0.00001). Brain FA of various areas was inversely associated with negative symptoms of schizophrenia (z-score -0.30 [-0.23, -0.36]; p %<0.00001) but was positively associated with positive symptoms of schizophrenia (z-score 0.16 [0.04, 0.27]; p = 0.007) and general psychopathology of schizophrenia (z-score 0.26 [0.15, 0.37]; p = 0.00001). Although, DTI-measured brain FA is found to be inversely associated with negative symptoms and positively associated with positive symptoms and general psychopathology of schizophrenia, the effect sizes of these correlations are low and may not be clinically significant. Moreover, brain FA was also negatively associated with age of patients. (orig.)
Yang, Xu; Cao, Ding; Liang, Xiumei; Zhao, Jiannong
2017-07-01
Several studies have examined the relationships between diffusion tensor imaging (DTI)-measured fractional anisotropy (FA) and the symptoms of schizophrenia, but results vary across the studies. The aim of this study was to carry out a meta-analysis of correlation coefficients reported by relevant studies to evaluate the correlative relationships between FA of various parts of the brain and schizophrenia symptomatic assessments. Literature was searched in several electronic databases, and study selection was based on précised eligibility criteria. Correlation coefficients between FA of a part of the brain and schizophrenia symptom were first converted into Fisher's z-scores for meta-analyses, and then overall effect sizes were back transformed to correlation coefficients. Thirty-three studies (1121 schizophrenia patients; age 32.66 years [95% confidence interval (CI) 30.19, 35.13]; 65.95 % [57.63, 74.28] males) were included in this meta-analysis. Age was inversely associated with brain FA (z-scores [95% CI] -0.23 [-0.14, -0.32]; p ˂ 0.00001). Brain FA of various areas was inversely associated with negative symptoms of schizophrenia (z-score -0.30 [-0.23, -0.36]; p ˂ 0.00001) but was positively associated with positive symptoms of schizophrenia (z-score 0.16 [0.04, 0.27]; p = 0.007) and general psychopathology of schizophrenia (z-score 0.26 [0.15, 0.37]; p = 0.00001). Although, DTI-measured brain FA is found to be inversely associated with negative symptoms and positively associated with positive symptoms and general psychopathology of schizophrenia, the effect sizes of these correlations are low and may not be clinically significant. Moreover, brain FA was also negatively associated with age of patients.
Tensor renormalization group analysis of ${\\rm CP}(N-1)$ model in two dimensions
Kawauchi, Hikaru
2015-01-01
We apply the higher order tensor renormalization group to lattice CP($N-1$) model in two dimensions. A tensor network representation of CP($N-1$) model is derived. We confirm that the numerical results of the CP(1) model without the $\\theta$-term using this method are consistent with that of the O(3) model which is analyzed by the same method in the region $\\beta \\gg 1$ and that obtained by Monte Carlo simulation in a wider range of $\\beta$.
Ji, Hongfei; Li, Jie; Lu, Rongrong; Gu, Rong; Cao, Lei; Gong, Xiaoliang
2016-01-01
Electroencephalogram- (EEG-) based brain-computer interface (BCI) systems usually utilize one type of changes in the dynamics of brain oscillations for control, such as event-related desynchronization/synchronization (ERD/ERS), steady state visual evoked potential (SSVEP), and P300 evoked potentials. There is a recent trend to detect more than one of these signals in one system to create a hybrid BCI. However, in this case, EEG data were always divided into groups and analyzed by the separate processing procedures. As a result, the interactive effects were ignored when different types of BCI tasks were executed simultaneously. In this work, we propose an improved tensor based multiclass multimodal scheme especially for hybrid BCI, in which EEG signals are denoted as multiway tensors, a nonredundant rank-one tensor decomposition model is proposed to obtain nonredundant tensor components, a weighted fisher criterion is designed to select multimodal discriminative patterns without ignoring the interactive effects, and support vector machine (SVM) is extended to multiclass classification. Experiment results suggest that the proposed scheme can not only identify the different changes in the dynamics of brain oscillations induced by different types of tasks but also capture the interactive effects of simultaneous tasks properly. Therefore, it has great potential use for hybrid BCI.
Analysis and control of Boolean networks a semi-tensor product approach
Cheng, Daizhan; Li, Zhiqiang
2010-01-01
This book presents a new approach to the investigation of Boolean control networks, using the semi-tensor product (STP), which can express a logical function as a conventional discrete-time linear system. This makes it possible to analyze basic control problems.
Performance of unscented Kalman filter tractography in edema: Analysis of the two-tensor model.
Liao, Ruizhi; Ning, Lipeng; Chen, Zhenrui; Rigolo, Laura; Gong, Shun; Pasternak, Ofer; Golby, Alexandra J; Rathi, Yogesh; O'Donnell, Lauren J
2017-01-01
Diffusion MRI tractography is increasingly used in pre-operative neurosurgical planning to visualize critical fiber tracts. However, a major challenge for conventional tractography, especially in patients with brain tumors, is tracing fiber tracts that are affected by vasogenic edema, which increases water content in the tissue and lowers diffusion anisotropy. One strategy for improving fiber tracking is to use a tractography method that is more sensitive than the traditional single-tensor streamline tractography. We performed experiments to assess the performance of two-tensor unscented Kalman filter (UKF) tractography in edema. UKF tractography fits a diffusion model to the data during fiber tracking, taking advantage of prior information from the previous step along the fiber. We studied UKF performance in a synthetic diffusion MRI digital phantom with simulated edema and in retrospective data from two neurosurgical patients with edema affecting the arcuate fasciculus and corticospinal tracts. We compared the performance of several tractography methods including traditional streamline, UKF single-tensor, and UKF two-tensor. To provide practical guidance on how the UKF method could be employed, we evaluated the impact of using various seed regions both inside and outside the edematous regions, as well as the impact of parameter settings on the tractography sensitivity. We quantified the sensitivity of different methods by measuring the percentage of the patient-specific fMRI activation that was reached by the tractography. We expected that diffusion anisotropy threshold parameters, as well as the inclusion of a free water model, would significantly influence the reconstruction of edematous WM fiber tracts, because edema increases water content in the tissue and lowers anisotropy. Contrary to our initial expectations, varying the fractional anisotropy threshold and including a free water model did not affect the UKF two-tensor tractography output appreciably in
Phase space analysis for a scalar-tensor model with kinetic and Gauss-Bonnet couplings
Granda, L N
2016-01-01
We study the phase space for an scalar-tensor string inspired model of dark energy with non minimal kinetic and Gauss Bonnet couplings. The form of the scalar potential and of the coupling terms is of the exponential type, which give rise to appealing cosmological solutions. The critical points describe a variety of cosmological scenarios that go from matter or radiation dominated universe to dark energy dominated universe. There were found trajectories in the phase space departing from unstable or saddle fixed points and arriving to the stable scalar field dominated point corresponding to late-time accelerated expansion.
Kassubek, Jan; Müller, Hans-Peter; Del Tredici, Kelly; Brettschneider, Johannes; Pinkhardt, Elmar H; Lulé, Dorothée; Böhm, Sarah; Braak, Heiko; Ludolph, Albert C
2014-06-01
Diffusion tensor imaging can identify amyotrophic lateral sclerosis-associated patterns of brain alterations at the group level. Recently, a neuropathological staging system for amyotrophic lateral sclerosis has shown that amyotrophic lateral sclerosis may disseminate in a sequential regional pattern during four disease stages. The objective of the present study was to apply a new methodological diffusion tensor imaging-based approach to automatically analyse in vivo the fibre tracts that are prone to be involved at each neuropathological stage of amyotrophic lateral sclerosis. Two data samples, consisting of 130 diffusion tensor imaging data sets acquired at 1.5 T from 78 patients with amyotrophic lateral sclerosis and 52 control subjects; and 55 diffusion-tensor imaging data sets at 3.0 T from 33 patients with amyotrophic lateral sclerosis and 22 control subjects, were analysed by a tract of interest-based fibre tracking approach to analyse five tracts that become involved during the course of amyotrophic lateral sclerosis: the corticospinal tract (stage 1); the corticorubral and the corticopontine tracts (stage 2); the corticostriatal pathway (stage 3); the proximal portion of the perforant path (stage 4); and two reference pathways. The statistical analyses of tracts of interest showed differences between patients with amyotrophic lateral sclerosis and control subjects for all tracts. The significance level of the comparisons at the group level was lower, the higher the disease stage with corresponding involved fibre tracts. Both the clinical phenotype as assessed by the amyotrophic lateral sclerosis functional rating scale-revised and disease duration correlated significantly with the resulting staging scheme. In summary, the tract of interest-based technique allowed for individual analysis of predefined tract structures, thus making it possible to image in vivo the disease stages in amyotrophic lateral sclerosis. This approach can be used not only for
Analysis of a Bianchi-like equation satisfied by the Mars-Simon tensor
Beyer, Florian; Paetz, Tim-Torben
2018-02-01
The Mars-Simon tensor (MST), which, e.g., plays a crucial role to provide gauge invariant characterizations of the Kerr-NUT-(A)(dS) family, satisfies a Bianchi-like equation. In this paper, we analyze this equation in close analogy to the Bianchi equation, in particular it will be shown that the constraints are preserved supposing that a generalized Buchdahl condition holds. This permits the systematic construction of solutions to this equation in terms of a well-posed Cauchy problem. A particular emphasis lies on the asymptotic Cauchy problem, where data are prescribed on a space-like I (i.e., for ∧ > 0). In contrast to the Bianchi equation, the MST equation is of Fuchsian type at I , for which existence and uniqueness results are derived.
Alizadeh, Mahdi; Conklin, Chris J; Middleton, Devon M; Shah, Pallav; Saksena, Sona; Krisa, Laura; Finsterbusch, Jürgen; Faro, Scott H; Mulcahey, M J; Mohamed, Feroze B
2017-11-15
Ghost artifacts are a major contributor to degradation of spinal cord diffusion tensor images. A multi-stage post-processing pipeline was designed, implemented and validated to automatically remove ghost artifacts arising from reduced field of view diffusion tensor imaging (DTI) of the pediatric spinal cord. A total of 12 pediatric subjects including 7 healthy subjects (mean age=11.34years) with no evidence of spinal cord injury or pathology and 5 patients (mean age=10.96years) with cervical spinal cord injury were studied. Ghost/true cords, labeled as region of interests (ROIs), in non-diffusion weighted b0 images were segmented automatically using mathematical morphological processing. Initially, 21 texture features were extracted from each segmented ROI including 5 first-order features based on the histogram of the image (mean, variance, skewness, kurtosis and entropy) and 16s-order feature vector elements, incorporating four statistical measures (contrast, correlation, homogeneity and energy) calculated from co-occurrence matrices in directions of 0°, 45°, 90° and 135°. Next, ten features with a high value of mutual information (MI) relative to the pre-defined target class and within the features were selected as final features which were input to a trained classifier (adaptive neuro-fuzzy interface system) to separate the true cord from the ghost cord. The implemented pipeline was successfully able to separate the ghost artifacts from true cord structures. The results obtained from the classifier showed a sensitivity of 91%, specificity of 79%, and accuracy of 84% in separating the true cord from ghost artifacts. The results show that the proposed method is promising for the automatic detection of ghost cords present in DTI images of the spinal cord. This step is crucial towards development of accurate, automatic DTI spinal cord post processing pipelines. Copyright © 2017 Elsevier Inc. All rights reserved.
Gurau, Razvan
2017-01-01
Written by the creator of the modern theory of random tensors, this book is the first self-contained introductory text to this rapidly developing theory. Starting from notions familiar to the average researcher or PhD student in mathematical or theoretical physics, the book presents in detail the theory and its applications to physics. The recent detections of the Higgs boson at the LHC and gravitational waves at LIGO mark new milestones in Physics confirming long standing predictions of Quantum Field Theory and General Relativity. These two experimental results only reinforce today the need to find an underlying common framework of the two: the elusive theory of Quantum Gravity. Over the past thirty years, several alternatives have been proposed as theories of Quantum Gravity, chief among them String Theory. While these theories are yet to be tested experimentally, key lessons have already been learned. Whatever the theory of Quantum Gravity may be, it must incorporate random geometry in one form or another....
Full in-plane strain tensor analysis using the microscale ring-core FIB milling and DIC approach
Lunt, Alexander J. G.; Salvati, Enrico; Ma, Lifeng; Dolbyna, Igor P.; Neo, Tee K.; Korsunsky, Alexander M.
2016-09-01
Microscale Full In-plane Strain Tensor (FIST) analysis is crucial for improving understanding of residual stress and mechanical failure in many applications. This study outlines the first Focused Ion Beam (FIB) milling and Digital Image Correlation (DIC) based technique capable of performing precise, reliable and rapid quantification of this behaviour. The nature of semi-destructive FIB milling overcomes the main limitations of X-Ray Diffraction (XRD) strain tensor quantification: unstrained lattice parameter estimates are not required, analysis is performed in within a precisely defined 3D microscale volume, both amorphous and crystalline materials can be studied and access to X-ray/neutron facilities is not required. The FIST FIB milling and DIC experimental technique is based on extending the ring-core milling geometry to quantify the strain variation with angle and therefore benefits from the excellent precision and simple analytical approach associated with this method. In this study in-plane strain analysis was performed on sample of commercial interest: a porcelain veneered Yttria Partially Stabilised Zirconia (YPSZ) dental prosthesis, and was compared with the results of XRD. The two methods sample different gauge volumes and mechanical states: approximately plane stress for ring-core milling, and a through-thickness average for XRD. We demonstrate using complex analysis methods and Finite Element (FE) modelling that valid comparisons can be drawn between these two stress states. Excellent agreement was obtained between principal stress orientation and magnitudes, leading to realistic residual stress estimates that agree well with the literature (σAv ≈ 460 MPa) . As a measure of validity of the matching approach we report the upper and lower bounds on the (101) interplanar spacing of YPSZ that are found to correspond to the range 2.9586 - 2.9596 Å , closely matching published values.
Koay, Cheng Guan; Yeh, Ping-Hong; Ollinger, John M; İrfanoğlu, M Okan; Pierpaoli, Carlo; Basser, Peter J; Oakes, Terrence R; Riedy, Gerard
2016-02-01
The purpose of this work is to develop a framework for single-subject analysis of diffusion tensor imaging (DTI) data. This framework is termed Tract Orientation and Angular Dispersion Deviation Indicator (TOADDI) because it is capable of testing whether an individual tract as represented by the major eigenvector of the diffusion tensor and its corresponding angular dispersion are significantly different from a group of tracts on a voxel-by-voxel basis. This work develops two complementary statistical tests based on the elliptical cone of uncertainty, which is a model of uncertainty or dispersion of the major eigenvector of the diffusion tensor. The orientation deviation test examines whether the major eigenvector from a single subject is within the average elliptical cone of uncertainty formed by a collection of elliptical cones of uncertainty. The shape deviation test is based on the two-tailed Wilcoxon-Mann-Whitney two-sample test between the normalized shape measures (area and circumference) of the elliptical cones of uncertainty of the single subject against a group of controls. The False Discovery Rate (FDR) and False Non-discovery Rate (FNR) were incorporated in the orientation deviation test. The shape deviation test uses FDR only. TOADDI was found to be numerically accurate and statistically effective. Clinical data from two Traumatic Brain Injury (TBI) patients and one non-TBI subject were tested against the data obtained from a group of 45 non-TBI controls to illustrate the application of the proposed framework in single-subject analysis. The frontal portion of the superior longitudinal fasciculus seemed to be implicated in both tests (orientation and shape) as significantly different from that of the control group. The TBI patients and the single non-TBI subject were well separated under the shape deviation test at the chosen FDR level of 0.0005. TOADDI is a simple but novel geometrically based statistical framework for analyzing DTI data. TOADDI may be
Tensor rank is not multiplicative under the tensor product
DEFF Research Database (Denmark)
Christandl, Matthias; Jensen, Asger Kjærulff; Zuiddam, Jeroen
2018-01-01
The tensor rank of a tensor t is the smallest number r such that t can be decomposed as a sum of r simple tensors. Let s be a k-tensor and let t be an ℓ-tensor. The tensor product of s and t is a (k+ℓ)-tensor. Tensor rank is sub-multiplicative under the tensor product. We revisit the connection b...
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Aldhafeeri, Faten M. [The University of Liverpool, Department of Medical Imaging, School of Health Sciences, Liverpool (United Kingdom); King Khalid General Hospital, Ministry of Health, Radiology Department, Hafral-batin (Saudi Arabia); Mackenzie, Ian; Kay, Tony [Aintree University Hospitals NHS Foundation Trust, Liverpool (United Kingdom); Alghamdi, Jamaan [The University of Liverpool, Department of Medical Imaging, School of Health Sciences, Liverpool (United Kingdom); King Abdul Aziz University, Physics Department, Faculty of Sciences, Jeddah (Saudi Arabia); Sluming, Vanessa [The University of Liverpool, Department of Medical Imaging, School of Health Sciences, Liverpool (United Kingdom); Magnetic Resonance and Image Analysis Research Centre, Liverpool (United Kingdom)
2012-08-15
Tinnitus is a poorly understood auditory perception of sound in the absence of external stimuli. Convergent evidence proposes that tinnitus perception involves brain structural alterations as part of its pathophysiology. The aim of this study is to investigate the structural brain changes that might be associated with tinnitus-related stress and negative emotions. Using high-resolution magnetic resonance imaging and diffusion tensor imaging, we investigated grey matter and white matter (WM) alterations by estimating cortical thickness measures, fractional anisotropy and mean diffusivity in 14 tinnitus subjects and 14 age- and sex-matched non-tinnitus subjects. Significant cortical thickness reductions were found in the prefrontal cortex (PFC), temporal lobe and limbic system in tinnitus subjects compared to non-tinnitus subjects. Tinnitus sufferers were found to have disrupted WM integrity in tracts involving connectivity of the PFC, temporal lobe, thalamus and limbic system. Our results suggest that such neural changes may represent neural origins for tinnitus or consequences of tinnitus and its associations. (orig.)
Link prediction via generalized coupled tensor factorisation
DEFF Research Database (Denmark)
Ermiş, Beyza; Evrim, Acar Ataman; Taylan Cemgil, A.
2012-01-01
This study deals with the missing link prediction problem: the problem of predicting the existence of missing connections between entities of interest. We address link prediction using coupled analysis of relational datasets represented as heterogeneous data, i.e., datasets in the form of matrices...... and higher-order tensors. We propose to use an approach based on probabilistic interpretation of tensor factorisation models, i.e., Generalised Coupled Tensor Factorisation, which can simultaneously fit a large class of tensor models to higher-order tensors/matrices with com- mon latent factors using...... different loss functions. Numerical experiments demonstrate that joint analysis of data from multiple sources via coupled factorisation improves the link prediction performance and the selection of right loss function and tensor model is crucial for accurately predicting missing links....
Son, Shuraku; Kubota, Manabu; Miyata, Jun; Fukuyama, Hidenao; Aso, Toshihiko; Urayama, Shin-ichi; Murai, Toshiya; Takahashi, Hidehiko
2015-05-01
Both creativity and schizotypy are suggested to be manifestations of the hyperactivation of unusual or remote concepts/words. However, the results of studies on creativity in schizophrenia are diverse, possibly due to the multifaceted aspects of creativity and difficulties of differentiating adaptive creativity from pathological schizotypy/positive symptoms. To date, there have been no detailed studies comprehensively investigating creativity, positive symptoms including delusions, and their neural bases in schizophrenia. In this study, we investigated 43 schizophrenia and 36 healthy participants using diffusion tensor imaging. We used idea, design, and verbal (semantic and phonological) fluency tests as creativity scores and Peters Delusions Inventory as delusion scores. Subsequently, we investigated group differences in every psychological score, correlations between fluency and delusions, and relationships between these scores and white matter integrity using tract-based spatial statistics (TBSS). In schizophrenia, idea and verbal fluency were significantly lower in general, and delusion score was higher than in healthy controls, whereas there were no group differences in design fluency. We also found positive correlation between phonological fluency and delusions in schizophrenia. By correlation analyses using TBSS, we found that the anterior part of corpus callosum was the substantially overlapped area, negatively correlated with both phonological fluency and delusion severity. Our results suggest that the anterior interhemispheric dysconnectivity might be associated with executive dysfunction, and disinhibited automatic spreading activation in the semantic network was manifested as uncontrollable phonological fluency or delusions. This dysconnectivity could be one possible neural basis that differentiates pathological positive symptoms from adaptive creativity. Copyright © 2015 Elsevier B.V. All rights reserved.
Liao, Yi; Huang, Xiaoqi; Wu, Qizhu; Yang, Chuang; Kuang, Weihong; Du, Mingying; Lui, Su; Yue, Qiang; Chan, Raymond C K; Kemp, Graham J; Gong, Qiyong
2013-01-01
Many studies using diffusion tensor imaging (DTI) have demonstrated impaired white matter integrity in patients with major depressive disorder (MDD), with significant results found in diverse brain regions. We sought to identify whether there are consistent changes of regional white matter integrity in patients with MDD, as shown by decreased fractional anisotropy in DTI. A systematic search strategy was used to identify relevant whole brain voxel-based DTI studies of patients with MDD in relation to comparison groups. Relevant databases were searched for studies published between January 1994 and February 2011 using combinations of the terms "DTI" or "diffusion tensor;" "whole brain" or "voxel-based;" and "depress*." Using the studies that met our inclusion criteria, we performed a meta-analysis of the coordinates of decreased fractional anisotropy using the activation likelihood estimation (ALE) method, which detects 3-dimensional conjunctions of coordinates from multiple studies, weighted by sample size. We then used DTIquery software for fibre tracking to locate the fascicles involved in each region. We included 11 studies with a combined sample of 231 patients with MDD and 261 comparison participants, providing 50 coordinates of decreased fractional anisotropy. Our meta-analysis identified 4 consistent locations of decreased fractional anisotropy in patients with MDD: white matter in the right frontal lobe, right fusiform gyrus, left frontal lobe and right occipital lobe. Fibre tracking showed that the main fascicles involved were the right inferior longitudinal fasciculus, right inferior fronto-occipital fasciculus, right posterior thalamic radiation and interhemispheric fibres running through the genu and body of the corpus callosum. The number of studies included was relatively small, and the DTI data acquisition and analysis techniques were heterogeneous. The ALE method cannot handle studies with no significant group differences. Voxel-based analysis of
Akakpo, Luis; Pierre, Wyston C; Jin, Chen; Londono, Irène; Pouliot, Philippe; Lodygensky, Gregory A
2017-11-01
Automated analysis of diffusion tensor imaging (DTI) data is an appealing way to process large datasets in an unbiased manner. However, automation can sometimes be linked to a lack of interpretability. Two whole-brain, automated and voxelwise methods exist: voxel-based analysis (VBA) and tract-based spatial statistics (TBSS). In VBA, the amount of smoothing has been shown to influence the results. TBSS is free of this step, but a projection procedure is introduced to correct for residual misalignments. This projection assigns the local highest fractional anisotropy (FA) value to the mean FA skeleton, which represents white matter tract centers. For both methods, the normalization procedure has a major impact. These issues are well documented in humans but, to our knowledge, not in rodents. In this study, we assessed the quality of three different registration algorithms (ANTs SyN, DTI-TK and FNIRT) using study-specific templates and their impact on automated analysis methods (VBA and TBSS) in a rat pup model of diffuse white matter injury presenting large unilateral deformations. VBA and TBSS results were stable and anatomically coherent across the three pipelines. For VBA, in regions around the large deformations, interpretability was limited because of the increased partial volume effect. With TBSS, two of the three pipelines found a significant decrease in axial diffusivity (AD) at the known injury site. These results demonstrate that automated voxelwise analyses can be used in an animal model with large deformations. Copyright © 2017 John Wiley & Sons, Ltd.
Müller, Hans-Peter; Unrath, Alexander; Huppertz, Hans-Jürgen; Ludolph, Albert C; Kassubek, Jan
2012-05-01
This study was designed to investigate differences of white matter (WM) involvement patterns in various motor neuron disorders (MND) by use of diffusion tensor imaging (DTI).DTI was acquired in ALS (n = 20), primary lateral sclerosis (n = 20), pure hereditary spastic paraparesis (HSP) (n = 20), and complicated HSP (n = 12). The data analysis was performed by voxelwise comparison of fractional anisotropy (FA) maps at group level together with fibre tracking in regions of interest (ROI) accompanied by tractwise fractional anisotropy statistics. DTI analysis revealed widespread patterns of alterations with a predominant deterioration of the motor system. These alterations encompassed, as the key structures, not only the corticospinal tracts (CST) but also distinct areas of the corpus callosum (CC), in particular its motor segment III. In conclusion, whole brain-based and tract-based DTI analysis was able to define a distinct WM pathoanatomy of different MND. These results may serve as an additional guidance in the identification of MRI-based parameters by showing a consistent CST and CC involvement, with differences in the extent of pathology, across a range of clinically different disorders. For potential future developments in MRI diagnostics in MND, a (perhaps multiparametric) ROI-based approach should include CST and the CC motor segment.
The Topology of Symmetric Tensor Fields
Levin, Yingmei; Batra, Rajesh; Hesselink, Lambertus; Levy, Yuval
1997-01-01
Combinatorial topology, also known as "rubber sheet geometry", has extensive applications in geometry and analysis, many of which result from connections with the theory of differential equations. A link between topology and differential equations is vector fields. Recent developments in scientific visualization have shown that vector fields also play an important role in the analysis of second-order tensor fields. A second-order tensor field can be transformed into its eigensystem, namely, eigenvalues and their associated eigenvectors without loss of information content. Eigenvectors behave in a similar fashion to ordinary vectors with even simpler topological structures due to their sign indeterminacy. Incorporating information about eigenvectors and eigenvalues in a display technique known as hyperstreamlines reveals the structure of a tensor field. The simplify and often complex tensor field and to capture its important features, the tensor is decomposed into an isotopic tensor and a deviator. A tensor field and its deviator share the same set of eigenvectors, and therefore they have a similar topological structure. A a deviator determines the properties of a tensor field, while the isotopic part provides a uniform bias. Degenerate points are basic constituents of tensor fields. In 2-D tensor fields, there are only two types of degenerate points; while in 3-D, the degenerate points can be characterized in a Q'-R' plane. Compressible and incompressible flows share similar topological feature due to the similarity of their deviators. In the case of the deformation tensor, the singularities of its deviator represent the area of vortex core in the field. In turbulent flows, the similarities and differences of the topology of the deformation and the Reynolds stress tensors reveal that the basic addie-viscosity assuptions have their validity in turbulence modeling under certain conditions.
Sirlin, Samuel W.
1993-01-01
Eight-page report describes systems of notation used most commonly to represent tensors of various ranks, with emphasis on tensors in Cartesian coordinate systems. Serves as introductory or refresher text for scientists, engineers, and others familiar with basic concepts of coordinate systems, vectors, and partial derivatives. Indicial tensor, vector, dyadic, and matrix notations, and relationships among them described.
Directory of Open Access Journals (Sweden)
Kuang-dai Leng
2012-01-01
Full Text Available Fabric tensor has proved to be an effective tool statistically characterizing directional data in a smooth and frame-indifferent form. Directional data arising from microscopic physics and mechanics can be summed up as tensor-valued orientation distribution functions (ODFs. Two characterizations of the tensor-valued ODFs are proposed, using the asymmetric and symmetric fabric tensors respectively. The later proves to be nonconvergent and less accurate but still an available solution for where fabric tensors are required in full symmetry. Analytic solutions of the two types of fabric tensors characterizing centrosymmetric and anticentrosymmetric tensor-valued ODFs are presented in terms of orthogonal irreducible decompositions in both two- and three-dimensional (2D and 3D spaces. Accuracy analysis is performed on normally distributed random ODFs to evaluate the approximation quality of the two characterizations, where fabric tensors of higher orders are employed. It is shown that the fitness is dominated by the dispersion degree of the original ODFs rather than the orders of fabric tensors. One application of tensor-valued ODF and fabric tensor in continuum damage mechanics is presented.
A study of diffusion tensor imaging by tissue-specific, smoothing-compensated voxel-based analysis.
Lee, Jee Eun; Chung, Moo K; Lazar, Mariana; DuBray, Molly B; Kim, Jinsuh; Bigler, Erin D; Lainhart, Janet E; Alexander, Andrew L
2009-02-01
Voxel-based analysis (VBA) is commonly used for statistical analysis of image data, including the detection of significant signal differences between groups. Typically, images are co-registered and then smoothed with an isotropic Gaussian kernel to compensate for image misregistration, to improve the signal-to-noise ratio (SNR), to reduce the number of multiple comparisons, and to apply random field theory. Problems with typical implementations of VBA include poor tissue specificity from image misregistration and smoothing. In this study, we developed a new tissue-specific, smoothing-compensated (T-SPOON) method for the VBA of diffusion tensor imaging (DTI) data with improved tissue specificity and compensation for image misregistration and smoothing. When compared with conventional VBA methods, the T-SPOON method introduced substantially less errors in the normalized and smoothed DTI maps. Another confound of the conventional DTI-VBA is that it is difficult to differentiate between differences in morphometry and DTI measures that describe tissue microstructure. T-SPOON VBA decreased the effects of differential morphometry in the DTI VBA studies. T-SPOON and conventional VBA were applied to a DTI study of white matter in autism. T-SPOON VBA results were found to be more consistent with region of interest (ROI) measurements in the corpus callosum and temporal lobe regions. The T-SPOON method may be also applicable to other quantitative imaging maps such as T1 or T2 relaxometry, magnetization transfer, or PET tracer maps.
Skidmore, F M; Spetsieris, P G; Anthony, T; Cutter, G R; von Deneen, K M; Liu, Y; White, K D; Heilman, K M; Myers, J; Standaert, D G; Lahti, A C; Eidelberg, D; Ulug, A M
2015-01-01
There is a compelling need for early, accurate diagnosis of Parkinson's disease (PD). Various magnetic resonance imaging modalities are being explored as an adjunct to diagnosis. A significant challenge in using MR imaging for diagnosis is developing appropriate algorithms for extracting diagnostically relevant information from brain images. In previous work, we have demonstrated that individual subject variability can have a substantial effect on identifying and determining the borders of regions of analysis, and that this variability may impact on prediction accuracy. In this paper we evaluate a new statistical algorithm to determine if we can improve accuracy of prediction using a subjects left-out validation of a DTI analysis. Twenty subjects with PD and 22 healthy controls were imaged to evaluate if a full brain diffusion tensor imaging-fractional anisotropy (DTI-FA) map might be capable of segregating PD from controls. In this paper, we present a new statistical algorithm based on bootstrapping. We compare the capacity of this algorithm to classify the identity of subjects left out of the analysis with the accuracy of other statistical techniques, including standard cluster-thresholding. The bootstrapped analysis approach was able to correctly discriminate the 20 subjects with PD from the 22 healthy controls (area under the receiver operator curve or AUROC 0.90); however the sensitivity and specificity of standard cluster-thresholding techniques at various voxel-specific thresholds were less effective (AUROC 0.72-0.75). Based on these results sufficient information to generate diagnostically relevant statistical maps may already be collected by current MRI scanners. We present one statistical technique that might be used to extract diagnostically relevant information from a full brain analysis.
Xu, Shi-da; Li, Yuan-hui; Liu, Jian-po
2017-05-01
An acoustic emission (AE) testing of rock cracking was performed under uniaxial loading conditions by precut varisized circular holes in selected brittle granites. Based on AE-source location technique and AE-theory for moment tensor analysis, rules of the temporal-spatial evolution of micro-cracks in different failure mechanisms were explored and types of micro-cracks were analyzed as well. The results revealed that the micro-cracks are uniquely easy to generate in the positions where stress are concentrated. Tensile fractures are easy to form on the roof and floor of a circular hole, while shear fractures are easy to be found on both sides. The locations of initial cracks generated around the holes in the loading process are the direction or vertical direction of maximum principle stress. Macroscopic crack orientation agrees with the direction of maximum principle stress approximately. As the size of circular opening increases and the relative size of pillar decreases, shear cracks are dominant with the percentage more than 45%, tension cracks are fewer, accounted for less than 40% of the total events, and mixed-mode cracks represent a minimum proportion, despite the decrease of percentage of shear cracks. The findings of this work can serve for supporting design of tunnel or roadway to avoid collapse.
Change-point analysis data of neonatal diffusion tensor MRI in preterm and term-born infants
Directory of Open Access Journals (Sweden)
Dan Wu
2017-06-01
Full Text Available The data presented in this article are related to the research article entitled “Mapping the Critical Gestational Age at Birth that Alters Brain Development in Preterm-born Infants using Multi-Modal MRI” (Wu et al., 2017 [1]. Brain immaturity at birth poses critical neurological risks in the preterm-born infants. We used a novel change-point model to analyze the critical gestational age at birth (GAB that could affect postnatal development, based on diffusion tensor MRI (DTI acquired from 43 preterm and 43 term-born infants in 126 brain regions. In the corresponding research article, we presented change-point analysis of fractional anisotropy (FA and mean diffusivities (MD measurements in these infants. In this article, we offered the relative changes of axonal and radial diffusivities (AD and RD in relation to the change of FA and FA-based change-points, and we also provided the AD- and RD-based change-point results.
Nortje, Gareth; Stein, Dan J; Radua, Joaquim; Mataix-Cols, David; Horn, Neil
2013-09-05
Diffusion tensor imaging (DTI) studies have shown changes in the microstructure of white matter in bipolar disorder. Studies suggest both localised, predominantly fronto-limbic, as well as more widespread changes in white matter, but with some apparent inconsistency. A meta-analysis of white matter alterations in adults with bipolar disorder was undertaken. Whole-brain DTI studies comparing adults with bipolar disorder to healthy controls on fractional anisotropy (FA) were retrieved using searches of MEDLINE and EMBASE from between 2003 and December 2012. White-matter tract involvement was collated and quantified. Clusters of significantly altered FA were meta-analysed using effect-size signed differential mapping (ES-SDM). Ten VBA studies (252 patients and 256 controls) and five TBSS studies (138 patients and 98 controls) met inclusion criteria. Sixty-one clusters of significantly different FA between bipolar disorder and healthy controls were identified. Analysis of white-matter tracts indicated that all major classes of tracts are implicated. ES-SDM meta-analysis of VBA studies revealed three significant clusters of decreased FA in bipolar disorder (a right posterior temporoparietal cluster and two left cingulate clusters). Findings limited to the Bipolar Type I papers were more robust. Voxel-based studies do not accurately identify tracts, and our ES-SDM analysis used only published peak voxels rather than raw DTI data. There is consistent data indicating widespread white matter involvement with decreased white matter FA demonstrated in three disparate areas in bipolar disorder. White matter alterations are not limited to anterior fronto-limbic pathways in bipolar disorder. Copyright © 2013 Elsevier B.V. All rights reserved.
Unrath, Alexander; Müller, Hans-Peter; Riecker, Axel; Ludolph, Albert C; Sperfeld, Anne-Dorte; Kassubek, Jan
2010-11-01
Different motor neuron disorders (MNDs) are mainly defined by the clinical presentation based on the predominance of upper or lower motor neuron impairment and the course of the disease. Magnetic resonance imaging (MRI) mostly serves as a tool to exclude other pathologies, but novel approaches such as diffusion tensor imaging (DTI) have begun to add information on the underlying pathophysiological processes of these disorders in vivo. The present study was designed to investigate three different rare MNDs, i.e., primary lateral sclerosis (PLS, N = 25), hereditary spastic paraparesis (HSP, N = 24), and X-linked spinobulbar muscular atrophy (X-SBMA, N = 20), by use of whole-brain-based DTI analysis in comparison with matched controls. This analysis of white matter (WM) impairment revealed widespread and characteristic patterns of alterations within the motor system with a predominant deterioration of the corticospinal tract (CST) in HSP and PLS patients according to the clinical presentation and also in patients with X-SBMA to a lesser degree, but also WM changes in projections to the limbic system and within distinct areas of the corpus callosum (CC), the latter both for HSP and PLS. In summary, DTI was able to define a characteristic WM pathoanatomy in motor and extra-motor brain areas, such as the CC and the limbic projectional system, for different MNDs via whole brain-based FA assessment and quantitative fiber tracking. Future advanced MRI-based investigations might help to provide a fingerprint-identification of MNDs. © 2010 Wiley-Liss, Inc.
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Kurki, Timo [Turku University Hospital, Department of Radiology, Turku (Finland); MRI Unit, Terveystalo Pulssi Medical Centre, Turku (Finland); Himanen, Leena; Vuorinen, Elina; Myllyniemi, Anna; Saarenketo, Anna-Riitta [NeuTera Neuropsychologist Centre, Turku (Finland); Kauko, Tommi [University of Turku, Department of Biostatistics, Turku (Finland); Brandstack, Nina [Turku University Hospital, Department of Radiology, Turku (Finland); Helsinki University Hospital, Department of Radiology, Helsinki (Finland); Tenovuo, Olli [Turku University Hospital and University of Turku, Department of Rehabilitation and Brain Trauma, Turku (Finland)
2014-10-15
To evaluate the clinical utility of quantitative diffusion tensor tractography (DTT) and tractography-based core analysis (TBCA) of the cingulum by defining the reproducibility, normal values, and findings in traumatic brain injury (TBI). Eighty patients with TBI and normal routine MRI and 78 controls underwent MRI at 3T. To determine reproducibility, 12 subjects were scanned twice. Superior (SC) and inferior (IC) cingulum were analyzed separately by DTT (fractional anisotropy (FA) thresholds 0.15 and 0.30). TBCA was performed from volumes defined by tractography with gradually changed FA thresholds. FA values were correlated with clinical and neuropsychological data. The lowest coefficient of variation was obtained at DTT threshold 0.30 (2.0 and 2.4 % for SC and IC, respectively), but in proportion to standard deviations of normal controls, the reproducibility of TBCA was better in SC and similar to that of DTT in IC. In patients with TBI, volume reduction with loss of peripheral fibers was relatively common; mean FA was mostly normal in these tractograms. The frequency of FA reductions (>2 SD) was in DTT smaller than in TBCA, in which FA decrease was present in 42 (13.1 %) of the 320 measurements. Central FA values in SC predicted visuoperceptual ability, and those in left IC predicted cognitive speed, language, and communication ability (p < 0.05). Tractography-based measurements have sufficient reproducibility for demonstration of severe abnormalities of the cingulum. TBCA is preferential for clinical FA analysis, because it measures corresponding areas in patients and controls without inaccuracies due to trauma-induced structural changes. (orig.)
New analysis of $\\eta\\pi$ tensor resonances measured at the COMPASS experiment
Jackura, A.; The COMPASS collaboration; Mikhasenko, M.; Pilloni, A.; Mathieu, V.; Nys, J.; Pauk, V.; Szczepaniak, A.P.; Fox, G.; Aghasyan, M.; Akhunzyanov, R.; Alexeev, M.G.; Alexeev, G.D.; Amoroso, A.; Andrieux, V.; Anfimov, N.V.; Anosov, V.; Antoshkin, A.; Augsten, K.; Augustyniak, W.; Austregesilo, A.; Azevedo, C.D.R.; Badełek, B.; Balestra, F.; Ball, M.; Barth, J.; Beck, R.; Bedfer, Y.; Bernhard, J.; Bicker, K.; Bielert, E.R.; Birsa, R.; Bodlak, M.; Bordalo, P.; Bradamante, F.; Bressan, A.; Büchele, M.; Burtsev, V.E.; Chang, W.-C.; Chatterjee, C.; Chiosso, M.; Choi, I.; Chumakov, A.G.; Chung, S.-U.; Cicuttin, A.; Crespo, M.L.; Dalla Torre, S.; Dasgupta, S.S.; Dasgupta, S.; Denisov, O.Yu.; Dhara, L.; Donskov, S.V.; Doshita, N.; Dreisbach, Ch.; Dünnweber, W.; Dusaev, R.R.; Dziewiecki, M.; Efremov, A.; Eversheim, P.D.; Faessler, M.; Ferrero, A.; Finger, M.; jr.,M.Finger; Fischer, H.; Franco, C.; du Fresne von Hohenesche, N.; Friedrich, J.M.; Frolov, V.; Fuchey, E.; Gautheron, F.; Gavrichtchouk, O.P.; Gerassimov, S.; Giarra, J.; Giordano, F.; Gnesi, I.; Gorzellik, M.; Grasso, A.; Grosse Perdekamp, M.; Grube, B.; Grussenmeyer, T.; Guskov, A.; Hahne, D.; Hamar, G.; von Harrach, D.; Heinsius, F.H.; Heitz, R.; Herrmann, F.; Horikawa, N.; d'Hose, N.; Hsieh, C.-Y.; Huber, S.; Ishimoto, S.; Ivanov, A.; Ivanshin, Yu.; Iwata, T.; Jary, V.; Joosten, R.; Jörg, P.; Kabuß, E.; Kerbizi, A.; Ketzer, B.; Khaustov, G.V.; Khokhlov, Yu.A.; Kisselev, Yu.; Klein, F.; Koivuniemi, J.H.; Kolosov, V.N.; Kondo, K.; Königsmann, K.; Konorov, I.; Konstantinov, V.F.; Kotzinian, A.M.; Kouznetsov, O.M.; Kral, Z.; Krämer, M.; Kremser, P.; Krinner, F.; Kroumchtein, Z.V.; Kulinich, Y.; Kunne, F.; Kurek, K.; Kurjata, R.P.; Kuznetsov, I.I.; Kveton, A.; Lednev, A.A.; Levchenko, E.A.; Levillain, M.; Levorato, S.; Lian, Y.-S.; Lichtenstadt, J.; Longo, R.; Lyubovitskij, V.E.; Maggiora, A.; Magnon, A.; Makins, N.; Makke, N.; Mallot, G.K.; Mamon, S.A.; Marianski, B.; Martin, A.; Marzec, J.; Matsuda, H.; Matsuda, T.; Meshcheryakov, G.V.; Meyer, M.; Meyer, W.; Mikhailov, Yu.V.; Mikhasenko, M.; Mitrofanov, E.; Mitrofanov, N.; Miyachi, Y.; Nagaytsev, A.; Nerling, F.; Neyret, D.; Nový, J.; Nowak, W.-D.; Nukazuka, G.; Nunes, A.S.; Olshevsky, A.G.; Orlov, I.; Ostrick, M.; Panzieri, D.; Parsamyan, B.; Paul, S.; Peng, J.-C.; Pereira, F.; Pešek, M.; Pešková, M.; Peshekhonov, D.V.; Pierre, N.; Platchkov, S.; Pochodzalla, J.; Polyakov, V.A.; Pretz, J.; Quaresma, M.; Quintans, C.; Ramos, S.; Regali, C.; Reicherz, G.; Riedl, C.; Rogacheva, N.S.; Ryabchikov, D.I.; Rybnikov, A.; Rychter, A.; Salac, R.; Samoylenko, V.D.; Sandacz, A.; Santos, C.; Sarkar, S.; Savin, I.A.; Sawada, T.; Sbrizzai, G.; Schiavon, P.; Schlüter, T.; Schmidt, K.; Schmieden, H.; Schönning, K.; Seder, E.; Selyunin, A.; Silva, L.; Sinha, L.; Sirtl, S.; Slunecka, M.; Smolik, J.; Srnka, A.; Steffen, D.; Stolarski, M.; Subrt, O.; Sulc, M.; Suzuki, H.; Szameitat, T.; Sznajder, P.; Tasevsky, M.; Tessaro, S.; Tessarotto, F.; Thiel, A.; Tomsa, J.; Tosello, F.; Tskhay, V.; Uhl, S.; Vasilishin, B.I.; Vauth, A.; Veloso, J.; Vidon, A.; Virius, M.; Wallner, S.; Weisrock, T.; Wilfert, M.; ter Wolbeek, J.; Zaremba, K.; Zavada, P.; Zavertyaev, M.; Zemlyanichkina, E.; Zhuravlev, N.; Ziembicki, M.
2017-01-01
We present a new amplitude analysis of the $\\eta\\pi$ $D$-wave in $\\pi^- p\\to \\eta\\pi^- p$ measured by COMPASS. Employing an analytical model based on the principles of the relativistic $S$-matrix, we find two resonances that can be identified with the $a_2(1320)$ and the excited $a_2^\\prime(1700)$, and perform a comprehensive analysis of their pole positions. For the mass and width of the $a_2$ we find $M=(1307 \\pm 1 \\pm 6)$~MeV and $\\Gamma=(112 \\pm 1 \\pm 8)$~MeV, and for the excited state $a_2^\\prime$ we obtain $M=(1720 \\pm 10 \\pm 60)$~MeV and $\\Gamma=(280\\pm 10 \\pm 70)$~MeV, respectively.
Electromagnetic game modeling through Tensor Analysis of Networks and Game Theory
Maurice, Olivier; Reineix, Alain; Lalléchère, Sébastien
2014-10-01
A complex system involves events coming from natural behaviors. Whatever is the complicated face of machines, they are still far from the complexity of natural systems. Currently, economy is one of the rare science trying to find out some ways to model human behavior. These attempts involve game theory and psychology. Our purpose is to develop a formalism able to take in charge both game and hardware modeling. We first present the Tensorial Analysis of Networks, used for the material part of the system. Then, we detail the mathematical objects defined in order to describe the evolution of the system and its gaming side. To illustrate the discussion we consider the case of a drone whose electronic can be disturbed by a radar field, but this drone must fly as near as possible close to this radar.
Analysis of diffusion tensor imaging metrics for gliomas grading at 3 T.
Server, Andrés; Graff, Bjørn A; Josefsen, Roger; Orheim, Tone E D; Schellhorn, Till; Nordhøy, Wibeke; Nakstad, Per H
2014-03-01
To assess the diagnostic accuracy of axial diffusivity (AD), radial diffusivity (RD), apparent diffusion coefficient (ADC) and fractional anisotropy (FA) values derived from DTI for grading of glial tumors, and to estimate the correlation between DTI parameters and tumor grades. Seventy-eight patients with glial tumors underwent DTI. AD, RD, ADC and FA values of tumor, peritumoral edema and contralateral normal-appearing white matter (NAWM) and AD, RD, ADC and FA ratios: lowest average AD, RD, ADC and FA values in tumor or peritumoral edema to AD, RD, ADC and FA of NAWM were calculated. DTI parameters and tumor grades were analyzed statistically and with Pearson correlation. Receiver operating characteristic (ROC) curve analysis was also performed. The differences in ADC, AD and RD tumor values, and ADC and RD tumor ratios were statistically significant between grades II and III, grades II and IV, and between grades II and III-IV. The AD tumor ratio differed significantly among all tumor grades. Tumor ADC, AD, RD and glial tumor grades were strongly correlated. In the ROC curve analysis, the area under the curve (AUC) of the parameter tumor ADC was the largest for distinguishing grade II from grades III to IV (98.5%), grade II from grade IV (98.9%) and grade II from grade III (97.0%). ADC, RD and AD are useful DTI parameters for differentiation between low- and high-grade gliomas with a diagnostic accuracy of more than 90%. Our study revealed a good inverse correlation between ADC, RD, AD and WHO grades II-IV astrocytic tumors. Copyright © 2014 Elsevier Ireland Ltd. All rights reserved.
Directory of Open Access Journals (Sweden)
E.M. Meintjes
2014-01-01
Full Text Available Reductions in brain volumes represent a neurobiological signature of fetal alcohol spectrum disorders (FASD. Less clear is how regional brain tissue reductions differ after normalizing for brain size differences linked with FASD and whether these profiles can predict the degree of prenatal exposure to alcohol. To examine associations of regional brain tissue excesses/deficits with degree of prenatal alcohol exposure and diagnosis with and without correction for overall brain volume, tensor-based morphometry (TBM methods were applied to structural imaging data from a well-characterized, demographically homogeneous sample of children diagnosed with FASD (n = 39, 9.6–11.0 years and controls (n = 16, 9.5–11.0 years. Degree of prenatal alcohol exposure was significantly associated with regionally pervasive brain tissue reductions in: (1 the thalamus, midbrain, and ventromedial frontal lobe, (2 the superior cerebellum and inferior occipital lobe, (3 the dorsolateral frontal cortex, and (4 the precuneus and superior parietal lobule. When overall brain size was factored out of the analysis on a subject-by-subject basis, no regions showed significant associations with alcohol exposure. FASD diagnosis was associated with a similar deformation pattern, but few of the regions survived FDR correction. In data-driven independent component analyses (ICA regional brain tissue deformations successfully distinguished individuals based on extent of prenatal alcohol exposure and to a lesser degree, diagnosis. The greater sensitivity of the continuous measure of alcohol exposure compared with the categorical diagnosis across diverse brain regions underscores the dose dependence of these effects. The ICA results illustrate that profiles of brain tissue alterations may be a useful indicator of prenatal alcohol exposure when reliable historical data are not available and facial features are not apparent.
Aliotta, Rachel; Cox, Jennifer L; Donohue, Katelyn; Weinstock-Guttman, Bianca; Yeh, E Ann; Polak, Paul; Dwyer, Michael G; Zivadinov, Robert
2014-01-01
White matter (WM) microstructure may vary significantly in pediatric-onset (PO) and adult-onset (AO) patients with multiple sclerosis (MS), a difference that could be explained by the effects of an inherent plasticity in the affected pediatric brains early in the disease, and a phenomenon that does not occur later in life. This hypothesis would support the observation that disease progression is much slower in POMS compared to AOMS patients. To examine WM microstructure in the brain of adults with POMS and AOMS, using tract based spatial statistics (TBSS) analysis of diffusion-tensor imaging (DTI). Adults with relapsing-remitting (RR) POMS, who were diagnosed before age of 18 years (n = 16), were compared with age-matched (AOA, n = 23) and disease duration-matched (AOD, n = 22) RR patients who developed MS after the age of 18 years. Scans were analyzed using the FSL software package (Oxford, UK) and statistics were performed using TBSS to evaluate WM microstructure between groups based on the mean fractional anisotropy (FA) values obtained from the DTI. Widespread cortical and deep WM area differences characterized by increased FA values were seen in the AOAMS compared with POMS group (P < 0.05, TFCE corrected). Significantly increased FA values of posterior WM areas were detected in the AODMS compared with POMS group (P < 0.05, TFCE corrected). Increased FA values in WM areas of the AOMS compared with the POMS patients suggest that diffuse WM microstructure changes are more attributable to age of onset than a simple function of disease duration and age. Copyright © 2012 Wiley Periodicals, Inc.
Structure of tensor operators in SU3
Energy Technology Data Exchange (ETDEWEB)
Biedenharn, L.C.; Flath, D.E.
1984-03-01
A global algebraic formulation of SU3 tensor operator structure is achieved. A single irreducible unitary representation (irrep), V, of kappa(6, 2) is constructed which contains every SU3 irrep precisely once. An algebra of polynomial differential operators A acting on V is given. The algebra A is shown to consist of linear combinations of all SU3 tensor operators with polynomial invariant operators as coefficients. By carrying out an analysis of A, the multiplicity problem for SU3 tensor operators is resolved.
Tensors and their applications
Islam, Nazrul
2006-01-01
About the Book: The book is written is in easy-to-read style with corresponding examples. The main aim of this book is to precisely explain the fundamentals of Tensors and their applications to Mechanics, Elasticity, Theory of Relativity, Electromagnetic, Riemannian Geometry and many other disciplines of science and engineering, in a lucid manner. The text has been explained section wise, every concept has been narrated in the form of definition, examples and questions related to the concept taught. The overall package of the book is highly useful and interesting for the people associated with the field. Contents: Preliminaries Tensor Algebra Metric Tensor and Riemannian Metric Christoffel`s Symbols and Covariant Differentiation Riemann-Christoffel Tensor The e-Systems and the Generalized Krönecker Deltas Geometry Analytical Mechanics Curvature of a Curve, Geodesic Parallelism of Vectors Ricci`s Coefficients of Rotation and Congruence Hyper Surfaces
Orthogonal tensor decompositions
Energy Technology Data Exchange (ETDEWEB)
Tamara G. Kolda
2000-03-01
The authors explore the orthogonal decomposition of tensors (also known as multi-dimensional arrays or n-way arrays) using two different definitions of orthogonality. They present numerous examples to illustrate the difficulties in understanding such decompositions. They conclude with a counterexample to a tensor extension of the Eckart-Young SVD approximation theorem by Leibovici and Sabatier [Linear Algebra Appl. 269(1998):307--329].
Pavan Kumar, G.; Kumar, Virender; Nagar, Mehul; Singh, Dilip; Mahendar, E.; Patel, Pruthul; Mahesh, P.
2017-07-01
The 2001 Bhuj earthquake (Mw 7.7) occurred in northwestern region of Indian peninsula has reactivated a couple of transverse faults to its surroundings. Intermediate to moderate magnitude earthquakes are occurring along these faults which includes recent Dholavira earthquake (Mw 5.1, 2012) suggesting distinct tectonic scenario in the region. We present the results of magnetotelluric (MT) impedance tensors analyses of 18 sites located along a profile cutting various faults in the uplifted Wagad block of the Kachchh basin. The MT time series of 4-5 days recording duration have been processed and the earth response functions are estimated in broad frequency range (0.01-1000 s). The observed impedance tensors are analyzed by using three decomposition techniques as well as by the phase tensor method constraining with the induction arrows. The analyses suggest distinct tectonic feature within the block bounded by the South Wagad Fault (SWF) and the North Wagad Fault (NWF) particularly in the period band of 1-10 s. In the south of NWF, the telluric vectors and the major axes of the phase ellipses are aligned in the NNW-SSE to NW-SE direction where as a dominant E-W strike is obtained for northern side of the NWF. The transverse geo-electric strike coincides with the prominent clustering of seismicity after the Bhuj earthquake and trend of the Manfara transverse fault is located in close vicinity of the study area. We therefore suggest the presence NNW-SSE trending transverse structural feature in the Wagad uplift of the basin appears to play significant role in the current seismicity of the active intraplate region.
Calculus of tensors and differential forms
Sinha, Rajnikant
2014-01-01
Calculus of tensors and differential forms is an introductory-level textbook. Through this book, students will familiarize themselves with tools they need in order to use for further study on general relativity and research, such as affine tensors, tensor calculus on manifolds, relative tensors, Lie derivatives, wedge products, differential forms, and Stokes' theorem. The treatment is concrete and in detail, so that abstract concepts do not deter even physics and engineering students. This self contained book requires undergraduate-level calculus of several variables and linear algebra as prerequisite. Fubini's theorem in real analysis, to be used in Stokes' theorem, has been proved earlier than Stokes' theorem so that students don't have to search elsewhere.
Tensors, relativity, and cosmology
Dalarsson, Mirjana
2015-01-01
Tensors, Relativity, and Cosmology, Second Edition, combines relativity, astrophysics, and cosmology in a single volume, providing a simplified introduction to each subject that is followed by detailed mathematical derivations. The book includes a section on general relativity that gives the case for a curved space-time, presents the mathematical background (tensor calculus, Riemannian geometry), discusses the Einstein equation and its solutions (including black holes and Penrose processes), and considers the energy-momentum tensor for various solutions. In addition, a section on relativistic astrophysics discusses stellar contraction and collapse, neutron stars and their equations of state, black holes, and accretion onto collapsed objects, with a final section on cosmology discussing cosmological models, observational tests, and scenarios for the early universe. This fully revised and updated second edition includes new material on relativistic effects, such as the behavior of clocks and measuring rods in m...
Symmetric Tensor Decomposition
DEFF Research Database (Denmark)
Brachat, Jerome; Comon, Pierre; Mourrain, Bernard
2010-01-01
We present an algorithm for decomposing a symmetric tensor, of dimension n and order d, as a sum of rank-1 symmetric tensors, extending the algorithm of Sylvester devised in 1886 for binary forms. We recall the correspondence between the decomposition of a homogeneous polynomial in n variables....... Exploiting this duality, we propose necessary and sufficient conditions for the existence of such a decomposition of a given rank, using the properties of Hankel (and quasi-Hankel) matrices, derived from multivariate polynomials and normal form computations. This leads to the resolution of systems...
Zhu, Lin; Guo, Wei-Li; Deng, Su-Ping; Huang, De-Shuang
2016-01-01
In recent years, thanks to the efforts of individual scientists and research consortiums, a huge amount of chromatin immunoprecipitation followed by high-throughput sequencing (ChIP-seq) experimental data have been accumulated. Instead of investigating them independently, several recent studies have convincingly demonstrated that a wealth of scientific insights can be gained by integrative analysis of these ChIP-seq data. However, when used for the purpose of integrative analysis, a serious drawback of current ChIP-seq technique is that it is still expensive and time-consuming to generate ChIP-seq datasets of high standard. Most researchers are therefore unable to obtain complete ChIP-seq data for several TFs in a wide variety of cell lines, which considerably limits the understanding of transcriptional regulation pattern. In this paper, we propose a novel method called ChIP-PIT to overcome the aforementioned limitation. In ChIP-PIT, ChIP-seq data corresponding to a diverse collection of cell types, TFs and genes are fused together using the three-mode pair-wise interaction tensor (PIT) model, and the prediction of unperformed ChIP-seq experimental results is formulated as a tensor completion problem. Computationally, we propose efficient first-order method based on extensions of coordinate descent method to learn the optimal solution of ChIP-PIT, which makes it particularly suitable for the analysis of massive scale ChIP-seq data. Experimental evaluation the ENCODE data illustrate the usefulness of the proposed model.
Energy Technology Data Exchange (ETDEWEB)
Alsing, Paul M; McDonald, Jonathan R [Information Directorate, Air Force Research Laboratory, Rome, NY 13441 (United States); Miller, Warner A, E-mail: jonathan.mcdonald.ctr@rl.af.mil [Department of Physics, Florida Atlantic University, Boca Raton, FL 33431 (United States)
2011-08-07
The Ricci tensor (Ric) is fundamental to Einstein's geometric theory of gravitation. The three-dimensional Ric of a spacelike surface vanishes at the moment of time symmetry for vacuum spacetimes. The four-dimensional Ric is the Einstein tensor for such spacetimes. More recently, the Ric was used by Hamilton to define a nonlinear, diffusive Ricci flow (RF) that was fundamental to Perelman's proof of the Poincare conjecture. Analytic applications of RF can be found in many fields including general relativity and mathematics. Numerically it has been applied broadly to communication networks, medical physics, computer design and more. In this paper, we use Regge calculus (RC) to provide the first geometric discretization of the Ric. This result is fundamental for higher dimensional generalizations of discrete RF. We construct this tensor on both the simplicial lattice and its dual and prove their equivalence. We show that the Ric is an edge-based weighted average of deficit divided by an edge-based weighted average of dual area-an expression similar to the vertex-based weighted average of the scalar curvature reported recently. We use this Ric in a third and independent geometric derivation of the RC Einstein tensor in arbitrary dimensions.
Evaluation of bayesian tensor estimation using tensor coherence.
Kim, Dae-Jin; Kim, In-Young; Jeong, Seok-Oh; Park, Hae-Jeong
2009-06-21
Fiber tractography, a unique and non-invasive method to estimate axonal fibers within white matter, constructs the putative streamlines from diffusion tensor MRI by interconnecting voxels according to the propagation direction defined by the diffusion tensor. This direction has uncertainties due to the properties of underlying fiber bundles, neighboring structures and image noise. Therefore, robust estimation of the diffusion direction is essential to reconstruct reliable fiber pathways. For this purpose, we propose a tensor estimation method using a Bayesian framework, which includes an a priori probability distribution based on tensor coherence indices, to utilize both the neighborhood direction information and the inertia moment as regularization terms. The reliability of the proposed tensor estimation was evaluated using Monte Carlo simulations in terms of accuracy and precision with four synthetic tensor fields at various SNRs and in vivo human data of brain and calf muscle. Proposed Bayesian estimation demonstrated the relative robustness to noise and the higher reliability compared to the simple tensor regression.
Evaluation of Bayesian tensor estimation using tensor coherence
Kim, Dae-Jin; Kim, In-Young; Jeong, Seok-Oh; Park, Hae-Jeong
2009-06-01
Fiber tractography, a unique and non-invasive method to estimate axonal fibers within white matter, constructs the putative streamlines from diffusion tensor MRI by interconnecting voxels according to the propagation direction defined by the diffusion tensor. This direction has uncertainties due to the properties of underlying fiber bundles, neighboring structures and image noise. Therefore, robust estimation of the diffusion direction is essential to reconstruct reliable fiber pathways. For this purpose, we propose a tensor estimation method using a Bayesian framework, which includes an a priori probability distribution based on tensor coherence indices, to utilize both the neighborhood direction information and the inertia moment as regularization terms. The reliability of the proposed tensor estimation was evaluated using Monte Carlo simulations in terms of accuracy and precision with four synthetic tensor fields at various SNRs and in vivo human data of brain and calf muscle. Proposed Bayesian estimation demonstrated the relative robustness to noise and the higher reliability compared to the simple tensor regression.
Quantum Critical Scaling of the Geometric Tensors
Campos Venuti, Lorenzo; Zanardi, Paolo
2007-08-01
Berry phases and the quantum-information theoretic notion of fidelity have been recently used to analyze quantum phase transitions from a geometrical perspective. In this Letter we unify these two approaches showing that the underlying mechanism is the critical singular behavior of a complex tensor over the Hamiltonian parameter space. This is achieved by performing a scaling analysis of this quantum geometric tensor in the vicinity of the critical points. In this way most of the previous results are understood on general grounds and new ones are found. We show that criticality is not a sufficient condition to ensure superextensive divergence of the geometric tensor, and state the conditions under which this is possible. The validity of this analysis is further checked by exact diagonalization of the spin-1/2 XXZ Heisenberg chain.
Gogny interactions with tensor terms
Energy Technology Data Exchange (ETDEWEB)
Anguiano, M.; Lallena, A.M.; Bernard, R.N. [Universidad de Granada, Departamento de Fisica Atomica, Molecular y Nuclear, Granada (Spain); Co' , G. [INFN, Lecce (Italy); De Donno, V. [Universita del Salento, Dipartimento di Matematica e Fisica ' ' E. De Giorgi' ' , Lecce (Italy); Grasso, M. [Universite Paris-Sud, Institut de Physique Nucleaire, IN2P3-CNRS, Orsay (France)
2016-07-15
We present a perturbative approach to include tensor terms in the Gogny interaction. We do not change the values of the usual parameterisations, with the only exception of the spin-orbit term, and we add tensor terms whose only free parameters are the strengths of the interactions. We identify observables sensitive to the presence of the tensor force in Hartree-Fock, Hartree-Fock-Bogoliubov and random phase approximation calculations. We show the need of including two tensor contributions, at least: a pure tensor term and a tensor-isospin term. We show results relevant for the inclusion of the tensor term for single-particle energies, charge-conserving magnetic excitations and Gamow-Teller excitations. (orig.)
DEFF Research Database (Denmark)
Ziegel, Johanna; Nyengaard, Jens Randel; Jensen, Eva B. Vedel
In the present paper, statistical procedures for estimating shape and orientation of arbitrary three-dimensional particles are developed. The focus of this work is on the case where the particles cannot be observed directly, but only via sections. Volume tensors are used for describing particle...... shape and orientation, and stereological estimators of the tensors are derived. It is shown that these estimators can be combined to provide consistent estimators of the moments of the so-called particle cover density. The covariance structure associated with the particle cover density depends...... on the orientation and shape of the particles. For instance, if the distribution of the typical particle is invariant under all rotations, then the covariance matrix is proportional to the identity matrix. A non-parametric test for such isotropy is developed. A flexible L\\'evy-based particle model is proposed, which...
Brown, Eric
2008-10-01
Some of the most beautiful and complex theories in physics are formulated in the language of tensors. While powerful, these methods are sometimes daunting to the uninitiated. I will introduce the use of Clifford Algebra as a practical alternative to the use of tensors. Many physical quantities can be represented in an indexless form. The boundary between the classical and the quantum worlds becomes a little more transparent. I will review some key concepts, and then talk about some of the things that I am doing with this interesting and powerful tool. Of note to some will be the development of rigid body dynamics for a game engine. Others may be interested in expressing the connection on a spin bundle. My intent is to prove to the audience that there exists an accessible mathematical tool that can be employed to probe the most difficult of topics in physics.
Tensor calculus for engineers and physicists
de Souza Sánchez Filho, Emil
2016-01-01
This textbook provides a rigorous approach to tensor manifolds in several aspects relevant for Engineers and Physicists working in industry or academia. With a thorough, comprehensive, and unified presentation, this book offers insights into several topics of tensor analysis, which covers all aspects of N dimensional spaces. The main purpose of this book is to give a self-contained yet simple, correct and comprehensive mathematical explanation of tensor calculus for undergraduate and graduate students and for professionals. In addition to many worked problems, this book features a selection of examples, solved step by step. Although no emphasis is placed on special and particular problems of Engineering or Physics, the text covers the fundamentals of these fields of science. The book makes a brief introduction into the basic concept of the tensorial formalism so as to allow the reader to make a quick and easy review of the essential topics that enable having the grounds for the subsequent themes, without need...
LENUS (Irish Health Repository)
Murphy, Melissa L
2011-09-01
Fractional anisotropy anomalies occurring in the white matter tracts in the brains of depressed patients may reflect microstructural changes underlying the pathophysiology of this disorder. We conducted a meta-analysis of fractional anisotropy abnormalities occurring in major depressive disorder using voxel-based diffusion tensor imaging studies. Using the Embase, PubMed and Google Scholar databases, 89 relevant data sets were identified, of which 7 (including 188 patients with major depressive disorder and 221 healthy controls) met our inclusion criteria. Authors were contacted to retrieve any additional data required. Coordinates were extracted from clusters of significant white matter fractional anisotropy differences between patients and controls. Relevant demographic, clinical and methodological variables were extracted from each study or obtained directly from authors. The meta-analysis was carried out using Signed Differential Mapping. Patients with depression showed decreased white matter fractional anisotropy values in the superior longitudinal fasciculus and increased fractional anisotropy values in the fronto-occipital fasciculus compared to controls. Using quartile and jackknife sensitivity analysis, we found that reduced fractional anisotropy in the left superior longitudinal fasciculus was very stable, with increases in the right fronto-occipital fasciculus driven by just one study. In conclusion, our meta-analysis revealed a significant reduction in fractional anisotropy values in the left superior longitudinal fasciculus, which may ultimately play an important role in the pathology of depression.
LENUS (Irish Health Repository)
Murphy, Melissa L
2011-09-27
Abstract Fractional anisotropy anomalies occurring in the white matter tracts in the brains of depressed patients may reflect microstructural changes underlying the pathophysiology of this disorder. We conducted a meta-analysis of fractional anisotropy abnormalities occurring in major depressive disorder using voxel-based diffusion tensor imaging studies. Using the Embase, PubMed and Google Scholar databases, 89 relevant data sets were identified, of which 7 (including 188 patients with major depressive disorder and 221 healthy controls) met our inclusion criteria. Authors were contacted to retrieve any additional data required. Coordinates were extracted from clusters of significant white matter fractional anisotropy differences between patients and controls. Relevant demographic, clinical and methodological variables were extracted from each study or obtained directly from authors. The meta-analysis was carried out using Signed Differential Mapping. Patients with depression showed decreased white matter fractional anisotropy values in the superior longitudinal fasciculus and increased fractional anisotropy values in the fronto-occipital fasciculus compared to controls. Using quartile and jackknife sensitivity analysis, we found that reduced fractional anisotropy in the left superior longitudinal fasciculus was very stable, with increases in the right fronto-occipital fasciculus driven by just one study. In conclusion, our meta-analysis revealed a significant reduction in fractional anisotropy values in the left superior longitudinal fasciculus, which may ultimately play an important role in the pathology of depression.
Tensor deep stacking networks.
Hutchinson, Brian; Deng, Li; Yu, Dong
2013-08-01
A novel deep architecture, the tensor deep stacking network (T-DSN), is presented. The T-DSN consists of multiple, stacked blocks, where each block contains a bilinear mapping from two hidden layers to the output layer, using a weight tensor to incorporate higher order statistics of the hidden binary (½0; 1) features. A learning algorithm for the T-DSN’s weight matrices and tensors is developed and described in which the main parameter estimation burden is shifted to a convex subproblem with a closed-form solution. Using an efficient and scalable parallel implementation for CPU clusters, we train sets of T-DSNs in three popular tasks in increasing order of the data size: handwritten digit recognition using MNIST (60k), isolated state/phone classification and continuous phone recognition using TIMIT (1.1 m), and isolated phone classification using WSJ0 (5.2 m). Experimental results in all three tasks demonstrate the effectiveness of the T-DSN and the associated learning methods in a consistent manner. In particular, a sufficient depth of the T-DSN, a symmetry in the two hidden layers structure in each T-DSN block, our model parameter learning algorithm, and a softmax layer on top of T-DSN are shown to have all contributed to the low error rates observed in the experiments for all three tasks.
Alsing, Paul M; Miller, Warner A; 10.1088/0264-9381/28/15/155007
2011-01-01
The Ricci tensor (Ric) is fundamental to Einstein's geometric theory of gravitation. The 3-dimensional Ric of a spacelike surface vanishes at the moment of time symmetry for vacuum spacetimes. The 4-dimensional Ric is the Einstein tensor for such spacetimes. More recently the Ric was used by Hamilton to define a non-linear, diffusive Ricci flow (RF) that was fundamental to Perelman's proof of the Poincare conjecture. Analytic applications of RF can be found in many fields including general relativity and mathematics. Numerically it has been applied broadly to communication networks, medical physics, computer design and more. In this paper, we use Regge calculus (RC) to provide the first geometric discretization of the Ric. This result is fundamental for higher-dimensional generalizations of discrete RF. We construct this tensor on both the simplicial lattice and its dual and prove their equivalence. We show that the Ric is an edge-based weighted average of deficit divided by an edge-based weighted average of ...
Andreev, Pavel A
2016-01-01
The dielectric permeability tensor for spin polarized plasmas is derived in terms of the spin-1/2 quantum kinetic model in six-dimensional phase space. Expressions for the distribution function and spin distribution function are derived in linear approximations on the path of dielectric permeability tensor derivation. The dielectric permeability tensor is derived the spin-polarized degenerate electron gas. It is also discussed at the finite temperature regime, where the equilibrium distribution function is presented by the spin-polarized Fermi-Dirac distribution. Consideration of the spin-polarized equilibrium states opens possibilities for the kinetic modeling of the thermal spin current contribution in the plasma dynamics.
Tensor Factorization for Low-Rank Tensor Completion.
Zhou, Pan; Lu, Canyi; Lin, Zhouchen; Zhang, Chao
2018-03-01
Recently, a tensor nuclear norm (TNN) based method was proposed to solve the tensor completion problem, which has achieved state-of-the-art performance on image and video inpainting tasks. However, it requires computing tensor singular value decomposition (t-SVD), which costs much computation and thus cannot efficiently handle tensor data, due to its natural large scale. Motivated by TNN, we propose a novel low-rank tensor factorization method for efficiently solving the 3-way tensor completion problem. Our method preserves the low-rank structure of a tensor by factorizing it into the product of two tensors of smaller sizes. In the optimization process, our method only needs to update two smaller tensors, which can be more efficiently conducted than computing t-SVD. Furthermore, we prove that the proposed alternating minimization algorithm can converge to a Karush-Kuhn-Tucker point. Experimental results on the synthetic data recovery, image and video inpainting tasks clearly demonstrate the superior performance and efficiency of our developed method over state-of-the-arts including the TNN and matricization methods.
The geomagnetic field gradient tensor
DEFF Research Database (Denmark)
Kotsiaros, Stavros; Olsen, Nils
2012-01-01
of the magnetic gradient tensor and provide explicit expressions of its elements in terms of spherical harmonics. Finally we discuss the benefit of using gradient measurements for exploring the Earth’s magnetic field from space, in particular the advantage of the various tensor elements for a better determination......We develop the general mathematical basis for space magnetic gradiometry in spherical coordinates. The magnetic gradient tensor is a second rank tensor consisting of 3 × 3 = 9 spatial derivatives. Since the geomagnetic field vector B is always solenoidal (∇ · B = 0) there are only eight independent...
Visualizing Tensor Normal Distributions at Multiple Levels of Detail.
Abbasloo, Amin; Wiens, Vitalis; Hermann, Max; Schultz, Thomas
2016-01-01
Despite the widely recognized importance of symmetric second order tensor fields in medicine and engineering, the visualization of data uncertainty in tensor fields is still in its infancy. A recently proposed tensorial normal distribution, involving a fourth order covariance tensor, provides a mathematical description of how different aspects of the tensor field, such as trace, anisotropy, or orientation, vary and covary at each point. However, this wealth of information is far too rich for a human analyst to take in at a single glance, and no suitable visualization tools are available. We propose a novel approach that facilitates visual analysis of tensor covariance at multiple levels of detail. We start with a visual abstraction that uses slice views and direct volume rendering to indicate large-scale changes in the covariance structure, and locations with high overall variance. We then provide tools for interactive exploration, making it possible to drill down into different types of variability, such as in shape or orientation. Finally, we allow the analyst to focus on specific locations of the field, and provide tensor glyph animations and overlays that intuitively depict confidence intervals at those points. Our system is demonstrated by investigating the effects of measurement noise on diffusion tensor MRI, and by analyzing two ensembles of stress tensor fields from solid mechanics.
Asymptotic tensor rank of graph tensors: beyond matrix multiplication
M. Christandl (Matthias); P. Vrana (Péter); J. Zuiddam (Jeroen)
2016-01-01
textabstractWe present an upper bound on the exponent of the asymptotic behaviour of the tensor rank of a family of tensors defined by the complete graph on $k$ vertices. For $k\\geq4$, we show that the exponent per edge is at most 0.77, outperforming the best known upper bound on the exponent per
Genten: Software for Generalized Tensor Decompositions v. 1.0.0
Energy Technology Data Exchange (ETDEWEB)
2017-06-22
Tensors, or multidimensional arrays, are a powerful mathematical means of describing multiway data. This software provides computational means for decomposing or approximating a given tensor in terms of smaller tensors of lower dimension, focusing on decomposition of large, sparse tensors. These techniques have applications in many scientific areas, including signal processing, linear algebra, computer vision, numerical analysis, data mining, graph analysis, neuroscience and more. The software is designed to take advantage of parallelism present emerging computer architectures such has multi-core CPUs, many-core accelerators such as the Intel Xeon Phi, and computation-oriented GPUs to enable efficient processing of large tensors.
Dark energy in scalar-tensor theories
Energy Technology Data Exchange (ETDEWEB)
Moeller, J.
2007-12-15
We investigate several aspects of dynamical dark energy in the framework of scalar-tensor theories of gravity. We provide a classification of scalar-tensor coupling functions admitting cosmological scaling solutions. In particular, we recover that Brans-Dicke theory with inverse power-law potential allows for a sequence of background dominated scaling regime and scalar field dominated, accelerated expansion. Furthermore, we compare minimally and non-minimally coupled models, with respect to the small redshift evolution of the dark energy equation of state. We discuss the possibility to discriminate between different models by a reconstruction of the equation-of-state parameter from available observational data. The non-minimal coupling characterizing scalar-tensor models can - in specific cases - alleviate fine tuning problems, which appear if (minimally coupled) quintessence is required to mimic a cosmological constant. Finally, we perform a phase-space analysis of a family of biscalar-tensor models characterized by a specific type of {sigma}-model metric, including two examples from recent literature. In particular, we generalize an axion-dilaton model of Sonner and Townsend, incorporating a perfect fluid background consisting of (dark) matter and radiation. (orig.)
Wiseman, S J; Bastin, M E; Hamilton, I F; Hunt, D; Ritchie, S J; Amft, E N; Thomson, S; Belch, J F F; Ralston, S H; Wardlaw, J M
2017-05-01
Objective The objective of this study was to investigate fatigue and cognitive impairments in systemic lupus erythematous (SLE) in relation to diffuse white matter microstructural brain damage. Methods Diffusion tensor MRI, used to generate biomarkers of brain white matter microstructural integrity, was obtained in patients with SLE and age-matched controls. Fatigue and cognitive function were assessed and related to SLE activity, clinical data and plasma biomarkers of inflammation and endothelial dysfunction. Results Fifty-one patients with SLE (mean age 48.8 ± 14.3 years) were included. Mean diffusivity (MD) was significantly higher in all white matter fibre tracts in SLE patients versus age-matched healthy controls ( p < 0.0001). Fatigue in SLE was higher than a normal reference range ( p < 0.0001) and associated with lower MD ( ß = -0.61, p = 0.02), depression ( ß = 0.17, p = 0.001), anxiety ( ß = 0.13, p = 0.006) and higher body mass index ( ß = 0.10, p = 0.004) in adjusted analyses. Poorer cognitive function was associated with longer SLE disease duration ( p = 0.003) and higher MD ( p = 0.03) and, in adjusted analysis, higher levels of IL-6 ( ß = -0.15, p = 0.02) but not with MD. Meta-analysis (10 studies, n = 261, including the present study) confirmed that patients with SLE have higher MD than controls. Conclusion Patients with SLE have more microstructural brain white matter damage for age than the general population, but this does not explain increased fatigue or lower cognition in SLE. The association between raised IL-6 and worse current cognitive function in SLE should be explored in larger datasets.
Tensor-based dynamic reconstruction method for electrical capacitance tomography
Lei, J.; Mu, H. P.; Liu, Q. B.; Li, Z. H.; Liu, S.; Wang, X. Y.
2017-03-01
Electrical capacitance tomography (ECT) is an attractive visualization measurement method, in which the acquisition of high-quality images is beneficial for the understanding of the underlying physical or chemical mechanisms of the dynamic behaviors of the measurement objects. In real-world measurement environments, imaging objects are often in a dynamic process, and the exploitation of the spatial-temporal correlations related to the dynamic nature will contribute to improving the imaging quality. Different from existing imaging methods that are often used in ECT measurements, in this paper a dynamic image sequence is stacked into a third-order tensor that consists of a low rank tensor and a sparse tensor within the framework of the multiple measurement vectors model and the multi-way data analysis method. The low rank tensor models the similar spatial distribution information among frames, which is slowly changing over time, and the sparse tensor captures the perturbations or differences introduced in each frame, which is rapidly changing over time. With the assistance of the Tikhonov regularization theory and the tensor-based multi-way data analysis method, a new cost function, with the considerations of the multi-frames measurement data, the dynamic evolution information of a time-varying imaging object and the characteristics of the low rank tensor and the sparse tensor, is proposed to convert the imaging task in the ECT measurement into a reconstruction problem of a third-order image tensor. An effective algorithm is developed to search for the optimal solution of the proposed cost function, and the images are reconstructed via a batching pattern. The feasibility and effectiveness of the developed reconstruction method are numerically validated.
Tensor Network Contractions for #SAT
Biamonte, Jacob D.; Morton, Jason; Turner, Jacob
2015-09-01
The computational cost of counting the number of solutions satisfying a Boolean formula, which is a problem instance of #SAT, has proven subtle to quantify. Even when finding individual satisfying solutions is computationally easy (e.g. 2-SAT, which is in ), determining the number of solutions can be #-hard. Recently, computational methods simulating quantum systems experienced advancements due to the development of tensor network algorithms and associated quantum physics-inspired techniques. By these methods, we give an algorithm using an axiomatic tensor contraction language for n-variable #SAT instances with complexity where c is the number of COPY-tensors, g is the number of gates, and d is the maximal degree of any COPY-tensor. Thus, n-variable counting problems can be solved efficiently when their tensor network expression has at most COPY-tensors and polynomial fan-out. This framework also admits an intuitive proof of a variant of the Tovey conjecture (the r,1-SAT instance of the Dubois-Tovey theorem). This study increases the theory, expressiveness and application of tensor based algorithmic tools and provides an alternative insight on these problems which have a long history in statistical physics and computer science.
Energy Technology Data Exchange (ETDEWEB)
Qin, Yuan-Yuan [Huazhong University of Science and Technology, Department of Radiology, Tongji Hospital, Tongji Medical College, Wuhan (China); The Johns Hopkins University School of Medicine, The Russell H. Morgan Department of Radiology and Radiological Science, Baltimore, MD (United States); Li, Mu-Wei; Oishi, Kenichi [The Johns Hopkins University School of Medicine, The Russell H. Morgan Department of Radiology and Radiological Science, Baltimore, MD (United States); Zhang, Shun; Zhang, Yan; Zhao, Ling-Yun; Zhu, Wen-Zhen [Huazhong University of Science and Technology, Department of Radiology, Tongji Hospital, Tongji Medical College, Wuhan (China); Lei, Hao [Chinese Academy of Sciences, Wuhan Center for Magnetic Resonance, State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Wuhan (China)
2013-08-15
Diffusion tensor imaging (DTI) has been applied to characterize the pathological features of Alzheimer's disease (AD) in a mouse model, although little is known about whether these features are structure specific. Voxel-based analysis (VBA) and atlas-based analysis (ABA) are good complementary tools for whole-brain DTI analysis. The purpose of this study was to identify the spatial localization of disease-related pathology in an AD mouse model. VBA and ABA quantification were used for the whole-brain DTI analysis of nine APP/PS1 mice and wild-type (WT) controls. Multiple scalar measurements, including fractional anisotropy (FA), trace, axial diffusivity (DA), and radial diffusivity (DR), were investigated to capture the various types of pathology. The accuracy of the image transformation applied for VBA and ABA was evaluated by comparing manual and atlas-based structure delineation using kappa statistics. Following the MR examination, the brains of the animals were analyzed for microscopy. Extensive anatomical alterations were identified in APP/PS1 mice, in both the gray matter areas (neocortex, hippocampus, caudate putamen, thalamus, hypothalamus, claustrum, amygdala, and piriform cortex) and the white matter areas (corpus callosum/external capsule, cingulum, septum, internal capsule, fimbria, and optic tract), evidenced by an increase in FA or DA, or both, compared to WT mice (p < 0.05, corrected). The average kappa value between manual and atlas-based structure delineation was approximately 0.8, and there was no significant difference between APP/PS1 and WT mice (p > 0.05). The histopathological changes in the gray matter areas were confirmed by microscopy studies. DTI did, however, demonstrate significant changes in white matter areas, where the difference was not apparent by qualitative observation of a single-slice histological specimen. This study demonstrated the structure-specific nature of pathological changes in APP/PS1 mouse, and also showed the
Jiang, Jing; Zhao, You-Jin; Hu, Xin-Yu; Du, Ming-Ying; Chen, Zi-Qi; Wu, Min; Li, Kai-Ming; Zhu, Hong-Yan; Kumar, Poornima; Gong, Qi-Yong
2017-01-01
Background Multiple meta-analyses of diffusion tensor imaging (DTI) studies have reported impaired white matter integrity in patients with major depressive disorder (MDD). However, owing to inclusion of medicated patients in these studies, it is difficult to conclude whether these reported alterations are associated with MDD or confounded by medication effects. A meta-analysis of DTI studies on medication-free (medication-naive and medication washout) patients with MDD would therefore be necessary to disentangle MDD-specific effects. Methods We analyzed white matter alterations between medication-free patients with MDD and healthy controls using anisotropic effect size–signed differential mapping (AES-SDM). We used DTI query software for fibre tracking. Results Both pooled and subgroup meta-analyses in medication washout patients showed robust fractional anisotropy (FA) reductions in white matter of the right cerebellum hemispheric lobule, body of the corpus callosum (CC) and bilateral superior longitudinal fasciculus III (SLF III), whereas FA reductions in the genu of the CC and right anterior thalamic projections were seen in only medication-naive patients. Fibre tracking showed that the main tracts with observed FA reductions included the right cerebellar tracts, body of the CC, bilateral SLF III and arcuate fascicle. Limitations The analytic techniques, patient characteristics and clinical variables of the included studies were heterogeneous; we could not exclude the effects of nondrug therapies owing to a lack of data. Conclusion By excluding the confounding influences of current medication status, findings from the present study may provide a better understanding of the underlying neuropathology of MDD. PMID:27780031
Sijens, PE; Irwan, R; Potze, JH; Mostert, JP; De Keyser, J; Oudkerk, M
Primary progressive multiple sclerosis (ppMS; n=4) patients and controls (n=4) were examined by 1H magnetic resonance spectroscopy (MRS) and diffusion tensor imaging (DTI) in order to map choline (Cho), creatine and N-acetylaspartate (NAA), the fractional anisotropy (FA) and the apparent diffusion
Energy Technology Data Exchange (ETDEWEB)
Yasmin, Hasina; Nakata, Yasuhiro; Abe, Osamu; Masutani, Yoshitaka; Ohtomo, Kuni [University of Tokyo, Department of Radiology, Tokyo (Japan); Aoki, Shigeki [University of Tokyo, Department of Radiology, Tokyo (Japan); Sato, Noriko [National Center of Neurology and Psychiatry, Department of Radiology, National Center Hospital for Mental, Nervous and Muscular Disorders, Tokyo (Japan); Nemoto, Kiyotaka [Ibaraki Prefectural Tomobe Hospital, Department of Psychiatry, Ibaraki (Japan); Arima, Kunimasa; Furuta, Nobuo [National Center of Neurology and Psychiatry, Department of Psychiatry, National Center Hospital for Mental, Nervous and Muscular Disorders, Tokyo (Japan); Uno, Masatake [Yoshioka Rehabilitation Clinic, Department of Psychiatry, Tokyo (Japan); Hirai, Shigeo [Iruma Hirai Clinic, Department of Psychiatry, Saitama (Japan)
2008-04-15
Our aim was to determine diffusion abnormalities in the uncinate fasciculus (UF) in Alzheimer's disease (AD) by diffusion tensor tractography (DTT) using a new method for measuring the core of the tract. We studied 19 patients with AD and 19 age-matched control subjects who underwent MRI using diffusion tensor imaging (DTI). DTT of the UF was generated. The mean diffusivity (MD) and fractional anisotropy (FA) of the core of the tract were measured after voxelized tract shape processing. Student's t-test was used to compare results between patients with AD and controls. Intraobserver correlation tests were also performed. FA was significantly lower (P < 0.0001) in the UF of patients with AD than of controls. There was no significant difference in MD along the UF between the two groups. Intraobserver reliability (intraclass correlation coefficient) for the first and second measurement was r > 0.93 for measured FA and r > 0.92 for measured MD. Our results suggest that FA reflects progression of AD-related histopathological changes in the UF of the white matter and may represent a useful biological index in monitoring AD. Diffusion tensor tract-specific analysis with voxelized tract shape processing to measure the core of the tract may be a sensitive tool for evaluation of diffusion abnormalities of white matter tracts in AD. (orig.)
Expression of strain tensor in orthogonal curvilinear coordinates
Directory of Open Access Journals (Sweden)
Xuyan Liu
2010-01-01
Full Text Available Based on an analysis of connotation and extension of the concept of the orthogonal curvilinear coordinates, we have deduced a platform of strain tensor expression of Cartesian coordinates, which turns out to be a function of Lame coefficient and unit vector. By using transform matrix between Cartesian coordinates and orthogonal curvilinear coordinates, we have deduced a mathematical expression for correcting displacement vector differential in orthogonal curvilinear coordinates, and given a general expression of strain tensor in orthogonal curvilinear coordinates.
Salo, Raimo A; Miettinen, Tuukka; Laitinen, Teemu; Gröhn, Olli; Sierra, Alejandra
2017-05-15
Imaging markers for monitoring disease progression, recovery, and treatment efficacy are a major unmet need for many neurological diseases, including epilepsy. Recent evidence suggests that diffusion tensor imaging (DTI) provides high microstructural contrast even outside major white matter tracts. We hypothesized that in vivo DTI could detect progressive microstructural changes in the dentate gyrus and the hippocampal CA3bc in the rat brain after status epilepticus (SE). To test this hypothesis, we induced SE with systemic kainic acid or pilocarpine in adult male Wistar rats and subsequently scanned them using in vivo DTI at five time-points: prior to SE, and 10, 20, 34, and 79 days post SE. In order to tie the DTI findings to changes in the tissue microstructure, myelin- and glial fibrillary acidic protein (GFAP)-stained sections from the same animals underwent Fourier analysis. We compared the Fourier analysis parameters, anisotropy index and angle of myelinated axons or astrocyte processes, to corresponding DTI parameters, fractional anisotropy (FA) and the orientation angle of the principal eigenvector. We found progressive detectable changes in DTI parameters in both the dentate gyrus (FA, axial diffusivity [D||], linear anisotropy [CL] and spherical anisotropy [CS], p<0.001, linear mixed-effects model [LMEM]) and the CA3bc (FA, D||, CS, and angle, p<0.001, LMEM; CL and planar anisotropy [CP], p<0.01, LMEM) post SE. The Fourier analysis revealed that both myelinated axons and astrocyte processes played a role in the water diffusion anisotropy changes detected by DTI in individual portions of the dentate gyrus (suprapyramidal blade, mid-portion, and infrapyramidal blade). In the whole dentate gyrus, myelinated axons markedly contributed to the water diffusion changes. In CA3bc as well as in CA3b and CA3c, both myelinated axons and astrocyte processes contributed to water diffusion anisotropy and orientation. Our study revealed that DTI is a promising method
Colored Tensor Models - a Review
Directory of Open Access Journals (Sweden)
Razvan Gurau
2012-04-01
Full Text Available Colored tensor models have recently burst onto the scene as a promising conceptual and computational tool in the investigation of problems of random geometry in dimension three and higher. We present a snapshot of the cutting edge in this rapidly expanding research field. Colored tensor models have been shown to share many of the properties of their direct ancestor, matrix models, which encode a theory of fluctuating two-dimensional surfaces. These features include the possession of Feynman graphs encoding topological spaces, a 1/N expansion of graph amplitudes, embedded matrix models inside the tensor structure, a resumable leading order with critical behavior and a continuum large volume limit, Schwinger-Dyson equations satisfying a Lie algebra (akin to the Virasoro algebra in two dimensions, non-trivial classical solutions and so on. In this review, we give a detailed introduction of colored tensor models and pointers to current and future research directions.
Generalized Slow Roll for Tensors
Hu, Wayne
2014-01-01
The recent BICEP2 detection of degree scale CMB B-mode polarization, coupled with a deficit of observed power in large angle temperature anisotropy, suggest that the slow-roll parameter $\\epsilon_H$, the fractional variation in the Hubble rate per efold, is both relatively large and may evolve from an even larger value on scales greater than the horizon at recombination. The relatively large tensor contribution implied also requires finite matching features in the tensor power spectrum for an...
An Introduction to Tensors for Students of Physics and Engineering
Kolecki, Joseph C.
2002-01-01
Tensor analysis is the type of subject that can make even the best of students shudder. My own post-graduate instructor in the subject took away much of the fear by speaking of an implicit rhythm in the peculiar notation traditionally used, and helped us to see how this rhythm plays its way throughout the various formalisms. Prior to taking that class, I had spent many years "playing" on my own with tensors. I found the going to be tremendously difficult but was able, over time, to back out some physical and geometrical considerations that helped to make the subject a little more transparent. Today, it is sometimes hard not to think in terms of tensors and their associated concepts. This article, prompted and greatly enhanced by Marlos Jacob, whom I've met only by e-mail, is an attempt to record those early notions concerning tensors. It is intended to serve as a bridge from the point where most undergraduate students "leave off" in their studies of mathematics to the place where most texts on tensor analysis begin. A basic knowledge of vectors, matrices, and physics is assumed. A semi-intuitive approach to those notions underlying tensor analysis is given via scalars, vectors, dyads, triads, and higher vector products. The reader must be prepared to do some mathematics and to think. For those students who wish to go beyond this humble start, I can only recommend my professor's wisdom: find the rhythm in the mathematics and you will fare pretty well.
Positivity and conservation of superenergy tensors
Pozo, J M
2002-01-01
Two essential properties of energy-momentum tensors T submu subnu are their positivity and conservation. This is mathematically formalized by, respectively, an energy condition, as the dominant energy condition, and the vanishing of their divergence nabla supmu T submu subnu = 0. The classical Bel and Bel-Robinson superenergy tensors, generated from the Riemann and Weyl tensors, respectively, are rank-4 tensors. But they share these two properties with energy-momentum tensors: the dominant property (DP) and the divergence-free property in the absence of sources (vacuum). Senovilla defined a universal algebraic construction which generates a basic superenergy tensor T left brace A right brace from any arbitrary tensor A. In this construction, the seed tensor A is structured as an r-fold multivector, which can always be done. The most important feature of the basic superenergy tensors is that they satisfy automatically the DP, independently of the generating tensor A. We presented a more compact definition of T...
Development of the Tensoral Computer Language
Ferziger, Joel; Dresselhaus, Eliot
1996-01-01
The research scientist or engineer wishing to perform large scale simulations or to extract useful information from existing databases is required to have expertise in the details of the particular database, the numerical methods and the computer architecture to be used. This poses a significant practical barrier to the use of simulation data. The goal of this research was to develop a high-level computer language called Tensoral, designed to remove this barrier. The Tensoral language provides a framework in which efficient generic data manipulations can be easily coded and implemented. First of all, Tensoral is general. The fundamental objects in Tensoral represent tensor fields and the operators that act on them. The numerical implementation of these tensors and operators is completely and flexibly programmable. New mathematical constructs and operators can be easily added to the Tensoral system. Tensoral is compatible with existing languages. Tensoral tensor operations co-exist in a natural way with a host language, which may be any sufficiently powerful computer language such as Fortran, C, or Vectoral. Tensoral is very-high-level. Tensor operations in Tensoral typically act on entire databases (i.e., arrays) at one time and may, therefore, correspond to many lines of code in a conventional language. Tensoral is efficient. Tensoral is a compiled language. Database manipulations are simplified optimized and scheduled by the compiler eventually resulting in efficient machine code to implement them.
The Perturbation Bound for the Spectral Radius of a Nonnegative Tensor
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Wen Li
2014-01-01
to estimate the spectral radius of a nonnegative tensor in general. On the other hand, we study the backward error matrix ΔA and obtain its smallest error bound for its perturbed largest eigenvalue and associated eigenvector of an irreducible nonnegative tensor. Based on the backward error analysis, we can estimate the stability of computation of the largest eigenvalue of an irreducible nonnegative tensor by the NQZ algorithm. Numerical examples are presented to illustrate the theoretical results of our perturbation analysis.
Obtaining orthotropic elasticity tensor using entries zeroing method.
Gierlach, Bartosz; Danek, Tomasz
2017-04-01
rotation. Computations were parallelized with OpenMP to decrease computational time what enables different tensors to be processed by different threads. As a result the distributions of rotated tensor entries values were obtained. For the entries which were to be zeroed we can observe almost normal distributions having mean equal to zero or sum of two normal distributions having inverse means. Non-zero entries represent different distributions with two or three maxima. Analysis of obtained results shows that described method produces consistent values of quaternions used to rotate tensors. Despite of less complex target function in a process of optimization in comparison to common approach, entries zeroing method provides results which can be applied to obtain an orthotropic tensor with good reliability. Modification of the method can produce also a tool for obtaining effective tensors belonging to another symmetry classes. This research was supported by the Polish National Science Center under contract No. DEC-2013/11/B/ST10/0472.
Octupolar tensors for liquid crystals
Chen, Yannan; Qi, Liqun; Virga, Epifanio G.
2018-01-01
A third-rank three-dimensional symmetric traceless tensor, called the octupolar tensor, has been introduced to study tetrahedratic nematic phases in liquid crystals. The octupolar potential, a scalar-valued function generated on the unit sphere by that tensor, should ideally have four maxima (on the vertices of a tetrahedron), but it was recently found to possess an equally generic variant with three maxima instead of four. It was also shown that the irreducible admissible region for the octupolar tensor in a three-dimensional parameter space is bounded by a dome-shaped surface, beneath which is a separatrix surface connecting the two generic octupolar states. The latter surface, which was obtained through numerical continuation, may be physically interpreted as marking a possible intra-octupolar transition. In this paper, by using the resultant theory of algebraic geometry and the E-characteristic polynomial of spectral theory of tensors, we give a closed-form, algebraic expression for both the dome-shaped surface and the separatrix surface. This turns the envisaged intra-octupolar transition into a quantitative, possibly observable prediction.
Kiriushcheva, N.; Kuzmin, S. V.; McKeon, D. G. C.
2005-01-01
The peculiarities of doing a canonical analysis of the first order formulation of the Einstein-Hilbert action in terms of either the metric tensor $g^{\\alpha \\beta}$ or the metric density $h^{\\alpha \\beta}= \\sqrt{-g}g^{\\alpha \\beta}$ along with the affine connection are discussed. It is shown that the difference between using $g^{\\alpha \\beta}$ as opposed to $h^{\\alpha \\beta}$ appears only in two spacetime dimensions. Despite there being a different number of constraints in these two approach...
Spectral Tensor-Train Decomposition
DEFF Research Database (Denmark)
Bigoni, Daniele; Engsig-Karup, Allan Peter; Marzouk, Youssef M.
2016-01-01
.e., the “cores”) comprising the functional TT decomposition. This result motivates an approximation scheme employing polynomial approximations of the cores. For functions with appropriate regularity, the resulting spectral tensor-train decomposition combines the favorable dimension-scaling of the TT......The accurate approximation of high-dimensional functions is an essential task in uncertainty quantification and many other fields. We propose a new function approximation scheme based on a spectral extension of the tensor-train (TT) decomposition. We first define a functional version of the TT...
STRUCTURE TENSOR IMAGE FILTERING USING RIEMANNIAN L1 AND L∞ CENTER-OF-MASS
Directory of Open Access Journals (Sweden)
Jesus Angulo
2014-06-01
Full Text Available Structure tensor images are obtained by a Gaussian smoothing of the dyadic product of gradient image. These images give at each pixel a n×n symmetric positive definite matrix SPD(n, representing the local orientation and the edge information. Processing such images requires appropriate algorithms working on the Riemannian manifold on the SPD(n matrices. This contribution deals with structure tensor image filtering based on Lp geometric averaging. In particular, L1 center-of-mass (Riemannian median or Fermat-Weber point and L∞ center-of-mass (Riemannian circumcenter can be obtained for structure tensors using recently proposed algorithms. Our contribution in this paper is to study the interest of L1 and L∞ Riemannian estimators for structure tensor image processing. In particular, we compare both for two image analysis tasks: (i structure tensor image denoising; (ii anomaly detection in structure tensor images.
Tensor calculus for physics a concise guide
Neuenschwander, Dwight E
2015-01-01
Understanding tensors is essential for any physics student dealing with phenomena where causes and effects have different directions. A horizontal electric field producing vertical polarization in dielectrics; an unbalanced car wheel wobbling in the vertical plane while spinning about a horizontal axis; an electrostatic field on Earth observed to be a magnetic field by orbiting astronauts—these are some situations where physicists employ tensors. But the true beauty of tensors lies in this fact: When coordinates are transformed from one system to another, tensors change according to the same rules as the coordinates. Tensors, therefore, allow for the convenience of coordinates while also transcending them. This makes tensors the gold standard for expressing physical relationships in physics and geometry. Undergraduate physics majors are typically introduced to tensors in special-case applications. For example, in a classical mechanics course, they meet the "inertia tensor," and in electricity and magnetism...
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Tachibana, Yasuhiko [National Institute of Radiological Sciences, Research Center for Charged Particle Therapy, Chiba (Japan); Yokohama City University Graduate School of Medicine, Department of Radiology, Yokohama (Japan); Juntendo University School of Medicine, Department of Radiology, Tokyo (Japan); Obata, Takayuki [National Institute of Radiological Sciences, Research Center for Charged Particle Therapy, Chiba (Japan); Yoshida, Mariko; Hori, Masaaki; Kamagata, Koji; Suzuki, Michimasa; Fukunaga, Issei; Kamiya, Kouhei; Aoki, Shigeki [Juntendo University School of Medicine, Department of Radiology, Tokyo (Japan); Yokoyama, Kazumasa; Hattori, Nobutaka [Juntendo University School of Medicine, Department of Neurology, Tokyo (Japan); Inoue, Tomio [Yokohama City University Graduate School of Medicine, Department of Radiology, Yokohama (Japan)
2015-06-01
To compare the significance of the two-compartment model, considering diffusional anisotropy with conventional diffusion analyzing methods regarding the detection of occult changes in normal-appearing white matter (NAWM) of multiple sclerosis (MS). Diffusion-weighted images (nine b-values with six directions) were acquired from 12 healthy female volunteers (22-52 years old, median 33 years) and 13 female MS patients (24-48 years old, median 37 years). Diffusion parameters based on the two-compartment model of water diffusion considering diffusional anisotropy was calculated by a proposed method. Other parameters including diffusion tensor imaging and conventional apparent diffusion coefficient (ADC) were also obtained. They were compared statistically between the control and MS groups. Diffusion of the slow diffusion compartment in the radial direction of neuron fibers was elevated in MS patients (0.121 x 10{sup -3} mm{sup 2}/s) in comparison to control (0.100 x 10{sup -3} mm{sup 2}/s), the difference being significant (P = 0.001). The difference between the groups was not significant in other comparisons, including conventional ADC and fractional anisotropy (FA) of diffusion tensor imaging. The proposed method was applicable to clinically acceptable small data. The parameters obtained by this method improved the detectability of occult changes in NAWM compared to the conventional methods. (orig.)
Vilanova, Anna; Burgeth, Bernhard; Visualization and Processing of Tensors and Higher Order Descriptors for Multi-Valued Data
2014-01-01
Arising from the fourth Dagstuhl conference entitled Visualization and Processing of Tensors and Higher Order Descriptors for Multi-Valued Data (2011), this book offers a broad and vivid view of current work in this emerging field. Topics covered range from applications of the analysis of tensor fields to research on their mathematical and analytical properties. Part I, Tensor Data Visualization, surveys techniques for visualization of tensors and tensor fields in engineering, discusses the current state of the art and challenges, and examines tensor invariants and glyph design, including an overview of common glyphs. The second Part, Representation and Processing of Higher-order Descriptors, describes a matrix representation of local phase, outlines mathematical morphological operations techniques, extended for use in vector images, and generalizes erosion to the space of diffusion weighted MRI. Part III, Higher Order Tensors and Riemannian-Finsler Geometry, offers powerful mathematical language to model and...
Surgery in colored tensor models
Pérez-Sánchez, Carlos I.
2017-10-01
Rooted in group field theory and matrix models, random tensor models are a recent background-invariant approach to quantum gravity in arbitrary dimensions. Colored tensor models (CTM) generate random triangulated orientable (pseudo)-manifolds. We analyze, in low dimensions, which known spaces are triangulated by specific CTM interactions. As a tool, we develop the graph-encoded surgery that is compatible with the quantum-field-theory-structure and use it to prove that a single model, the complex φ4-interaction in rank- 2, generates all orientable 2-bordisms, thus, in particular, also all orientable, closed surfaces. We show that certain quartic rank- 3 CTM, the φ34 -theory, has as boundary sector all closed, possibly disconnected, orientable surfaces. Hence all closed orientable surfaces are cobordant via manifolds generated by the φ34 -theory.
Hyperinvariant Tensor Networks and Holography
Evenbly, Glen
2017-10-01
We propose a new class of tensor network state as a model for the AdS /CFT correspondence and holography. This class is demonstrated to retain key features of the multiscale entanglement renormalization ansatz (MERA), in that they describe quantum states with algebraic correlation functions, have free variational parameters, and are efficiently contractible. Yet, unlike the MERA, they are built according to a uniform tiling of hyperbolic space, without inherent directionality or preferred locations in the holographic bulk, and thus circumvent key arguments made against the MERA as a model for AdS /CFT . Novel holographic features of this tensor network class are examined, such as an equivalence between the causal cones C (R ) and the entanglement wedges E (R ) of connected boundary regions R .
The metric theory of tensor products Grothendieck's resume revisited
Diestel, Joe; Swart, Johan; Swarte, Johannes Laurentius; Diestel, Joseph
2008-01-01
Grothendieck's Resumé is a landmark in functional analysis. Despite having appeared more than a half century ago, its techniques and results are still not widely known nor appreciated. This is due, no doubt, to the fact that Grothendieck included practically no proofs, and the presentation is based on the theory of the very abstract notion of tensor products. This book aims at providing the details of Grothendieck's constructions and laying bare how the important classes of operators are a consequence of the abstract operations on tensor norms. Particular attention is paid to how the classical
Diffusion tensor optical coherence tomography
Marks, Daniel L.; Blackmon, Richard L.; Oldenburg, Amy L.
2018-01-01
In situ measurements of diffusive particle transport provide insight into tissue architecture, drug delivery, and cellular function. Analogous to diffusion-tensor magnetic resonance imaging (DT-MRI), where the anisotropic diffusion of water molecules is mapped on the millimeter scale to elucidate the fibrous structure of tissue, here we propose diffusion-tensor optical coherence tomography (DT-OCT) for measuring directional diffusivity and flow of optically scattering particles within tissue. Because DT-OCT is sensitive to the sub-resolution motion of Brownian particles as they are constrained by tissue macromolecules, it has the potential to quantify nanoporous anisotropic tissue structure at micrometer resolution as relevant to extracellular matrices, neurons, and capillaries. Here we derive the principles of DT-OCT, relating the detected optical signal from a minimum of six probe beams with the six unique diffusion tensor and three flow vector components. The optimal geometry of the probe beams is determined given a finite numerical aperture, and a high-speed hardware implementation is proposed. Finally, Monte Carlo simulations are employed to assess the ability of the proposed DT-OCT system to quantify anisotropic diffusion of nanoparticles in a collagen matrix, an extracellular constituent that is known to become highly aligned during tumor development.
Shape anisotropy: tensor distance to anisotropy measure
Weldeselassie, Yonas T.; El-Hilo, Saba; Atkins, M. S.
2011-03-01
Fractional anisotropy, defined as the distance of a diffusion tensor from its closest isotropic tensor, has been extensively studied as quantitative anisotropy measure for diffusion tensor magnetic resonance images (DT-MRI). It has been used to reveal the white matter profile of brain images, as guiding feature for seeding and stopping in fiber tractography and for the diagnosis and assessment of degenerative brain diseases. Despite its extensive use in DT-MRI community, however, not much attention has been given to the mathematical correctness of its derivation from diffusion tensors which is achieved using Euclidean dot product in 9D space. But, recent progress in DT-MRI has shown that the space of diffusion tensors does not form a Euclidean vector space and thus Euclidean dot product is not appropriate for tensors. In this paper, we propose a novel and robust rotationally invariant diffusion anisotropy measure derived using the recently proposed Log-Euclidean and J-divergence tensor distance measures. An interesting finding of our work is that given a diffusion tensor, its closest isotropic tensor is different for different tensor distance metrics used. We demonstrate qualitatively that our new anisotropy measure reveals superior white matter profile of DT-MR brain images and analytically show that it has a higher signal to noise ratio than fractional anisotropy.
Interactive Volume Rendering of Diffusion Tensor Data
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Hlawitschka, Mario; Weber, Gunther; Anwander, Alfred; Carmichael, Owen; Hamann, Bernd; Scheuermann, Gerik
2007-03-30
As 3D volumetric images of the human body become an increasingly crucial source of information for the diagnosis and treatment of a broad variety of medical conditions, advanced techniques that allow clinicians to efficiently and clearly visualize volumetric images become increasingly important. Interaction has proven to be a key concept in analysis of medical images because static images of 3D data are prone to artifacts and misunderstanding of depth. Furthermore, fading out clinically irrelevant aspects of the image while preserving contextual anatomical landmarks helps medical doctors to focus on important parts of the images without becoming disoriented. Our goal was to develop a tool that unifies interactive manipulation and context preserving visualization of medical images with a special focus on diffusion tensor imaging (DTI) data. At each image voxel, DTI provides a 3 x 3 tensor whose entries represent the 3D statistical properties of water diffusion locally. Water motion that is preferential to specific spatial directions suggests structural organization of the underlying biological tissue; in particular, in the human brain, the naturally occuring diffusion of water in the axon portion of neurons is predominantly anisotropic along the longitudinal direction of the elongated, fiber-like axons [MMM+02]. This property has made DTI an emerging source of information about the structural integrity of axons and axonal connectivity between brain regions, both of which are thought to be disrupted in a broad range of medical disorders including multiple sclerosis, cerebrovascular disease, and autism [Mos02, FCI+01, JLH+99, BGKM+04, BJB+03].
Tensor decomposition of EEG signals: a brief review.
Cong, Fengyu; Lin, Qiu-Hua; Kuang, Li-Dan; Gong, Xiao-Feng; Astikainen, Piia; Ristaniemi, Tapani
2015-06-15
Electroencephalography (EEG) is one fundamental tool for functional brain imaging. EEG signals tend to be represented by a vector or a matrix to facilitate data processing and analysis with generally understood methodologies like time-series analysis, spectral analysis and matrix decomposition. Indeed, EEG signals are often naturally born with more than two modes of time and space, and they can be denoted by a multi-way array called as tensor. This review summarizes the current progress of tensor decomposition of EEG signals with three aspects. The first is about the existing modes and tensors of EEG signals. Second, two fundamental tensor decomposition models, canonical polyadic decomposition (CPD, it is also called parallel factor analysis-PARAFAC) and Tucker decomposition, are introduced and compared. Moreover, the applications of the two models for EEG signals are addressed. Particularly, the determination of the number of components for each mode is discussed. Finally, the N-way partial least square and higher-order partial least square are described for a potential trend to process and analyze brain signals of two modalities simultaneously. Copyright © 2015 The Authors. Published by Elsevier B.V. All rights reserved.
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Sijens, Paul E.; Irwan, Roy; Potze, Jan Hendrik; Oudkerk, Matthijs [University Medical Center Groningen, Department of Radiology, Hanzeplein 1, Groningen (Netherlands); Mostert, Jop P.; Keyser, Jacques de [University Medical Center Groningen, Department of Neurology, Groningen (Netherlands)
2005-08-01
Primary progressive multiple sclerosis (ppMS; n=4) patients and controls (n=4) were examined by 1H magnetic resonance spectroscopy (MRS) and diffusion tensor imaging (DTI) in order to map choline (Cho), creatine and N-acetylaspartate (NAA), the fractional anisotropy (FA) and the apparent diffusion constant (ADC). After chemical shift imaging (point-resolved spectroscopy, repetition time/echo time 1,500 ms/135 ms) of a supraventricular volume of interest of 8 x 8 x 2 cm{sup 3} (64 voxels) MRS peak areas were matched to the results of DTI for the corresponding volume elements. Mean FA and NAA values were reduced in the ppMS patients (P<0.01, both) and the ADC increased (P<0.02). The spatial distribution of NAA showed strong correlation to ADC in both ppMS patients and controls (r =-0.74 and r= -0.70; P<0.00001, both), and weaker correlations to FA (r=0.49 and r=0.41; P<0.00001, all). FA and ADC also correlated significantly with Cho in patients and controls (P<0.00001, all). The relationship of Cho and NAA to the ADC and the FA and thus to the content of neuronal structures suggests that these metabolite signals essentially originate from axons (NAA) and the myelin sheath (Cho). This is of interest in view of previous reports in which Cho increases were associated with demyelination and the subsequent breakdown of neurons. (orig.)
Tensor power spectrum and disformal transformations
Fumagalli, Jacopo; Postma, Marieke
2016-01-01
In a general effective theory description of inflation a disformal transformation can be used to set the tensor sound speed to one. After the transformation, the tensor power spectrum then automatically only depends on the Hubble parameter. We show that this disformal transformation, however, is nothing else than a change of units. It is a very useful tool for simplifying and interpreting computations, but it cannot change any physics. While the apparent parametrical dependence of the tensor power spectrum does change under a disformal transformation, the physics described is frame invariant. We further illustrate the frame invariance of the tensor power spectrum by writing it exclusively in terms of separately invariant quantities.
Diffusion Tensor Estimation by Maximizing Rician Likelihood.
Landman, Bennett; Bazin, Pierre-Louis; Prince, Jerry
2007-01-01
Diffusion tensor imaging (DTI) is widely used to characterize white matter in health and disease. Previous approaches to the estimation of diffusion tensors have either been statistically suboptimal or have used Gaussian approximations of the underlying noise structure, which is Rician in reality. This can cause quantities derived from these tensors - e.g., fractional anisotropy and apparent diffusion coefficient - to diverge from their true values, potentially leading to artifactual changes that confound clinically significant ones. This paper presents a novel maximum likelihood approach to tensor estimation, denoted Diffusion Tensor Estimation by Maximizing Rician Likelihood (DTEMRL). In contrast to previous approaches, DTEMRL considers the joint distribution of all observed data in the context of an augmented tensor model to account for variable levels of Rician noise. To improve numeric stability and prevent non-physical solutions, DTEMRL incorporates a robust characterization of positive definite tensors and a new estimator of underlying noise variance. In simulated and clinical data, mean squared error metrics show consistent and significant improvements from low clinical SNR to high SNR. DTEMRL may be readily supplemented with spatial regularization or a priori tensor distributions for Bayesian tensor estimation.
The tensor network theory library
Al-Assam, S.; Clark, S. R.; Jaksch, D.
2017-09-01
In this technical paper we introduce the tensor network theory (TNT) library—an open-source software project aimed at providing a platform for rapidly developing robust, easy to use and highly optimised code for TNT calculations. The objectives of this paper are (i) to give an overview of the structure of TNT library, and (ii) to help scientists decide whether to use the TNT library in their research. We show how to employ the TNT routines by giving examples of ground-state and dynamical calculations of one-dimensional bosonic lattice system. We also discuss different options for gaining access to the software available at www.tensornetworktheory.org.
Analyzing vortex breakdown flow structures by assignment of colors to tensor invariants.
Rütten, Markus; Chong, Min S
2006-01-01
Topological methods are often used to describe flow structures in fluid dynamics and topological flow field analysis usually relies on the invariants of the associated tensor fields. A visual impression of the local properties of tensor fields is often complex and the search of a suitable technique for achieving this is an ongoing topic in visualization. This paper introduces and assesses a method of representing the topological properties of tensor fields and their respective flow patterns with the use of colors. First, a tensor norm is introduced, which preserves the properties of the tensor and assigns the tensor invariants to values of the RGB color space. Secondly, the RGB colors of the tensor invariants are transferred to corresponding hue values as an alternative color representation. The vectorial tensor invariants field is reduced to a scalar hue field and visualization of iso-surfaces of this hue value field allows us to identify locations with equivalent flow topology. Additionally highlighting by the maximum of the eigenvalue difference field reflects the magnitude of the structural change of the flow. The method is applied on a vortex breakdown flow structure inside a cylinder with a rotating lid.
Tensor decomposition of EEG signals: A brief review
Cong, Fengyu; Lin, Qiu-Hua; Kuang, Li-Dan; Gong, Xiao-Feng; Astikainen, Piia; Ristaniemi, Tapani
2015-01-01
Electroencephalography (EEG) is one fundamental tool for functional brain imaging. EEG signals tend to be represented by a vector or a matrix to facilitate data processing and analysis with generally understood methodologies like time-series analysis, spectral analysis and matrix decomposition. Indeed, EEG signals are often naturally born with more than two modes of time and space, and they can be denoted by a multi-way array called as tensor. This review summarizes the current pr...
An optimization approach for fitting canonical tensor decompositions.
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Dunlavy, Daniel M. (Sandia National Laboratories, Albuquerque, NM); Acar, Evrim; Kolda, Tamara Gibson
2009-02-01
Tensor decompositions are higher-order analogues of matrix decompositions and have proven to be powerful tools for data analysis. In particular, we are interested in the canonical tensor decomposition, otherwise known as the CANDECOMP/PARAFAC decomposition (CPD), which expresses a tensor as the sum of component rank-one tensors and is used in a multitude of applications such as chemometrics, signal processing, neuroscience, and web analysis. The task of computing the CPD, however, can be difficult. The typical approach is based on alternating least squares (ALS) optimization, which can be remarkably fast but is not very accurate. Previously, nonlinear least squares (NLS) methods have also been recommended; existing NLS methods are accurate but slow. In this paper, we propose the use of gradient-based optimization methods. We discuss the mathematical calculation of the derivatives and further show that they can be computed efficiently, at the same cost as one iteration of ALS. Computational experiments demonstrate that the gradient-based optimization methods are much more accurate than ALS and orders of magnitude faster than NLS.
3D reconstruction of tensors and vectors
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Defrise, Michel; Gullberg, Grant T.
2005-02-17
Here we have developed formulations for the reconstruction of 3D tensor fields from planar (Radon) and line-integral (X-ray) projections of 3D vector and tensor fields. Much of the motivation for this work is the potential application of MRI to perform diffusion tensor tomography. The goal is to develop a theory for the reconstruction of both Radon planar and X-ray or line-integral projections because of the flexibility of MRI to obtain both of these type of projections in 3D. The development presented here for the linear tensor tomography problem provides insight into the structure of the nonlinear MRI diffusion tensor inverse problem. A particular application of tensor imaging in MRI is the potential application of cardiac diffusion tensor tomography for determining in vivo cardiac fiber structure. One difficulty in the cardiac application is the motion of the heart. This presents a need for developing future theory for tensor tomography in a motion field. This means developing a better understanding of the MRI signal for diffusion processes in a deforming media. The techniques developed may allow the application of MRI tensor tomography for the study of structure of fiber tracts in the brain, atherosclerotic plaque, and spine in addition to fiber structure in the heart. However, the relations presented are also applicable to other fields in medical imaging such as diffraction tomography using ultrasound. The mathematics presented can also be extended to exponential Radon transform of tensor fields and to other geometric acquisitions such as cone beam tomography of tensor fields.
A few cosmological implications of tensor nonlocalities
Ferreira, Pedro G.; Maroto, Antonio L.
2013-12-01
We consider nonlocal gravity theories that include tensor nonlocalities. We show that in the cosmological context, the tensor nonlocalities, unlike scalar ones, generically give rise to growing modes. An explicit example with quadratic curvature terms is studied in detail. Possible consequences for recent nonlocal cosmological models proposed in the literature are also discussed.
A Simplified Algorithm for Inverting Higher Order Diffusion Tensors
Directory of Open Access Journals (Sweden)
Laura Astola
2014-11-01
Full Text Available In Riemannian geometry, a distance function is determined by an inner product on the tangent space. In Riemann–Finsler geometry, this distance function can be determined by a norm. This gives more freedom on the form of the so-called indicatrix or the set of unit vectors. This has some interesting applications, e.g., in medical image analysis, especially in diffusion weighted imaging (DWI. An important application of DWI is in the inference of the local architecture of the tissue, typically consisting of thin elongated structures, such as axons or muscle fibers, by measuring the constrained diffusion of water within the tissue. From high angular resolution diffusion imaging (HARDI data, one can estimate the diffusion orientation distribution function (dODF, which indicates the relative diffusivity in all directions and can be represented by a spherical polynomial. We express this dODF as an equivalent spherical monomial (higher order tensor to directly generalize the (second order diffusion tensor approach. To enable efficient computation of Riemann–Finslerian quantities on diffusion weighted (DW-images, such as the metric/norm tensor, we present a simple and efficient algorithm to invert even order spherical monomials, which extends the familiar inversion of diffusion tensors, i.e., symmetric matrices.
Elasticity $\\mathscr{M}$-tensors and the Strong Ellipticity Condition
Ding, Weiyang; Liu, Jinjie; Qi, Liqun; Yan, Hong
2017-01-01
In this paper, we propose a class of tensors satisfying the strong ellipticity condition. The elasticity $\\mathscr{M}$-tensor is defined with respect to the M-eigenvalues of elasticity tensors. We prove that any nonsingular elasticity $\\mathscr{M}$-tensor satisfies the strong ellipticity condition by employing a Perron-Frobenius-type theorem for M-spectral radii of nonnegative elasticity tensors. We also establish other equivalent definitions of nonsingular elasticity $\\mathscr{M}$-tensors.
Malecki, A.; Potdevin, G.; Biernath, T.; Eggl, E.; Willer, K.; Lasser, T.; Maisenbacher, J.; Gibmeier, J.; Wanner, A.; Pfeiffer, F.
2014-02-01
Here we introduce a new concept for x-ray computed tomography that yields information about the local micro-morphology and its orientation in each voxel of the reconstructed 3D tomogram. Contrary to conventional x-ray CT, which only reconstructs a single scalar value for each point in the 3D image, our approach provides a full scattering tensor with multiple independent structural parameters in each volume element. In the application example shown in this study, we highlight that our method can visualize sub-pixel fiber orientations in a carbon composite sample, hence demonstrating its value for non-destructive testing applications. Moreover, as the method is based on the use of a conventional x-ray tube, we believe that it will also have a great impact in the wider range of material science investigations and in future medical diagnostics. The authors declare no competing financial interests.
Depth inpainting by tensor voting.
Kulkarni, Mandar; Rajagopalan, Ambasamudram N
2013-06-01
Depth maps captured by range scanning devices or by using optical cameras often suffer from missing regions due to occlusions, reflectivity, limited scanning area, sensor imperfections, etc. In this paper, we propose a fast and reliable algorithm for depth map inpainting using the tensor voting (TV) framework. For less complex missing regions, local edge and depth information is utilized for synthesizing missing values. The depth variations are modeled by local planes using 3D TV, and missing values are estimated using plane equations. For large and complex missing regions, we collect and evaluate depth estimates from self-similar (training) datasets. We align the depth maps of the training set with the target (defective) depth map and evaluate the goodness of depth estimates among candidate values using 3D TV. We demonstrate the effectiveness of the proposed approaches on real as well as synthetic data.
On the possibility of blue tensor spectrum within single field inflation
Directory of Open Access Journals (Sweden)
Yi-Fu Cai
2015-11-01
Full Text Available We present a series of theoretical constraints on the potentially viable inflation models that might yield a blue spectrum for primordial tensor perturbations. By performing a detailed dynamical analysis we show that, while there exists such possibility, the corresponding phase space is strongly bounded. Our result implies that, in order to achieve a blue tilt for inflationary tensor perturbations, one may either construct a non-canonical inflation model delicately, or study the generation of primordial tensor modes beyond the standard scenario of single slow-roll field.
On the possibility of blue tensor spectrum within single field inflation
Energy Technology Data Exchange (ETDEWEB)
Cai, Yi-Fu, E-mail: yifucai@ustc.edu.cn [CAS Key Laboratory for Research in Galaxies and Cosmology, Department of Astronomy, University of Science and Technology of China, Chinese Academy of Sciences, Hefei, Anhui 230026 (China); Department of Physics, McGill University, Montréal, Quebec H3A 2T8 (Canada); Gong, Jinn-Ouk, E-mail: jinn-ouk.gong@apctp.org [Asia Pacific Center for Theoretical Physics, Pohang 790-784 (Korea, Republic of); Department of Physics, Postech, Pohang 790-784 (Korea, Republic of); Pi, Shi, E-mail: spi@apctp.org [Asia Pacific Center for Theoretical Physics, Pohang 790-784 (Korea, Republic of); Saridakis, Emmanuel N., E-mail: Emmanuel_Saridakis@baylor.edu [Physics Division, National Technical University of Athens, Zografou Campus, 15780 Athens (Greece); Instituto de Física, Pontificia Universidad de Católica de Valparaíso, Casilla 4950, Valparaíso (Chile); Wu, Shang-Yu, E-mail: loganwu@gmail.com [Department of Electrophysics, National Center for Theoretical Science, National Chiao Tung University, Hsinchu 300, Taiwan (China); Shing-Tung Yau Center, National Chiao Tung University, Hsinchu 300, Taiwan (China)
2015-11-15
We present a series of theoretical constraints on the potentially viable inflation models that might yield a blue spectrum for primordial tensor perturbations. By performing a detailed dynamical analysis we show that, while there exists such possibility, the corresponding phase space is strongly bounded. Our result implies that, in order to achieve a blue tilt for inflationary tensor perturbations, one may either construct a non-canonical inflation model delicately, or study the generation of primordial tensor modes beyond the standard scenario of single slow-roll field.
Conformal field theories and tensor categories. Proceedings
Energy Technology Data Exchange (ETDEWEB)
Bai, Chengming [Nankai Univ., Tianjin (China). Chern Institute of Mathematics; Fuchs, Juergen [Karlstad Univ. (Sweden). Theoretical Physics; Huang, Yi-Zhi [Rutgers Univ., Piscataway, NJ (United States). Dept. of Mathematics; Kong, Liang [Tsinghua Univ., Beijing (China). Inst. for Advanced Study; Runkel, Ingo; Schweigert, Christoph (eds.) [Hamburg Univ. (Germany). Dept. of Mathematics
2014-08-01
First book devoted completely to the mathematics of conformal field theories, tensor categories and their applications. Contributors include both mathematicians and physicists. Some long expository articles are especially suitable for beginners. The present volume is a collection of seven papers that are either based on the talks presented at the workshop ''Conformal field theories and tensor categories'' held June 13 to June 17, 2011 at the Beijing International Center for Mathematical Research, Peking University, or are extensions of the material presented in the talks at the workshop. These papers present new developments beyond rational conformal field theories and modular tensor categories and new applications in mathematics and physics. The topics covered include tensor categories from representation categories of Hopf algebras, applications of conformal field theories and tensor categories to topological phases and gapped systems, logarithmic conformal field theories and the corresponding non-semisimple tensor categories, and new developments in the representation theory of vertex operator algebras. Some of the papers contain detailed introductory material that is helpful for graduate students and researchers looking for an introduction to these research directions. The papers also discuss exciting recent developments in the area of conformal field theories, tensor categories and their applications and will be extremely useful for researchers working in these areas.
Local Tensor Radiation Conditions For Elastic Waves
DEFF Research Database (Denmark)
Krenk, S.; Kirkegaard, Poul Henning
2001-01-01
A local boundary condition is formulated, representing radiation of elastic waves from an arbitrary point source. The boundary condition takes the form of a tensor relation between the stress at a point on an arbitrarily oriented section and the velocity and displacement vectors at the point....... The tensor relation generalizes the traditional normal incidence impedance condition by accounting for the angle between wave propagation and the surface normal and by including a generalized stiffness term due to spreading of the waves. The effectiveness of the local tensor radiation condition...
Local transformations of units in scalar-tensor cosmology
Energy Technology Data Exchange (ETDEWEB)
Catena, R. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Pietroni, M. [INFN, Sezione di Padova (Italy); Scarabello, L. [INFN, Sezione di Padova (Italy)]|[Padua Univ. (Italy). Dipt. di Fisica
2006-10-15
The physical equivalence of Einstein and Jordan frame in Scalar Tensor theories has been explained by Dicke in 1962: they are related by a local transformation of units. We discuss this point in a cosmological framework. Our main result is the construction of a formalism in which all the physical observables are frame-invariant. The application of this approach to CMB codes is at present under analysis. (orig.)
Poincare Algebra Extension with Tensor Generator
Soroka, Dmitrij V.; Soroka, Vyacheslav A.
2005-01-01
A tensor extension of the Poincar\\'e algebra is proposed for the arbitrary dimensions. Casimir operators of the extension are constructed. A possible supersymmetric generalization of this extension is also found in the dimensions $D=2,3,4$.
Seamless warping of diffusion tensor fields
DEFF Research Database (Denmark)
Xu, Dongrong; Hao, Xuejun; Bansal, Ravi
2008-01-01
To warp diffusion tensor fields accurately, tensors must be reoriented in the space to which the tensors are warped based on both the local deformation field and the orientation of the underlying fibers in the original image. Existing algorithms for warping tensors typically use forward mapping...... deformations in an attempt to ensure that the local deformations in the warped image remains true to the orientation of the underlying fibers; forward mapping, however, can also create "seams" or gaps and consequently artifacts in the warped image by failing to define accurately the voxels in the template...... space where the magnitude of the deformation is large (e.g., |Jacobian| > 1). Backward mapping, in contrast, defines voxels in the template space by mapping them back to locations in the original imaging space. Backward mapping allows every voxel in the template space to be defined without the creation...
Entangled scalar and tensor fluctuations during inflation
Energy Technology Data Exchange (ETDEWEB)
Collins, Hael; Vardanyan, Tereza [Department of Physics, Carnegie Mellon University,5000 Forbes Avenue, Pittsburgh, Pennsylvania (United States)
2016-11-29
We show how the choice of an inflationary state that entangles scalar and tensor fluctuations affects the angular two-point correlation functions of the T, E, and B modes of the cosmic microwave background. The propagators for a state starting with some general quadratic entanglement are solved exactly, leading to predictions for the primordial scalar-scalar, tensor-tensor, and scalar-tensor power spectra. These power spectra are expressed in terms of general functions that describe the entangling structure of the initial state relative to the standard Bunch-Davies vacuum. We illustrate how such a state would modify the angular correlations in the CMB with a simple example where the initial state is a small perturbation away from the Bunch-Davies state. Because the state breaks some of the rotational symmetries, the angular power spectra no longer need be strictly diagonal.
Quantum theory with bold operator tensors.
Hardy, Lucien
2015-08-06
In this paper, we present a formulation of quantum theory in terms of bold operator tensors. A circuit is built up of operations where an operation corresponds to a use of an apparatus. We associate collections of operator tensors (which together comprise a bold operator) with these apparatus uses. We give rules for combining bold operator tensors such that, for a circuit, they give a probability distribution over the possible outcomes. If we impose certain physicality constraints on the bold operator tensors, then we get exactly the quantum formalism. We provide both symbolic and diagrammatic ways to represent these calculations. This approach is manifestly covariant in that it does not require us to foliate the circuit into time steps and then evolve a state. Thus, the approach forms a natural starting point for an operational approach to quantum field theory. © 2015 The Author(s) Published by the Royal Society. All rights reserved.
An introduction to linear algebra and tensors
Akivis, M A; Silverman, Richard A
1978-01-01
Eminently readable, completely elementary treatment begins with linear spaces and ends with analytic geometry, covering multilinear forms, tensors, linear transformation, and more. 250 problems, most with hints and answers. 1972 edition.
Tensor Field Visualization in Geomechanics Applications
Hotz, I.; Feng, L.; Hamann, B.; Joy, K.; Manaker, D.; Billen, M. I.; Kellogg, L. H.
2004-12-01
Scalar and vector fields, and especially tensor fields like stress and strain tensor fields, play an important role in the study of geophysics, including earthquakes. For example, time-varying tensor data result from modeling the behavior of bending plates. Application areas we focus on are concerned with a better understanding of bending phenomena in rocks, in the Earth's lithosphere, and in subducting slabs. The associated mathematical models and numerical simulations generate stress and strain data that are tensors. Tensors contain so much information and related components in each point that it is not easy to capture and visualize all information. Typically, researchers plot cross-sections or maps of individual components, which do not allow a view of all the information included in models or observational data. Therefore, it is important to provide scientists with an overview of an entire tensor field. We have developed a tensor field visualization method tailored specifically to the class of tensor fields exhibiting properties similar to stress and strain tensors, which are commonly encountered in geophysics/geomechanics. These tensor fields are characterized by the property that they have positive and negative eigenvalues. The sign of the eigenvalues indicates regions of expansion and compression. To understand field behavior visually, it is important to express these features in an intuitive way. Our technique is a global method providing an overview of an entire tensor field by using a continuous representation. The main idea it to represent a tensor field as a ``texture-deforming operator,'' which resembles deforming a piece of fabric to express the characteristic properties of a tensor field. The texture is stretched or compressed and bended according to the physical meaning of the tensor field. Large positive eigenvalues, which indicate tension, are illustrated by a texture with low density or a stretched piece of fabric. For negative eigenvalues
Correlators in tensor models from character calculus
Mironov, A.; Morozov, A.
2017-11-01
We explain how the calculations of [20], which provided the first evidence for non-trivial structures of Gaussian correlators in tensor models, are efficiently performed with the help of the (Hurwitz) character calculus. This emphasizes a close similarity between technical methods in matrix and tensor models and supports a hope to understand the emerging structures in very similar terms. We claim that the 2m-fold Gaussian correlators of rank r tensors are given by r-linear combinations of dimensions with the Young diagrams of size m. The coefficients are made from the characters of the symmetric group Sm and their exact form depends on the choice of the correlator and on the symmetries of the model. As the simplest application of this new knowledge, we provide simple expressions for correlators in the Aristotelian tensor model as tri-linear combinations of dimensions.
Correlators in tensor models from character calculus
Directory of Open Access Journals (Sweden)
A. Mironov
2017-11-01
Full Text Available We explain how the calculations of [20], which provided the first evidence for non-trivial structures of Gaussian correlators in tensor models, are efficiently performed with the help of the (Hurwitz character calculus. This emphasizes a close similarity between technical methods in matrix and tensor models and supports a hope to understand the emerging structures in very similar terms. We claim that the 2m-fold Gaussian correlators of rank r tensors are given by r-linear combinations of dimensions with the Young diagrams of size m. The coefficients are made from the characters of the symmetric group Sm and their exact form depends on the choice of the correlator and on the symmetries of the model. As the simplest application of this new knowledge, we provide simple expressions for correlators in the Aristotelian tensor model as tri-linear combinations of dimensions.
Tensor extension of the Poincare algebra
Energy Technology Data Exchange (ETDEWEB)
Soroka, Dmitrij V. [Kharkov Institute of Physics and Technology, 61108 Kharkov (Ukraine)]. E-mail: dsoroka@kipt.kharkov.ua; Soroka, Vyacheslav A. [Kharkov Institute of Physics and Technology, 61108 Kharkov (Ukraine)]. E-mail: vsoroka@kipt.kharkov.ua
2005-02-10
A tensor extension of the Poincare algebra is proposed for the arbitrary dimensions. Casimir operators of the extension are constructed. A possible supersymmetric generalization of this extension is also found in the dimensions D=2,3,4.
The energy–momentum tensor(s) in classical gauge theories
Energy Technology Data Exchange (ETDEWEB)
Blaschke, Daniel N., E-mail: dblaschke@lanl.gov [Los Alamos National Laboratory, Los Alamos, NM 87545 (United States); Gieres, François, E-mail: gieres@ipnl.in2p3.fr [Institut de Physique Nucléaire de Lyon, Université de Lyon, Université Claude Bernard Lyon 1 and CNRS/IN2P3, Bat. P. Dirac, 4 rue Enrico Fermi, F-69622 Villeurbanne (France); Reboud, Méril, E-mail: meril.reboud@ens-lyon.fr [Institut de Physique Nucléaire de Lyon, Université de Lyon, Université Claude Bernard Lyon 1 and CNRS/IN2P3, Bat. P. Dirac, 4 rue Enrico Fermi, F-69622 Villeurbanne (France); Ecole Normale Supérieure de Lyon, 46 allée d' Italie, F-69364 Lyon CEDEX 07 (France); Schweda, Manfred, E-mail: mschweda@tph.tuwien.ac.at [Institute for Theoretical Physics, Vienna University of Technology, Wiedner Hauptstraße 8-10, A-1040 Vienna (Austria)
2016-11-15
We give an introduction to, and review of, the energy–momentum tensors in classical gauge field theories in Minkowski space, and to some extent also in curved space–time. For the canonical energy–momentum tensor of non-Abelian gauge fields and of matter fields coupled to such fields, we present a new and simple improvement procedure based on gauge invariance for constructing a gauge invariant, symmetric energy–momentum tensor. The relationship with the Einstein–Hilbert tensor following from the coupling to a gravitational field is also discussed.
The energy–momentum tensor(s in classical gauge theories
Directory of Open Access Journals (Sweden)
Daniel N. Blaschke
2016-11-01
Full Text Available We give an introduction to, and review of, the energy–momentum tensors in classical gauge field theories in Minkowski space, and to some extent also in curved space–time. For the canonical energy–momentum tensor of non-Abelian gauge fields and of matter fields coupled to such fields, we present a new and simple improvement procedure based on gauge invariance for constructing a gauge invariant, symmetric energy–momentum tensor. The relationship with the Einstein–Hilbert tensor following from the coupling to a gravitational field is also discussed.
Chen, Guangxiang; Hu, Xinyu; Li, Lei; Huang, Xiaoqi; Lui, Su; Kuang, Weihong; Ai, Hua; Bi, Feng; Gu, Zhongwei; Gong, Qiyong
2016-01-01
White matter (WM) abnormalities have long been suspected in major depressive disorder (MDD). Tract-based spatial statistics (TBSS) studies have detected abnormalities in fractional anisotropy (FA) in MDD, but the available evidence has been inconsistent. We performed a quantitative meta-analysis of TBSS studies contrasting MDD patients with healthy control subjects (HCS). A total of 17 studies with 18 datasets that included 641 MDD patients and 581 HCS were identified. Anisotropic effect size-signed differential mapping (AES-SDM) meta-analysis was performed to assess FA alterations in MDD patients compared to HCS. FA reductions were identified in the genu of the corpus callosum (CC) extending to the body of the CC and left anterior limb of the internal capsule (ALIC) in MDD patients relative to HCS. Descriptive analysis of quartiles, sensitivity analysis and subgroup analysis further confirmed these findings. Meta-regression analysis revealed that individuals with more severe MDD were significantly more likely to have FA reductions in the genu of the CC. This study provides a thorough profile of WM abnormalities in MDD and evidence that interhemispheric connections and frontal-striatal-thalamic pathways are the most convergent circuits affected in MDD. PMID:26906716
Measuring Nematic Susceptibilities from the Elastoresistivity Tensor
Hristov, A. T.; Shapiro, M. C.; Hlobil, Patrick; Maharaj, Akash; Chu, Jiun-Haw; Fisher, Ian
The elastoresistivity tensor mijkl relates changes in resistivity to the strain on a material. As a fourth-rank tensor, it contains considerably more information about the material than the simpler (second-rank) resistivity tensor; in particular, certain elastoresistivity coefficients can be related to thermodynamic susceptibilities and serve as a direct probe of symmetry breaking at a phase transition. The aim of this talk is twofold. First, we enumerate how symmetry both constrains the structure of the elastoresistivity tensor into an easy-to-understand form and connects tensor elements to thermodynamic susceptibilities. In the process, we generalize previous studies of elastoresistivity to include the effects of magnetic field. Second, we describe an approach to measuring quantities in the elastoresistivity tensor with a novel transverse measurement, which is immune to relative strain offsets. These techniques are then applied to BaFe2As2 in a proof of principle measurement. This work is supported by the Department of Energy, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division, under Contract DE-AC02-76SF00515.
Data fusion in metabolomics using coupled matrix and tensor factorizations
DEFF Research Database (Denmark)
Evrim, Acar Ataman; Bro, Rasmus; Smilde, Age Klaas
2015-01-01
With a goal of identifying biomarkers/patterns related to certain conditions or diseases, metabolomics focuses on the detection of chemical substances in biological samples such as urine and blood using a number of analytical techniques, including nuclear magnetic resonance (NMR) spectroscopy...... vast amounts of data using different analytical methods, data fusion remains a challenging task, in particular, when the goal is to capture the underlying factors and use them for interpretation, e.g., for biomarker identification. Furthermore, many data fusion applications require joint analysis...... of heterogeneous (i.e., in the form of higher order tensors and matrices) data sets with shared/unshared factors. In order to jointly analyze such heterogeneous data sets, we formulate data fusion as a coupled matrix and tensor factorization (CMTF) problem, which has already proved useful in many data mining...
All-at-once Optimization for Coupled Matrix and Tensor Factorizations
DEFF Research Database (Denmark)
Evrim, Acar Ataman; Kolda, Tamara G.; Dunlavy, Daniel M.
2011-01-01
Joint analysis of data from multiple sources has the potential to improve our understanding of the underlying structures in complex data sets. For instance, in restaurant recommendation systems, recommendations can be based on rating histories of customers. In addition to rating histories.......g., the person by person social network matrix or the restaurant by category matrix, and higher-order tensors, e.g., the "ratings" tensor of the form restaurant by meal by person. In this paper, we are particularly interested in fusing data sets with the goal of capturing their underlying latent structures. We...... formulate this problem as a coupled matrix and tensor factorization (CMTF) problem where heterogeneous data sets are modeled by fitting outer-product models to higher-order tensors and matrices in a coupled manner. Unlike traditional approaches solving this problem using alternating algorithms, we propose...
Fundamentals of tensor calculus for engineers with a primer on smooth manifolds
Mühlich, Uwe
2017-01-01
This book presents the fundamentals of modern tensor calculus for students in engineering and applied physics, emphasizing those aspects that are crucial for applying tensor calculus safely in Euclidian space and for grasping the very essence of the smooth manifold concept. After introducing the subject, it provides a brief exposition on point set topology to familiarize readers with the subject, especially with those topics required in later chapters. It then describes the finite dimensional real vector space and its dual, focusing on the usefulness of the latter for encoding duality concepts in physics. Moreover, it introduces tensors as objects that encode linear mappings and discusses affine and Euclidean spaces. Tensor analysis is explored first in Euclidean space, starting from a generalization of the concept of differentiability and proceeding towards concepts such as directional derivative, covariant derivative and integration based on differential forms. The final chapter addresses the role of smooth...
Energy Technology Data Exchange (ETDEWEB)
Saur, R. [Sektion fuer Experimentelle Kernspinresonanz des ZNS, Abt. Neuroradiologie, Universitaetsklinikum Tuebingen (Germany); Augenklinik des Universitaetsklinikums Tuebingen (Germany); Klinik fuer Psychiatrie und Psychotherapie des Universitaetsklinikums Tuebingen (Germany); Gharabaghi, A. [Klinik fuer Neurochirurgie des Universitaetsklinikums Tuebingen (Germany); Erb, M. [Sektion fuer Experimentelle Kernspinresonanz des ZNS, Abt. Neuroradiologie, Universitaetsklinikum Tuebingen (Germany)
2007-07-01
Knowledge about integrity and location of fibre tracts arising from eloquent cortical areas is important to plan neurosurgical interventions and to allow maximization of resection of pathological tissue while preserving vital white matter tracts. Diffusion Tensor Imaging (DTI) is so far the only method to get preoperatively an impression of the individual complexity of nerve bundles. Thereby nerve fibres are not mapped directly. They are derived indirectly by analysis of the directional distribution of diffusion of water molecules which is influenced mainly by large fibre tracts. From acquisition to reconstruction and visualisation of the fibre tracts many representational stages and working steps have to be passed. Exact knowledge about problems of Diffusion Imaging is important for interpretation of the results. Particularly, brain tumor edema, intraoperative brain shift, MR-artefacts and limitations of the mathematical models and algorithms challenge DTI-developers and applicants. (orig.)
Tensor network state correspondence and holography
Singh, Sukhwinder
2018-01-01
In recent years, tensor network states have emerged as a very useful conceptual and simulation framework to study quantum many-body systems at low energies. In this paper, we describe a particular way in which any given tensor network can be viewed as a representation of two different quantum many-body states. The two quantum many-body states are said to correspond to each other by means of the tensor network. We apply this "tensor network state correspondence"—a correspondence between quantum many-body states mediated by tensor networks as we describe—to the multi-scale entanglement renormalization ansatz (MERA) representation of ground states of one dimensional (1D) quantum many-body systems. Since the MERA is a 2D hyperbolic tensor network (the extra dimension is identified as the length scale of the 1D system), the two quantum many-body states obtained from the MERA, via tensor network state correspondence, are seen to live in the bulk and on the boundary of a discrete hyperbolic geometry. The bulk state so obtained from a MERA exhibits interesting features, some of which caricature known features of the holographic correspondence of String theory. We show how (i) the bulk state admits a description in terms of "holographic screens", (ii) the conformal field theory data associated with a critical ground state can be obtained from the corresponding bulk state, in particular, how pointlike boundary operators are identified with extended bulk operators. (iii) We also present numerical results to illustrate that bulk states, dual to ground states of several critical spin chains, have exponentially decaying correlations, and that the bulk correlation length generally decreases with increase in central charge for these spin chains.
Parallel Tensor Compression for Large-Scale Scientific Data.
Energy Technology Data Exchange (ETDEWEB)
Kolda, Tamara G. [Sandia National Lab. (SNL-CA), Livermore, CA (United States); Ballard, Grey [Sandia National Lab. (SNL-CA), Livermore, CA (United States); Austin, Woody Nathan [Univ. of Texas, Austin, TX (United States)
2015-10-01
As parallel computing trends towards the exascale, scientific data produced by high-fidelity simulations are growing increasingly massive. For instance, a simulation on a three-dimensional spatial grid with 512 points per dimension that tracks 64 variables per grid point for 128 time steps yields 8 TB of data. By viewing the data as a dense five way tensor, we can compute a Tucker decomposition to find inherent low-dimensional multilinear structure, achieving compression ratios of up to 10000 on real-world data sets with negligible loss in accuracy. So that we can operate on such massive data, we present the first-ever distributed memory parallel implementation for the Tucker decomposition, whose key computations correspond to parallel linear algebra operations, albeit with nonstandard data layouts. Our approach specifies a data distribution for tensors that avoids any tensor data redistribution, either locally or in parallel. We provide accompanying analysis of the computation and communication costs of the algorithms. To demonstrate the compression and accuracy of the method, we apply our approach to real-world data sets from combustion science simulations. We also provide detailed performance results, including parallel performance in both weak and strong scaling experiments.
Huf, P. A.; Carminati, J.
2015-09-01
In this paper we: (1) introduce TensorPack, a software package for the algebraic manipulation of tensors in covariant index format in Maple; (2) briefly demonstrate the use of the package with an orthonormal tensor proof of the shearfree conjecture for dust. TensorPack is based on the Riemann and Canon tensor software packages and uses their functions to express tensors in an indexed covariant format. TensorPack uses a string representation as input and provides functions for output in index form. It extends the functionality to basic algebra of tensors, substitution, covariant differentiation, contraction, raising/lowering indices, symmetry functions and other accessory functions. The output can be merged with text in the Maple environment to create a full working document with embedded dynamic functionality. The package offers potential for manipulation of indexed algebraic tensor expressions in a flexible software environment.
The Racah-Wigner algebra and coherent tensors
Rowe, D. J.; Repka, J.
1996-05-01
We present a set of tensors which are shift tensors (Wigner tensors) in accordance with the definitions of Biedenharn and Louck and satisfy the coherence conditions of Flath and Towber. Our tensors are defined for all connected compact Lie groups and for finite-dimensional representations of connected reductive Lie groups. Thus, we have a realization of the coherent tensors in a rather general setting. Moreover, this realization enables us to confirm most of the conjectures of Flath and Towber concerning the properties of coherent tensors.
Geodesic-loxodromes for diffusion tensor interpolation and difference measurement.
Kindlmann, Gordon; Estépar, Raúl San José; Niethammer, Marc; Haker, Steven; Westin, Carl-Fredrik
2007-01-01
In algorithms for processing diffusion tensor images, two common ingredients are interpolating tensors, and measuring the distance between them. We propose a new class of interpolation paths for tensors, termed geodesic-loxodromes, which explicitly preserve clinically important tensor attributes, such as mean diffusivity or fractional anisotropy, while using basic differential geometry to interpolate tensor orientation. This contrasts with previous Riemannian and Log-Euclidean methods that preserve the determinant. Path integrals of tangents of geodesic-loxodromes generate novel measures of over-all difference between two tensors, and of difference in shape and in orientation.
Permittivity and permeability tensors for cloaking applications
Choudhury, Balamati; Jha, Rakesh Mohan
2016-01-01
This book is focused on derivations of analytical expressions for stealth and cloaking applications. An optimal version of electromagnetic (EM) stealth is the design of invisibility cloak of arbitrary shapes in which the EM waves can be controlled within the cloaking shell by introducing a prescribed spatial variation in the constitutive parameters. The promising challenge in design of invisibility cloaks lies in the determination of permittivity and permeability tensors for all the layers. This book provides the detailed derivation of analytical expressions of the permittivity and permeability tensors for various quadric surfaces within the eleven Eisenhart co-ordinate systems. These include the cylinders and the surfaces of revolutions. The analytical modeling and spatial metric for each of these surfaces are provided along with their tensors. This mathematical formulation will help the EM designers to analyze and design of various quadratics and their hybrids, which can eventually lead to design of cloakin...
Spacetime Encodings III - Second Order Killing Tensors
Brink, Jeandrew
2009-01-01
This paper explores the Petrov type D, stationary axisymmetric vacuum (SAV) spacetimes that were found by Carter to have separable Hamilton-Jacobi equations, and thus admit a second-order Killing tensor. The derivation of the spacetimes presented in this paper borrows from ideas about dynamical systems, and illustrates concepts that can be generalized to higher- order Killing tensors. The relationship between the components of the Killing equations and metric functions are given explicitly. The origin of the four separable coordinate systems found by Carter is explained and classified in terms of the analytic structure associated with the Killing equations. A geometric picture of what the orbital invariants may represent is built. Requiring that a SAV spacetime admits a second-order Killing tensor is very restrictive, selecting very few candidates from the group of all possible SAV spacetimes. This restriction arises due to the fact that the consistency conditions associated with the Killing equations require...
The pressure tensor in tangential equilibria
Directory of Open Access Journals (Sweden)
F. Mottez
2004-09-01
Full Text Available The tangential equilibria are characterized by a bulk plasma velocity and a magnetic field that are perpendicular to the gradient direction. Such equilibria can be spatially periodic (like waves, or they can separate two regions with asymptotic uniform conditions (like MHD tangential discontinuities. It is possible to compute the velocity moments of the particle distribution function. Even in very simple cases, the pressure tensor is not isotropic and not gyrotropic. The differences between a scalar pressure and the pressure tensor derived in the frame of the Maxwell-Vlasov theory are significant when the gradient scales are of the order of the Larmor radius; they concern mainly the ion pressure tensor.
Tensor network models of multiboundary wormholes
Peach, Alex; Ross, Simon F.
2017-05-01
We study the entanglement structure of states dual to multiboundary wormhole geometries using tensor network models. Perfect and random tensor networks tiling the hyperbolic plane have been shown to provide good models of the entanglement structure in holography. We extend this by quotienting the plane by discrete isometries to obtain models of the multiboundary states. We show that there are networks where the entanglement structure is purely bipartite, extending results obtained in the large temperature limit. We analyse the entanglement structure in a range of examples.
Improving Tensor Based Recommenders with Clustering
DEFF Research Database (Denmark)
Leginus, Martin; Dolog, Peter; Zemaitis, Valdas
2012-01-01
Social tagging systems (STS) model three types of entities (i.e. tag-user-item) and relationships between them are encoded into a 3-order tensor. Latent relationships and patterns can be discovered by applying tensor factorization techniques like Higher Order Singular Value Decomposition (HOSVD),...... of the recommendations and execution time are improved and memory requirements are decreased. The clustering is motivated by the fact that many tags in a tag space are semantically similar thus the tags can be grouped. Finally, promising experimental results are presented...
Blue running of the primordial tensor spectrum
Energy Technology Data Exchange (ETDEWEB)
Gong, Jinn-Ouk, E-mail: jinn-ouk.gong@apctp.org [Asia Pacific Center for Theoretical Physics, Pohang 790-784 (Korea, Republic of)
2014-07-01
We examine the possibility of positive spectral index of the power spectrum of the primordial tensor perturbation produced during inflation in the light of the detection of the B-mode polarization by the BICEP2 collaboration. We find a blue tilt is in general possible when the slow-roll parameter decays rapidly. We present two known examples in which a positive spectral index for the tensor power spectrum can be obtained. We also briefly discuss other consistency tests for further studies on inflationary dynamics.
Reconstruction of convex bodies from surface tensors
DEFF Research Database (Denmark)
Kousholt, Astrid; Kiderlen, Markus
We present two algorithms for reconstruction of the shape of convex bodies in the two-dimensional Euclidean space. The first reconstruction algorithm requires knowledge of the exact surface tensors of a convex body up to rank s for some natural number s. The second algorithm uses harmonic intrinsic...... volumes which are certain values of the surface tensors and allows for noisy measurements. From a generalized version of Wirtinger's inequality, we derive stability results that are utilized to ensure consistency of both reconstruction procedures. Consistency of the reconstruction procedure based...
Magnetotelluric impedance tensor analysis for identification of ...
Indian Academy of Sciences (India)
G Pavan Kumar
2017-07-18
Jul 18, 2017 ... Kachchh region is due to differential movement along the major E–W trending faults (Biswas and. Khattri 2002). However, couple of NW–SE to NE– ..... 2013), the kinematics of the fault structures need to. Figure 9. Epicentral distribution of earthquakes in the study region. The focal mechanism solutions are ...
Delvaux, D.
2012-04-01
The Win-Tensor program is an interactive computer program for fracture analysis and crustal stress reconstruction, freely distributed to the scientific and academic community and widely used by structural geologists. It was developed with a constant feed-back from the users and is regularly upgraded. Version 4.0 released in January 2012 provides as a new feature the standard deviation of the horizontal stress axes (SHmax/SHmin) and the stress regime Index R'. The latter expresses the relative stress magnitudes and the nature of the vertical stress in a continuous scale, ranging from 1 to 3. Computation of the standard deviations is based on the examination of all possible reduced stress tensors for a particular stress solution obtained from the inversion of fault-slip or focal mechanism data. They are defined by combining the possible values of each individual stress axes (sigma 1, sigma 2, sigma 3) and the stress ratio R = (sigma2-sigma3)/(sigma1-sigma3). For each possible reduced tensors, the horizontal paleostress directions (SHmax/SHmin) and regime (R') are computed and the related 1 sigma standard deviations determined. This way, the 4 dimensions of the reduced stress tensor are reduced to a two dimensional expression with is commonly used to depict the horizontal stress trajectories as in the World Stress Map project. This procedure has been implemented for the three different methods for reconstructing the reduced stress tensors in Win-Tensor: PBT Right Dihedron and Rotational Optimisation. The advantages of this statistical expression of stress parameters are demonstrated using practical examples. Win-Tensor program can be downloaded from the Tensor web site: http://www.damiendelvaux.be/Tensor/tensor-index.html
Observations About the Projective Tensor Product of Banach Spaces
African Journals Online (AJOL)
, 46B, 46E, 47B. Keywords: tensor, Banach, banach space, tensor product, projective norm, greatest crossnorm, semi-embedding, Radon-Nikodym property, absolutely p-summable sequence, strongly p-summable sequence, topological linear ...
Poya, Roman; Gil, Antonio J.; Ortigosa, Rogelio
2017-07-01
The paper presents aspects of implementation of a new high performance tensor contraction framework for the numerical analysis of coupled and multi-physics problems on streaming architectures. In addition to explicit SIMD instructions and smart expression templates, the framework introduces domain specific constructs for the tensor cross product and its associated algebra recently rediscovered by Bonet et al. (2015, 2016) in the context of solid mechanics. The two key ingredients of the presented expression template engine are as follows. First, the capability to mathematically transform complex chains of operations to simpler equivalent expressions, while potentially avoiding routes with higher levels of computational complexity and, second, to perform a compile time depth-first or breadth-first search to find the optimal contraction indices of a large tensor network in order to minimise the number of floating point operations. For optimisations of tensor contraction such as loop transformation, loop fusion and data locality optimisations, the framework relies heavily on compile time technologies rather than source-to-source translation or JIT techniques. Every aspect of the framework is examined through relevant performance benchmarks, including the impact of data parallelism on the performance of isomorphic and nonisomorphic tensor products, the FLOP and memory I/O optimality in the evaluation of tensor networks, the compilation cost and memory footprint of the framework and the performance of tensor cross product kernels. The framework is then applied to finite element analysis of coupled electro-mechanical problems to assess the speed-ups achieved in kernel-based numerical integration of complex electroelastic energy functionals. In this context, domain-aware expression templates combined with SIMD instructions are shown to provide a significant speed-up over the classical low-level style programming techniques.
Tensor completion for PDEs with uncertain coefficients and Bayesian Update
Litvinenko, Alexander
2017-03-05
In this work, we tried to show connections between Bayesian update and tensor completion techniques. Usually, only a small/sparse vector/tensor of measurements is available. The typical measurement is a function of the solution. The solution of a stochastic PDE is a tensor, the measurement as well. The idea is to use completion techniques to compute all "missing" values of the measurement tensor and only then apply the Bayesian technique.
Gravitational Metric Tensor Exterior to Rotating Homogeneous ...
African Journals Online (AJOL)
... ω is constructed. The constructed metric tensors in this gravitational field have seven non-zero distinct components.The Lagrangian for this gravitational field is constructed. It is used to derive Einstein's planetary equation of motion and photon equation of motion in the vicinity of the rotating homogeneous spherical mass.
Scalable Tensor Factorizations with Missing Data
DEFF Research Database (Denmark)
Acar, Evrim; Dunlavy, Daniel M.; Kolda, Tamara G.
2010-01-01
is shown to successfully factor tensors with noise and up to 70% missing data. Moreover, our approach is significantly faster than the leading alternative and scales to larger problems. To show the real-world usefulness of CP-WOPT, we illustrate its applicability on a novel EEG (electroencephalogram...
Families of twisted tensor product codes
Giuzzi, Luca; Pepe, Valentina
2011-01-01
Using geometric properties of the variety $\\cV_{r,t}$, the image under the Grassmannian map of a Desarguesian $(t-1)$-spread of $\\PG(rt-1,q)$, we introduce error correcting codes related to the twisted tensor product construction, producing several families of constacyclic codes. We exactly determine the parameters of these codes and characterise the words of minimum weight.
Tensors in image processing and computer vision
De Luis García, Rodrigo; Tao, Dacheng; Li, Xuelong
2009-01-01
Tensor signal processing is an emerging field with important applications to computer vision and image processing. This book presents the developments in this branch of signal processing, offering research and discussions by experts in the area. It is suitable for advanced students working in the area of computer vision and image processing.
Fermionic topological quantum states as tensor networks
Wille, C.; Buerschaper, O.; Eisert, J.
2017-06-01
Tensor network states, and in particular projected entangled pair states, play an important role in the description of strongly correlated quantum lattice systems. They do not only serve as variational states in numerical simulation methods, but also provide a framework for classifying phases of quantum matter and capture notions of topological order in a stringent and rigorous language. The rapid development in this field for spin models and bosonic systems has not yet been mirrored by an analogous development for fermionic models. In this work, we introduce a tensor network formalism capable of capturing notions of topological order for quantum systems with fermionic components. At the heart of the formalism are axioms of fermionic matrix-product operator injectivity, stable under concatenation. Building upon that, we formulate a Grassmann number tensor network ansatz for the ground state of fermionic twisted quantum double models. A specific focus is put on the paradigmatic example of the fermionic toric code. This work shows that the program of describing topologically ordered systems using tensor networks carries over to fermionic models.
Visualization and processing of tensor fields
Weickert, Joachim
2007-01-01
Presents information on the visualization and processing of tensor fields. This book serves as an overview for the inquiring scientist, as a basic foundation for developers and practitioners, and as a textbook for specialized classes and seminars for graduate and doctoral students.
Radiation Forces and Torques without Stress (Tensors)
Bohren, Craig F.
2011-01-01
To understand radiation forces and torques or to calculate them does not require invoking photon or electromagnetic field momentum transfer or stress tensors. According to continuum electromagnetic theory, forces and torques exerted by radiation are a consequence of electric and magnetic fields acting on charges and currents that the fields induce…
Tensor B mode and stochastic Faraday mixing
Giovannini, Massimo
2014-01-01
This paper investigates the Faraday effect as a different source of B mode polarization. The E mode polarization is Faraday rotated provided a stochastic large-scale magnetic field is present prior to photon decoupling. In the first part of the paper we discuss the case where the tensor modes of the geometry are absent and we argue that the B mode recently detected by the Bicep2 collaboration cannot be explained by a large-scale magnetic field rotating, through the Faraday effect, the well established E mode polarization. In this case, the observed temperature autocorrelations would be excessively distorted by the magnetic field. In the second part of the paper the formation of Faraday rotation is treated as a stationary, random and Markovian process with the aim of generalizing a set of scaling laws originally derived in the absence of the tensor modes of the geometry. We show that the scalar, vector and tensor modes of the brightness perturbations can all be Faraday rotated even if the vector and tensor par...
Holographic coherent states from random tensor networks
Qi, Xiao-Liang; Yang, Zhao; You, Yi-Zhuang
2017-08-01
Random tensor networks provide useful models that incorporate various important features of holographic duality. A tensor network is usually defined for a fixed graph geometry specified by the connection of tensors. In this paper, we generalize the random tensor network approach to allow quantum superposition of different spatial geometries. We setup a framework in which all possible bulk spatial geometries, characterized by weighted adjacient matrices of all possible graphs, are mapped to the boundary Hilbert space and form an overcomplete basis of the boundary. We name such an overcomplete basis as holographic coherent states. A generic boundary state can be expanded in this basis, which describes the state as a superposition of different spatial geometries in the bulk. We discuss how to define distinct classical geometries and small fluctuations around them. We show that small fluctuations around classical geometries define "code subspaces" which are mapped to the boundary Hilbert space isometrically with quantum error correction properties. In addition, we also show that the overlap between different geometries is suppressed exponentially as a function of the geometrical difference between the two geometries. The geometrical difference is measured in an area law fashion, which is a manifestation of the holographic nature of the states considered.
Anisotropy without tensors: a novel approach using geometric algebra.
Matos, Sérgio A; Ribeiro, Marco A; Paiva, Carlos R
2007-11-12
The most widespread approach to anisotropic media is dyadic analysis. However, to get a geometrical picture of a dielectric tensor, one has to resort to a coordinate system for a matrix form in order to obtain, for example, the index-ellipsoid, thereby obnubilating the deeper coordinate-free meaning of anisotropy itself. To overcome these shortcomings we present a novel approach to anisotropy: using geometric algebra we introduce a direct geometrical interpretation without the intervention of any coordinate system. By applying this new approach to biaxial crystals we show the effectiveness and insight that geometric algebra can bring to the optics of anisotropic media.
Efficient MATLAB computations with sparse and factored tensors.
Energy Technology Data Exchange (ETDEWEB)
Bader, Brett William; Kolda, Tamara Gibson (Sandia National Lab, Livermore, CA)
2006-12-01
In this paper, the term tensor refers simply to a multidimensional or N-way array, and we consider how specially structured tensors allow for efficient storage and computation. First, we study sparse tensors, which have the property that the vast majority of the elements are zero. We propose storing sparse tensors using coordinate format and describe the computational efficiency of this scheme for various mathematical operations, including those typical to tensor decomposition algorithms. Second, we study factored tensors, which have the property that they can be assembled from more basic components. We consider two specific types: a Tucker tensor can be expressed as the product of a core tensor (which itself may be dense, sparse, or factored) and a matrix along each mode, and a Kruskal tensor can be expressed as the sum of rank-1 tensors. We are interested in the case where the storage of the components is less than the storage of the full tensor, and we demonstrate that many elementary operations can be computed using only the components. All of the efficiencies described in this paper are implemented in the Tensor Toolbox for MATLAB.
The operator tensor formulation of quantum theory.
Hardy, Lucien
2012-07-28
In this paper, we provide what might be regarded as a manifestly covariant presentation of discrete quantum theory. A typical quantum experiment has a bunch of apparatuses placed so that quantum systems can pass between them. We regard each use of an apparatus, along with some given outcome on the apparatus (a certain detector click or a certain meter reading for example), as an operation. An operation (e.g. B(b(2)a(3))(a(1))) can have zero or more quantum systems inputted into it and zero or more quantum systems outputted from it. The operation B(b(2)a(3))(a(1)) has one system of type a inputted, and one system of type b and one system of type a outputted. We can wire together operations to form circuits, for example, A(a(1))B(b(2)a(3))(a(1))C(b(2)a(3)). Each repeated integer label here denotes a wire connecting an output to an input of the same type. As each operation in a circuit has an outcome associated with it, a circuit represents a set of outcomes that can happen in a run of the experiment. In the operator tensor formulation of quantum theory, each operation corresponds to an operator tensor. For example, the operation B(b(2)a(3))(a(1)) corresponds to the operator tensor B(b(2)a(3))(a(1)). Further, the probability for a general circuit is given by replacing operations with corresponding operator tensors as in Prob(A(a(1))B(b(2)a(3))(a(1))C(b(2)a(3))) = Â(a(1))B(b(2)a(3))(a(1))C(b(2)a(3)). Repeated integer labels indicate that we multiply in the associated subspace and then take the partial trace over that subspace. Operator tensors must be physical (namely, they must have positive input transpose and satisfy a certain normalization condition).
Modeling the evolution of lithium-ion particle contact distributions using a fabric tensor approach
Energy Technology Data Exchange (ETDEWEB)
Stershic, Andrew [Duke University; Simunovic, Srdjan [ORNL; Nanda, Jagjit [ORNL
2015-08-25
Electrode microstructure and processing can strongly influence lithium-ion battery performance such as capacity retention, power, and rate. Battery electrodes are multi-phase composite structures wherein conductive diluents and binder bond active material to a current collector. The structure and response of this composite network during repeated electrochemical cycling directly affects battery performance characteristics. We propose the fabric tensor formalism for describing the structure and evolution of the electrode microstructure. Fabric tensors are directional measures of particulate assemblies based on inter-particle connectivity, relating to the structural and transport properties of the electrode. Fabric tensor analysis is applied to experimental data-sets for positive electrode made of lithium nickel manganese cobalt oxide, captured by X-ray tomography for several compositions and consolidation pressures. We show that fabric tensors capture the evolution of inter-particle contact distribution and are therefore good measures for the internal state of and electronic transport within the electrode. The fabric tensor analysis is also applied to Discrete Element Method (DEM) simulations of electrode microstructures using spherical particles with size distributions from the tomography. Furthermore, these results do not follow the experimental trends, which indicates that the particle size distribution alone is not a sufficient measure for the electrode microstructures in DEM simulations.
Hyperspectral Image Denoising Based on Tensor Group Sparse Representation
Directory of Open Access Journals (Sweden)
WANG Zhongmei
2017-05-01
Full Text Available A novel algorithm for hyperspectral image (HSI denoising is proposed based on tensor group sparse representation. A HSI is considering as 3 order tensor. First, a HSI is divided into small tensor blocks. Second, similar blocks are gathered into clusters, and then a tensor group sparse representation model is constructed based on every cluster. Through exploiting HSI spectral correlation and nonlocal similarity over space, the model constrained tensor group sparse representation can be decomposed into a series of unconstrained low-rank tensor approximation problems, which can be solved using the tensor decomposition technique. The experiment results on the synthetic and real hyperspectral remote sensing images demonstrate the effectiveness of the proposed approach.
Algebraic and computational aspects of real tensor ranks
Sakata, Toshio; Miyazaki, Mitsuhiro
2016-01-01
This book provides comprehensive summaries of theoretical (algebraic) and computational aspects of tensor ranks, maximal ranks, and typical ranks, over the real number field. Although tensor ranks have been often argued in the complex number field, it should be emphasized that this book treats real tensor ranks, which have direct applications in statistics. The book provides several interesting ideas, including determinant polynomials, determinantal ideals, absolutely nonsingular tensors, absolutely full column rank tensors, and their connection to bilinear maps and Hurwitz-Radon numbers. In addition to reviews of methods to determine real tensor ranks in details, global theories such as the Jacobian method are also reviewed in details. The book includes as well an accessible and comprehensive introduction of mathematical backgrounds, with basics of positive polynomials and calculations by using the Groebner basis. Furthermore, this book provides insights into numerical methods of finding tensor ranks through...
Tensor modes on the string theory landscape
Energy Technology Data Exchange (ETDEWEB)
Westphal, Alexander
2012-06-15
We attempt an estimate for the distribution of the tensor mode fraction r over the landscape of vacua in string theory. The dynamics of eternal inflation and quantum tunneling lead to a kind of democracy on the landscape, providing no bias towards large-field or small-field inflation regardless of the class of measure. The tensor mode fraction then follows the number frequency distributions of inflationary mechanisms of string theory over the landscape. We show that an estimate of the relative number frequencies for small-field vs large-field inflation, while unattainable on the whole landscape, may be within reach as a regional answer for warped Calabi-Yau flux compactifications of type IIB string theory.
Numerical CP Decomposition of Some Difficult Tensors
Czech Academy of Sciences Publication Activity Database
Tichavský, Petr; Phan, A. H.; Cichocki, A.
2017-01-01
Roč. 317, č. 1 (2017), s. 362-370 ISSN 0377-0427 R&D Projects: GA ČR(CZ) GA14-13713S Institutional support: RVO:67985556 Keywords : Small matrix multiplication * Canonical polyadic tensor decomposition * Levenberg-Marquardt method Subject RIV: BB - Applied Statistics, Operational Research Impact factor: 1.357, year: 2016 http://library.utia.cas.cz/separaty/2017/SI/tichavsky-0468385. pdf
Vector-tensor interaction of gravitation
Energy Technology Data Exchange (ETDEWEB)
Zhang Yuan-zhong; Guo han-ying
1982-11-01
In the paper, by using the equation of motion a particle, we show that the antigravity exist in the vector-tensor model of gravitation. Thus the motion of a particle deviates from the geodesic equation. In Newtonian approximation and weak gravitational field, acceleration of a particle in a spherically symmetric and astatic gravitation field is zero. The result is obviously not in agreement with gravitational phenomena.
Monte Carlo Volcano Seismic Moment Tensors
Waite, G. P.; Brill, K. A.; Lanza, F.
2015-12-01
Inverse modeling of volcano seismic sources can provide insight into the geometry and dynamics of volcanic conduits. But given the logistical challenges of working on an active volcano, seismic networks are typically deficient in spatial and temporal coverage; this potentially leads to large errors in source models. In addition, uncertainties in the centroid location and moment-tensor components, including volumetric components, are difficult to constrain from the linear inversion results, which leads to a poor understanding of the model space. In this study, we employ a nonlinear inversion using a Monte Carlo scheme with the objective of defining robustly resolved elements of model space. The model space is randomized by centroid location and moment tensor eigenvectors. Point sources densely sample the summit area and moment tensors are constrained to a randomly chosen geometry within the inversion; Green's functions for the random moment tensors are all calculated from modeled single forces, making the nonlinear inversion computationally reasonable. We apply this method to very-long-period (VLP) seismic events that accompany minor eruptions at Fuego volcano, Guatemala. The library of single force Green's functions is computed with a 3D finite-difference modeling algorithm through a homogeneous velocity-density model that includes topography, for a 3D grid of nodes, spaced 40 m apart, within the summit region. The homogenous velocity and density model is justified by long wavelength of VLP data. The nonlinear inversion reveals well resolved model features and informs the interpretation through a better understanding of the possible models. This approach can also be used to evaluate possible station geometries in order to optimize networks prior to deployment.
Numerical Approximation of Elasticity Tensor Associated With Green-Naghdi Rate.
Liu, Haofei; Sun, Wei
2017-08-01
Objective stress rates are often used in commercial finite element (FE) programs. However, deriving a consistent tangent modulus tensor (also known as elasticity tensor or material Jacobian) associated with the objective stress rates is challenging when complex material models are utilized. In this paper, an approximation method for the tangent modulus tensor associated with the Green-Naghdi rate of the Kirchhoff stress is employed to simplify the evaluation process. The effectiveness of the approach is demonstrated through the implementation of two user-defined fiber-reinforced hyperelastic material models. Comparisons between the approximation method and the closed-form analytical method demonstrate that the former can simplify the material Jacobian evaluation with satisfactory accuracy while retaining its computational efficiency. Moreover, since the approximation method is independent of material models, it can facilitate the implementation of complex material models in FE analysis using shell/membrane elements in abaqus.
Correlation functions of the energy-momentum tensor in SU(2) gauge theory at finite temperature
DEFF Research Database (Denmark)
Huebner, K.; Karsch, F.; Pica, Claudio
2008-01-01
We calculate correlation functions of the energy-momentum tensor in the vicinity of the deconfinement phase transition of (3+1)-dimensional SU(2) gauge theory and discuss their critical behavior in the vicinity of the second order deconfinement transition. We show that correlation functions...... of the trace of the energy momentum tensor diverge uniformly at the critical point in proportion to the specific heat singularity. Correlation functions of the pressure, on the other hand, stay finite at the critical point. We discuss the consequences of these findings for the analysis of transport...
Tensor integrand reduction via Laurent expansion
Energy Technology Data Exchange (ETDEWEB)
Hirschi, Valentin [SLAC, National Accelerator Laboratory,2575 Sand Hill Road, Menlo Park, CA 94025-7090 (United States); Peraro, Tiziano [Higgs Centre for Theoretical Physics, School of Physics and Astronomy,The University of Edinburgh,Edinburgh EH9 3JZ, Scotland (United Kingdom)
2016-06-09
We introduce a new method for the application of one-loop integrand reduction via the Laurent expansion algorithm, as implemented in the public C++ library Ninja. We show how the coefficients of the Laurent expansion can be computed by suitable contractions of the loop numerator tensor with cut-dependent projectors, making it possible to interface Ninja to any one-loop matrix element generator that can provide the components of this tensor. We implemented this technique in the Ninja library and interfaced it to MADLOOP, which is part of the public MADGRAPH5{sub A}MC@NLO framework. We performed a detailed performance study, comparing against other public reduction tools, namely CUTTOOLS, SAMURAI, IREGI, PJFRY++ and GOLEM95. We find that Ninja outperforms traditional integrand reduction in both speed and numerical stability, the latter being on par with that of the tensor integral reduction tool GOLEM95 which is however more limited and slower than Ninja. We considered many benchmark multi-scale processes of increasing complexity, involving QCD and electro-weak corrections as well as effective non-renormalizable couplings, showing that Ninja’s performance scales well with both the rank and multiplicity of the considered process.
A hitchhiker’s guide to Diffusion Tensor Imaging
Directory of Open Access Journals (Sweden)
Jose eSoares
2013-03-01
Full Text Available Diffusion Tensor Imaging (DTI studies are increasingly popular among clinicians and researchers as they provide unique insights into brain network connectivity. However, in order to optimize the use of DTI, several technical and methodological aspects must be factored in. These include decisions on: acquisition protocol, artifact handling, data quality control, reconstruction algorithm and visualization approaches, and quantitative analysis methodology. Furthermore, the researcher and/or clinician also needs to take into account and decide on the most suited software tool(s for each stage of the DTI analysis pipeline. Herein, we provide a straightforward hitchhiker’s guide, covering all of the workflow’s major stages. Ultimately, this guide will help newcomers navigate the most critical roadblocks in the analysis and further encourage the use of DTI.
Masses of the tensor mesons with JP=2-
Chen, Wei; Cai, Zi-Xing; Zhu, Shi-Lin
2014-10-01
We calculate the two-point correlation function using the interpolating current with JPC=2-. After performing the Borel sum rule analysis, the extracted masses of the 2 tensor charmonium and bottomonium are 3.97±0.25 GeV and 10.13±0.34 GeV respectively. For comparison, we also perform the moment sum rule analysis for the charmonium and bottomonium systems. We extend the same analysis to study the qbarq,qbars,sbars,qbarc,sbarc,qbarb,sbarb and cbarb systems. Their masses are 1.78±0.12,1.85±0.14,2.00±0.16,2.86±0.14,3.01±0.21,5.66±0.33,6.40±0.25, and 7.08±0.34 GeV respectively.
Levine, Lyle E; Okoro, Chukwudi; Xu, Ruqing
2015-11-01
Nondestructive measurements of the full elastic strain and stress tensors from individual dislocation cells distributed along the full extent of a 50 µm-long polycrystalline copper via in Si is reported. Determining all of the components of these tensors from sub-micrometre regions within deformed metals presents considerable challenges. The primary issues are ensuring that different diffraction peaks originate from the same sample volume and that accurate determination is made of the peak positions from plastically deformed samples. For these measurements, three widely separated reflections were examined from selected, individual grains along the via. The lattice spacings and peak positions were measured for multiple dislocation cell interiors within each grain and the cell-interior peaks were sorted out using the measured included angles. A comprehensive uncertainty analysis using a Monte Carlo uncertainty algorithm provided uncertainties for the elastic strain tensor and stress tensor components.
Directory of Open Access Journals (Sweden)
Lyle E. Levine
2015-11-01
Full Text Available Nondestructive measurements of the full elastic strain and stress tensors from individual dislocation cells distributed along the full extent of a 50 µm-long polycrystalline copper via in Si is reported. Determining all of the components of these tensors from sub-micrometre regions within deformed metals presents considerable challenges. The primary issues are ensuring that different diffraction peaks originate from the same sample volume and that accurate determination is made of the peak positions from plastically deformed samples. For these measurements, three widely separated reflections were examined from selected, individual grains along the via. The lattice spacings and peak positions were measured for multiple dislocation cell interiors within each grain and the cell-interior peaks were sorted out using the measured included angles. A comprehensive uncertainty analysis using a Monte Carlo uncertainty algorithm provided uncertainties for the elastic strain tensor and stress tensor components.
Visualizing MR diffusion tensor fields by dynamic fiber tracking and uncertainty mapping
Ehricke, HH; Klose, U; Grodd, W
Recent advances in magnetic resonance imaging have provided methods for the acquisition of high-resolution diffusion tensor fields. Their 3D-visualization with streamline-based techniques-called fiber tracking-allow analysis of cerebral white matter tracts for diagnostic, therapeutic as well as
Tensors and Differential Geometry Applied to Analytic and Numerical Coordinate Generation
1981-01-01
and Tarapov [20], Stoker [21], Spivak [22], do Carmo [23], FlUgge [24], Howard [25], and Eiseman [26]. Part III of this monograph is the culmination...Mass. 02154 (1970). [23] do Carmo , M. P., Differential Geometry of Curves and Surfaces, Prentice-Hall, Inc. (1976). [24] Fligge, W., Tensor Analysis
Gasbarra, Dario; Pajevic, Sinisa; Basser, Peter J.
2017-01-01
Tensor-valued and matrix-valued measurements of different physical properties are increasingly available in material sciences and medical imaging applications. The eigenvalues and eigenvectors of such multivariate data provide novel and unique information, but at the cost of requiring a more complex statistical analysis. In this work we derive the distributions of eigenvalues and eigenvectors in the special but important case of m×m symmetric random matrices, D, observed with isotropic matrix-variate Gaussian noise. The properties of these distributions depend strongly on the symmetries of the mean tensor/matrix, D̄. When D̄ has repeated eigenvalues, the eigenvalues of D are not asymptotically Gaussian, and repulsion is observed between the eigenvalues corresponding to the same D̄ eigenspaces. We apply these results to diffusion tensor imaging (DTI), with m = 3, addressing an important problem of detecting the symmetries of the diffusion tensor, and seeking an experimental design that could potentially yield an isotropic Gaussian distribution. In the 3-dimensional case, when the mean tensor is spherically symmetric and the noise is Gaussian and isotropic, the asymptotic distribution of the first three eigenvalue central moment statistics is simple and can be used to test for isotropy. In order to apply such tests, we use quadrature rules of order t ≥ 4 with constant weights on the unit sphere to design a DTI-experiment with the property that isotropy of the underlying true tensor implies isotropy of the Fisher information. We also explain the potential implications of the methods using simulated DTI data with a Rician noise model. PMID:28989561
The Cauchy problem of scalar-tensor theories of gravity
Energy Technology Data Exchange (ETDEWEB)
Salgado, Marcelo [Instituto de Ciencias Nucleares, Universidad Nacional Autonoma de Mexico, Apdo. Postal 70-543 Mexico 04510 DF (Mexico)
2006-07-21
The 3 + 1 formulation of scalar-tensor theories of gravity (STT) is obtained in the physical (Jordan) frame departing from the 4 + 0 covariant field equations. Contrary to common belief (folklore), the new system of ADM-like equations shows that the Cauchy problem of STT is well formulated (in the sense that the whole system of evolution equations is of first order in the time derivative). This is the first step towards a full first-order (in time and space) formulation from which a subsequent hyperbolicity analysis (a well-posedness determination) can be performed. Several gauge (lapse and shift) conditions are considered and implemented for STT. In particular, a generalization of the harmonic gauge for STT allows us to prove the well posedness of the STT using a second-order analysis which is very similar to the one employed in general relativity. Several appendices complement the ideas of the main part of the paper.
Diffusion Tensor Tractography Reveals Disrupted Structural Connectivity during Brain Aging
Lin, Lan; Tian, Miao; Wang, Qi; Wu, Shuicai
2017-10-01
Brain aging is one of the most crucial biological processes that entail many physical, biological, chemical, and psychological changes, and also a major risk factor for most common neurodegenerative diseases. To improve the quality of life for the elderly, it is important to understand how the brain is changed during the normal aging process. We compared diffusion tensor imaging (DTI)-based brain networks in a cohort of 75 healthy old subjects by using graph theory metrics to describe the anatomical networks and connectivity patterns, and network-based statistic (NBS) analysis was used to identify pairs of regions with altered structural connectivity. The NBS analysis revealed a significant network comprising nine distinct fiber bundles linking 10 different brain regions showed altered white matter structures in young-old group compare with middle-aged group (p < .05, family-wise error-corrected). Our results might guide future studies and help to gain a better understanding of brain aging.
An introduction to tensors and group theory for physicists
Jeevanjee, Nadir
2011-01-01
An Introduction to Tensors and Group Theory for Physicists provides both an intuitive and rigorous approach to tensors and groups and their role in theoretical physics and applied mathematics. A particular aim is to demystify tensors and provide a unified framework for understanding them in the context of classical and quantum physics. Connecting the component formalism prevalent in physics calculations with the abstract but more conceptual formulation found in many mathematical texts, the work will be a welcome addition to the literature on tensors and group theory. Part I of the text begins with linear algebraic foundations, follows with the modern component-free definition of tensors, and concludes with applications to classical and quantum physics through the use of tensor products. Part II introduces abstract groups along with matrix Lie groups and Lie algebras, then intertwines this material with that of Part I by introducing representation theory. Exercises and examples are provided throughout for go...
Redberry: a computer algebra system designed for tensor manipulation
Poslavsky, Stanislav; Bolotin, Dmitry
2015-05-01
In this paper we focus on the main aspects of computer-aided calculations with tensors and present a new computer algebra system Redberry which was specifically designed for algebraic tensor manipulation. We touch upon distinctive features of tensor software in comparison with pure scalar systems, discuss the main approaches used to handle tensorial expressions and present the comparison of Redberry performance with other relevant tools.
Symmetric Topological Phases and Tensor Network States
Jiang, Shenghan
Classification and simulation of quantum phases are one of main themes in condensed matter physics. Quantum phases can be distinguished by their symmetrical and topological properties. The interplay between symmetry and topology in condensed matter physics often leads to exotic quantum phases and rich phase diagrams. Famous examples include quantum Hall phases, spin liquids and topological insulators. In this thesis, I present our works toward a more systematically understanding of symmetric topological quantum phases in bosonic systems. In the absence of global symmetries, gapped quantum phases are characterized by topological orders. Topological orders in 2+1D are well studied, while a systematically understanding of topological orders in 3+1D is still lacking. By studying a family of exact solvable models, we find at least some topological orders in 3+1D can be distinguished by braiding phases of loop excitations. In the presence of both global symmetries and topological orders, the interplay between them leads to new phases termed as symmetry enriched topological (SET) phases. We develop a framework to classify a large class of SET phases using tensor networks. For each tensor class, we can write down generic variational wavefunctions. We apply our method to study gapped spin liquids on the kagome lattice, which can be viewed as SET phases of on-site symmetries as well as lattice symmetries. In the absence of topological order, symmetry could protect different topological phases, which are often referred to as symmetry protected topological (SPT) phases. We present systematic constructions of tensor network wavefunctions for bosonic symmetry protected topological (SPT) phases respecting both onsite and spatial symmetries.
CONSTRUCTION A CORING FROM TENSOR PRODUCT OF BIALGEBRA
Directory of Open Access Journals (Sweden)
Nikken Prima Puspita
2015-01-01
Full Text Available In this Paper introduced a coring from tensor product of bialgebra. An algebra with compatible coalgebrastructure are known as bialgebra. For any bialgebra B we can obtained tensor product between B anditself. Defined a right and left B -action on the tensor product of bialgebra B such that we have tensorproduct of B and itself is a bimodule over B. In this note we expect that the tensor product B anditself becomes a B -coring with comultiplication and counit.Keywords : action, algebra, coalgebra, coring.
The Topology of Three-Dimensional Symmetric Tensor Fields
Lavin, Yingmei; Levy, Yuval; Hesselink, Lambertus
1994-01-01
We study the topology of 3-D symmetric tensor fields. The goal is to represent their complex structure by a simple set of carefully chosen points and lines analogous to vector field topology. The basic constituents of tensor topology are the degenerate points, or points where eigenvalues are equal to each other. First, we introduce a new method for locating 3-D degenerate points. We then extract the topological skeletons of the eigenvector fields and use them for a compact, comprehensive description of the tensor field. Finally, we demonstrate the use of tensor field topology for the interpretation of the two-force Boussinesq problem.
3D Inversion of SQUID Magnetic Tensor Data
DEFF Research Database (Denmark)
Zhdanov, Michael; Cai, Hongzhu; Wilson, Glenn
2012-01-01
Developments in SQUID-based technology have enabled direct measurement of magnetic tensor data for geophysical exploration. For quantitative interpretation, we introduce 3D regularized inversion for magnetic tensor data. For mineral exploration-scale targets, our model studies show that magnetic...... tensor data have significantly improved resolution compared to magnetic vector data for the same model. We present a case study for the 3D regularized inversion of magnetic tensor data acquired over a magnetite skarn at Tallawang, Australia. The results obtained from our 3D regularized inversion agree...
p-Norm SDD tensors and eigenvalue localization
Directory of Open Access Journals (Sweden)
Qilong Liu
2016-07-01
Full Text Available Abstract We present a new class of nonsingular tensors (p-norm strictly diagonally dominant tensors, which is a subclass of strong H $\\mathcal{H}$ -tensors. As applications of the results, we give a new eigenvalue inclusion set, which is tighter than those provided by Li et al. (Linear Multilinear Algebra 64:727-736, 2016 in some case. Based on this set, we give a checkable sufficient condition for the positive (semidefiniteness of an even-order symmetric tensor.
TENSOR MODELING BASED FOR AIRBORNE LiDAR DATA CLASSIFICATION
Li, N.; Liu, C; Pfeifer, N; Yin, J. F.; Liao, Z.Y.; Zhou, Y
2016-01-01
Feature selection and description is a key factor in classification of Earth observation data. In this paper a classification method based on tensor decomposition is proposed. First, multiple features are extracted from raw LiDAR point cloud, and raster LiDAR images are derived by accumulating features or the “raw” data attributes. Then, the feature rasters of LiDAR data are stored as a tensor, and tensor decomposition is used to select component features. This tensor representation could kee...
TENSOR MODELING BASED FOR AIRBORNE LiDAR DATA CLASSIFICATION
Directory of Open Access Journals (Sweden)
N. Li
2016-06-01
Full Text Available Feature selection and description is a key factor in classification of Earth observation data. In this paper a classification method based on tensor decomposition is proposed. First, multiple features are extracted from raw LiDAR point cloud, and raster LiDAR images are derived by accumulating features or the “raw” data attributes. Then, the feature rasters of LiDAR data are stored as a tensor, and tensor decomposition is used to select component features. This tensor representation could keep the initial spatial structure and insure the consideration of the neighborhood. Based on a small number of component features a k nearest neighborhood classification is applied.
Tensor Decompositions for Learning Latent Variable Models
2012-12-08
for several popular latent variable models Tensor Decompositions for Learning Latent Variable Models Anima Anandkumar1, Rong Ge2, Daniel Hsu3, Sham M...the ARO Award W911NF-12-1-0404. References [AFH+12] A. Anandkumar, D. P. Foster, D. Hsu, S. M. Kakade, and Y.-K. Liu . A spectral algorithm for latent...volume 13. Cambridge University Press, 2005. [PSX11] A. Parikh, L. Song , and E. P. Xing. A spectral algorithm for latent tree graphical models. In
Scalable tensor factorizations for incomplete data
DEFF Research Database (Denmark)
Acar, Evrim; Dunlavy, Daniel M.; KOlda, Tamara G.
2011-01-01
experiments, our algorithm is shown to successfully factorize tensors with noise and up to 99% missing data. A unique aspect of our approach is that it scales to sparse large-scale data, e.g., 1000 × 1000 × 1000 with five million known entries (0.5% dense). We further demonstrate the usefulness of CP......-WOPT on two real-world applications: a novel EEG (electroencephalogram) application where missing data is frequently encountered due to disconnections of electrodes and the problem of modeling computer network traffic where data may be absent due to the expense of the data collection process....
A Case of Tensor Fasciae Suralis Muscle
Miyauchi, Ryosuke; Kurihara, Kazushige; Tachibana, Gen
1985-01-01
An anomalous muscle was found on the dorsum of the right lower limb of a 67-year-old Japanese male. It originated by two heads from the semitendinosus and long head of the biceps femoris and ran distally to insert into the deep surface of the sural fascia. The origin, insertion and location of the muscle were compared with those of the various supernumerary muscles hitherto published. The muscle is consequently regarded as being the tensor fasciae suralis. This is the fifth case in Japan.
Holographic duality from random tensor networks
Energy Technology Data Exchange (ETDEWEB)
Hayden, Patrick; Nezami, Sepehr; Qi, Xiao-Liang; Thomas, Nathaniel; Walter, Michael; Yang, Zhao [Stanford Institute for Theoretical Physics, Department of Physics, Stanford University,382 Via Pueblo, Stanford, CA 94305 (United States)
2016-11-02
Tensor networks provide a natural framework for exploring holographic duality because they obey entanglement area laws. They have been used to construct explicit toy models realizing many of the interesting structural features of the AdS/CFT correspondence, including the non-uniqueness of bulk operator reconstruction in the boundary theory. In this article, we explore the holographic properties of networks of random tensors. We find that our models naturally incorporate many features that are analogous to those of the AdS/CFT correspondence. When the bond dimension of the tensors is large, we show that the entanglement entropy of all boundary regions, whether connected or not, obey the Ryu-Takayanagi entropy formula, a fact closely related to known properties of the multipartite entanglement of assistance. We also discuss the behavior of Rényi entropies in our models and contrast it with AdS/CFT. Moreover, we find that each boundary region faithfully encodes the physics of the entire bulk entanglement wedge, i.e., the bulk region enclosed by the boundary region and the minimal surface. Our method is to interpret the average over random tensors as the partition function of a classical ferromagnetic Ising model, so that the minimal surfaces of Ryu-Takayanagi appear as domain walls. Upon including the analog of a bulk field, we find that our model reproduces the expected corrections to the Ryu-Takayanagi formula: the bulk minimal surface is displaced and the entropy is augmented by the entanglement of the bulk field. Increasing the entanglement of the bulk field ultimately changes the minimal surface behavior topologically, in a way similar to the effect of creating a black hole. Extrapolating bulk correlation functions to the boundary permits the calculation of the scaling dimensions of boundary operators, which exhibit a large gap between a small number of low-dimension operators and the rest. While we are primarily motivated by the AdS/CFT duality, the main
Radiation forces and torques without stress (tensors)
Energy Technology Data Exchange (ETDEWEB)
Bohren, Craig F, E-mail: bohren@meteo.psu.edu [Department of Meteorology, Pennsylvania State University, University Park, PA 16802 (United States)
2011-11-15
To understand radiation forces and torques or to calculate them does not require invoking photon or electromagnetic field momentum transfer or stress tensors. According to continuum electromagnetic theory, forces and torques exerted by radiation are a consequence of electric and magnetic fields acting on charges and currents that the fields induce within illuminated objects. This can be shown directly by deriving the radiation force and torque resulting from normal-incidence illumination of a planar interface between free space and an arbitrary medium. Every point of the medium contributes to the total force and torque, which are therefore not localized.
Reconstruction of convex bodies from surface tensors
DEFF Research Database (Denmark)
Kousholt, Astrid; Kiderlen, Markus
2016-01-01
We present two algorithms for reconstruction of the shape of convex bodies in the two-dimensional Euclidean space. The first reconstruction algorithm requires knowledge of the exact surface tensors of a convex body up to rank s for some natural number s. When only measurements subject to noise...... measurements. From a generalized version of Wirtinger's inequality, we derive stability results that are utilized to ensure consistency of both reconstruction procedures. Consistency of the reconstruction procedure based on measurements subject to noise is established under certain assumptions on the noise...
Gürses, Bengi; Kiliçkesmez, Ozgür; Taşdelen, Neslihan; Firat, Zeynep; Gürmen, Nevzat
2011-12-01
To evaluate the feasibility of renal diffusion tensor imaging and determine the normative fractional anisotropy and apparent diffusion coefficient values at 3 Tesla magnetic resonance imaging (MRI) using parallel imaging and free breathing technique. A total of 52 young healthy volunteers with no history of renal disease were included in the study. MRI examinations were performed with 3 Tesla MRI equipment, using six-channel phased array SENSE Torso coil. In all subjects, T2-weighted turbo spin echo and diffusion tensor imaging using single shot echo planar imaging sequences were obtained in the coronal plane with free breathing. Field of view, slice thickness, and slice gap values were identical for both sequences for anatomic correlation during analysis of diffusion tensor imaging data. Parallel imaging method was used with a SENSE factor of 2. Diffusion tensor parameters of the cortex and medulla were determined and the intra- and inter-observer measurement variances were calculated. The mean fractional anisotropy of the medulla was significantly higher than that of the cortex, whereas the mean apparent diffusion coefficient of the medulla was lower when compared with that of the cortex. According to the two-sided paired samples Student's t test, the intra- and inter-observer measurements correlated well. This study shows the feasibility of renal diffusion tensor imaging and repeatibility of diffusion tensor parameter measurements in 3 Tesla MRI.
Black holes in vector-tensor theories
Heisenberg, Lavinia; Kase, Ryotaro; Minamitsuji, Masato; Tsujikawa, Shinji
2017-08-01
We study static and spherically symmetric black hole (BH) solutions in second-order generalized Proca theories with nonminimal vector field derivative couplings to the Ricci scalar, the Einstein tensor, and the double dual Riemann tensor. We find concrete Lagrangians which give rise to exact BH solutions by imposing two conditions of the two identical metric components and the constant norm of the vector field. These exact solutions are described by either Reissner-Nordström (RN), stealth Schwarzschild, or extremal RN solutions with a non-trivial longitudinal mode of the vector field. We then numerically construct BH solutions without imposing these conditions. For cubic and quartic Lagrangians with power-law couplings which encompass vector Galileons as the specific cases, we show the existence of BH solutions with the difference between two non-trivial metric components. The quintic-order power-law couplings do not give rise to non-trivial BH solutions regular throughout the horizon exterior. The sixth-order and intrinsic vector-mode couplings can lead to BH solutions with a secondary hair. For all the solutions, the vector field is regular at least at the future or past horizon. The deviation from General Relativity induced by the Proca hair can be potentially tested by future measurements of gravitational waves in the nonlinear regime of gravity.
Automated hydraulic tensor for Total Knee Arthroplasty.
Marmignon, C; Leimnei, A; Lavallée, S; Cinquin, P
2005-12-01
To obtain a long lifespan of knee prosthesis, it is necessary to restore the alignment of the lower limb. In some cases of severe arthrosis, the ligament envelope of the joint may be deformed, inducing an asymmetric laxity once the lower limb is realigned. Because there is not yet unanimity regarding how to optimally measure or implement soft tissue balance, we provide a means to acquire a variety of measurements. In traditional surgery, the surgeon sometimes uses a "tensor", which acts like a forceps. This system was redesigned, instrumented, actuated, and integrated into a navigation system for orthopaedic surgery. Improving the perception of the surgeon, it helps him to address the ligament balancing problem. Our first prototype has been tested on sawbones before being validated in an experiment on two cadavers. In our first attempt, the surgeon was able to assess soft tissue balance but judged the device not powerful enough, which led us to develop a new more powerful hydraulic system. In this paper, we present our approach and the first results of the new hydraulic tensor which is currently in an integration process. Copyright 2005 John Wiley & Sons, Ltd.
Regional, Local, and In-mine Moment Tensors for the 2013 Rudna Mine collapse
Whidden, K. M.; Rudzinski, L.; Lizurek, G.; Pankow, K. L.
2013-12-01
On March 19, 2013, the room-and-pillar Rudna copper mine in southwest Poland experienced a collapse (mb 4.7) that trapped 19 miners who were all rescued hours later. News outlets reported that the collapse occurred as the result of an earthquake on a fault. We use three different moment tensor methods and seismic networks to study the source of this event. The velocity structure at regional distances is complex. To the southwest are the Sudetic Mountains and to the north and east a deep sedimentary basin extends towards the Baltic Sea. A single 1-D velocity model is unlikely to adequately account for the paths to all stations. Regional moment tensors were calculated for this event using two sets of velocity models: 1) those used for routine regional moment tensor calculation in Utah, with slight modifications for stations in the deepest part of the basin, and 2) velocity models derived from the POLONAISE'97 seismic refraction experiment (Janik et al. 2002, Sroda et al. 2002, Grad et al. 2003). All models were validated for use in Poland by calculating a moment tensor for the M4.4 earthquake on 2004/11/03 in southeast Poland that has regional moment tensor estimates from two different agencies (see International Seismological Centre event 7443851 for solutions by the Swiss Seismological Service and MedNet Regional Centroid Moment Tensors). Both sets of velocity models were able to generate synthetics that were a good match to the data for the 2004 earthquake, and the resulting moment tensor solutions closely match those from previous investigators, confirming that the velocity models used in the analysis are adequate. A full waveform moment tensor using the velocity models described above and a broadband regional network with event to station distances of 75 to 220 km reveals a source with a dominant and statistically significant implosive component. A local network consisting of four short-period three axial sensors, with event to station distances of 3.5 to 7 km
Square Deal: Lower Bounds and Improved Relaxations for Tensor Recovery
2013-08-16
drawn uniformly at random (by the command orth(randn(·, ·)) in Matlab ). The observed entries are chosen uniformly with ratio ρ. We increase the...and 4d pre-stack seismic data completion using tensor nuclear norm (tnn). preprint, 2013. [GQ12] D. Goldfarb and Z. Qin. Robust low-rank tensor
Transversely isotropic higher-order averaged structure tensors
Hashlamoun, Kotaybah; Federico, Salvatore
2017-08-01
For composites or biological tissues reinforced by statistically oriented fibres, a probability distribution function is often used to describe the orientation of the fibres. The overall effect of the fibres on the material response is accounted for by evaluating averaging integrals over all possible directions in space. The directional average of the structure tensor (tensor product of the unit vector describing the fibre direction by itself) is of high significance. Higher-order averaged structure tensors feature in several models and carry similarly important information. However, their evaluation has a quite high computational cost. This work proposes to introduce mathematical techniques to minimise the computational cost associated with the evaluation of higher-order averaged structure tensors, for the case of a transversely isotropic probability distribution of orientation. A component expression is first introduced, using which a general tensor expression is obtained, in terms of an orthonormal basis in which one of the vectors coincides with the axis of symmetry of transverse isotropy. Then, a higher-order transversely isotropic averaged structure tensor is written in an appropriate basis, constructed starting from the basis of the space of second-order transversely isotropic tensors, which is constituted by the structure tensor and its complement to the identity.
Exploring the tensor networks/AdS correspondence
Energy Technology Data Exchange (ETDEWEB)
Bhattacharyya, Arpan [Department of Physics and Center for Field Theory and Particle Physics, Fudan University,220 Handan Road, 200433 Shanghai (China); Centre For High Energy Physics, Indian Institute of Science,560012 Bangalore (India); Gao, Zhe-Shen [Department of Physics and Center for Field Theory and Particle Physics, Fudan University,220 Handan Road, 200433 Shanghai (China); Hung, Ling-Yan [Department of Physics and Center for Field Theory and Particle Physics, Fudan University,220 Handan Road, 200433 Shanghai (China); State Key Laboratory of Surface Physics and Department of Physics, Fudan University,220 Handan Road, 200433 Shanghai (China); Collaborative Innovation Center of Advanced Microstructures, Nanjing University,Nanjing, 210093 (China); Liu, Si-Nong [Department of Physics and Center for Field Theory and Particle Physics, Fudan University,220 Handan Road, 200433 Shanghai (China)
2016-08-11
In this paper we study the recently proposed tensor networks/AdS correspondence. We found that the Coxeter group is a useful tool to describe tensor networks in a negatively curved space. Studying generic tensor network populated by perfect tensors, we find that the physical wave function generically do not admit any connected correlation functions of local operators. To remedy the problem, we assume that wavefunctions admitting such semi-classical gravitational interpretation are composed of tensors close to, but not exactly perfect tensors. Computing corrections to the connected two point correlation functions, we find that the leading contribution is given by structures related to geodesics connecting the operators inserted at the boundary physical dofs. Such considerations admit generalizations at least to three point functions. This is highly suggestive of the emergence of the analogues of Witten diagrams in the tensor network. The perturbations alone however do not give the right entanglement spectrum. Using the Coxeter construction, we also constructed the tensor network counterpart of the BTZ black hole, by orbifolding the discrete lattice on which the network resides. We found that the construction naturally reproduces some of the salient features of the BTZ black hole, such as the appearance of RT surfaces that could wrap the horizon, depending on the size of the entanglement region A.
Black holes with surrounding matter in scalar-tensor theories.
Cardoso, Vitor; Carucci, Isabella P; Pani, Paolo; Sotiriou, Thomas P
2013-09-13
We uncover two mechanisms that can render Kerr black holes unstable in scalar-tensor gravity, both associated with the presence of matter in the vicinity of the black hole and the fact that this introduces an effective mass for the scalar. Our results highlight the importance of understanding the structure of spacetime in realistic, astrophysical black holes in scalar-tensor theories.
Cosmic no-hair conjecture in scalar–tensor theories
Indian Academy of Sciences (India)
In fact, during inflation there is no difference between scalar–tensor theories, Lyra's manifold and general relativity (GR). Keywords. Scalar–tensor theories; cosmic no-hair. PACS Nos 04.20.jb; 98.80.Hw. 1. Introduction. With regard to the question whether the Universe evolves to a homogeneous and isotropic state during ...
Secoond order parallel tensors on some paracontact manifolds | Liu ...
African Journals Online (AJOL)
The object of the present paper is to study the symmetric and skewsymmetric properties of a second order parallel tensor on paracontact metric (k;μ)- spaces and almost β-para-Kenmotsu (k;μ)-spaces. In this paper, we prove that if there exists a second order symmetric parallel tensor on a paracontact metric (k;μ)- space M, ...
Time-optimized high-resolution readout-segmented diffusion tensor imaging.
Directory of Open Access Journals (Sweden)
Gernot Reishofer
Full Text Available Readout-segmented echo planar imaging with 2D navigator-based reacquisition is an uprising technique enabling the sampling of high-resolution diffusion images with reduced susceptibility artifacts. However, low signal from the small voxels and long scan times hamper the clinical applicability. Therefore, we introduce a regularization algorithm based on total variation that is applied directly on the entire diffusion tensor. The spatially varying regularization parameter is determined automatically dependent on spatial variations in signal-to-noise ratio thus, avoiding over- or under-regularization. Information about the noise distribution in the diffusion tensor is extracted from the diffusion weighted images by means of complex independent component analysis. Moreover, the combination of those features enables processing of the diffusion data absolutely user independent. Tractography from in vivo data and from a software phantom demonstrate the advantage of the spatially varying regularization compared to un-regularized data with respect to parameters relevant for fiber-tracking such as Mean Fiber Length, Track Count, Volume and Voxel Count. Specifically, for in vivo data findings suggest that tractography results from the regularized diffusion tensor based on one measurement (16 min generates results comparable to the un-regularized data with three averages (48 min. This significant reduction in scan time renders high resolution (1 × 1 × 2.5 mm(3 diffusion tensor imaging of the entire brain applicable in a clinical context.
On the energy-momentum tensor in Moyal space
Energy Technology Data Exchange (ETDEWEB)
Balasin, Herbert; Schweda, Manfred [Vienna University of Technology, Institute for Theoretical Physics, Vienna (Austria); Blaschke, Daniel N. [Los Alamos National Laboratory, Theory Division, Los Alamos, NM (United States); Gieres, Francois [Universite de Lyon, Universite Claude Bernard Lyon 1 et CNRS/IN2P3, Institut de Physique Nucleaire de Lyon, Villeurbanne (France)
2015-06-15
We study the properties of the energy-momentum tensor of gauge fields coupled to matter in non-commutative (Moyal) space. In general, the non-commutativity affects the usual conservation law of the tensor as well as its transformation properties (gauge covariance instead of gauge invariance). It is well known that the conservation of the energy-momentum tensor can be achieved by a redefinition involving another star-product. Furthermore, for a pure gauge theory it is always possible to define a gauge invariant energy-momentum tensor by means of a Wilson line. We show that the last two procedures are incompatible with each other if couplings of gauge fields to matter fields (scalars or fermions) are considered: The gauge invariant tensor (constructed via Wilson line) does not allow for a redefinition assuring its conservation, and vice versa the introduction of another star-product does not allow for gauge invariance by means of a Wilson line. (orig.)
The atomistic representation of first strain-gradient elastic tensors
Admal, Nikhil Chandra; Marian, Jaime; Po, Giacomo
2017-02-01
We derive the atomistic representations of the elastic tensors appearing in the linearized theory of first strain-gradient elasticity for an arbitrary multi-lattice. In addition to the classical second-Piola) stress and elastic moduli tensors, these include the rank-three double-stress tensor, the rank-five tensor of mixed elastic moduli, and the rank-six tensor of strain-gradient elastic moduli. The atomistic representations are closed-form analytical expressions in terms of the first and second derivatives of the interatomic potential with respect to interatomic distances, and dyadic products of relative atomic positions. Moreover, all expressions are local, in the sense that they depend only on the atomic neighborhood of a lattice site. Our results emanate from the condition of energetic equivalence between continuum and atomistic representations of a crystal, when the kinematics of the latter is governed by the Cauchy-Born rule. Using the derived expressions, we prove that the odd-order tensors vanish if the lattice basis admits central-symmetry. The analytical expressions are implemented as a KIM compliant algorithm to compute the strain gradient elastic tensors for various materials. Numerical results are presented to compare representative interatomic potentials used in the literature for cubic crystals, including simple lattices (fcc Al and Cu and bcc Fe and W) and multi-lattices (diamond-cubic Si). We observe that central potentials exhibit generalized Cauchy relations for the rank-six tensor of strain-gradient elastic moduli. In addition, this tensor is found to be indefinite for many potentials. We discuss the relationship between indefiniteness and material stability. Finally, the atomistic representations are specialized to central potentials in simple lattices. These expressions are used with analytical potentials to study the sensitivity of the elastic tensors to the choice of the cutoff radius.
Tensor renormalization group methods for spin and gauge models
Zou, Haiyuan
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.
Chiral perturbation theory with tensor sources
Energy Technology Data Exchange (ETDEWEB)
Cata, Oscar; Cata, Oscar; Mateu, Vicent
2007-05-21
We construct the most general chirally-invariant Lagrangian for mesons in the presence of external sources coupled to the tensor current \\bar psi sigma_mu nu psi. In order to have only even terms in the chiral expansion, we consider the new source of O(p2). With this choice, we build the even-parity effective Lagrangian up to the p6-order (NLO). While there are only 4 new terms at the p4-order, at p6-order we find 78 terms for n_f=2 and 113 terms for n_f=3. We provide a detailed discussion on the different mechanisms that ensure that our final set of operators is complete and non-redundant. We also examine the odd-parity sector, to conclude that the first operators appear at the p8-order (NNLO).
Anisotropic diffusion tensor applied to temporal mammograms
DEFF Research Database (Denmark)
Karemore, Gopal; Brandt, Sami; Sporring, Jon
2010-01-01
Breast density is considered a structural property of a mammogram that can change in various ways explaining different effects of medicinal treatments. The aim of the present work is to provide a framework for obtaining more accurate and sensitive measurements of breast density...... changes related to specific effects like Hormonal Replacement Therapy (HRT) and aging. Given effect-grouped patient data, we demonstrated how anisotropic diffusion tensor and its coherence features computed in an anatomically oriented breast coordinate system followed by statistical learning...
Sato, Yuiko; Ito, Kenji; Ogasawara, Kuniaki; Sasaki, Makoto; Kudo, Kohsuke; Murakami, Toshiyuki; Nanba, Takamasa; Nishimoto, Hideaki; Yoshida, Kenji; Kobayashi, Masakazu; Kubo, Yoshitaka; Mase, Tomohiko; Ogawa, Akira
2013-10-01
Carotid endarterectomy (CEA) might improve cognitive function. Fractional anisotropy (FA) values in the cerebral white matter derived from diffusion tensor magnetic resonance imaging (DTI) correlate with cognitive function in patients with various central nervous system diseases. To use tract-based spatial statistics to determine whether postoperative changes of FA values in the cerebral white matter derived from DTI are associated with cognitive improvement after uncomplicated CEA. In 80 patients undergoing CEA for ipsilateral internal carotid artery stenosis (≥70%), FA values in the cerebral white matter were derived from DTI before and 1 month after surgery and were analyzed by using tract-based spatial statistics. Neuropsychological testing, consisting of the Wechsler Adult Intelligence Scale Revised, the Wechsler Memory Scale and the Rey-Osterreith Complex Figure test, was also performed preoperatively and after the first postoperative month. Based on the neuropsychological assessments, 11 (14%) patients were defined as having postoperatively improved cognition. The difference between the 2 mean FA values (postoperative values minus preoperative values) in the cerebral hemisphere ipsilateral to surgery was significantly associated with postoperative cognitive improvement (95% confidence intervals, 2.632-9.877; P = .008). White matter FA values in patients with postoperative cognitive improvement were significantly increased after surgery in the whole ipsilateral cerebral hemisphere, in the contralateral anterior cerebral artery territory, and in the watershed zone between the contralateral anterior and middle cerebral arteries. Postoperative increase in cerebral white matter FA on DTI is associated with cognitive improvement after uncomplicated CEA.
Holographic spin networks from tensor network states
Singh, Sukhwinder; McMahon, Nathan A.; Brennen, Gavin K.
2018-01-01
In the holographic correspondence of quantum gravity, a global on-site symmetry at the boundary generally translates to a local gauge symmetry in the bulk. We describe one way how the global boundary on-site symmetries can be gauged within the formalism of the multiscale renormalization ansatz (MERA), in light of the ongoing discussion between tensor networks and holography. We describe how to "lift" the MERA representation of the ground state of a generic one dimensional (1D) local Hamiltonian, which has a global on-site symmetry, to a dual quantum state of a 2D "bulk" lattice on which the symmetry appears gauged. The 2D bulk state decomposes in terms of spin network states, which label a basis in the gauge-invariant sector of the bulk lattice. This decomposition is instrumental to obtain expectation values of gauge-invariant observables in the bulk, and also reveals that the bulk state is generally entangled between the gauge and the remaining ("gravitational") bulk degrees of freedom that are not fixed by the symmetry. We present numerical results for ground states of several 1D critical spin chains to illustrate that the bulk entanglement potentially depends on the central charge of the underlying conformal field theory. We also discuss the possibility of emergent topological order in the bulk using a simple example, and also of emergent symmetries in the nongauge (gravitational) sector in the bulk. More broadly, our holographic model translates the MERA, a tensor network state, to a superposition of spin network states, as they appear in lattice gauge theories in one higher dimension.
Dispersive transport and symmetry of the dispersion tensor in porous media
Pride, Steven R.; Vasco, Donald W.; Flekkoy, Eirik G.; Holtzman, Ran
2017-04-01
The macroscopic laws controlling the advection and diffusion of solute at the scale of the porous continuum are derived in a general manner that does not place limitations on the geometry and time evolution of the pore space. Special focus is given to the definition and symmetry of the dispersion tensor that is controlling how a solute plume spreads out. We show that the dispersion tensor is not symmetric and that the asymmetry derives from the advective derivative in the pore-scale advection-diffusion equation. When flow is spatially variable across a voxel, such as in the presence of a permeability gradient, the amount of asymmetry can be large. As first shown by Auriault [J.-L. Auriault et al. Transp. Porous Med. 85, 771 (2010), 10.1007/s11242-010-9591-y] in the limit of low Péclet number, we show that at any Péclet number, the dispersion tensor Di j satisfies the flow-reversal symmetry Di j(+q ) =Dj i(-q ) where q is the mean flow in the voxel under analysis; however, Reynold's number must be sufficiently small that the flow is reversible when the force driving the flow changes sign. We also demonstrate these symmetries using lattice-Boltzmann simulations and discuss some subtle aspects of how to measure the dispersion tensor numerically. In particular, the numerical experiments demonstrate that the off-diagonal components of the dispersion tensor are antisymmetric which is consistent with the analytical dependence on the average flow gradients that we propose for these off-diagonal components.
Paniagua, Beatriz; Ehlers, Cindy; Crews, Fulton; Budin, Francois; Larson, Garrett; Styner, Martin; Oguz, Ipek
2011-03-01
Understanding the effects of adolescent binge drinking that persist into adulthood is a crucial public health issue. Adolescent intermittent ethanol exposure (AIE) is an animal model that can be used to investigate these effects in rodents. In this work, we investigate the application of a particular image analysis technique, tensor-based morphometry, for detecting anatomical differences between AIE and control rats using Diffusion Tensor Imaging (DTI). Deformation field analysis is a popular method for detecting volumetric changes analyzing Jacobian determinants calculated on deformation fields. Recent studies showed that computing deformation field metrics on the full deformation tensor, often referred to as tensor-based morphometry (TBM), increases the sensitivity to anatomical differences. In this paper we conduct a comprehensive TBM study for precisely locating differences between control and AIE rats. Using a DTI RARE sequence designed for minimal geometric distortion, 12-directional images were acquired postmortem for control and AIE rats (n=9). After preprocessing, average images for the two groups were constructed using an unbiased atlas building approach. We non-rigidly register the two atlases using Large Deformation Diffeomorphic Metric Mapping, and analyze the resulting deformation field using TBM. In particular, we evaluate the tensor determinant, geodesic anisotropy, and deformation direction vector (DDV) on the deformation field to detect structural differences. This yields data on the local amount of growth, shrinkage and the directionality of deformation between the groups. We show that TBM can thus be used to measure group morphological differences between rat populations, demonstrating the potential of the proposed framework.
Magnetotelluric Phase Tensor Applications to Geothermal Assessment in New Zealand and New Mexico
Jiracek, G. R.; Feucht, D. W.; Brown, D.; Castro, B.; Chang, J.; Goff, D.; Hardwick, C.; Hollingshaus, B.; Bowles-martinez, E.; Nakai, J.; Wilson, C.; Bertrand, E. A.; Bennie, S.; Caldwell, G.; Hill, G. J.; Wallin, E.; Bedrosian, P. A.; Hasterok, D. P.; Pellerin, L.
2012-12-01
Magnetotelluric (MT) phase tensor analysis preserves the background (regional) phase response irrespective of galvanic distortion even if distorting inhomogeneities change between multiple MT deployments. This characteristic is the basis for repeat MT monitoring of the South Karapiti, New Zealand region near the Wairakei Power Station where 1-2 km-deep reinjection of spent geothermal fluids will commence soon. Deep electrical conductivity changes caused by this injection may be detected by background phase tensor changes independent of possible surficial changes, e.g., from drilling operations, or from differing sensor alignments during the multi-MT occupations. In 2010-2012 twenty MT sites within 1.5 km of a newly-drilled injection well were reoccupied by New Zealand GNS scientists and US students from NSF's International Research Experiences for Students program. Maps of phase tensor ellipses at various frequencies have identified frequency bands exhibiting good repeatability, therefore, they are potentially useful for detection of future brine injection. Final reoccupation of the MT sites is scheduled in 2013 after a large brine injection. In New Mexico, the 2012 SAGE program (Summer of Applied Geophysical Experience) applied phase tensor analysis to 8 MT soundings aimed at understanding the occurrence of anomalously high vertical and horizontal temperature gradients located approximately 25 km NW of Santa Fe. Plots of phase tensor ellipses allowed unique, distortion-free visualization of the dimensionality and directions of background geoelectric variations. Analysis of the plots as functions of frequency and location revealed a nearly one-dimensional (1-D) upper conductive (sedimentary) section. Variations in the orientations of the principal axes of phase tensor ellipses exposed an overall, deeper three-dimensional (3-D) geoelectric structure in the region. However, two sequential frequency bands revealed dominantly two-dimensional (2-D) regional features
Kusumoto, Shigekazu
2016-09-01
We estimated the dip distribution of Oita-Kumamoto Tectonic Line located in central Kyushu, Japan, by using the dip of the maximum eigenvector of the gravity gradient tensor. A series of earthquakes in Kumamoto and Oita beginning on 14 April 2016 occurred along this tectonic line, the largest of which was M = 7.3. Because a gravity gradiometry survey has not been conducted in the study area, we calculated the gravity gradient tensor from the Bouguer gravity anomaly and employed it to the analysis. The general dip distribution of the Oita-Kumamoto Tectonic Line was found to be about 65° and tends to be higher towards its eastern end. In addition, we estimated the dip around the largest earthquake to be about 60° from the gravity gradient tensor. This result agrees with the dip of the earthquake source fault obtained by Global Navigation Satellite System data analysis.[Figure not available: see fulltext.
Bayesian approach to magnetotelluric tensor decomposition
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Michel Menvielle
2010-05-01
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Magnetotelluric directional analysis and impedance tensor decomposition are basic tools to validate a local/regional composite electrical model of the underlying structure. Bayesian stochastic methods approach the problem of the parameter estimation and their uncertainty characterization in a fully probabilistic fashion, through the use of posterior model probabilities.We use the standard GroomBailey 3D local/2D regional composite model in our bayesian approach. We assume that the experimental impedance estimates are contamined with the Gaussian noise and define the likelihood of a particular composite model with respect to the observed data. We use noninformative, flat priors over physically reasonable intervals for the standard GroomBailey decomposition parameters. We apply two numerical methods, the Markov chain Monte Carlo procedure based on the Gibbs sampler and a singlecomponent adaptive Metropolis algorithm. From the posterior samples, we characterize the estimates and uncertainties of the individual decomposition parameters by using the respective marginal posterior probabilities. We conclude that the stochastic scheme performs reliably for a variety of models, including the multisite and multifrequency case with up to
Tensor-based Dictionary Learning for Spectral CT Reconstruction
Zhang, Yanbo; Wang, Ge
2016-01-01
Spectral computed tomography (CT) produces an energy-discriminative attenuation map of an object, extending a conventional image volume with a spectral dimension. In spectral CT, an image can be sparsely represented in each of multiple energy channels, and are highly correlated among energy channels. According to this characteristics, we propose a tensor-based dictionary learning method for spectral CT reconstruction. In our method, tensor patches are extracted from an image tensor, which is reconstructed using the filtered backprojection (FBP), to form a training dataset. With the Candecomp/Parafac decomposition, a tensor-based dictionary is trained, in which each atom is a rank-one tensor. Then, the trained dictionary is used to sparsely represent image tensor patches during an iterative reconstruction process, and the alternating minimization scheme is adapted for optimization. The effectiveness of our proposed method is validated with both numerically simulated and real preclinical mouse datasets. The results demonstrate that the proposed tensor-based method generally produces superior image quality, and leads to more accurate material decomposition than the currently popular popular methods. PMID:27541628
Exact tensor network ansatz for strongly interacting systems
Zaletel, Michael P.
It appears that the tensor network ansatz, while not quite complete, is an efficient coordinate system for the tiny subset of a many-body Hilbert space which can be realized as a low energy state of a local Hamiltonian. However, we don't fully understand precisely which phases are captured by the tensor network ansatz, how to compute their physical observables (even numerically), or how to compute a tensor network representation for a ground state given a microscopic Hamiltonian. These questions are algorithmic in nature, but their resolution is intimately related to understanding the nature of quantum entanglement in many-body systems. For this reason it is useful to compute the tensor network representation of various `model' wavefunctions representative of different phases of matter; this allows us to understand how the entanglement properties of each phase are expressed in the tensor network ansatz, and can serve as test cases for algorithm development. Condensed matter physics has many illuminating model wavefunctions, such as Laughlin's celebrated wave function for the fractional quantum Hall effect, the Bardeen-Cooper-Schrieffer wave function for superconductivity, and Anderson's resonating valence bond ansatz for spin liquids. This thesis presents some results on exact tensor network representations of these model wavefunctions. In addition, a tensor network representation is given for the time evolution operator of a long-range one-dimensional Hamiltonian, which allows one to numerically simulate the time evolution of power-law interacting spin chains as well as two-dimensional strips and cylinders.
Volume in moment tensor space in terms of distance
Tape, Walter; Tape, Carl
2017-07-01
Suppose that we want to assess the extent to which some large collection of moment tensors is concentrated near a fixed moment tensor m. We are naturally led to consider the distribution of the distances of the moment tensors from m. This distribution, however, can only be judged in conjunction with the distribution of distances from m for randomly chosen moment tensors. In cumulative form, the latter distribution is the same as the fractional volume \\hat{V}(ω ) of the set of all moment tensors that are within distance ω of m. This definition of \\hat{V}(ω ) assumes that a reasonable universe {M} of moment tensors has been specified at the outset and that it includes the original collection as a subset. Our main goal in this article is to derive a formula for \\hat{V}(ω ) when {M} is the set [Λ]_{U} of all moment tensors having a specified eigenvalue triple Λ. We find that \\hat{V}(ω ) depends strongly on Λ, and we illustrate the dependence by plotting the derivative curves \\hat{V}^' }(ω ) for various seismologically relevant Λs. The exotic and unguessable shapes of these curves underscores the futility of interpreting the distribution of distances for the original moment tensors without knowing \\hat{V}(ω ) or \\hat{V}^' }(ω ). The derivation of the formula for \\hat{V}(ω ) relies on a certain ϕ σz coordinate system for [Λ]_{U}, which we treat in detail. Our underlying motivation for the paper is the estimation of uncertainties in moment tensor inversion.
Tensor-based fusion of EEG and FMRI to understand neurological changes in Schizophrenia
DEFF Research Database (Denmark)
Evrim, Acar Ataman; Levin-Schwartz, Yuri; Calhoun, Vince D.
2016-01-01
Neuroimaging modalities such as functional magnetic resonance imaging (fMRI) and electroencephalography (EEG) provide information about neurological functions in complementary spatiotemporal resolutions; therefore, fusion of these modalities is expected to provide better understanding of brain...... activity. In this paper, we jointly analyze fMRI and multi-channel EEG signals collected during an auditory oddball task with the goal of capturing brain activity patterns that differ between patients with schizophrenia and healthy controls. Rather than selecting a single electrode or matricizing the third......-order tensor that can be naturally used to represent multi-channel EEG signals, we preserve the multi-way structure of EEG data and use a coupled matrix and tensor factorization (CMTF) model to jointly analyze fMRI and EEG signals. Our analysis reveals that (i) joint analysis of EEG and fMRI using a CMTF model...
Tensor valuations and their applications in stochastic geometry and imaging
Kiderlen, Markus
2017-01-01
The purpose of this volume is to give an up-to-date introduction to tensor valuations and their applications. Starting with classical results concerning scalar-valued valuations on the families of convex bodies and convex polytopes, it proceeds to the modern theory of tensor valuations. Product and Fourier-type transforms are introduced and various integral formulae are derived. New and well-known results are presented, together with generalizations in several directions, including extensions to the non-Euclidean setting and to non-convex sets. A variety of applications of tensor valuations to models in stochastic geometry, to local stereology and to imaging are also discussed.
The general dielectric tensor for bi-kappa magnetized plasmas
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Gaelzer, R., E-mail: rudi.gaelzer@ufrgs.br; Ziebell, L. F., E-mail: luiz.ziebell@ufrgs.br; Meneses, A. R., E-mail: anemeneses@gmail.com [Instituto de Física, UFRGS, 91501-970 Porto Alegre, RS (Brazil)
2016-06-15
In this paper, we derive the dielectric tensor for a plasma containing particles described by an anisotropic superthermal (bi-kappa) velocity distribution function. The tensor components are written in terms of the two-variables kappa plasma special functions, recently defined by Gaelzer and Ziebell [Phys. Plasmas 23, 022110 (2016)]. We also obtain various new mathematical properties for these functions, which are useful for the analytical treatment, numerical implementation, and evaluation of the functions and, consequently, of the dielectric tensor. The formalism developed here and in the previous paper provides a mathematical framework for the study of electromagnetic waves propagating at arbitrary angles and polarizations in a superthermal plasma.
Scalar-Tensor Black Holes Embedded in an Expanding Universe
Tretyakova, Daria; Latosh, Boris
2018-02-01
In this review we focus our attention on scalar-tensor gravity models and their empirical verification in terms of black hole and wormhole physics. We focus on a black hole, embedded in an expanding universe, describing both cosmological and astrophysical scales. We show that in scalar-tensor gravity it is quite common that the local geometry is isolated from the cosmological expansion, so that it does not backreact on the black hole metric. We try to extract common features of scalar-tensor black holes in an expanding universe and point out the gaps that must be filled.
Scalar-Tensor Black Holes Embedded in an Expanding Universe
Directory of Open Access Journals (Sweden)
Daria Tretyakova
2018-02-01
Full Text Available In this review, we focus our attention on scalar-tensor gravity models and their empirical verification in terms of black hole and wormhole physics. We focus on black holes, embedded in an expanding universe, describing both cosmological and astrophysical scales. We show that in scalar-tensor gravity it is quite common that the local geometry is isolated from the cosmological expansion, so that it does not backreact on the black hole metric. We try to extract common features of scalar-tensor black holes in an expanding universe and point out the issues that are not fully investigated.
The general dielectric tensor for bi-kappa magnetized plasmas
Gaelzer, Rudi; Meneses, Anelise Ramires
2016-01-01
In this paper we derive the dielectric tensor for a plasma containing particles described by an anisotropic superthermal (bi-kappa) velocity distribution function. The tensor components are written in terms of the two-variables kappa plasma special functions, recently defined by Gaelzer and Ziebell [Phys. Plasmas 23, 022110 (2016)]. We also obtain various new mathematical properties for these functions, which are useful for the analytical treatment, numerical implementation and evaluation of the functions and, consequently, of the dielectric tensor. The formalism developed here and in the previous paper provides a mathematical framework for the study of electromagnetic waves propagating at arbitrary angles and polarizations in a superthermal plasma.
Energy-momentum tensor within the 1/N expansion
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Gaigg, P.; Schaller, P.; Schweda, M. (Technische Univ., Vienna (Austria). 1. Inst. fuer Theoretische Physik)
1985-01-01
The authors extend the 1/N expansion for the O(N)-symmetric field models in lowest nontrivial order to incorporate the energy-momentum tensor consistently. They demonstrate the idea on the basis of an O(N)-model consisting of N real scalar fields with a quartic self-interaction. It is shown that the corresponding Green's functions with the energy-momentum tensor insertion are renormalizable in the usual sense. It can be proved that the energy-momentum tensor is a conserved quantity in this approximation.
Masses of the tensor mesons with JP=2−
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Wei Chen
2014-10-01
Full Text Available We calculate the two-point correlation function using the interpolating current with JPC=2−. After performing the Borel sum rule analysis, the extracted masses of the 2−− tensor charmonium and bottomonium are 3.97±0.25 GeV and 10.13±0.34 GeV respectively. For comparison, we also perform the moment sum rule analysis for the charmonium and bottomonium systems. We extend the same analysis to study the q¯q,q¯s,s¯s,q¯c,s¯c,q¯b,s¯b and c¯b systems. Their masses are 1.78±0.12,1.85±0.14,2.00±0.16,2.86±0.14,3.01±0.21,5.66±0.33,6.40±0.25, and 7.08±0.34 GeV respectively.
On the joint numerical status and tensor products
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Ram Verma
1990-01-01
Full Text Available We prove a result on the joint numerical status of the bounded Hilbert space operators on the tensor products. The result seems to have nice applications in the multiparameter spectral theory.
Two new eigenvalue localization sets for tensors and theirs applications
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Zhao Jianxing
2017-10-01
Full Text Available A new eigenvalue localization set for tensors is given and proved to be tighter than those presented by Qi (J. Symbolic Comput., 2005, 40, 1302-1324 and Li et al. (Numer. Linear Algebra Appl., 2014, 21, 39-50. As an application, a weaker checkable sufficient condition for the positive (semi-definiteness of an even-order real symmetric tensor is obtained. Meanwhile, an S-type E-eigenvalue localization set for tensors is given and proved to be tighter than that presented by Wang et al. (Discrete Cont. Dyn.-B, 2017, 22(1, 187-198. As an application, an S-type upper bound for the Z-spectral radius of weakly symmetric nonnegative tensors is obtained. Finally, numerical examples are given to verify the theoretical results.
An eigenvalue localization set for tensors and its applications
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Jianxing Zhao
2017-03-01
Full Text Available Abstract A new eigenvalue localization set for tensors is given and proved to be tighter than those presented by Li et al. (Linear Algebra Appl. 481:36-53, 2015 and Huang et al. (J. Inequal. Appl. 2016:254, 2016. As an application of this set, new bounds for the minimum eigenvalue of M $\\mathcal{M}$ -tensors are established and proved to be sharper than some known results. Compared with the results obtained by Huang et al., the advantage of our results is that, without considering the selection of nonempty proper subsets S of N = { 1 , 2 , … , n } $N=\\{1,2,\\ldots,n\\}$ , we can obtain a tighter eigenvalue localization set for tensors and sharper bounds for the minimum eigenvalue of M $\\mathcal{M}$ -tensors. Finally, numerical examples are given to verify the theoretical results.
Tensor extension of the Poincar\\'e algebra
Soroka, Dmitrij V.; Soroka, Vyacheslav A.
2004-01-01
A tensor extension of the Poincar\\'e algebra is proposed for the arbitrary dimensions. Casimir operators of the extension are constructed. A possible supersymmetric generalization of this extension is also found in the dimensions $D=2,3,4$.
An introduction to tensors and group theory for physicists
Jeevanjee, Nadir
2015-01-01
The second edition of this highly praised textbook provides an introduction to tensors, group theory, and their applications in classical and quantum physics. Both intuitive and rigorous, it aims to demystify tensors by giving the slightly more abstract but conceptually much clearer definition found in the math literature, and then connects this formulation to the component formalism of physics calculations. New pedagogical features, such as new illustrations, tables, and boxed sections, as well as additional “invitation” sections that provide accessible introductions to new material, offer increased visual engagement, clarity, and motivation for students. Part I begins with linear algebraic foundations, follows with the modern component-free definition of tensors, and concludes with applications to physics through the use of tensor products. Part II introduces group theory, including abstract groups and Lie groups and their associated Lie algebras, then intertwines this material with that of Part...
Renormalization of nonabelian gauge theories with tensor matter fields
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Lemes, Vitor; Renan, Ricardo [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil); Sorella, Silvio Paolo [Universidade do Estado, Rio de Janeiro, RJ (Brazil). Inst. de Fisica
1996-03-01
The renormalizability of a nonabelian model describing the coupling between antisymmetric second rank tensor matter fields and Yang-Mills gauge fields is discussed within the BRS algebraic framework. (author). 12 refs.
Non-convex Statistical Optimization for Sparse Tensor Graphical Model.
Sun, Wei; Wang, Zhaoran; Liu, Han; Cheng, Guang
2015-01-01
We consider the estimation of sparse graphical models that characterize the dependency structure of high-dimensional tensor-valued data. To facilitate the estimation of the precision matrix corresponding to each way of the tensor, we assume the data follow a tensor normal distribution whose covariance has a Kronecker product structure. The penalized maximum likelihood estimation of this model involves minimizing a non-convex objective function. In spite of the non-convexity of this estimation problem, we prove that an alternating minimization algorithm, which iteratively estimates each sparse precision matrix while fixing the others, attains an estimator with the optimal statistical rate of convergence as well as consistent graph recovery. Notably, such an estimator achieves estimation consistency with only one tensor sample, which is unobserved in previous work. Our theoretical results are backed by thorough numerical studies.
Comparison of two global digital algorithms for Minkowski tensor estimation
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are confirmed by simulations on test sets, and recommendations for input arguments of the algorithms are given. For increasing resolutions, we obtain more accurate estimators for the Minkowski tensors. Digitisations of more complicated objects are shown to require higher resolutions....
Ward identities and combinatorics of rainbow tensor models
Itoyama, H.; Mironov, A.; Morozov, A.
2017-06-01
We discuss the notion of renormalization group (RG) completion of non-Gaussian Lagrangians and its treatment within the framework of Bogoliubov-Zimmermann theory in application to the matrix and tensor models. With the example of the simplest non-trivial RGB tensor theory (Aristotelian rainbow), we introduce a few methods, which allow one to connect calculations in the tensor models to those in the matrix models. As a byproduct, we obtain some new factorization formulas and sum rules for the Gaussian correlators in the Hermitian and complex matrix theories, square and rectangular. These sum rules describe correlators as solutions to finite linear systems, which are much simpler than the bilinear Hirota equations and the infinite Virasoro recursion. Search for such relations can be a way to solving the tensor models, where an explicit integrability is still obscure.
The tensor hierarchy of 8-dimensional field theories
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Andino, Óscar Lasso; Ortín, Tomás [Instituto de Física Teórica UAM/CSIC,C/ Nicolás Cabrera, 13-15, C.University Cantoblanco, E-28049 Madrid (Spain)
2016-10-18
We construct the tensor hierarchy of generic, bosonic, 8-dimensional field theories. We first study the form of the most general 8-dimensional bosonic theory with Abelian gauge symmetries only and no massive deformations. This study determines the tensors that occur in the Chern-Simons terms of the (electric and magnetic) field strengths and the action for the electric fields, which we determine. Having constructed the most general Abelian theory we study the most general gaugings of its global symmetries and the possible massive deformations using the embedding tensor formalism, constructing the complete tensor hierarchy using the Bianchi identities. We find the explicit form of all the field strengths of the gauged theory up to the 6-forms. Finally, we find the equations of motion comparing the Noether identities with the identities satisfied by the Bianchi identities themselves. We find that some equations of motion are not simply the Bianchi identities of the dual fields, but combinations of them.
Vectors, tensors and the basic equations of fluid mechanics
Aris, Rutherford
1962-01-01
Introductory text, geared toward advanced undergraduate and graduate students, applies mathematics of Cartesian and general tensors to physical field theories and demonstrates them in terms of the theory of fluid mechanics. 1962 edition.
Traffic Speed Data Imputation Method Based on Tensor Completion
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Bin Ran
2015-01-01
Full Text Available Traffic speed data plays a key role in Intelligent Transportation Systems (ITS; however, missing traffic data would affect the performance of ITS as well as Advanced Traveler Information Systems (ATIS. In this paper, we handle this issue by a novel tensor-based imputation approach. Specifically, tensor pattern is adopted for modeling traffic speed data and then High accurate Low Rank Tensor Completion (HaLRTC, an efficient tensor completion method, is employed to estimate the missing traffic speed data. This proposed method is able to recover missing entries from given entries, which may be noisy, considering severe fluctuation of traffic speed data compared with traffic volume. The proposed method is evaluated on Performance Measurement System (PeMS database, and the experimental results show the superiority of the proposed approach over state-of-the-art baseline approaches.
Tweeting Earthquakes using TensorFlow
Casarotti, E.; Comunello, F.; Magnoni, F.
2016-12-01
The use of social media is emerging as a powerful tool for disseminating trusted information about earthquakes. Since 2009, the Twitter account @INGVterremoti provides constant and timely details about M2+ seismic events detected by the Italian National Seismic Network, directly connected with the seismologists on duty at Istituto Nazionale di Geofisica e Vulcanologia (INGV). Currently, it updates more than 150,000 followers. Nevertheless, since it provides only the manual revision of seismic parameters, the timing (approximately between 10 and 20 minutes after an event) has started to be under evaluation. Undeniably, mobile internet, social network sites and Twitter in particular require a more rapid and "real-time" reaction. During the last 36 months, INGV tested the tweeting of the automatic detection of M3+ earthquakes, studying the reliability of the information both in term of seismological accuracy that from the point of view of communication and social research. A set of quality parameters (i.e. number of seismic stations, gap, relative error of the location) has been recognized to reduce false alarms and the uncertainty of the automatic detection. We present an experiment to further improve the reliability of this process using TensorFlow™ (an open source software library originally developed by researchers and engineers working on the Google Brain Team within Google's Machine Intelligence research organization).
Smartphone dependence classification using tensor factorization.
Choi, Jingyun; Rho, Mi Jung; Kim, Yejin; Yook, In Hye; Yu, Hwanjo; Kim, Dai-Jin; Choi, In Young
2017-01-01
Excessive smartphone use causes personal and social problems. To address this issue, we sought to derive usage patterns that were directly correlated with smartphone dependence based on usage data. This study attempted to classify smartphone dependence using a data-driven prediction algorithm. We developed a mobile application to collect smartphone usage data. A total of 41,683 logs of 48 smartphone users were collected from March 8, 2015, to January 8, 2016. The participants were classified into the control group (SUC) or the addiction group (SUD) using the Korean Smartphone Addiction Proneness Scale for Adults (S-Scale) and a face-to-face offline interview by a psychiatrist and a clinical psychologist (SUC = 23 and SUD = 25). We derived usage patterns using tensor factorization and found the following six optimal usage patterns: 1) social networking services (SNS) during daytime, 2) web surfing, 3) SNS at night, 4) mobile shopping, 5) entertainment, and 6) gaming at night. The membership vectors of the six patterns obtained a significantly better prediction performance than the raw data. For all patterns, the usage times of the SUD were much longer than those of the SUC. From our findings, we concluded that usage patterns and membership vectors were effective tools to assess and predict smartphone dependence and could provide an intervention guideline to predict and treat smartphone dependence based on usage data.
Smartphone dependence classification using tensor factorization.
Directory of Open Access Journals (Sweden)
Jingyun Choi
Full Text Available Excessive smartphone use causes personal and social problems. To address this issue, we sought to derive usage patterns that were directly correlated with smartphone dependence based on usage data. This study attempted to classify smartphone dependence using a data-driven prediction algorithm. We developed a mobile application to collect smartphone usage data. A total of 41,683 logs of 48 smartphone users were collected from March 8, 2015, to January 8, 2016. The participants were classified into the control group (SUC or the addiction group (SUD using the Korean Smartphone Addiction Proneness Scale for Adults (S-Scale and a face-to-face offline interview by a psychiatrist and a clinical psychologist (SUC = 23 and SUD = 25. We derived usage patterns using tensor factorization and found the following six optimal usage patterns: 1 social networking services (SNS during daytime, 2 web surfing, 3 SNS at night, 4 mobile shopping, 5 entertainment, and 6 gaming at night. The membership vectors of the six patterns obtained a significantly better prediction performance than the raw data. For all patterns, the usage times of the SUD were much longer than those of the SUC. From our findings, we concluded that usage patterns and membership vectors were effective tools to assess and predict smartphone dependence and could provide an intervention guideline to predict and treat smartphone dependence based on usage data.
Smartphone dependence classification using tensor factorization
Kim, Yejin; Yook, In Hye; Yu, Hwanjo; Kim, Dai-Jin
2017-01-01
Excessive smartphone use causes personal and social problems. To address this issue, we sought to derive usage patterns that were directly correlated with smartphone dependence based on usage data. This study attempted to classify smartphone dependence using a data-driven prediction algorithm. We developed a mobile application to collect smartphone usage data. A total of 41,683 logs of 48 smartphone users were collected from March 8, 2015, to January 8, 2016. The participants were classified into the control group (SUC) or the addiction group (SUD) using the Korean Smartphone Addiction Proneness Scale for Adults (S-Scale) and a face-to-face offline interview by a psychiatrist and a clinical psychologist (SUC = 23 and SUD = 25). We derived usage patterns using tensor factorization and found the following six optimal usage patterns: 1) social networking services (SNS) during daytime, 2) web surfing, 3) SNS at night, 4) mobile shopping, 5) entertainment, and 6) gaming at night. The membership vectors of the six patterns obtained a significantly better prediction performance than the raw data. For all patterns, the usage times of the SUD were much longer than those of the SUC. From our findings, we concluded that usage patterns and membership vectors were effective tools to assess and predict smartphone dependence and could provide an intervention guideline to predict and treat smartphone dependence based on usage data. PMID:28636614
Parametric diffusion tensor imaging of the breast.
Eyal, Erez; Shapiro-Feinberg, Myra; Furman-Haran, Edna; Grobgeld, Dov; Golan, Talia; Itzchak, Yacov; Catane, Raphael; Papa, Moshe; Degani, Hadassa
2012-05-01
To investigate the ability of parametric diffusion tensor imaging (DTI), applied at 3 Tesla, to dissect breast tissue architecture and evaluate breast lesions. All protocols were approved and a signed informed consent was obtained from all subjects. The study included 21 healthy women, 26 women with 33 malignant lesions, and 14 women with 20 benign lesions. Images were recorded at 3 Tesla with a protocol optimized for breast DTI at a spatial resolution of 1.9 × 1.9 × (2-2.5) mm3. Image processing algorithms and software, applied at pixel resolution, yielded vector maps of prime diffusion direction and parametric maps of the 3 orthogonal diffusion coefficients and of the fractional anisotropy and maximal anisotropy. The DTI-derived vector maps and parametric maps revealed the architecture of the entire mammary fibroglandular tissue and allowed a reliable detection of malignant lesions. Cancer lesions exhibited significantly lower values of the orthogonal diffusion coefficients, λ1, λ2, λ3, and of the maximal anisotropy index λ1-λ3 as compared with normal breast tissue (P architecture. Parametric maps of λ1 and λ1-λ3 facilitate the detection and diagnosis of breast cancer.
Diffusion Tensor Imaging, Structural Connectivity, and Schizophrenia
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Thomas J. Whitford
2011-01-01
Full Text Available A fundamental tenet of the “disconnectivity” theories of schizophrenia is that the disorder is ultimately caused by abnormal communication between spatially disparate brain structures. Given that the white matter fasciculi represent the primary infrastructure for long distance communication in the brain, abnormalities in these fiber bundles have been implicated in the etiology of schizophrenia. Diffusion tensor imaging (DTI is a magnetic resonance imaging (MRI technique that enables the visualization of white matter macrostructure in vivo, and which has provided unprecedented insight into the existence and nature of white matter abnormalities in schizophrenia. The paper begins with an overview of DTI and more commonly used diffusion metrics and moves on to a brief review of the schizophrenia literature. The functional implications of white matter abnormalities are considered, particularly with respect to myelin's role in modulating the transmission velocity of neural discharges. The paper concludes with a speculative hypothesis about the relationship between gray and white matter abnormalities associated with schizophrenia.
PHYSLIB: A C++ tensor class library
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Budge, K.G.
1991-10-09
C++ is the first object-oriented programming language which produces sufficiently efficient code for consideration in computation-intensive physics and engineering applications. In addition, the increasing availability of massively parallel architectures requires novel programming techniques which may prove to be relatively easy to implement in C++. For these reasons, Division 1541 at Sandia National Laboratories is devoting considerable resources to the development of C++ libraries. This document describes the first of these libraries to be released, PHYSLIB, which defines classes representing Cartesian vectors and (second-order) tensors. This library consists of the header file physlib.h, the inline code file physlib.inl, and the source file physlib.C. The library is applicable to both three-dimensional and two-dimensional problems; the user selects the 2-D version of the library by defining the symbol TWO D in the header file physlib.h and recompiling physlib.C and his own code. Alternately, system managers may wish to provide duplicate header and object modules of each dimensionality. This code was produced under the auspices of Sandia National Laboratories, a federally-funded research center administered for the United States Department of Energy on a non-profit basis by AT T. This code is available to US citizens, and institutions under research, government use and/or commercial license agreements.
Evolution of Dark Energy Perturbations in Scalar-Tensor Cosmologies
Sanchez, J. C. Bueno; Perivolaropoulos, L.
2010-01-01
We solve analytically and numerically the generalized Einstein equations in scalar-tensor cosmologies to obtain the evolution of dark energy and matter linear perturbations. We compare our results with the corresponding results for minimally coupled quintessence perturbations. Our results for natural (O(1)) values of parameters in the Lagrangian which lead to a background expansion similar to LCDM are summarized as follows: 1. Scalar-Tensor dark energy density perturbations are amplified by a...
Review of diffusion tensor imaging and its application in children
Energy Technology Data Exchange (ETDEWEB)
Vorona, Gregory A. [Children' s Hospital of Richmond at Virginia Commonwealth University, Department of Radiology, Richmond, VA (United States); Berman, Jeffrey I. [Children' s Hospital of Philadelphia, Department of Radiology, Philadelphia, PA (United States)
2015-09-15
Diffusion MRI is an imaging technique that uses the random motion of water to probe tissue microstructure. Diffusion tensor imaging (DTI) can quantitatively depict the organization and connectivity of white matter. Given the non-invasiveness of the technique, DTI has become a widely used tool for researchers and clinicians to examine the white matter of children. This review covers the basics of diffusion-weighted imaging and diffusion tensor imaging and discusses examples of their clinical application in children. (orig.)
Optimization via separated representations and the canonical tensor decomposition
Reynolds, Matthew J.; Beylkin, Gregory; Doostan, Alireza
2017-11-01
We introduce a new, quadratically convergent algorithm for finding maximum absolute value entries of tensors represented in the canonical format. The computational complexity of the algorithm is linear in the dimension of the tensor. We show how to use this algorithm to find global maxima of non-convex multivariate functions in separated form. We demonstrate the performance of the new algorithms on several examples.
Batch derivation of piezoresistive coefficient tensor by matrix algebra
Bao, Minhang; Huang, Yiping
2004-03-01
To commemorate the important discovery of the piezoresistance effect of germanium and silicon by C S Smith half a century ago, we present a new method of deriving the piezoresistive (PR) coefficient tensor for diamond structure material using matrix algebra. Using this method, all the components of the PR coefficient tensor (of the fourth rank) in an arbitrary Cartesian coordinate system can be obtained in a batch and the relation between the components is clearly shown.
Overview of recent advances in numerical tensor algebra
Bergqvist G.; Larsson E.G.
2010-01-01
We present a survey of some recent developments for decompositions of multi-way arrays or tensors, with special emphasis on results relevant for applications and modeling in signal processing. A central problem is how to find lowrank approximations of tensors, and we describe some new results, including numerical methods, algorithms and theory, for the higher order singular value decomposition (HOSVD) and the parallel factors expansion or canonical decomposition (CP expansion).
Beyond-Standard-Model Tensor Interaction and Hadron Phenomenology.
Courtoy, Aurore; Baeßler, Stefan; González-Alonso, Martín; Liuti, Simonetta
2015-10-16
We evaluate the impact of recent developments in hadron phenomenology on extracting possible fundamental tensor interactions beyond the standard model. We show that a novel class of observables, including the chiral-odd generalized parton distributions, and the transversity parton distribution function can contribute to the constraints on this quantity. Experimental extractions of the tensor hadronic matrix elements, if sufficiently precise, will provide a, so far, absent testing ground for lattice QCD calculations.
A linear support higher-order tensor machine for classification.
Hao, Zhifeng; He, Lifang; Chen, Bingqian; Yang, Xiaowei
2013-07-01
There has been growing interest in developing more effective learning machines for tensor classification. At present, most of the existing learning machines, such as support tensor machine (STM), involve nonconvex optimization problems and need to resort to iterative techniques. Obviously, it is very time-consuming and may suffer from local minima. In order to overcome these two shortcomings, in this paper, we present a novel linear support higher-order tensor machine (SHTM) which integrates the merits of linear C-support vector machine (C-SVM) and tensor rank-one decomposition. Theoretically, SHTM is an extension of the linear C-SVM to tensor patterns. When the input patterns are vectors, SHTM degenerates into the standard C-SVM. A set of experiments is conducted on nine second-order face recognition datasets and three third-order gait recognition datasets to illustrate the performance of the proposed SHTM. The statistic test shows that compared with STM and C-SVM with the RBF kernel, SHTM provides significant performance gain in terms of test accuracy and training speed, especially in the case of higher-order tensors.
Guilhem, A.; Dreger, D. S.; Hutchings, L. J.; Johnson, L.
2012-12-01
We investigate moment tensor solutions and their uncertainties for magnitude (M) ~3 earthquakes located in the northwest Geysers geothermal field, California. We are exploiting an unusual opportunity where data for M~3 events have been recorded by three different networks and have moment tensor solutions calculated by three different methods. We solve for both deviatoric and full moment tensor solutions. The data sets include local short-period instruments (4.5 Hz) of the 30 stations of the Lawrence Berkeley National Laboratory (LBNL), with which we obtain waveform inversion solutions at relatively high frequencies (i.e., up to 2.5 Hz), and regionally distributed broadband stations operated by the Berkeley Seismological Laboratory (BSL), with which are used to provide waveform inversion solutions with data filtered at longer periods (i.e., > 10 sec). We also utilize the LBNL data to obtain moment tensor solutions by fitting the P-wave first motions. The USGS, LBNL, and BSL obtain different event locations, utilize different velocity models, and analyze different frequency bands and wave types (i.e., body waves for LBNL method and primarily surface waves for the BSL analysis). Preliminary results indicate that the BSL and LBNL waveform modeling analyses give similar results in terms of nodal plane characteristics, moment magnitude, and moment tensor decomposition. Analysis of the P-wave first motions recorded by LBNL stations can illuminate complexities in the source processes when compared to waveform moment tensor solutions. We discuss uncertainties in the source inversions that use broadband and/or short-period waveform modeling, and in the source inversions from first motions only. We also combine the different datasets and compare their individual importance as they can help illustrate the complex source processes happening in the Geysers. This study introduces the possibility to interpret the seismic sources as complex processes in which both shear and tensile
Four-point correlation function of stress-energy tensors in N=4 superconformal theories
Korchemsky, G P
2015-01-01
We derive the explicit expression for the four-point correlation function of stress-energy tensors in four-dimensional N=4 superconformal theory. We show that it has a remarkably simple and suggestive form allowing us to predict a large class of four-point correlation functions involving the stress-energy tensor and other conserved currents. We then apply the obtained results on the correlation functions to computing the energy-energy correlations, which measure the flow of energy in the final states created from the vacuum by a source. We demonstrate that they are given by a universal function independent of the choice of the source. Our analysis relies only on N=4 superconformal symmetry and does not use the dynamics of the theory.
Resonances at the LHC beyond the Higgs. The Scalar/Tensor case
Energy Technology Data Exchange (ETDEWEB)
Kilian, Wolfgang [Department of Physics, University of Siegen (Germany); Ohl, Thorsten [Faculty of Physics and Astronomy, Wuerzburg University (Germany); Reuter, Juergen [DESY, Theory Group, Hamburg (Germany); Sekulla, Marco [Institute for Theoretical Physics, Karlsruhe Institute of Technology (Germany)
2016-07-01
Weak vector boson scattering (VBS) at high energies will be one of the key measurements in current and upcoming LHC runs. It is most sensitive to any new physics associated with electroweak symmetry breaking. However, a conventional EFT analysis will fail at high energies. In this talk I present an extension of the bottom-up EFT, which includes the 125 GeV Higgs boson. Within a simplified model the effects of generic tensor and scalar resonances are considered. The spurious degrees of freedom of tensor resonances that would lead to bad high-energy behavior are treated using a generalization of the Stueckelberg formalism. To ensure that the scattering amplitudes are well behaved on the whole phase space, the T-matrix unitarization procedure is used. The implementation of this model into the Monte Carlo generator WHIZARD can be used for further studies at the LHC as I will show with exemplary plots.
Clinical prediction of fall risk and white matter abnormalities: a diffusion tensor imaging study.
Koo, Bang-Bon; Bergethon, Peter; Qiu, Wei Qiao; Scott, Tammy; Hussain, Mohammed; Rosenberg, Irwin; Caplan, Louis R; Bhadelia, Rafeeque A
2012-06-01
The Tinetti scale is a simple clinical tool designed to predict risk of falling by focusing on gait and stance impairment in elderly persons. Gait impairment is also associated with white matter (WM) abnormalities. To test the hypothesis that elderly subjects at risk for falling, as determined by the Tinetti scale, have specific patterns of WM abnormalities on diffusion tensor imaging. Community-based cohort of 125 homebound elderly individuals. Diffusion tensor imaging scans were analyzed using tract-based spatial statistics analysis to determine the location of WM abnormalities in subjects with Tinetti scale scores of 25 or higher (without risk of falls) and lower than 25 (with risk of falls).Multivariate linear least squares correlation analysis was performed to determine the association between Tinetti scale scores and local fractional anisotropy values on each skeletal voxel controlling for possible confounders. In subjects with risk of falls (Tinetti scale score Tinetti scale have WM abnormalities in specific locations on diffusion tensor imaging, some of which correlate with cognitive function scores.
Effective field theory approaches for tensor potentials
Energy Technology Data Exchange (ETDEWEB)
Jansen, Maximilian
2016-11-14
Effective field theories are a widely used tool to study physical systems at low energies. We apply them to systematically analyze two and three particles interacting via tensor potentials. Two examples are addressed: pion interactions for anti D{sup 0}D{sup *0} scattering to dynamically generate the X(3872) and dipole interactions for two and three bosons at low energies. For the former, the one-pion exchange and for the latter, the long-range dipole force induce a tensor-like structure of the potential. We apply perturbative as well as non-perturbative methods to determine low-energy observables. The X(3872) is of major interest in modern high-energy physics. Its exotic characteristics require approaches outside the range of the quark model for baryons and mesons. Effective field theories represent such methods and provide access to its peculiar nature. We interpret the X(3872) as a hadronic molecule consisting of neutral D and D{sup *} mesons. It is possible to apply an effective field theory with perturbative pions. Within this framework, we address chiral as well as finite volume extrapolations for low-energy observables, such as the binding energy and the scattering length. We show that the two-point correlation function for the D{sup *0} meson has to be resummed to cure infrared divergences. Moreover, next-to-leading order coupling constants, which were introduced by power counting arguments, appear to be essential to renormalize the scattering amplitude. The binding energy as well as the scattering length display a moderate dependence on the light quark masses. The X(3872) is most likely deeper bound for large light quark masses. In a finite volume on the other hand, the binding energy significantly increases. The dependence on the light quark masses and the volume size can be simultaneously obtained. For bosonic dipoles we apply a non-perturbative, numerical approach. We solve the Lippmann-Schwinger equation for the two-dipole system and the Faddeev
Nearest-neighbor interaction systems in the tensor-train format
Gelß, Patrick; Klus, Stefan; Matera, Sebastian; Schütte, Christof
2017-07-01
Low-rank tensor approximation approaches have become an important tool in the scientific computing community. The aim is to enable the simulation and analysis of high-dimensional problems which cannot be solved using conventional methods anymore due to the so-called curse of dimensionality. This requires techniques to handle linear operators defined on extremely large state spaces and to solve the resulting systems of linear equations or eigenvalue problems. In this paper, we present a systematic tensor-train decomposition for nearest-neighbor interaction systems which is applicable to a host of different problems. With the aid of this decomposition, it is possible to reduce the memory consumption as well as the computational costs significantly. Furthermore, it can be shown that in some cases the rank of the tensor decomposition does not depend on the network size. The format is thus feasible even for high-dimensional systems. We will illustrate the results with several guiding examples such as the Ising model, a system of coupled oscillators, and a CO oxidation model.
Direct solution of the Chemical Master Equation using quantized tensor trains.
Kazeev, Vladimir; Khammash, Mustafa; Nip, Michael; Schwab, Christoph
2014-03-01
The Chemical Master Equation (CME) is a cornerstone of stochastic analysis and simulation of models of biochemical reaction networks. Yet direct solutions of the CME have remained elusive. Although several approaches overcome the infinite dimensional nature of the CME through projections or other means, a common feature of proposed approaches is their susceptibility to the curse of dimensionality, i.e. the exponential growth in memory and computational requirements in the number of problem dimensions. We present a novel approach that has the potential to "lift" this curse of dimensionality. The approach is based on the use of the recently proposed Quantized Tensor Train (QTT) formatted numerical linear algebra for the low parametric, numerical representation of tensors. The QTT decomposition admits both, algorithms for basic tensor arithmetics with complexity scaling linearly in the dimension (number of species) and sub-linearly in the mode size (maximum copy number), and a numerical tensor rounding procedure which is stable and quasi-optimal. We show how the CME can be represented in QTT format, then use the exponentially-converging hp-discontinuous Galerkin discretization in time to reduce the CME evolution problem to a set of QTT-structured linear equations to be solved at each time step using an algorithm based on Density Matrix Renormalization Group (DMRG) methods from quantum chemistry. Our method automatically adapts the "basis" of the solution at every time step guaranteeing that it is large enough to capture the dynamics of interest but no larger than necessary, as this would increase the computational complexity. Our approach is demonstrated by applying it to three different examples from systems biology: independent birth-death process, an example of enzymatic futile cycle, and a stochastic switch model. The numerical results on these examples demonstrate that the proposed QTT method achieves dramatic speedups and several orders of magnitude storage
Direct solution of the Chemical Master Equation using quantized tensor trains.
Directory of Open Access Journals (Sweden)
Vladimir Kazeev
2014-03-01
Full Text Available The Chemical Master Equation (CME is a cornerstone of stochastic analysis and simulation of models of biochemical reaction networks. Yet direct solutions of the CME have remained elusive. Although several approaches overcome the infinite dimensional nature of the CME through projections or other means, a common feature of proposed approaches is their susceptibility to the curse of dimensionality, i.e. the exponential growth in memory and computational requirements in the number of problem dimensions. We present a novel approach that has the potential to "lift" this curse of dimensionality. The approach is based on the use of the recently proposed Quantized Tensor Train (QTT formatted numerical linear algebra for the low parametric, numerical representation of tensors. The QTT decomposition admits both, algorithms for basic tensor arithmetics with complexity scaling linearly in the dimension (number of species and sub-linearly in the mode size (maximum copy number, and a numerical tensor rounding procedure which is stable and quasi-optimal. We show how the CME can be represented in QTT format, then use the exponentially-converging hp-discontinuous Galerkin discretization in time to reduce the CME evolution problem to a set of QTT-structured linear equations to be solved at each time step using an algorithm based on Density Matrix Renormalization Group (DMRG methods from quantum chemistry. Our method automatically adapts the "basis" of the solution at every time step guaranteeing that it is large enough to capture the dynamics of interest but no larger than necessary, as this would increase the computational complexity. Our approach is demonstrated by applying it to three different examples from systems biology: independent birth-death process, an example of enzymatic futile cycle, and a stochastic switch model. The numerical results on these examples demonstrate that the proposed QTT method achieves dramatic speedups and several orders of
Ultrasound elastic tensor imaging: comparison with MR diffusion tensor imaging in the myocardium
Lee, Wei-Ning; Larrat, Benoît; Pernot, Mathieu; Tanter, Mickaël
2012-08-01
We have previously proven the feasibility of ultrasound-based shear wave imaging (SWI) to non-invasively characterize myocardial fiber orientation in both in vitro porcine and in vivo ovine hearts. The SWI-estimated results were in good correlation with histology. In this study, we proposed a new and robust fiber angle estimation method through a tensor-based approach for SWI, coined together as elastic tensor imaging (ETI), and compared it with magnetic resonance diffusion tensor imaging (DTI), a current gold standard and extensively reported non-invasive imaging technique for mapping fiber architecture. Fresh porcine (n = 5) and ovine (n = 5) myocardial samples (20 × 20 × 30 mm3) were studied. ETI was firstly performed to generate shear waves and to acquire the wave events at ultrafast frame rate (8000 fps). A 2.8 MHz phased array probe (pitch = 0.28 mm), connected to a prototype ultrasound scanner, was mounted on a customized MRI-compatible rotation device, which allowed both the rotation of the probe from -90° to 90° at 5° increments and co-registration between two imaging modalities. Transmural shear wave speed at all propagation directions realized was firstly estimated. The fiber angles were determined from the shear wave speed map using the least-squares method and eigen decomposition. The test myocardial sample together with the rotation device was then placed inside a 7T MRI scanner. Diffusion was encoded in six directions. A total of 270 diffusion-weighted images (b = 1000 s mm-2, FOV = 30 mm, matrix size = 60 × 64, TR = 6 s, TE = 19 ms, 24 averages) and 45 B0 images were acquired in 14 h 30 min. The fiber structure was analyzed by the fiber-tracking module in software, MedINRIA. The fiber orientation in the overlapped myocardial region which both ETI and DTI accessed was therefore compared, thanks to the co-registered imaging system. Results from all ten samples showed good correlation (r2 = 0.81, p 0.05, unpaired, one-tailed t-test, N = 10). In
Tensor completion for estimating missing values in visual data
Liu, Ji
2013-01-01
In this paper, we propose an algorithm to estimate missing values in tensors of visual data. The values can be missing due to problems in the acquisition process or because the user manually identified unwanted outliers. Our algorithm works even with a small amount of samples and it can propagate structure to fill larger missing regions. Our methodology is built on recent studies about matrix completion using the matrix trace norm. The contribution of our paper is to extend the matrix case to the tensor case by proposing the first definition of the trace norm for tensors and then by building a working algorithm. First, we propose a definition for the tensor trace norm that generalizes the established definition of the matrix trace norm. Second, similarly to matrix completion, the tensor completion is formulated as a convex optimization problem. Unfortunately, the straightforward problem extension is significantly harder to solve than the matrix case because of the dependency among multiple constraints. To tackle this problem, we developed three algorithms: simple low rank tensor completion (SiLRTC), fast low rank tensor completion (FaLRTC), and high accuracy low rank tensor completion (HaLRTC). The SiLRTC algorithm is simple to implement and employs a relaxation technique to separate the dependant relationships and uses the block coordinate descent (BCD) method to achieve a globally optimal solution; the FaLRTC algorithm utilizes a smoothing scheme to transform the original nonsmooth problem into a smooth one and can be used to solve a general tensor trace norm minimization problem; the HaLRTC algorithm applies the alternating direction method of multipliers (ADMMs) to our problem. Our experiments show potential applications of our algorithms and the quantitative evaluation indicates that our methods are more accurate and robust than heuristic approaches. The efficiency comparison indicates that FaLTRC and HaLRTC are more efficient than SiLRTC and between Fa
Experience of Google's latest deep learning library, TensorFlow, in a large-scale WLCG cluster
Energy Technology Data Exchange (ETDEWEB)
Kawamura, Gen; Smith, Joshua Wyatt; Quadt, Arnulf [II. Physikalisches Institut, Georg-August-Universitaet Goettingen (Germany)
2016-07-01
The researchers at the Google Brain team released their second generation's Deep Learning library, TensorFlow, as an open-source package under the Apache 2.0 license in November, 2015. Google has already deployed the first generation's library using DistBlief in various systems such as Google Search, advertising systems, speech recognition systems, Google Images, Google Maps, Street View, Google Translate and many other latest products. In addition, many researchers in high energy physics have recently started to understand and use Deep Learning algorithms in their own research and analysis. We conceive a first use-case scenario of TensorFlow to create the Deep Learning models from high-dimensional inputs like physics analysis data in a large-scale WLCG computing cluster. TensorFlow carries out computations using a dataflow model and graph structure onto a wide variety of different hardware platforms and systems, such as many CPU architectures, GPUs and smartphone platforms. Having a single library that can distribute the computations to create a model to the various platforms and systems would significantly simplify the use of Deep Learning algorithms in high energy physics. We deploy TensorFlow with the Docker container environments and present the first use in our grid system.
Energy Technology Data Exchange (ETDEWEB)
Walder, Brennan J.; Davis, Michael C.; Grandinetti, Philip J. [Department of Chemistry, Ohio State University, 100 West 18th Avenue, Columbus, Ohio 43210 (United States); Dey, Krishna K. [Department of Physics, Dr. H. S. Gour University, Sagar, Madhya Pradesh 470003 (India); Baltisberger, Jay H. [Division of Natural Science, Mathematics, and Nursing, Berea College, Berea, Kentucky 40403 (United States)
2015-01-07
A new two-dimensional Nuclear Magnetic Resonance (NMR) experiment to separate and correlate the first-order quadrupolar and chemical/paramagnetic shift interactions is described. This experiment, which we call the shifting-d echo experiment, allows a more precise determination of tensor principal components values and their relative orientation. It is designed using the recently introduced symmetry pathway concept. A comparison of the shifting-d experiment with earlier proposed methods is presented and experimentally illustrated in the case of {sup 2}H (I = 1) paramagnetic shift and quadrupolar tensors of CuCl{sub 2}⋅2D{sub 2}O. The benefits of the shifting-d echo experiment over other methods are a factor of two improvement in sensitivity and the suppression of major artifacts. From the 2D lineshape analysis of the shifting-d spectrum, the {sup 2}H quadrupolar coupling parameters are 〈C{sub q}〉 = 118.1 kHz and 〈η{sub q}〉 = 0.88, and the {sup 2}H paramagnetic shift tensor anisotropy parameters are 〈ζ{sub P}〉 = − 152.5 ppm and 〈η{sub P}〉 = 0.91. The orientation of the quadrupolar coupling principal axis system (PAS) relative to the paramagnetic shift anisotropy principal axis system is given by (α,β,γ)=((π)/2 ,(π)/2 ,0). Using a simple ligand hopping model, the tensor parameters in the absence of exchange are estimated. On the basis of this analysis, the instantaneous principal components and orientation of the quadrupolar coupling are found to be in excellent agreement with previous measurements. A new point dipole model for predicting the paramagnetic shift tensor is proposed yielding significantly better agreement than previously used models. In the new model, the dipoles are displaced from nuclei at positions associated with high electron density in the singly occupied molecular orbital predicted from ligand field theory.
One-loop tensor Feynman integral reduction with signed minors
DEFF Research Database (Denmark)
Fleischer, Jochem; Riemann, Tord; Yundin, Valery
2012-01-01
of the formalism is the immediate evaluation of complete contractions of the tensor integrals with external momenta. This leads to the problem of evaluating sums over products of signed minors with scalar products of chords. Chords are differences of external momenta. These sums may be evaluated analytically......We present an algebraic approach to one-loop tensor integral reduction. The integrals are presented in terms of scalar one- to four-point functions. The reduction is worked out explicitly until five-point functions of rank five. The numerical C++ package PJFry evaluates tensor coefficients in terms...... of a basis of scalar integrals, which is provided by an external library, e.g. QCDLoop. We shortly describe installation and use of PJFry. Examples for numerical results are shown, including a special treatment for small or vanishing inverse four-point Gram determinants. An extremely efficient application...
Robust Tensor Preserving Projection for Multispectral Face Recognition
Directory of Open Access Journals (Sweden)
Shaoyuan Sun
2014-01-01
Full Text Available Multiple imaging modalities based face recognition has become a hot research topic. A great number of multispectral face recognition algorithms/systems have been designed in the last decade. How to extract features of different spectrum has still been an important issue for face recognition. To address this problem, we propose a robust tensor preserving projection (RTPP algorithm which represents a multispectral image as a third-order tensor. RTPP constructs sparse neighborhoods and then computes weights of the tensor. RTPP iteratively obtains one spectral space transformation matrix through preserving the sparse neighborhoods. Due to sparse representation, RTPP can not only keep the underlying spatial structure of multispectral images but also enhance robustness. The experiments on both Equinox and DHUFO face databases show that the performance of the proposed method is better than those of related algorithms.
CMB bounds on tensor-scalar-scalar inflationary correlations
Shiraishi, Maresuke; Liguori, Michele; Fergusson, James R.
2018-01-01
The nonlinear interaction between one graviton and two scalars is enhanced in specific inflationary models, potentially leading to distinguishable signatures in the bispectrum of the cosmic microwave background (CMB) anisotropies. We develop the tools to examine such bispectrum signatures, and show a first application using WMAP temperature data. We consider several l-ranges, estimating the gtss amplitude parameter, by means of the so-called separable modal methodology. We do not find any evidence of a tensor-scalar-scalar signal at any scale. Our tightest bound on the size of the tensor-scalar-scalar correlator is derived from our measurement including all the multipoles in the range 2 first direct observational constraint on the primordial tensor-scalar-scalar correlation, and it will be cross-checked and improved by applying the same pipeline to high-resolution temperature and polarization data from Planck and forthcoming CMB experiments.
High spatial resolution diffusion tensor imaging and its applications
Wang, J J
2002-01-01
Introduction Magnetic Resonance Imaging is at present the only imaging technique available to measure diffusion of water and metabolites in humans. It provides vital insights to brain connectivity and has proved to be an important tool in diagnosis and therapy planning in many neurological diseases such as brain tumour, ischaemia and multiple sclerosis. This project focuses on the development of a high resolution diffusion tensor imaging technique. In this thesis, the basic theory of diffusion tensor MR Imaging is presented. The technical challenges encountered during development of these techniques will be discussed, with proposed solutions. New sequences with high spatial resolution have been developed and the results are compared with the standard technique more commonly used. Overview The project aims at the development of diffusion tensor imaging techniques with a high spatial resolution. Chapter 2 will describe the basic physics of MRI, the phenomenon of diffusion and the measurement of diffusion by MRI...
Spinal cord diffusion tensor imaging in patients with sensory neuronopathy
Energy Technology Data Exchange (ETDEWEB)
Fernandes Casseb, Raphael [University of Campinas - UNICAMP, Department of Neurology, School of Medicine, Campinas, SP (Brazil); University of Campinas - UNICAMP, Neurophysics Group, Department of Cosmic Rays and Chronology, Institute of Physics Gleb Wataghin, Campinas, SP (Brazil); Ribeiro de Paiva, Jean Levi; Teixeira Branco, Lucas Melo; Muro Martinez, Alberto Rolim; Cavalcante Franca, Marcondes Jr. [University of Campinas - UNICAMP, Department of Neurology, School of Medicine, Campinas, SP (Brazil); Reis, Fabiano [University of Campinas - UNICAMP, Department of Radiology, School of Medicine, Campinas, SP (Brazil); Lima-Junior, Jose Carlos de [University of Campinas - UNICAMP, Laboratory of Cell Signaling, Department of Internal Medicine, Campinas, SP (Brazil); Castellano, Gabriela [University of Campinas - UNICAMP, Neurophysics Group, Department of Cosmic Rays and Chronology, Institute of Physics Gleb Wataghin, Campinas, SP (Brazil)
2016-11-15
We investigated whether MR diffusion tensor imaging (DTI) analysis of the cervical spinal cord could aid the (differential) diagnosis of sensory neuronopathies, an underdiagnosed group of diseases of the peripheral nervous system. We obtained spinal cord DTI and T2WI at 3 T from 28 patients, 14 diabetic subjects with sensory-motor distal polyneuropathy, and 20 healthy controls. We quantified DTI-based parameters and looked at the hyperintense T2W signal at the spinal cord posterior columns. Fractional anisotropy and mean diffusivity values at C2-C3 and C3-C4 levels were compared between groups. We also compared average fractional anisotropy (mean of values at C2-C3 and C3-C4 levels). A receiver operating characteristic (ROC) curve was used to determine diagnostic accuracy of average fractional anisotropy, and we compared its sensitivity against the hyperintense signal in segregating patients from the other subjects. Mean age and disease duration were 52 ± 10 and 11.4 ± 9.3 years in the patient group. Eighteen subjects had idiopathic disease and 6 dysimmune etiology. Fractional anisotropy at C3-C4 level and average fractional anisotropy were significantly different between patients and healthy controls (p < 0.001 and <0.001) and between patients and diabetic subjects (p = 0.019 and 0.027). Average fractional anisotropy presented an area under the curve of 0.838. Moreover, it had higher sensitivity than visual detection of the hyperintense signal (0.86 vs. 0.54), particularly for patients with short disease duration. DTI-based analysis enables in vivo detection of posterior column damage in sensory neuronopathy patients and is a useful diagnostic test for this condition. It also helps the differential diagnosis between sensory neuronopathy and distal polyneuropathies. (orig.)
Baker, Ben; Stachnik, Joshua; Rozhkov, Mikhail
2017-04-01
International Data Center is required to conduct expert technical analysis and special studies to improve event parameters and assist State Parties in identifying the source of specific event according to the protocol to the Protocol to the Comprehensive Nuclear Test Ban Treaty. Determination of seismic event source mechanism and its depth is closely related to these tasks. It is typically done through a strategic linearized inversion of the waveforms for a complete or subset of source parameters, or similarly defined grid search through precomputed Greens Functions created for particular source models. In this presentation we demonstrate preliminary results obtained with the latter approach from an improved software design. In this development we tried to be compliant with different modes of CTBT monitoring regime and cover wide range of source-receiver distances (regional to teleseismic), resolve shallow source depths, provide full moment tensor solution based on body and surface waves recordings, be fast to satisfy both on-demand studies and automatic processing and properly incorporate observed waveforms and any uncertainties a priori as well as accurately estimate posteriori uncertainties. Posterior distributions of moment tensor parameters show narrow peaks where a significant number of reliable surface wave observations are available. For earthquake examples, fault orientation (strike, dip, and rake) posterior distributions also provide results consistent with published catalogues. Inclusion of observations on horizontal components will provide further constraints. In addition, the calculation of teleseismic P wave Green's Functions are improved through prior analysis to determine an appropriate attenuation parameter for each source-receiver path. Implemented HDF5 based Green's Functions pre-packaging allows much greater flexibility in utilizing different software packages and methods for computation. Further additions will have the rapid use of Instaseis
Tensor fields on orbits of quantum states and applications
Energy Technology Data Exchange (ETDEWEB)
Volkert, Georg Friedrich
2010-07-19
On classical Lie groups, which act by means of a unitary representation on finite dimensional Hilbert spaces H, we identify two classes of tensor field constructions. First, as pull-back tensor fields of order two from modified Hermitian tensor fields, constructed on Hilbert spaces by means of the property of having the vertical distributions of the C{sub 0}-principal bundle H{sub 0} {yields} P(H) over the projective Hilbert space P(H) in the kernel. And second, directly constructed on the Lie group, as left-invariant representation-dependent operator-valued tensor fields (LIROVTs) of arbitrary order being evaluated on a quantum state. Within the NP-hard problem of deciding whether a given state in a n-level bi-partite quantum system is entangled or separable (Gurvits, 2003), we show that both tensor field constructions admit a geometric approach to this problem, which evades the traditional ambiguity on defining metrical structures on the convex set of mixed states. In particular by considering manifolds associated to orbits passing through a selected state when acted upon by the local unitary group U(n) x U(n) of Schmidt coefficient decomposition inducing transformations, we find the following results: In the case of pure states we show that Schmidt-equivalence classes which are Lagrangian submanifolds define maximal entangled states. This implies a stronger statement as the one proposed by Bengtsson (2007). Moreover, Riemannian pull-back tensor fields split on orbits of separable states and provide a quantitative characterization of entanglement which recover the entanglement measure proposed by Schlienz and Mahler (1995). In the case of mixed states we highlight a relation between LIROVTs of order two and a class of computable separability criteria based on the Bloch-representation (de Vicente, 2007). (orig.)
Inflationary tensor fossils in large-scale structure
Energy Technology Data Exchange (ETDEWEB)
Dimastrogiovanni, Emanuela [School of Physics and Astronomy, University of Minnesota, Minneapolis, MN 55455 (United States); Fasiello, Matteo [Department of Physics, Case Western Reserve University, Cleveland, OH 44106 (United States); Jeong, Donghui [Department of Astronomy and Astrophysics, The Pennsylvania State University, University Park, PA 16802 (United States); Kamionkowski, Marc, E-mail: ema@physics.umn.edu, E-mail: mrf65@case.edu, E-mail: duj13@psu.edu, E-mail: kamion@jhu.edu [Department of Physics and Astronomy, 3400 N. Charles St., Johns Hopkins University, Baltimore, MD 21218 (United States)
2014-12-01
Inflation models make specific predictions for a tensor-scalar-scalar three-point correlation, or bispectrum, between one gravitational-wave (tensor) mode and two density-perturbation (scalar) modes. This tensor-scalar-scalar correlation leads to a local power quadrupole, an apparent departure from statistical isotropy in our Universe, as well as characteristic four-point correlations in the current mass distribution in the Universe. So far, the predictions for these observables have been worked out only for single-clock models in which certain consistency conditions between the tensor-scalar-scalar correlation and tensor and scalar power spectra are satisfied. Here we review the requirements on inflation models for these consistency conditions to be satisfied. We then consider several examples of inflation models, such as non-attractor and solid-inflation models, in which these conditions are put to the test. In solid inflation the simplest consistency conditions are already violated whilst in the non-attractor model we find that, contrary to the standard scenario, the tensor-scalar-scalar correlator probes directly relevant model-dependent information. We work out the predictions for observables in these models. For non-attractor inflation we find an apparent local quadrupolar departure from statistical isotropy in large-scale structure but that this power quadrupole decreases very rapidly at smaller scales. The consistency of the CMB quadrupole with statistical isotropy then constrains the distance scale that corresponds to the transition from the non-attractor to attractor phase of inflation to be larger than the currently observable horizon. Solid inflation predicts clustering fossils signatures in the current galaxy distribution that may be large enough to be detectable with forthcoming, and possibly even current, galaxy surveys.
Quantum group symmetry and q-tensor algebras
Biedenharn, Lawrence Christian
1995-01-01
Quantum groups are a generalization of the classical Lie groups and Lie algebras and provide a natural extension of the concept of symmetry fundamental to physics. This monograph is a survey of the major developments in quantum groups, using an original approach based on the fundamental concept of a tensor operator. Using this concept, properties of both the algebra and co-algebra are developed from a single uniform point of view, which is especially helpful for understanding the noncommuting co-ordinates of the quantum plane, which we interpret as elementary tensor operators. Representations
Tables of Products of Tensor Operators and Stevens Operators
DEFF Research Database (Denmark)
Lindgård, Per-Anker
1975-01-01
Numerical tables of products of tensor (Racah) operators, Rl,m(J), and Stevens operators Olm(J), working within a J-multiplet are given as a function of X=J(J+1). Examples of the use of the tables, such as the calculation of commutation relations and thermal averages are given.......Numerical tables of products of tensor (Racah) operators, Rl,m(J), and Stevens operators Olm(J), working within a J-multiplet are given as a function of X=J(J+1). Examples of the use of the tables, such as the calculation of commutation relations and thermal averages are given....
3D inversion of full tensor magnetic gradiometry (FTMG) data
DEFF Research Database (Denmark)
Zhdanov, Michael; Cai, Hongzhu; Wilson, Glenn
2011-01-01
Following recent advances in SQUID technology, full tensor magnetic gradiometry (FTMG) is emerging as a practical exploration method. We introduce 3D regularized focusing inversion for FTMG data. Our model studies show that inversion of magnetic tensor data can significantly improve resolution...... compared to inversion of magnetic vector data for the same model. We present a case study for the 3D inversion of GETMAG® FTMG data acquired over a magnetite skarn at Tallawang, Australia. The results obtained from our 3D inversion agree very well with the known geology of the area....
Dipole modulation in tensor modes: signatures in CMB polarization
Energy Technology Data Exchange (ETDEWEB)
Zarei, Moslem [Isfahan University of Technology, Department of Physics, Isfahan (Iran, Islamic Republic of); Institute for Research in Fundamental Sciences (IPM), School of Astronomy, P. O. Box 19395-5531, Tehran (Iran, Islamic Republic of)
2015-06-15
In this work we consider a dipole asymmetry in tensor modes and study the effects of this asymmetry on the angular power spectra of CMB. We derive analytical expressions for the C{sub l}{sup TT} and C{sub l}{sup BB} in the presence of such dipole modulation in tensor modes for l < 100. We also discuss on the amplitude of modulation term and show that the C{sub l}{sup BB} is considerably modified due to this term. (orig.) 3.
Analytical effective tensor for flow-through composites
Sviercoski, Rosangela De Fatima [Los Alamos, NM
2012-06-19
A machine, method and computer-usable medium for modeling an average flow of a substance through a composite material. Such a modeling includes an analytical calculation of an effective tensor K.sup.a suitable for use with a variety of media. The analytical calculation corresponds to an approximation to the tensor K, and follows by first computing the diagonal values, and then identifying symmetries of the heterogeneity distribution. Additional calculations include determining the center of mass of the heterogeneous cell and its angle according to a defined Cartesian system, and utilizing this angle into a rotation formula to compute the off-diagonal values and determining its sign.
Tensores polares atomicos e energias das camadas internas
Anselmo Elcana de Oliveira
1999-01-01
Resumo: Tensores polares atômicos foram calculados para os hidretos do grupo IV: CH4, SiH4, GeH4 e SnH4 com base na resolução dos sinais das derivadas do momento de dipolo, utilizando componentes principais e resultados de cálculos ab initio. Os tensores propostos decorrem da análise para os diferentes valores de intensidades de bandas vibracionais fundamentais no infravermelho para estes hidretos, em fase gasosa. Análise de coordenadas normais foi realizada para o benzeno e .além deste, os t...
Scalar-tensor theory of gravitation with negative coupling constant
Smalley, L. L.; Eby, P. B.
1976-01-01
The possibility of a Brans-Dicke scalar-tensor gravitation theory with a negative coupling constant is considered. The admissibility of a negative-coupling theory is investigated, and a simplified cosmological solution is obtained which allows a negative derivative of the gravitation constant. It is concluded that a Brans-Dicke theory with a negative coupling constant can be a viable alternative to general relativity and that a large negative value for the coupling constant seems to bring the original scalar-tensor theory into close agreement with perihelion-precession results in view of recent observations of small solar oblateness.
Testing a time-domain regional momtent tensor inversion program for large worldwide earthquakes
Richter, G.; Hoffmann, M.; Hanka, W.; Saul, J.
2009-04-01
After gaining an accurate source location and magnitude estimate of large earthquakes the direction of plate movement is the next important information for reliable hazard assessment. For this purpose rapid moment tensor inversions are necessary. In this study the time-domain moment tensor inversion program by Dreger (2001) is tested. This program for regional moment tensor solutions is applied to seismic data from regional stations of the GEOFON net and international cooperating partner networks (InaTEWS, IRIS, GEOFON Extended Virtual Network) to obtain moment tensor solutions for large earthquakes worldwide. The motivation of the study is to have rapid information on the plate motion direction for the verification of tsunami generation hazard by earthquakes. A special interest lies on the application in the Indonesian archipelago to integrate the program in German-Indonesian Tsunami Early Warning System (GITEWS). Performing the inversion on a single CPU of a normal PC most solutions are achieved within half an hour after origin time. The program starts automatically for large earthquakes detected by the seismic analysis tool SeisComP3 (Hanka et al, 2008). The data from seismic stations in the distance range up to 2000 km are selected, prepared and quality controlled. First the program searches the best automatic solution by varying the source depth. Testing different stations combinations for the inversion enables to identify the stability of the solution. For further optimization of the solution the interactive selection of available stations is facilitated. The results of over 200 events are compared to centroid moment tensor solutions from the Global CMT-Project, from MedNet/INGV and NEID to evaluate the accuracy of the results. The inversion in the time-domain is sensitive to uncertainties in the velocity model and in the source location. These resolution limits are visible in the waveform fits. Another reason for misfits are strong structural inhomogeneities
A Class of Homogeneous Scalar Tensor Cosmologies with a Radiation Fluid
Yazadjiev, Stoytcho S.
We present a new class of exact homogeneous cosmological solutions with a radiation fluid for all scalar tensor theories. The solutions belong to Bianchi type VIh cosmologies. Explicit examples of nonsingular homogeneous scalar tensor cosmologies are also given.
Improved tensor scale computation with application to medical image interpolation.
Xu, Ziyue; Sonka, Milan; Saha, Punam K
2011-01-01
Tensor scale (t-scale) is a parametric representation of local structure morphology that simultaneously describes its orientation, shape and isotropic scale. At any image location, t-scale represents the largest ellipse (an ellipsoid in three dimensions) centered at that location and contained in the same homogeneous region. Here, we present an improved algorithm for t-scale computation and study its application to image interpolation. Specifically, the t-scale computation algorithm is improved by: (1) enhancing the accuracy of identifying local structure boundary and (2) combining both algebraic and geometric approaches in ellipse fitting. In the context of interpolation, a closed form solution is presented to determine the interpolation line at each image location in a gray level image using t-scale information of adjacent slices. At each location on an image slice, the method derives normal vector from its t-scale that yields trans-orientation of the local structure and points to the closest edge point. Normal vectors at the matching two-dimensional locations on two adjacent slices are used to compute the interpolation line using a closed form equation. The method has been applied to BrainWeb data sets and to several other images from clinical applications and its accuracy and response to noise and other image-degrading factors have been examined and compared with those of current state-of-the-art interpolation methods. Experimental results have established the superiority of the new t-scale based interpolation method as compared to existing interpolation algorithms. Also, a quantitative analysis based on the paired t-test of residual errors has ascertained that the improvements observed using the t-scale based interpolation are statistically significant. Copyright © 2010 Elsevier Ltd. All rights reserved.
Vacuum Polarisation Tensors in Constant Electromagnetic Fields Part III
Gies, Holger; Gies, Holger; Schubert, Christian
2001-01-01
The string-inspired technique is used for a first calculation of the one-loop axialvector vacuum polarisation in a general constant electromagnetic field. A compact result is reached for the difference between this tensor and the corresponding vector vacuum polarisation. This result is confirmed by a Feynman diagram calculation. Its physical relevance is briefly discussed.
Refresher Course on Tensors and their Applications in Engineering ...
Indian Academy of Sciences (India)
... and a brief write up on your academic activities etc. to: Prof C S. Jog, Coordinator, Refresher Course on Tensors, Department of Mechanical Engineering,. Bangalore-560012, Email: jogc@mecheng.iisc.ernet.in. Research Fellows who wish to participate should also submit a letter of recommendation from their supervisors.
Stress Energy Tensor in c=0 Logarithmic Conformal Field Theory
Kogan, I. I.; Nichols, A.
2002-01-01
We discuss the partners of the stress energy tensor and their structure in Logarithmic conformal field theories. In particular we draw attention to the fundamental differences between theories with zero and non-zero central charge. We analyze the OPE for T, \\bar{T} and the logarithmic partners t and \\bar{t} for c=0 theories.
Tensor models, Kronecker coefficients and permutation centralizer algebras
Geloun, Joseph Ben; Ramgoolam, Sanjaye
2017-11-01
We show that the counting of observables and correlators for a 3-index tensor model are organized by the structure of a family of permutation centralizer algebras. These algebras are shown to be semi-simple and their Wedderburn-Artin decompositions into matrix blocks are given in terms of Clebsch-Gordan coefficients of symmetric groups. The matrix basis for the algebras also gives an orthogonal basis for the tensor observables which diagonalizes the Gaussian two-point functions. The centres of the algebras are associated with correlators which are expressible in terms of Kronecker coefficients (Clebsch-Gordan multiplicities of symmetric groups). The color-exchange symmetry present in the Gaussian model, as well as a large class of interacting models, is used to refine the description of the permutation centralizer algebras. This discussion is extended to a general number of colors d: it is used to prove the integrality of an infinite family of number sequences related to color-symmetrizations of colored graphs, and expressible in terms of symmetric group representation theory data. Generalizing a connection between matrix models and Belyi maps, correlators in Gaussian tensor models are interpreted in terms of covers of singular 2-complexes. There is an intriguing difference, between matrix and higher rank tensor models, in the computational complexity of superficially comparable correlators of observables parametrized by Young diagrams.
Energy-Momentum Tensor Improvements in Two Dimensions
Deser, S.; Jackiw, R.
1995-01-01
We discuss some aspects of the two-dimensional scalar field, considering particularly the action for the conformal anomaly as an ``improved'' gravitational coupling, and the possibility of introducing a dual coupling, which provides a ``chiral'' energy-momentum tensor improvement.
On the projective curvature tensor of generalized Sasakian-space ...
African Journals Online (AJOL)
... some conditions regarding projective curvature tensor. All the results obtained in this paper are in the form of necessary and sufficient conditions. Keywords: Generalized Sasakian-space-forms; projectively flat; projectively-semisymmetric; projectively symmetric; projectively recurrent; Einstein manifold; scalar curvature
Quantum Analogs of Tensor Product Representations of su(1; 1)*
Groenevelt, W.
2011-01-01
Abstract. We study representations of Uq(su(1; 1)) that can be considered as quantum analogs of tensor products of irreducible -representations of the Lie algebra su(1; 1). We determine the decomposition of these representations into irreducible -representations of Uq(su(1; 1)) by diagonalizing the
Anisotropic cosmological models and generalized scalar tensor theory
Indian Academy of Sciences (India)
Abstract. In this paper generalized scalar tensor theory has been considered in the background of anisotropic cosmological models, namely, axially symmetric Bianchi-I, Bianchi-III and Kortowski–. Sachs space-time. For bulk viscous fluid, both exponential and power-law solutions have been stud- ied and some assumptions ...
Cosmic no-hair conjecture in scalar–tensor theories
Indian Academy of Sciences (India)
We have shown that, within the context of scalar–tensor theories, the anisotropic Bianchi-type cosmological models evolve towards de Sitter Universe. A similar result holds in the case of cosmology in Lyra manifold. Thus the analogue of cosmic no-hair theorem of Wald [1] hold in both the cases. In fact, during inflation there ...
Collineations of the curvature tensor in general relativity
Indian Academy of Sciences (India)
Curvature collineations for the curvature tensor, constructed from a fundamental Bianchi Type-V metric, are studied. We are concerned with a symmetry property of space-time which is called curvature collineation, and we briefly discuss the physical and kinematical properties of the models.
Refresher Course on Tensors and their Applications in Engineering ...
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 11; Issue 7. Refresher Course on Tensors and their Applications in Engineering Sciences. Information and Announcements Volume 11 Issue 7 July 2006 pp 100-100. Fulltext. Click here to view fulltext PDF. Permanent link:
Theoretical study of the relativistic molecular rotational g-tensor
Energy Technology Data Exchange (ETDEWEB)
Aucar, I. Agustín, E-mail: agustin.aucar@conicet.gov.ar; Gomez, Sergio S., E-mail: ssgomez@exa.unne.edu.ar [Institute for Modeling and Technological Innovation, IMIT (CONICET-UNNE) and Faculty of Exact and Natural Sciences, Northeastern University of Argentina, Avenida Libertad 5400, W3404AAS Corrientes (Argentina); Giribet, Claudia G.; Ruiz de Azúa, Martín C. [Physics Department, Faculty of Exact and Natural Sciences, University of Buenos Aires and IFIBA CONICET, Ciudad Universitaria, Pab. I, 1428 Buenos Aires (Argentina)
2014-11-21
An original formulation of the relativistic molecular rotational g-tensor valid for heavy atom containing compounds is presented. In such formulation, the relevant terms of a molecular Hamiltonian for non-relativistic nuclei and relativistic electrons in the laboratory system are considered. Terms linear and bilinear in the nuclear rotation angular momentum and an external uniform magnetic field are considered within first and second order (relativistic) perturbation theory to obtain the rotational g-tensor. Relativistic effects are further analyzed by carrying out the linear response within the elimination of the small component expansion. Quantitative results for model systems HX (X=F, Cl, Br, I), XF (X=Cl, Br, I), and YH{sup +} (Y=Ne, Ar, Kr, Xe, Rn) are obtained both at the RPA and density functional theory levels of approximation. Relativistic effects are shown to be small for this molecular property. The relation between the rotational g-tensor and susceptibility tensor which is valid in the non-relativistic theory does not hold within the relativistic framework, and differences between both molecular parameters are analyzed for the model systems under study. It is found that the non-relativistic relation remains valid within 2% even for the heavy HI, IF, and XeH{sup +} systems. Only for the sixth-row Rn atom a significant deviation of this relation is found.
Numerical evaluation of tensor Feynman integrals in Euclidean kinematics
Energy Technology Data Exchange (ETDEWEB)
Gluza, J.; Kajda [Silesia Univ., Katowice (Poland). Inst. of Physics; Riemann, T.; Yundin, V. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany)
2010-10-15
For the investigation of higher order Feynman integrals, potentially with tensor structure, it is highly desirable to have numerical methods and automated tools for dedicated, but sufficiently 'simple' numerical approaches. We elaborate two algorithms for this purpose which may be applied in the Euclidean kinematical region and in d=4-2{epsilon} dimensions. One method uses Mellin-Barnes representations for the Feynman parameter representation of multi-loop Feynman integrals with arbitrary tensor rank. Our Mathematica package AMBRE has been extended for that purpose, and together with the packages MB (M. Czakon) or MBresolve (A. V. Smirnov and V. A. Smirnov) one may perform automatically a numerical evaluation of planar tensor Feynman integrals. Alternatively, one may apply sector decomposition to planar and non-planar multi-loop {epsilon}-expanded Feynman integrals with arbitrary tensor rank. We automatized the preparations of Feynman integrals for an immediate application of the package sectordecomposition (C. Bogner and S. Weinzierl) so that one has to give only a proper definition of propagators and numerators. The efficiency of the two implementations, based on Mellin-Barnes representations and sector decompositions, is compared. The computational packages are publicly available. (orig.)
Endomorphism Algebras of Tensor Powers of Modules for Quantum Groups
DEFF Research Database (Denmark)
Andersen, Therese Søby
the group algebra of the braid group to the endomorphism algebra of any tensor power of the Weyl module with highest weight 2. We take a first step towards determining the kernel of this map by reformulating well-known results on the semisimplicity of the Birman-Murakami-Wenzl algebra in terms of the order...
Gravity in warped compactications and the holographic stress tensor
Haro, S. de; Skenderis, K.; Solodukhin, S.N.
2001-01-01
We study gravitational aspects of Brane-World scenarios. We show that the bulk Einstein equations together with the junction condition imply that the induced metric on the brane satisfies the full non-linear Einstein equations with a specific effective stress energy tensor. This result holds for
Two loop stress-energy tensor for inflationary scalar electrodynamics
Prokopec, T.; Tsamis, N.C.; Woodard, R.P.
2008-01-01
We calculate the expectation value of the coincident product of two field strength tensors at two loop order in scalar electrodynamics on de Sitter background. The result agrees with the stochastic formulation which we have developed in a companion paper [2] for the nonperturbative resummation of
Incompressible Steady Flow with Tensor Conductivity Leaving a Transverse Magnetic Field
Energy Technology Data Exchange (ETDEWEB)
Witalis, E.A.
1965-12-15
The straight channel flow of an inviscid, incompressible fluid with tensor conductivity is considered when the flow leaves a region of constant transverse magnetic field. The channel walls are taken to be insulating, and an eddy current system arises. This is investigated by the method of magnetic field analysis as given by Witalis. The spatial distribution of magnetic field and ohmic power loss, both parallel and transverse to the flow, are given as functions of the Hall parameter with consideration also to the magnetic Reynolds number of the fluid. MHD power generator aspects of this problem and the results are discussed.
Atomic orbital-based SOS-MP2 with tensor hypercontraction. II. Local tensor hypercontraction
Song, Chenchen; Martínez, Todd J.
2017-01-01
In the first paper of the series [Paper I, C. Song and T. J. Martinez, J. Chem. Phys. 144, 174111 (2016)], we showed how tensor-hypercontracted (THC) SOS-MP2 could be accelerated by exploiting sparsity in the atomic orbitals and using graphical processing units (GPUs). This reduced the formal scaling of the SOS-MP2 energy calculation to cubic with respect to system size. The computational bottleneck then becomes the THC metric matrix inversion, which scales cubically with a large prefactor. In this work, the local THC approximation is proposed to reduce the computational cost of inverting the THC metric matrix to linear scaling with respect to molecular size. By doing so, we have removed the primary bottleneck to THC-SOS-MP2 calculations on large molecules with O(1000) atoms. The errors introduced by the local THC approximation are less than 0.6 kcal/mol for molecules with up to 200 atoms and 3300 basis functions. Together with the graphical processing unit techniques and locality-exploiting approaches introduced in previous work, the scaled opposite spin MP2 (SOS-MP2) calculations exhibit O(N2.5) scaling in practice up to 10 000 basis functions. The new algorithms make it feasible to carry out SOS-MP2 calculations on small proteins like ubiquitin (1231 atoms/10 294 atomic basis functions) on a single node in less than a day.
Cockayne syndrome: a diffusion tensor imaging and volumetric study.
Koob, Mériam; Rousseau, François; Laugel, Vincent; Meyer, Nicolas; Armspach, Jean-Paul; Girard, Nadine; Dietemann, Jean-Louis
2016-11-01
Cockayne syndrome (CS) is a rare disorder characterized by severe brain atrophy, white matter (WM) hypomyelination and basal ganglia calcifications. This study aimed to quantify atrophy and WM abnormalities using diffusion tensor imaging (DTI) and volumetric analysis, to evaluate possible differences between CS subtypes and to determine whether DTI findings may correspond to a hypomyelinating disorder. 14 patients with CS and 14 controls underwent brain MRI including DTI and a volumetric three-dimensional T 1 weighted sequence. DTI analysis was made through regions of interest within the whole brain to obtain fractional anisotropy (FA) and apparent diffusion coefficient (ADC) values and in the left centrum semiovale to obtain DTI eigenvalues. The Student's t-test was used to compare patients and controls, and CS subtypes. Given the small number of patients with CS, they were pooled into two groups: moderate (CS1/CS3) and severe (CS2/cerebro-oculo-facio-skeletal syndrome). Total brain volume in CS was reduced by 57%, predominantly in the infratentorial area (68%) (p < 0.001). Total brain volume reduction was greater in the severe group, but there was no difference in the degree of infratentorial atrophy in the two groups (p = 0.7). Mean FA values were lower, whereas ADC was higher in most of the WM in patients with CS (p < 0.05). ADC in the splenium of the corpus callosum and the posterior limb of the internal capsule and FA in the cerebral peduncles were significantly different between the two groups (p < 0.05). Mean ADC values corresponded to a hypomyelinating disorder. All DTI eigenvalues were higher in patients with CS, mainly for transverse diffusivity (+51%) (p < 0.001). DTI and volumetric analysis provide quantitative information for the characterization of CS and may be particularly useful for evaluating therapeutic intervention. Advances in knowledge: DTI combined with volumetric analysis provides additional information useful for not
Frames and bases in tensor products of Hilbert spaces and Hilbert C ...
Indian Academy of Sciences (India)
and K, tensor product of resolutions of the identities of H and K, and tensor product of frame representations ... of the identity and prove that tensor product of any resolutions of H and K, is a resolution of the identity. 1 ...... Press) (1993). [19] Young R, An introduction to nonharmonic Fourier series (New York: Academic Press).
On large N limit of symmetric traceless tensor models
Klebanov, Igor R.; Tarnopolsky, Grigory
2017-10-01
For some theories where the degrees of freedom are tensors of rank 3 or higher, there exist solvable large N limits dominated by the melonic diagrams. Simple examples are provided by models containing one rank 3 tensor in the tri-fundamental representation of the O( N)3 symmetry group. When the quartic interaction is assumed to have a special tetrahedral index structure, the coupling constant g must be scaled as N -3/2 in the melonic large N limit. In this paper we consider the combinatorics of a large N theory of one fully symmetric and traceless rank-3 tensor with the tetrahedral quartic interaction; this model has a single O( N ) symmetry group. We explicitly calculate all the vacuum diagrams up to order g 8, as well as some diagrams of higher order, and find that in the large N limit where g 2 N 3 is held fixed only the melonic diagrams survive. While some non-melonic diagrams are enhanced in the O( N ) symmetric theory compared to the O( N )3 one, we have not found any diagrams where this enhancement is strong enough to make them comparable with the melonic ones. Motivated by these results, we conjecture that the model of a real rank-3 symmetric traceless tensor possesses a smooth large N limit where g 2 N 3 is held fixed and all the contributing diagrams are melonic. A feature of the symmetric traceless tensor models is that some vacuum diagrams containing odd numbers of vertices are suppressed only by N -1/2 relative to the melonic graphs.
The total position-spread tensor: Spin partition
Energy Technology Data Exchange (ETDEWEB)
El Khatib, Muammar, E-mail: elkhatib@irsamc.ups-tlse.fr; Evangelisti, Stefano, E-mail: stefano@irsamc.ups-tlse.fr; Leininger, Thierry, E-mail: Thierry.Leininger@irsamc.ups-tlse.fr [Laboratoire de Chimie et Physique Quantiques - LCPQ/IRSAMC, Université de Toulouse (UPS) et CNRS (UMR-5626), 118, Route de Narbonne, 31062 Toulouse Cedex (France); Brea, Oriana, E-mail: oriana.brea@uam.es [Laboratoire de Chimie et Physique Quantiques - LCPQ/IRSAMC, Université de Toulouse (UPS) et CNRS (UMR-5626), 118, Route de Narbonne, 31062 Toulouse Cedex (France); Departamento de Química, Facultad de Ciencias, Módulo 13, Universidad Autónoma de Madrid, Cantoblanco, 28049 Madrid (Spain); Fertitta, Edoardo [Institut für Chemie und Biochemie - Physikalische und Theoretische Chemie, Freie Universität Berlin, Takustr. 3, D-14195 Berlin (Germany); Bendazzoli, Gian Luigi, E-mail: gianluigi.bendazzoli@unibo.it [Dipartimento di Chimica Industriale “Toso Montanari”, Università di Bologna, Viale Risorgimento 4, I–40136 Bologna (Italy)
2015-03-07
The Total Position Spread (TPS) tensor, defined as the second moment cumulant of the position operator, is a key quantity to describe the mobility of electrons in a molecule or an extended system. In the present investigation, the partition of the TPS tensor according to spin variables is derived and discussed. It is shown that, while the spin-summed TPS gives information on charge mobility, the spin-partitioned TPS tensor becomes a powerful tool that provides information about spin fluctuations. The case of the hydrogen molecule is treated, both analytically, by using a 1s Slater-type orbital, and numerically, at Full Configuration Interaction (FCI) level with a V6Z basis set. It is found that, for very large inter-nuclear distances, the partitioned tensor growths quadratically with the distance in some of the low-lying electronic states. This fact is related to the presence of entanglement in the wave function. Non-dimerized open chains described by a model Hubbard Hamiltonian and linear hydrogen chains H{sub n} (n ≥ 2), composed of equally spaced atoms, are also studied at FCI level. The hydrogen systems show the presence of marked maxima for the spin-summed TPS (corresponding to a high charge mobility) when the inter-nuclear distance is about 2 bohrs. This fact can be associated to the presence of a Mott transition occurring in this region. The spin-partitioned TPS tensor, on the other hand, has a quadratical growth at long distances, a fact that corresponds to the high spin mobility in a magnetic system.
Jenkins, Samantha; Blancafort, Lluís; Kirk, Steven R; Bearpark, Michael J
2014-04-21
New insights into the double bond isomerization of fulvene in the ground and excited electronic states are provided by newly developed QTAIM and stress tensor tools. The S0 and S1 states follow the 'biradical' torsion model, but the double bond is stiffer in the S0 state; by contrast, the S2 state follows the 'zwitterionic' torsion. Differences are explained in terms of the ellipticity and bond critical point (BCP) stiffness for both QTAIM and the stress tensor. Overall, the wave-function based analysis is found to be in agreement with the work of Bonačić-Koutecký and Michl that the bond-twisted species can have biradical or zwitterionic character, depending on the state. Using QTAIM and the stress tensor a new understanding of bond torsion is revealed; the electronic charge density around the twisted bond is found not to rotate in concert with the nuclei of the rotated -CH2 methylene group. The ability to visualize how the bond stiffness varies between individual electronic states and how this correlates with the QTAIM and stress tensor bond stiffness is highlighted. In addition, the most and least preferred morphologies of bond-path torsion are visualized. Briefly we discuss the prospects for using this new QTAIM and stress tensor analysis for excited state chemistry.
Full moment tensor analyses to investigate the dynamics of the 2001 Etna eruption
Sarao, A.; Cocina, O.; Privitera, E.; Panza, G. F.
2009-12-01
The Mt. Etna eruption of July 2001 was announced by a severe seismic activity (2645 earthquakes between 12 and 18 July) and by the opening of a 7 km long field of fractures. Results from multidisciplinary approaches suggest that the observed phenomenology was related to the rapid intrusion of a vertical dike located few km south of the summit region. To add new constraints on the dynamics of the eruption process, we determine the full seismic moment tensors of 61 earthquakes (Md ≥ 2.2), selected among those occurred between July 12 and July 18, located in a depth ranging from 1 km above sea level to 3 km under the volcano. Short period seismograms recorded by the INGV-Catania seismic network have been used for the moment tensor retrieval. For our analyses we employed the INPAR method (Šílený et al., GJI 1992; Šílený, GJI 1998) that has been widely tested to define the realiability of solutions against the influence of random noise, station geometry and wave propagation effects in volcanic and geothermal environments. Our analysis revealed the presence of high percentage of double couple events, well related with the system of fractures bred just before the eruption, but also meaningful non-double couple components that can be explained as the response of the confining rocks to the magma uprising and degassing process. Most of the studied earthquakes show normal fault type mechanisms with significant strike slip components, in addition, pure strike slip and reverse fault mechanisms can be observed, in agreement with the stress regime induced by a dike injection. The space-time analysis of seismic source locations and source moment tensors 1) confirms the evidence of a vertical dike emplacement that fed the 2001 lateral eruption and 2) adds new insights supporting the hypothesis of the injection of a second aborted dike, 2 km SE far from the fractures zone.
Yepes-Calderon, Fernando; Brun, Caroline; Sant, Nishita; Thompson, Paul; Lepore, Natasha
2015-01-01
Tensor-Based Morphometry (TBM) is an increasingly popular method for group analysis of brain MRI data. The main steps in the analysis consist of a nonlinear registration to align each individual scan to a common space, and a subsequent statistical analysis to determine morphometric differences, or difference in fiber structure between groups. Recently, we implemented the Statistically-Assisted Fluid Registration Algorithm or SAFIRA,1 which is designed for tracking morphometric differences among populations. To this end, SAFIRA allows the inclusion of statistical priors extracted from the populations being studied as regularizers in the registration. This flexibility and degree of sophistication limit the tool to expert use, even more so considering that SAFIRA was initially implemented in command line mode. Here, we introduce a new, intuitive, easy to use, Matlab-based graphical user interface for SAFIRA's multivariate TBM. The interface also generates different choices for the TBM statistics, including both the traditional univariate statistics on the Jacobian matrix, and comparison of the full deformation tensors.2 This software will be freely disseminated to the neuroimaging research community.
Directory of Open Access Journals (Sweden)
B. Palombo
1994-06-01
Full Text Available e present a method for the inversion of complete waveforms in the 5-30 mHz frequency band for moment tensor determination. The method is based on the calibration of phase and group velocity dispersion curves for Rayleigh and Love fundamental modes to account for heterogeneous lithospheric structure, and is applied to the analysis of single station records of the VSL MEDNET station for the 1990 NW Iran earthquake sequence (the events of June 20, 21 and 24. The revised seismic moment of the June 20, 1990 Iranian earthquake is Mo = 1.56 x 1027 dyne-cm, corresponding to Mw = 7.4. The method proves to be a very robust tool for the analysis of moderate and large earthquakes at regional distances, producing consistent moment tensor solutions trom single station inversions in narrow (2-4 mHz and wide (up to 20 mHz frequency bands across the whole band of interest.
A stress tensor eigenvector projection space for the (H2O)5 potential energy surface
Xu, Tianlv; Farrell, James; Momen, Roya; Azizi, Alireza; Kirk, Steven R.; Jenkins, Samantha; Wales, David J.
2017-01-01
A stress tensor eigenvector projection space is created to describe reaction pathways on the (H2O)5 MP2 potential energy surface. Evidence for the stabilizing role of the O--O bonding interactions is found from the length of the recently introduced stress tensor trajectory in the stress tensor eigenvector projection space. The stress tensor trajectories demonstrate coupling behavior of the adjoining covalent (σ) O-H and hydrogen bonds due to sharing of covalent character. Additionally, the stress tensor trajectories can show dynamic coupling effects of pairs of σ bonds and of pairs of hydrogen bonds.
Interplay between tensor force and deformation in even–even nuclei
Energy Technology Data Exchange (ETDEWEB)
Bernard, Rémi N., E-mail: rbernard@ugr.es; Anguiano, Marta
2016-09-15
In this work we study the effect of the nuclear tensor force on properties related with deformation. We focus on isotopes in the Mg, Si, S, Ar, Sr and Zr chains within the Hartree–Fock–Bogoliubov theory using the D1ST2a Gogny interaction. Contributions to the tensor energy in terms of saturated and unsaturated subshells are analyzed. Like–particle and proton–neutron parts of the tensor term are independently examinated. We found that the tensor term may considerably modify the potential energy landscapes and change the ground state shape. We analyze too how the pairing characteristics of the ground state change when the tensor force is included.
Directory of Open Access Journals (Sweden)
Saurav Z. K. Sajib
2016-06-01
Full Text Available Anisotropy of biological tissues is a low-frequency phenomenon that is associated with the function and structure of cell membranes. Imaging of anisotropic conductivity has potential for the analysis of interactions between electromagnetic fields and biological systems, such as the prediction of current pathways in electrical stimulation therapy. To improve application to the clinical environment, precise approaches are required to understand the exact responses inside the human body subjected to the stimulated currents. In this study, we experimentally evaluate the anisotropic conductivity tensor distribution of canine brain tissues, using a recently developed diffusion tensor-magnetic resonance electrical impedance tomography method. At low frequency, electrical conductivity of the biological tissues can be expressed as a product of the mobility and concentration of ions in the extracellular space. From diffusion tensor images of the brain, we can obtain directional information on diffusive movements of water molecules, which correspond to the mobility of ions. The position dependent scale factor, which provides information on ion concentration, was successfully calculated from the magnetic flux density, to obtain the equivalent conductivity tensor. By combining the information from both techniques, we can finally reconstruct the anisotropic conductivity tensor images of brain tissues. The reconstructed conductivity images better demonstrate the enhanced signal intensity in strongly anisotropic brain regions, compared with those resulting from previous methods using a global scale factor.
Energy Technology Data Exchange (ETDEWEB)
Sajib, Saurav Z. K.; Jeong, Woo Chul; Oh, Tong In; Kim, Hyung Joong, E-mail: bmekim@khu.ac.kr, E-mail: ejwoo@khu.ac.kr; Woo, Eung Je, E-mail: bmekim@khu.ac.kr, E-mail: ejwoo@khu.ac.kr [Department of Biomedical Engineering, Kyung Hee University, Seoul 02447 (Korea, Republic of); Kyung, Eun Jung [Department of Pharmacology, Chung-Ang University, Seoul 06974 (Korea, Republic of); Kim, Hyun Bum [Department of East-West Medical Science, Kyung Hee University, Yongin 17104 (Korea, Republic of); Kwon, Oh In [Department of Mathematics, Konkuk University, Seoul 05029 (Korea, Republic of)
2016-06-15
Anisotropy of biological tissues is a low-frequency phenomenon that is associated with the function and structure of cell membranes. Imaging of anisotropic conductivity has potential for the analysis of interactions between electromagnetic fields and biological systems, such as the prediction of current pathways in electrical stimulation therapy. To improve application to the clinical environment, precise approaches are required to understand the exact responses inside the human body subjected to the stimulated currents. In this study, we experimentally evaluate the anisotropic conductivity tensor distribution of canine brain tissues, using a recently developed diffusion tensor-magnetic resonance electrical impedance tomography method. At low frequency, electrical conductivity of the biological tissues can be expressed as a product of the mobility and concentration of ions in the extracellular space. From diffusion tensor images of the brain, we can obtain directional information on diffusive movements of water molecules, which correspond to the mobility of ions. The position dependent scale factor, which provides information on ion concentration, was successfully calculated from the magnetic flux density, to obtain the equivalent conductivity tensor. By combining the information from both techniques, we can finally reconstruct the anisotropic conductivity tensor images of brain tissues. The reconstructed conductivity images better demonstrate the enhanced signal intensity in strongly anisotropic brain regions, compared with those resulting from previous methods using a global scale factor.
Pre- and post-operative diffusion tensor imaging of the median nerve in carpal tunnel syndrome
Energy Technology Data Exchange (ETDEWEB)
Hiltunen, Jaana [Aalto University School of Science, Brain Research Unit, Low Temperature Laboratory, Aalto (Finland); Aalto University School of Science, Advanced Magnetic Imaging Centre, Aalto (Finland); Kirveskari, Erika [Aalto University School of Science, Brain Research Unit, Low Temperature Laboratory, Aalto (Finland); Helsinki University Central Hospital, Department of Clinical Neurophysiology, Helsinki (Finland); Numminen, Jussi [Aalto University School of Science, Brain Research Unit, Low Temperature Laboratory, Aalto (Finland); University of Helsinki, Helsinki Medical Imaging Center, Helsinki (Finland); Lindfors, Nina; Goeransson, Harry [Helsinki University Central Hospital, Department of Hand Surgery, Helsinki (Finland); Hari, Riitta [Aalto University School of Science, Brain Research Unit, Low Temperature Laboratory, Aalto (Finland); Aalto University School of Science, Advanced Magnetic Imaging Centre, Aalto (Finland); Helsinki University Central Hospital, Department of Clinical Neurophysiology, Helsinki (Finland)
2012-06-15
To use pre- and post-operative diffusion tensor imaging (DTI) to monitor median nerve integrity in patients suffering from carpal tunnel syndrome (CTS). Diffusivity and anisotropy images along the median nerve were compared among 12 patients, 12 age-matched and 12 young control subjects and correlated with electrophysiological neurography results. Slice-wise DTI parameter values were calculated to focus on local changes. Results of pre-operative patients and age-matched control subjects differed only in the distal nerve. Moreover, pre-operative patients differed significantly from young controls and post-operative patients. The main abnormalities were increased diffusivity and decreased anisotropy in the carpal tunnel and distal median nerve. Post-operative clinical improvement was reflected in diffusivity, but not in anisotropy. Slice-wise analysis showed high pre-operative diffusivity at the distal nerve. All groups had relatively large inter-subject variation in both diffusivity and anisotropy. DTI can provide information complementary to clinical examination, electrophysiological recordings and anatomical MRI of diseases and injuries of peripheral nerves. However, similar age-related changes in diffusivity and anisotropy may weaken DTI specificity. Slice-wise analysis is necessary for detection of local changes in nerve integrity. circle Diffusion tensor magnetic resonance imaging provides information complementary to conventional diagnostic methods. circle Age caused similar changes to diffusivity and anisotropy as carpal tunnel syndrome. circle Post-operative clinical improvement was reflected in diffusivity, but not in anisotropy. circle Inter-subject variation in diffusivity and anisotropy was considerable. (orig.)
C7-Decompositions of the Tensor Product of Complete Graphs
Directory of Open Access Journals (Sweden)
Manikandan R.S.
2017-08-01
Full Text Available In this paper we consider a decomposition of Km × Kn, where × denotes the tensor product of graphs, into cycles of length seven. We prove that for m, n ≥ 3, cycles of length seven decompose the graph Km × Kn if and only if (1 either m or n is odd and (2 14 | m(m − 1n(n − 1. The results of this paper together with the results of [Cp-Decompositions of some regular graphs, Discrete Math. 306 (2006 429–451] and [C5-Decompositions of the tensor product of complete graphs, Australasian J. Combinatorics 37 (2007 285–293], give necessary and sufficient conditions for the existence of a p-cycle decomposition, where p ≥ 5 is a prime number, of the graph Km × Kn.
Fitting alignment tensor components to experimental RDCs, CSAs and RQCs.
Wirz, Lukas N; Allison, Jane R
2015-05-01
Residual dipolar couplings, chemical shift anisotropies and quadrupolar couplings provide information about the orientation of inter-spin vectors and the anisotropic contribution of the local environment to the chemical shifts of nuclei, respectively. Structural interpretation of these observables requires parameterization of their angular dependence in terms of an alignment tensor. We compare and evaluate two algorithms for generating the optimal alignment tensor for a given molecular structure and set of experimental data, namely SVD (Losonczi et al. in J Magn Reson 138(2):334-342, 1999), which scales as [Formula: see text], and the linear least squares algorithm (Press et al. in Numerical recipes in C. The art of scientific computing, 2nd edn. Cambridge University Press, Cambridge, 1997), which scales as [Formula: see text].
Closed String Thermodynamics and a Blue Tensor Spectrum
Brandenberger, Robert H; Patil, Subodh P
2014-01-01
The BICEP-2 team has reported the detection of primordial cosmic microwave background B-mode polarization, with hints of a suppression of power at large angular scales relative to smaller scales. Provided that the B-mode polarization is due to primordial gravitational waves, this might imply a blue tilt of the primordial gravitational wave spectrum. Such a tilt would be incompatible with standard inflationary models, although it was predicted some years ago in the context of a mechanism that thermally generates the primordial perturbations through a Hagedorn phase of string cosmology. The purpose of this note is to encourage greater scrutiny of the data with priors informed by a model that is immediately falsifiable, but which \\textit{predicts} features that might be favoured by the data-- namely a blue tensor tilt with an induced and complimentary red tilt to the scalar spectrum, with a naturally large tensor to scalar ratio that relates to both.
Near-wall diffusion tensor of an axisymmetric colloidal particle
Lisicki, Maciej; Wajnryb, Eligiusz
2016-01-01
Hydrodynamic interactions with confining boundaries often lead to drastic changes in the diffusive behaviour of microparticles in suspensions. For axially symmetric particles, earlier numerical studies have suggested a simple form of the near-wall diffusion matrix which depends on the distance and orientation of the particle with respect to the wall, which is usually calculated numerically. In this work, we derive explicit analytical formulae for the dominant correction to the bulk diffusion tensor of an axially symmetric colloidal particle due to the presence of a nearby no-slip wall. The relative correction scales as powers of inverse wall-particle distance and its angular structure is represented by simple polynomials in sines and cosines of the particle's inclination angle to the wall. We analyse the correction for translational and rotational motion, as well as the translation-rotation coupling. Our findings provide a simple approximation to the anisotropic diffusion tensor near a wall, which completes a...
Quantum Gravity Effects in Scalar, Vector and Tensor Field Propagation
Dutta, Anindita
Quantum theory of gravity deals with the physics of the gravitational field at Planck length scale (10-35 m). Even though it is experimentally hard to reach the Planck length scale, on can look for evidence of quantum gravity that is detectable in astrophysics. In this thesis, we try to find effects of loop quantum gravity corrections on observable phenomena. We show that the quantum fluctuation strain for LIGO data would be 10 -125 on the Earth. Th correction is, however, substantial near the black hole horizon. We discuss the effect of this for scalar field propagation followed by vector and tensor fields. For the scalar field, the correction introduces a new asymmetry; for the vector field, we found a new perturbation solution and for the tensor field, we found the corrected Einstein equations which are yet to solve. These will affect phenomena like Hawking radiation, black hole entropy and gravitational waves.
Abelian tensor hierarchy in 4D, N=1 superspace
Energy Technology Data Exchange (ETDEWEB)
Becker, Katrin; Becker, Melanie; III, William D. Linch; Robbins, Daniel [George P. and Cynthia W. Mitchell Institute for Fundamental Physics and Astronomy,Texas A& M University, College Station, TX 77843 (United States)
2016-03-09
With the goal of constructing the supersymmetric action for all fields, massless and massive, obtained by Kaluza-Klein compactification from type II theory or M-theory in a closed form, we embed the (Abelian) tensor hierarchy of p-forms in four-dimensional, N=1 superspace and construct its Chern-Simons-like invariants. When specialized to the case in which the tensors arise from a higher-dimensional theory, the invariants may be interpreted as higher-dimensional Chern-Simons forms reduced to four dimensions. As an application of the formalism, we construct the eleven-dimensional Chern-Simons form in terms of four-dimensional, N=1 superfields.
Chiral tensor particles in the early Universe — Present status
Kirilova, D. P.; Chizhov, V. M.
2017-11-01
In this work, an update of the cosmological role and place of the chiral tensor particles in the Universe history is provided. We discuss an extended model with chiral tensor particles. The influence of these particles on the early Universe evolution is studied. Namely, the increase of the Universe expansion rate caused by the additional particles in this extended model is calculated, their characteristic interactions with the particles of the hot Universe plasma are studied and the corresponding times of their creation, scattering, annihilation and decay are estimated for accepted values of their masses and couplings, based on the recent experimental constraints. The period of abundant presence of these particles in the Universe evolution is determined.
Unified cosmology with scalar-tensor theory of gravity
Energy Technology Data Exchange (ETDEWEB)
Tajahmad, Behzad [Faculty of Physics, University of Tabriz, Tabriz (Iran, Islamic Republic of); Sanyal, Abhik Kumar [Jangipur College, Department of Physics, Murshidabad (India)
2017-04-15
Unlike the Noether symmetry, a metric independent general conserved current exists for non-minimally coupled scalar-tensor theory of gravity if the trace of the energy-momentum tensor vanishes. Thus, in the context of cosmology, a symmetry exists both in the early vacuum and radiation dominated era. For slow roll, symmetry is sacrificed, but at the end of early inflation, such a symmetry leads to a Friedmann-like radiation era. Late-time cosmic acceleration in the matter dominated era is realized in the absence of symmetry, in view of the same decayed and redshifted scalar field. Thus, unification of early inflation with late-time cosmic acceleration with a single scalar field may be realized. (orig.)
Making tensor factorizations robust to non-gaussian noise.
Energy Technology Data Exchange (ETDEWEB)
Chi, Eric C. (Rice University, Houston, TX); Kolda, Tamara Gibson
2011-03-01
Tensors are multi-way arrays, and the CANDECOMP/PARAFAC (CP) tensor factorization has found application in many different domains. The CP model is typically fit using a least squares objective function, which is a maximum likelihood estimate under the assumption of independent and identically distributed (i.i.d.) Gaussian noise. We demonstrate that this loss function can be highly sensitive to non-Gaussian noise. Therefore, we propose a loss function based on the 1-norm because it can accommodate both Gaussian and grossly non-Gaussian perturbations. We also present an alternating majorization-minimization (MM) algorithm for fitting a CP model using our proposed loss function (CPAL1) and compare its performance to the workhorse algorithm for fitting CP models, CP alternating least squares (CPALS).
Two photon couplings of scalar and tensor mesons
Feindt, Michael; Harjes, Jens
1991-06-01
Experimental data on exclusive two photon reactions are investigated with respect to formation of tensor and scalar mesons. Theoretical and experimental status and progress is reviewed. Furthermore, new CELLO results on γγ → π-π- and γγ → ϱ0ϱ0 are presented. Clear evidence for a large scalar contribution is found in both reactions. The implications of these new results are discussed.
Compact stars in vector-tensor-Horndeski theory of gravity
Energy Technology Data Exchange (ETDEWEB)
Momeni, Davood; Myrzakulov, Kairat; Myrzakulov, Ratbay [Eurasian National University, Department of General and Theoretical Physics, Eurasian International Center for Theoretical Physics, Astana (Kazakhstan); Faizal, Mir [University of British Columbia-Okanagan, Irving K. Barber School of Arts and Sciences, Kelowna, BC (Canada); University of Lethbridge, Department of Physics and Astronomy, Lethbridge, AB (Canada)
2017-01-15
In this paper, we will analyze a theory of modified gravity, in which the field content of general relativity will be increased to include a vector field. We will use the Horndeski formalism to non-minimally couple this vector field to the metric. As we will be using the Horndeski formalism, this theory will not contain Ostrogradsky ghost degree of freedom. We will analyze compact stars using this vector-tensor-Horndeski theory. (orig.)
Irreducible tensor phenomenology for pd→3Heπ+π-
Ramachandran, G.; Deepak, P. N.
2000-03-01
A phenomenology based on the irreducible tensor formalism is developed for the reaction pdicons/Journals/Common/to" ALT="to" ALIGN="TOP"/> 3 Heicons/Journals/Common/pi" ALT="pi" ALIGN="TOP"/> + icons/Journals/Common/pi" ALT="pi" ALIGN="TOP"/> - , to study incisively the P-wave dominance noticed in the recent kinematically complete experiment at c.m. excess energy of 70 MeV at the MOMO facility.
Duality and Confinement in Massive Antisymmetric Tensor Gauge Theories
Diamantini, M Cristina
2001-01-01
We extend the duality between massive and topologically massive antisymmetric tensor gauge theories in arbitrary space-time dimensions to include topological defects. We show explicitly that the condensation of these defects leads, in 4 dimensions, to confinement of electric strings in the two dual models. The dual phase, in which magnetic strings are confined is absent. The presence of the confinement phase explicitely found in the 4-dimensional case, is generalized, using duality arguments, to arbitrary space-time dimensions.
Parallel Flux Tensor Analysis for Efficient Moving Object Detection
2011-07-01
1107. [7] S. Ali and M. Shah, “ COCOA - Tracking in aerial imagery,” in SPIE Airborne Intelligence, Surveillance, Reconnaissance (ISR) Systems and...Grauer-Gray, C. Kambhamettu, and K. Palaniappan, “GPU implementation of belief propagation using CUDA for cloud tracking and reconstruction,” in 5th IAPR Workshop on Pattern Recognition in Remote Sensing (ICPR), 2008, pp. 1–4. 1233
Regional Moment Tensor Source-Type Discrimination Analysis
2015-11-16
geothermal environment, those occurring as the result of the collapse of a brine cavity in a salt dome, and for a shallow mining related explosion. 3...the Napoleonville Salt Dome, Louisiana, an industrial quarry explosion and an earthquake at The Geysers geothermal field, Northern California are...for industrial applications (Chiang, A., et al, 2015), and (3) event TE3, an earthquake at The Geysers geothermal field, Northern California (Table 1
Human action recognition based on point context tensor shape descriptor
Li, Jianjun; Mao, Xia; Chen, Lijiang; Wang, Lan
2017-07-01
Motion trajectory recognition is one of the most important means to determine the identity of a moving object. A compact and discriminative feature representation method can improve the trajectory recognition accuracy. This paper presents an efficient framework for action recognition using a three-dimensional skeleton kinematic joint model. First, we put forward a rotation-scale-translation-invariant shape descriptor based on point context (PC) and the normal vector of hypersurface to jointly characterize local motion and shape information. Meanwhile, an algorithm for extracting the key trajectory based on the confidence coefficient is proposed to reduce the randomness and computational complexity. Second, to decrease the eigenvalue decomposition time complexity, a tensor shape descriptor (TSD) based on PC that can globally capture the spatial layout and temporal order to preserve the spatial information of each frame is proposed. Then, a multilinear projection process is achieved by tensor dynamic time warping to map the TSD to a low-dimensional tensor subspace of the same size. Experimental results show that the proposed shape descriptor is effective and feasible, and the proposed approach obtains considerable performance improvement over the state-of-the-art approaches with respect to accuracy on a public action dataset.
Controlling sign problems in spin models using tensor renormalization
Denbleyker, Alan; Liu, Yuzhi; Meurice, Y.; Qin, M. P.; Xiang, T.; Xie, Z. Y.; Yu, J. F.; Zou, Haiyuan
2014-01-01
We consider the sign problem for classical spin models at complex β =1/g02 on L ×L lattices. We show that the tensor renormalization group method allows reliable calculations for larger Imβ than the reweighting Monte Carlo method. For the Ising model with complex β we compare our results with the exact Onsager-Kaufman solution at finite volume. The Fisher zeros can be determined precisely with the tensor renormalization group method. We check the convergence of the tensor renormalization group method for the O(2) model on L×L lattices when the number of states Ds increases. We show that the finite size scaling of the calculated Fisher zeros agrees very well with the Kosterlitz-Thouless transition assumption and predict the locations for larger volume. The location of these zeros agree with Monte Carlo reweighting calculation for small volume. The application of the method for the O(2) model with a chemical potential is briefly discussed.
One-loop tensor Feynman integral reduction with signed minors
Energy Technology Data Exchange (ETDEWEB)
Fleischer, J. [Bielefeld Univ. (Germany). Fakultaet fuer Physik; Riemann, T. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Yundin, V. [Copenhagen Univ. (Denmark). Niels Bohr International Academy and Discovery Center
2011-12-15
We present an algebraic approach to one-loop tensor integral reduction. The integrals are presented in terms of scalar one- to four-point functions. The reduction is worked out explicitly until five-point functions of rank five. The numerical C++ package PJFry evaluates tensor coefficients in terms of a basis of scalar integrals, which is provided by an external library, e.g. QCDLoop. We shortly describe installation and use of PJFry. Examples for numerical results are shown, including a special treatment for small or vanishing inverse four-point Gram determinants. An extremely efficient application of the formalism is the immediate evaluation of complete contractions of the tensor integrals with external momenta. This leads to the problem of evaluating sums over products of signed minors with scalar products of chords. Chords are differences of external momenta. These sums may be evaluated analytically in a systematic way. The final expressions for the numerical evaluation are then compact combinations of the contributing basic scalar functions. (orig.)
Automated Moment Tensor Solution for the Southern California Seismic Network
Clinton, J. F.; Hauksson, E.; Solanki, K.
2004-12-01
Automatically generated moment tensor solutions have recently been added to the suite of real-time products produced by the Southern California Seismic Network (SCSN/CISN). The moment magnitude, Mw, and the moment tensor are available within minutes for all regional earthquakes that trigger the network with Ml>4.0, and in special cases for events between Ml 3.5-4.0. The method uses the 1-D Time-Domain INVerse Code (TDMT_INVC) software package developed by Doug Dreger, which is routinely used in real-time by the UC Berkeley Seismological Laboratory. Green's Functions are determined for various velocity profiles in Southern California, which are used in the inversion of observed three component broadband waveforms (10s-100s) for a number of stations. The duty seismologists will review the automatically generated solution before distribution. A web-interface has been developed to evaluate the quality of the automatic solution, and determine whether it meets the minimum requirements for an immediate distribution. Simple modifications to the stations selected for the inversion are possible, and the inversion can be re-run to optimise the solution. The Mw determined with this method will be the official SCSN/CISN Mw solution for the event. Comparisons of the moment tensors determined using this 1-D model are made with 3-D models generated for larger earthquakes in the Southern California to facilitate calibration of the automated algorithm.
DEFF Research Database (Denmark)
Nielsen, Søren Føns Vind; Mørup, Morten
2014-01-01
Non-negative Tensor Factorization (NTF) has become a prominent tool for analyzing high dimensional multi-way structured data. In this paper we set out to analyze gene expression across brain regions in multiple subjects based on data from the Allen Human Brain Atlas [1] with more than 40 % data...... from all subjects the model based predictions are useful. When analyzing the structure of the components derived for one of the best predicting model orders the components identified in general constitute localized regions of the brain. Non-negative tensor factorization based on marginalization thus...... missing in our problem. Our analysis is based on the non-negativity constrained Canonical Polyadic (CP) decomposition where we handle the missing data using marginalization considering three prominent alternating least squares procedures; multiplicative updates, column-wise, and row-wise updating...
High spatial resolution diffusion tensor imaging and its applications
Energy Technology Data Exchange (ETDEWEB)
Wang, Jiun-Jie
2002-07-01
Introduction Magnetic Resonance Imaging is at present the only imaging technique available to measure diffusion of water and metabolites in humans. It provides vital insights to brain connectivity and has proved to be an important tool in diagnosis and therapy planning in many neurological diseases such as brain tumour, ischaemia and multiple sclerosis. This project focuses on the development of a high resolution diffusion tensor imaging technique. In this thesis, the basic theory of diffusion tensor MR Imaging is presented. The technical challenges encountered during development of these techniques will be discussed, with proposed solutions. New sequences with high spatial resolution have been developed and the results are compared with the standard technique more commonly used. Overview The project aims at the development of diffusion tensor imaging techniques with a high spatial resolution. Chapter 2 will describe the basic physics of MRI, the phenomenon of diffusion and the measurement of diffusion by MRI. The basic parameters used all through the projects will be presented. In Chapter 3, a reproducibility study on DTI with the single shot EPI sequence will be conducted. The single shot DT-EPI was carried out on a stroke patient. In Chapter 4, current techniques on high spatial resolution DTI will be explored. Sequences of Interleaved EPI of two segments and EPI with Half Fourier acquisition will be developed. The sources of artefacts which contaminate most DT images will be discussed with solution proposed. Chapter 5 proposed a new selective averaging algorithm for the data acquired by the sequences of interleaved EPI. It does not require cardiac gating during data acquisition period and thus increase the speed of data collection. A new ghost free segmented EPI sequence will be presented in Chapter 6: Half-FOV EPI. The technique will be tested on a phantom in vitro as well as in two normal male volunteers in vivo. A comparison study on diffusion tensor imaging
Ortega, Roberto; Quintanar, Luis; Huesca-Pérez, Eduardo
2016-10-01
The East Pacific Rise (EPR) and the Gulf of California (GC) have different tectonic histories. While the EPR has been present for 75 Ma, the GC started only 12.5 Myr. The region that links both systems is the Tamayo Fracture Zone, where a diffuse triple junction is located. A key question to be solved is whether the source mechanisms in this region reflect important variations from the GC to the EPR. Therefore, we analyzed the seismic moment tensors of the GC and the EPR using a full moment tensor inversion. This source model is useful in extensional regimes where isotropic components or complex faults are present. The full moment tensor is the best representation of the fault and slip direction in a rifting process because it resolves for six free parameters, including complex sources of pure shear dislocations. The analysis is similar to the deviatoric case, but the interpretation is different, because physical characteristics in the model allow for choosing a realistic style of rupture. Our results show that there are similarities between focal mechanisms determined by full moment tensors computed for the southern part of the GC and the EPR. We suggest that the EPR is tectonically linked to the GC not only at the diffuse triple junction region but also along the entire province. The rupture patterns of the GC and the EPR are slightly different: whereas the GC is partitioned by means of NW-SE faults, the EPR ruptures through a faulting system NE-SW. The geometrical relations of the extensional province of the GC and the EPR were present since the crustal thinning of the rifting process. Strain partitioning of faults explains easily the nature of the oblique divergence of the GC and the EPR. In addition, in our analysis, we observe clockwise rotation in the structures of the southern part of the GC, suggesting that there is a change in the spatial partitioning of this region.
Classical limits of scalar and tensor gauge operators based on the overlap Dirac matrix
Alexandru, Andrei; Horváth, Ivan; Liu, Keh-Fei
2008-10-01
It was recently proposed by the second author to consider lattice formulations of QCD in which complete actions, including the gauge part, are built explicitly from a given Dirac operator D. In a simple example of such theory, the gauge action is proportional to the trace of Ginsparg Wilson operator D chosen to define the quark dynamics. This construction relies on the proposition that the classical limit of lattice gauge operator trD(x,x) is proportional to trF2(x) (up to an additive constant). Here we show this for the case of the overlap Dirac operator using both analytical and numerical methods. We carry out the same analysis also for the tensor component of D, which is similarly related to the field-strength tensor F, and obtain results identical to our previous derivation that used a different approach. The corresponding proportionality constants are computed to high precision for a wide range of the negative mass parameter values, and it is verified that they are the same in finite and infinite volumes.
Energy Technology Data Exchange (ETDEWEB)
Ferraz-Filho, Jose R.L.; Muniz, Marcos P.; Souza, Antonio S. [Medical School in Sao Jose do Rio Preto (FAMERP), Radiology Department, Sao Paulo (Brazil); Rocha, Antonio J. da [School Medical Sciences of the Santa Casa de Sao Paulo, Radiology Department, Sao Paulo (Brazil); Goloni-Bertollo, Eny M.; Pavarino-Bertelli, Erika C. [Center of Research and attendace in Neurofibromatosis (CEPAN) of Medical School in Sao Jose do Rio Preto (FAMERP), Sao Paulo (Brazil)
2012-04-15
Neurofibromatosis type 1 (NF1) is a hereditary disease with a dominant autosomal pattern. In children and adolescents, it is frequently associated with the appearance of T2-weighted hyperintensities in the brain's white matter. MRI with diffusion tensor imaging (DTI) is used to detect white matter abnormalities by measuring fractional anisotropy (FA). This study employed DTI to evaluate the relationship between FA patterns and the findings of T2 sequences, with the aim of improving our understanding of anatomical changes and microstructural brain abnormalities in individuals with NF1. Forty-four individuals with NF1 and 20 control subjects were evaluated. The comparative analysis of FA between NF1 and control groups was based on four predetermined anatomical regions of the brain hemispheres (basal ganglia, cerebellum, pons, thalamus) and related the presence or absence of T2-weighted hyperintensities in the brain, which are called unidentified bright objects (UBOs). The FA values between the groups demonstrated statistically significant differences (P {<=} 0.05) for the cerebellum and thalamus in patients with NF1, independent of the occurrence of UBOs. Diffusion tensor MR imaging confirms the influence of UBOs in the decrease of FA values in this series of patients with NF1. Additionally, this technique allows the characterization of microstructural abnormalities even in some brain regions that appear normal in conventional MR sequences. (orig.)
Representation of light pressure resultant force and moment as a tensor series
Nerovny, Nikolay; Zimin, Vladimir; Fedorchuk, Sergey; Golubev, Evgeny
2017-08-01
In this article, we address the problem of the determination of light pressure upon space structures with a complex geometric shape. For each surface element, we enforce a condition that it can interact with light only from its front side, a condition represented in the form of series of Chebyshev polynomials of the first kind. This Chebyshev expansion enables the use of a series of tensors of increasing rank for determination of the force and moment acting on the sail. We obtain expressions for the determination of light pressure on space structures of complex geometry, taking into account self-shadowing and reflections within the structure. We also give the expressions for tensor parametrization using the specularity coefficient in case of specular -diffuse reflection. For these expressions, we calculated the principal moment and force upon two-sided flat solar sail, spherical and cylindrical bodies, and approximated light pressure upon the proposed space-based observatory Millimetron. The proposed expressions can be used in the ballistic analysis of solar sails and other space objects significantly affected by radiation pressure. Also, these results can be used to analyze the dynamics of large-scale space structures around their center of gravity under light pressure.
2016-05-11
AFRL-AFOSR-JP-TR-2016-0046 Designing Feature and Data Parallel Stochastic Coordinate Descent Method for Matrix and Tensor Factorization U Kang Korea...Designing Feature and Data Parallel Stochastic Coordinate Descent Method for Matrix and Tensor Factorization 5a. CONTRACT NUMBER 5b. GRANT NUMBER FA2386...AOARD Grant FA2386-14-1-4036 “Designing Feature and Data Parallel Stochastic Coordinate Descent Method for Matrix and Tensor Factorization” 29
Akinobu, DOTE; Yoshiko, KANADA-EN'YO; Hisashi, HORIUCHI; Yoshinori, AKAISHI; Kiyomi, IKEDA; High Energy Accelerator Research Organization (KEK); Yukawa Institute for Theoretical Physics; Department of Physics, Kyoto University; College of Science and Technology, Nihon University; The Institute of Physical and Chemical Research (RIKEN)
2006-01-01
In order to treat the tensor force explicitly, we propose a microscopic model of nuclear structure based on antisymmetrized molecular dynamics (AMD). It is found that some extensions of the AMD method are effective for incorporating the tensor correlation into wave functions. Calculating the wave functions for deuteron, triton and He^4 with the extended version of AMD, we obtained solutions for which the contribution of the tensor force is large. By analyzing the wave function of He^4, it is ...
Identifying Isotropic Events Using a Regional Moment Tensor Inversion
Energy Technology Data Exchange (ETDEWEB)
Ford, S R; Dreger, D S; Walter, W R
2008-11-04
We calculate the deviatoric and isotropic source components for 17 explosions at the Nevada Test Site, as well as 12 earthquakes and 3 collapses in the surrounding region of the western US, using a regional time-domain full waveform inversion for the complete moment tensor. The events separate into specific populations according to their deviation from a pure double-couple and ratio of isotropic to deviatoric energy. The separation allows for anomalous event identification and discrimination between explosions, earthquakes, and collapses. Confidence regions of the model parameters are estimated from the data misfit by assuming normally distributed parameter values. We investigate the sensitivity of the resolved parameters of an explosion to imperfect Earth models, inaccurate event depths, and data with low signal-to-noise ratio (SNR) assuming a reasonable azimuthal distribution of stations. In the band of interest (0.02-0.10 Hz) the source-type calculated from complete moment tensor inversion is insensitive to velocity models perturbations that cause less than a half-cycle shift (<5 sec) in arrival time error if shifting of the waveforms is allowed. The explosion source-type is insensitive to an incorrect depth assumption (for a true depth of 1 km), and the goodness-of-fit of the inversion result cannot be used to resolve the true depth of the explosion. Noise degrades the explosive character of the result, and a good fit and accurate result are obtained when the signal-to-noise ratio (SNR) is greater than 5. We assess the depth and frequency dependence upon the resolved explosive moment. As the depth decreases from 1 km to 200 m, the isotropic moment is no longer accurately resolved and is in error between 50-200%. However, even at the most shallow depth the resultant moment tensor is dominated by the explosive component when the data have a good SNR.
National Research Council Canada - National Science Library
Sajjadi, Seyed A; Acosta-Cabronero, Julio; Patterson, Karalyn; Diaz-de-Grenu, Lara Z; Williams, Guy B; Nestor, Peter J
2013-01-01
.... This report presents evidence to indicate that corticobasal degeneration and progressive supranuclear palsy, in particular, might be identifiable at a single subject level with diffusion tensor imaging...
Validation of buoyancy driven spectral tensor model using HATS data
DEFF Research Database (Denmark)
Chougule, A.; Mann, Jakob; Kelly, Mark C.
2016-01-01
We present a homogeneous spectral tensor model for wind velocity and temperature fluctuations, driven by mean vertical shear and mean temperature gradient. Results from the model, including one-dimensional velocity and temperature spectra and the associated co-spectra, are shown in this paper. Th...... is described via five parameters: the dissipation rate (ε), length scale of energy-containing eddies (L), a turbulence anisotropy parameter (Γ), gradient Richardson number (Ri) representing the atmospheric stability and the rate of destruction of temperature variance (ηθ)....
Bayesian ISOLA: new tool for automated centroid moment tensor inversion
Vackář, Jiří; Burjánek, Jan; Gallovič, František; Zahradník, Jiří; Clinton, John
2017-04-01
Focal mechanisms are important for understanding seismotectonics of a region, and they serve as a basic input for seismic hazard assessment. Usually, the point source approximation and the moment tensor (MT) are used. We have developed a new, fully automated tool for the centroid moment tensor (CMT) inversion in a Bayesian framework. It includes automated data retrieval, data selection where station components with various instrumental disturbances and high signal-to-noise are rejected, and full-waveform inversion in a space-time grid around a provided hypocenter. The method is innovative in the following aspects: (i) The CMT inversion is fully automated, no user interaction is required, although the details of the process can be visually inspected latter on many figures which are automatically plotted.(ii) The automated process includes detection of disturbances based on MouseTrap code, so disturbed recordings do not affect inversion.(iii) A data covariance matrix calculated from pre-event noise yields an automated weighting of the station recordings according to their noise levels and also serves as an automated frequency filter suppressing noisy frequencies.(iv) Bayesian approach is used, so not only the best solution is obtained, but also the posterior probability density function.(v) A space-time grid search effectively combined with the least-squares inversion of moment tensor components speeds up the inversion and allows to obtain more accurate results compared to stochastic methods. The method has been tested on synthetic and observed data. It has been tested by comparison with manually processed moment tensors of all events greater than M≥3 in the Swiss catalogue over 16 years using data available at the Swiss data center (http://arclink.ethz.ch). The quality of the results of the presented automated process is comparable with careful manual processing of data. The software package programmed in Python has been designed to be as versatile as possible in
Rainbow tensor model with enhanced symmetry and extreme melonic dominance
Itoyama, H.; Mironov, A.; Morozov, A.
2017-08-01
We introduce and briefly analyze the rainbow tensor model where all planar diagrams are melonic. This leads to considerable simplification of the large N limit as compared to that of the matrix model: in particular, what are dressed in this limit are propagators only, which leads to an oversimplified closed set of Schwinger-Dyson equations for multi-point correlators. We briefly touch upon the Ward identities, the substitute of the spectral curve and the AMM/EO topological recursion and their possible connections to Connes-Kreimer theory and forest formulas.
Tensor tomography of stresses in cubic single crystals
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Dmitry D. Karov
2015-03-01
Full Text Available The possibility of optical tomography applying to investigation of a two-dimensional and a three-dimensional stressed state in single cubic crystals has been studied. Stresses are determined within the framework of the Maxwell piezo-optic law (linear dependence of the permittivity tensor on stresses and weak optical anisotropy. It is shown that a complete reconstruction of stresses in a sample is impossible both by translucence it in the parallel planes system and by using of the elasticity theory equations. For overcoming these difficulties, it is offered to use a method of magnetophotoelasticity.
Statistical Texture Modeling for Medical Volume Using Linear Tensor Coding
Directory of Open Access Journals (Sweden)
Junping Deng
2013-01-01
Full Text Available We introduced a compact representation method named Linear Tensor Coding (LTC for medical volume. With LTC, medical volumes can be represented by a linear combination of bases which are mutually independent. Furthermore, it is possible to choose the distinctive basis for classification. Before classification, correlations between category labels and the coefficients of LTC basis are used to choose the basis. Then we use the selected basis for classification. The classification accuracy can be significantly improved by the use of selected distinctive basis.
Finite-Size Geometric Entanglement from Tensor Network Algorithms
Shi, Qian-Qian; Orus, Roman; Fjaerestad, John Ove; Zhou, Huan-Qiang
2009-01-01
The global geometric entanglement is studied in the context of newly-developed tensor network algorithms for finite systems. For one-dimensional quantum spin systems it is found that, at criticality, the leading finite-size correction to the global geometric entanglement per site behaves as $b/n$, where $n$ is the size of the system and $b$ a given coefficient. Our conclusion is based on the computation of the geometric entanglement per spin for the quantum Ising model in a transverse magneti...
Scalar, vector and tensor harmonics on the three-sphere
Lindblom, Lee; Taylor, Nicholas W.; Zhang, Fan
2017-11-01
Scalar, vector and tensor harmonics on the three-sphere were introduced originally to facilitate the study of various problems in gravitational physics. These harmonics are defined as eigenfunctions of the covariant Laplace operator which satisfy certain divergence and trace identities, and ortho-normality conditions. This paper provides a summary of these properties, along with a new notation that simplifies and clarifies some of the key expressions. Practical methods are described for accurately and efficiently computing these harmonics numerically, and test results are given that illustrate how well the analytical identities are satisfied by the harmonics computed numerically in this way.
Moment tensors, state of stress and their relation to faulting processes in Gujarat, western India
Aggarwal, Sandeep Kumar; Khan, Prosanta Kumar; Mohanty, Sarada Prasad; Roumelioti, Zafeiria
2016-10-01
Time domain moment tensor analysis of 145 earthquakes (Mw 3.2 to 5.1), occurring during the period 2006-2014 in Gujarat region, has been performed. The events are mainly confined in the Kachchh area demarcated by the Island belt and Kachchh Mainland faults to its north and south, and two transverse faults to its east and west. Libraries of Green's functions were established using the 1D velocity model of Kachchh, Saurashtra and Mainland Gujarat. Green's functions and broadband displacement waveforms filtered at low frequency (0.5-0.8 Hz) were inverted to determine the moment tensor solutions. The estimated solutions were rigorously tested through number of iterations at different source depths for finding reliable source locations. The identified heterogeneous nature of the stress fields in the Kachchh area allowed us to divide this into four Zones 1-4. The stress inversion results indicate that the Zone 1 is dominated with radial compression, Zone 2 with strike-slip compression, and Zones 3 and 4 with strike-slip extensions. The analysis further shows that the epicentral region of 2001 MW 7.7 Bhuj mainshock, located at the junction of Zones 2, 3 and 4, was associated with predominant compressional stress and strike-slip motion along ∼ NNE-SSW striking fault on the western margin of the Wagad uplift. Other tectonically active parts of Gujarat (e.g. Jamnagar, Talala and Mainland) show earthquake activities are dominantly associated with strike-slip extension/compression faulting. Stress inversion analysis shows that the maximum compressive stress axes (σ1) are vertical for both the Jamnagar and Talala regions and horizontal for the Mainland Gujarat. These stress regimes are distinctly different from those of the Kachchh region.
Directory of Open Access Journals (Sweden)
A.M. Auriat
2015-01-01
Full Text Available Diffusion tensor imaging (DTI-based tractography has been used to demonstrate functionally relevant differences in white matter pathway status after stroke. However, it is now known that the tensor model is insensitive to the complex fiber architectures found in the vast majority of voxels in the human brain. The inability to resolve intra-voxel fiber orientations may have important implications for the utility of standard DTI-based tract reconstruction methods. Intra-voxel fiber orientations can now be identified using novel, tensor-free approaches. Constrained spherical deconvolution (CSD is one approach to characterize intra-voxel diffusion behavior. In the current study, we performed DTI- and CSD-based tract reconstruction of the corticospinal tract (CST and corpus callosum (CC to test the hypothesis that characterization of complex fiber orientations may improve the robustness of fiber tract reconstruction and increase the sensitivity to identify functionally relevant white matter abnormalities in individuals with chronic stroke. Diffusion weighted magnetic resonance imaging was performed in 27 chronic post-stroke participants and 12 healthy controls. Transcallosal pathways and the CST bilaterally were reconstructed using DTI- and CSD-based tractography. Mean fractional anisotropy (FA, apparent diffusion coefficient (ADC, axial diffusivity (AD, and radial diffusivity (RD were calculated across the tracts of interest. The total number and volume of reconstructed tracts was also determined. Diffusion measures were compared between groups (Stroke, Control and methods (CSD, DTI. The relationship between post-stroke motor behavior and diffusion measures was evaluated. Overall, CSD methods identified more tracts than the DTI-based approach for both CC and CST pathways. Mean FA, ADC, and RD differed between DTI and CSD for CC-mediated tracts. In these tracts, we discovered a difference in FA for the CC between stroke and healthy control groups
Identifying key nodes in multilayer networks based on tensor decomposition
Wang, Dingjie; Wang, Haitao; Zou, Xiufen
2017-06-01
The identification of essential agents in multilayer networks characterized by different types of interactions is a crucial and challenging topic, one that is essential for understanding the topological structure and dynamic processes of multilayer networks. In this paper, we use the fourth-order tensor to represent multilayer networks and propose a novel method to identify essential nodes based on CANDECOMP/PARAFAC (CP) tensor decomposition, referred to as the EDCPTD centrality. This method is based on the perspective of multilayer networked structures, which integrate the information of edges among nodes and links between different layers to quantify the importance of nodes in multilayer networks. Three real-world multilayer biological networks are used to evaluate the performance of the EDCPTD centrality. The bar chart and ROC curves of these multilayer networks indicate that the proposed approach is a good alternative index to identify real important nodes. Meanwhile, by comparing the behavior of both the proposed method and the aggregated single-layer methods, we demonstrate that neglecting the multiple relationships between nodes may lead to incorrect identification of the most versatile nodes. Furthermore, the Gene Ontology functional annotation demonstrates that the identified top nodes based on the proposed approach play a significant role in many vital biological processes. Finally, we have implemented many centrality methods of multilayer networks (including our method and the published methods) and created a visual software based on the MATLAB GUI, called ENMNFinder, which can be used by other researchers.
Quadratic third-order tensor optimization problem with quadratic constraints
Directory of Open Access Journals (Sweden)
Lixing Yang
2014-05-01
Full Text Available Quadratically constrained quadratic programs (QQPs problems play an important modeling role for many diverse problems. These problems are in general NP hard and numerically intractable. Semidenite programming (SDP relaxations often provide good approximate solutions to these hard problems. For several special cases of QQP, e.g., convex programs and trust region subproblems, SDP relaxation provides the exact optimal value, i.e., there is a zero duality gap. However, this is not true for the general QQP, or even the QQP with two convex constraints, but a nonconvex objective.In this paper, we consider a certain QQP where the variable is neither vector nor matrix but a third-order tensor. This problem can be viewed as a generalization of the ordinary QQP with vector or matrix as it's variant. Under some mild conditions, we rst show that SDP relaxation provides exact optimal solutions for the original problem. Then we focus on two classes of homogeneous quadratic tensor programming problems which have no requirements on the constraints number. For one, we provide an easily implemental polynomial time algorithm to approximately solve the problem and discuss the approximation ratio. For the other, we show there is no gap between the SDP relaxation and itself.
Structure-adaptive sparse denoising for diffusion-tensor MRI.
Bao, Lijun; Robini, Marc; Liu, Wanyu; Zhu, Yuemin
2013-05-01
Diffusion tensor magnetic resonance imaging (DT-MRI) is becoming a prospective imaging technique in clinical applications because of its potential for in vivo and non-invasive characterization of tissue organization. However, the acquisition of diffusion-weighted images (DWIs) is often corrupted by noise and artifacts, and the intensity of diffusion-weighted signals is weaker than that of classical magnetic resonance signals. In this paper, we propose a new denoising method for DT-MRI, called structure-adaptive sparse denoising (SASD), which exploits self-similarity in DWIs. We define a similarity measure based on the local mean and on a modified structure-similarity index to find sets of similar patches that are arranged into three-dimensional arrays, and we propose a simple and efficient structure-adaptive window pursuit method to achieve sparse representation of these arrays. The noise component of the resulting structure-adaptive arrays is attenuated by Wiener shrinkage in a transform domain defined by two-dimensional principal component decomposition and Haar transformation. Experiments on both synthetic and real cardiac DT-MRI data show that the proposed SASD algorithm outperforms state-of-the-art methods for denoising images with structural redundancy. Moreover, SASD achieves a good trade-off between image contrast and image smoothness, and our experiments on synthetic data demonstrate that it produces more accurate tensor fields from which biologically relevant metrics can then be computed. Copyright © 2013 Elsevier B.V. All rights reserved.
Tensor Spectral Clustering for Partitioning Higher-order Network Structures.
Benson, Austin R; Gleich, David F; Leskovec, Jure
2015-01-01
Spectral graph theory-based methods represent an important class of tools for studying the structure of networks. Spectral methods are based on a first-order Markov chain derived from a random walk on the graph and thus they cannot take advantage of important higher-order network substructures such as triangles, cycles, and feed-forward loops. Here we propose a Tensor Spectral Clustering (TSC) algorithm that allows for modeling higher-order network structures in a graph partitioning framework. Our TSC algorithm allows the user to specify which higher-order network structures (cycles, feed-forward loops, etc.) should be preserved by the network clustering. Higher-order network structures of interest are represented using a tensor, which we then partition by developing a multilinear spectral method. Our framework can be applied to discovering layered flows in networks as well as graph anomaly detection, which we illustrate on synthetic networks. In directed networks, a higher-order structure of particular interest is the directed 3-cycle, which captures feedback loops in networks. We demonstrate that our TSC algorithm produces large partitions that cut fewer directed 3-cycles than standard spectral clustering algorithms.
Explicit Determination of Piezoelectric Eshelby Tensors for a Spheroidal Inclusion
Energy Technology Data Exchange (ETDEWEB)
Yozo Mikata
2001-06-21
In this paper, by systematically treating the integrals involved in the piezoelectric inclusion problem, explicit results were obtained for the piezoelectric Eshelby tensors for a spheroidal inclusion aligned along the axis of the anisotropy in a transversely isotropic piezoelectric material. This problem was first treated by Dunn and Wienecke (1996) using a Green's function approach, which closely follows Withers' approach (1989) for an ellipsoidal inclusion problem in a transversely isotropic elastic medium. The same problem was recently treated by Michelitsch and Levin (2000) also using a Green's function approach. In this paper, a different method was used to obtain the explicit results for the piezoelectric Eshelby tensors for a spheroidal inclusion. The method is a direct extension of a more unified approach, which has been recently developed by Mikata (2000), which is based on Deeg's results (1980) on a piezoelectric inclusion problem. The main advantage of this method is that it is more straightforward and simpler than Dunn and Wienecke (1996), or Michelitsch and Levin (2000), and the results are a little bit more explicit than their solutions. The key step of this paper is an analytical closed form evaluation of several integrals, which was made possible after a careful treatment of a certain bi-cubic equation.
Operator Algebras in Rigid C*-Tensor Categories
Jones, Corey; Penneys, David
2017-11-01
In this article, we define operator algebras internal to a rigid C*-tensor category C. A C*/W*-algebra object in C is an algebra object A in ind-C whose category of free modules {FreeMod_C(A)} is a C-module C*/W*-category respectively. When C= Hilb_fd, the category of finite dimensional Hilbert spaces, we recover the usual notions of operator algebras. We generalize basic representation theoretic results, such as the Gelfand-Naimark and von Neumann bicommutant theorems, along with the GNS construction. We define the notion of completely positive morphisms between C*-algebra objects in C and prove the analog of the Stinespring dilation theorem. As an application, we discuss approximation and rigidity properties, including amenability, the Haagerup property, and property (T) for a connected W*-algebra M in C. Our definitions simultaneously unify the definitions of analytic properties for discrete quantum groups and rigid C*-tensor categories.
Stereological estimation of particle shape and orientation from volume tensors.
Rafati, A H; Ziegel, J F; Nyengaard, J R; Jensen, E B Vedel
2016-09-01
In the present paper, we describe new robust methods of estimating cell shape and orientation in 3D from sections. The descriptors of 3D cell shape and orientation are based on volume tensors which are used to construct an ellipsoid, the Miles ellipsoid, approximating the average cell shape and orientation in 3D. The estimators of volume tensors are based on observations in several optical planes through sampled cells. This type of geometric sampling design is known as the optical rotator. The statistical behaviour of the estimator of the Miles ellipsoid is studied under a flexible model for 3D cell shape and orientation. In a simulation study, the lengths of the axes of the Miles ellipsoid can be estimated with coefficients of variation of about 2% if 100 cells are sampled. Finally, we illustrate the use of the developed methods in an example, involving neurons in the medial prefrontal cortex of rat. © 2016 The Authors Journal of Microscopy © 2016 Royal Microscopical Society.
Tensor Networks for Lattice Gauge Theories with Continuous Groups
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L. Tagliacozzo
2014-11-01
Full Text Available We discuss how to formulate lattice gauge theories in the tensor-network language. In this way, we obtain both a consistent-truncation scheme of the Kogut-Susskind lattice gauge theories and a tensor-network variational ansatz for gauge-invariant states that can be used in actual numerical computations. Our construction is also applied to the simplest realization of the quantum link models or gauge magnets and provides a clear way to understand their microscopic relation with the Kogut-Susskind lattice gauge theories. We also introduce a new set of gauge-invariant operators that modify continuously Rokhsar-Kivelson wave functions and can be used to extend the phase diagrams of known models. As an example, we characterize the transition between the deconfined phase of the Z_{2} lattice gauge theory and the Rokhsar-Kivelson point of the U(1 gauge magnet in 2D in terms of entanglement entropy. The topological entropy serves as an order parameter for the transition but not the Schmidt gap.
Towards overcoming the Monte Carlo sign problem with tensor networks
Energy Technology Data Exchange (ETDEWEB)
Banuls, Mari Carmen; Cirac, J. Ignacio; Kuehn, Stefan [Max-Planck-Institut fuer Quantenoptik (MPQ), Garching (Germany); Cichy, Krzysztof [Frankfurt Univ. (Germany). Inst. fuer Theoretische Physik; Adam Mickiewicz Univ., Poznan (Poland). Faculty of Physics; Jansen, Karl [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Saito, Hana [AISIN AW Co., Ltd., Aichi (Japan)
2016-11-15
The study of lattice gauge theories with Monte Carlo simulations is hindered by the infamous sign problem that appears under certain circumstances, in particular at non-zero chemical potential. So far, there is no universal method to overcome this problem. However, recent years brought a new class of non-perturbative Hamiltonian techniques named tensor networks, where the sign problem is absent. In previous work, we have demonstrated that this approach, in particular matrix product states in 1+1 dimensions, can be used to perform precise calculations in a lattice gauge theory, the massless and massive Schwinger model. We have computed the mass spectrum of this theory, its thermal properties and real-time dynamics. In this work, we review these results and we extend our calculations to the case of two flavours and non-zero chemical potential. We are able to reliably reproduce known analytical results for this model, thus demonstrating that tensor networks can tackle the sign problem of a lattice gauge theory at finite density.
Lithospheric Stress Tensor from Gravity and Lithospheric Structure Models
Eshagh, Mehdi; Tenzer, Robert
2017-07-01
In this study we investigate the lithospheric stresses computed from the gravity and lithospheric structure models. The functional relation between the lithospheric stress tensor and the gravity field parameters is formulated based on solving the boundary-value problem of elasticity in order to determine the propagation of stresses inside the lithosphere, while assuming the horizontal shear stress components (computed at the base of the lithosphere) as lower boundary values for solving this problem. We further suppress the signature of global mantle flow in the stress spectrum by subtracting the long-wavelength harmonics (below the degree of 13). This numerical scheme is applied to compute the normal and shear stress tensor components globally at the Moho interface. The results reveal that most of the lithospheric stresses are accumulated along active convergent tectonic margins of oceanic subductions and along continent-to-continent tectonic plate collisions. These results indicate that, aside from a frictional drag caused by mantle convection, the largest stresses within the lithosphere are induced by subduction slab pull forces on the side of subducted lithosphere, which are coupled by slightly less pronounced stresses (on the side of overriding lithospheric plate) possibly attributed to trench suction. Our results also show the presence of (intra-plate) lithospheric loading stresses along Hawaii islands. The signature of ridge push (along divergent tectonic margins) and basal shear traction resistive forces is not clearly manifested at the investigated stress spectrum (between the degrees from 13 to 180).
Stealth configurations in vector-tensor theories of gravity
Chagoya, Javier; Tasinato, Gianmassimo
2018-01-01
Studying the physics of compact objects in modified theories of gravity is important for understanding how future observations can test alternatives to General Relativity. We consider a subset of vector-tensor Galileon theories of gravity characterized by new symmetries, which can prevent the propagation of the vector longitudinal polarization, even in absence of Abelian gauge invariance. We investigate new spherically symmetric and slowly rotating solutions for these systems, including an arbitrary matter Lagrangian. We show that, under certain conditions, there always exist stealth configurations whose geometry coincides with solutions of Einstein gravity coupled with the additional matter. Such solutions have a non-trivial profile for the vector field, characterized by independent integration constants, which extends to asymptotic infinity. We interpret our findings in terms of the symmetries and features of the original vector-tensor action, and on the number of degrees of freedom that it propagates. These results are important to eventually describe gravitationally bound configurations in modified theories of gravity, such as black holes and neutron stars, including realistic matter fields forming or surrounding the object.
Vulnerability parameters of tensor product of complete equipartite graphs
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P. Paulraja
2013-01-01
Full Text Available Let \\(G_{1}\\ and \\(G_{2}\\ be two simple graphs. The tensor product of \\(G_{1}\\ and \\(G_{2}\\, denoted by \\(G_{1}\\times G_{2}\\, has vertex set \\(V(G_{1}\\times G_{2}=V(G_{1}\\times V(G_{2}\\ and edge set \\(E(G_{1}\\times G_{2}=\\{(u_{1},v_{1}(u_{2},v_{2}:u_{1}u_{2}\\in E(G_{1}\\ and \\(v_{1}v_{2}\\in E(G_{2}\\}\\. In this paper, we determine vulnerability parameters such as toughness, scattering number, integrity and tenacity of the tensor product of the graphs \\(K_{r(s}\\times K_{m(n}\\ for \\(r\\geq 3, m\\geq 3, s\\geq 1\\ and \\(n\\geq 1,\\ where \\(K_{r(s}\\ denotes the complete \\(r\\-partite graph in which each part has \\(s\\ vertices. Using the results obtained here the theorems proved in [Aygul Mamut, Elkin Vumar, Vertex Vulnerability Parameters of Kronecker Products of Complete Graphs, Information Processing Letters 106 (2008, 258-262] are obtained as corollaries.
Traffic Volume Data Outlier Recovery via Tensor Model
Directory of Open Access Journals (Sweden)
Huachun Tan
2013-01-01
Full Text Available Traffic volume data is already collected and used for a variety of purposes in intelligent transportation system (ITS. However, the collected data might be abnormal due to the problem of outlier data caused by malfunctions in data collection and record systems. To fully analyze and operate the collected data, it is necessary to develop a validate method for addressing the outlier data. Many existing algorithms have studied the problem of outlier recovery based on the time series methods. In this paper, a multiway tensor model is proposed for constructing the traffic volume data based on the intrinsic multilinear correlations, such as day to day and hour to hour. Then, a novel tensor recovery method, called ADMM-TR, is proposed for recovering outlier data of traffic volume data. The proposed method is evaluated on synthetic data and real world traffic volume data. Experimental results demonstrate the practicability, effectiveness, and advantage of the proposed method, especially for the real world traffic volume data.
Comparison of quality control software tools for diffusion tensor imaging.
Liu, Bilan; Zhu, Tong; Zhong, Jianhui
2015-04-01
Image quality of diffusion tensor imaging (DTI) is critical for image interpretation, diagnostic accuracy and efficiency. However, DTI is susceptible to numerous detrimental artifacts that may impair the reliability and validity of the obtained data. Although many quality control (QC) software tools are being developed and are widely used and each has its different tradeoffs, there is still no general agreement on an image quality control routine for DTIs, and the practical impact of these tradeoffs is not well studied. An objective comparison that identifies the pros and cons of each of the QC tools will be helpful for the users to make the best choice among tools for specific DTI applications. This study aims to quantitatively compare the effectiveness of three popular QC tools including DTI studio (Johns Hopkins University), DTIprep (University of North Carolina at Chapel Hill, University of Iowa and University of Utah) and TORTOISE (National Institute of Health). Both synthetic and in vivo human brain data were used to quantify adverse effects of major DTI artifacts to tensor calculation as well as the effectiveness of different QC tools in identifying and correcting these artifacts. The technical basis of each tool was discussed, and the ways in which particular techniques affect the output of each of the tools were analyzed. The different functions and I/O formats that three QC tools provide for building a general DTI processing pipeline and integration with other popular image processing tools were also discussed. Copyright © 2015 Elsevier Inc. All rights reserved.
Adaptive stochastic Galerkin FEM with hierarchical tensor representations
Eigel, Martin
2016-01-08
PDE with stochastic data usually lead to very high-dimensional algebraic problems which easily become unfeasible for numerical computations because of the dense coupling structure of the discretised stochastic operator. Recently, an adaptive stochastic Galerkin FEM based on a residual a posteriori error estimator was presented and the convergence of the adaptive algorithm was shown. While this approach leads to a drastic reduction of the complexity of the problem due to the iterative discovery of the sparsity of the solution, the problem size and structure is still rather limited. To allow for larger and more general problems, we exploit the tensor structure of the parametric problem by representing operator and solution iterates in the tensor train (TT) format. The (successive) compression carried out with these representations can be seen as a generalisation of some other model reduction techniques, e.g. the reduced basis method. We show that this approach facilitates the efficient computation of different error indicators related to the computational mesh, the active polynomial chaos index set, and the TT rank. In particular, the curse of dimension is avoided.
Euclidean supersymmetric solutions with the self-dual Weyl tensor
Directory of Open Access Journals (Sweden)
Masato Nozawa
2017-07-01
Full Text Available We explore the Euclidean supersymmetric solutions admitting the self-dual gauge field in the framework of N=2 minimal gauged supergravity in four dimensions. According to the classification scheme utilizing the spinorial geometry or the bilinears of Killing spinors, the general solution preserves one quarter of supersymmetry and is described by the Przanowski–Tod class with the self-dual Weyl tensor. We demonstrate that there exists an additional Killing spinor, provided the Przanowski–Tod metric admits a Killing vector that commutes with the principal one. The proof proceeds by recasting the metric into another Przanowski–Tod form. This formalism enables us to show that the self-dual Reissner–Nordström–Taub–NUT–AdS metric possesses a second Killing spinor, which has been missed over many years. We also address the supersymmetry when the Przanowski–Tod space is conformal to each of the self-dual ambi-toric Kähler metrics. It turns out that three classes of solutions are all reduced to the self-dual Carter family, by virtue of the nondegenerate Killing–Yano tensor.
Segmentation of the pectoral muscle in breast MR images using structure tensor and deformable model
Lee, Myungeun; Kim, Jong Hyo
2012-02-01
Recently, breast MR images have been used in wider clinical area including diagnosis, treatment planning, and treatment response evaluation, which requests quantitative analysis and breast tissue segmentation. Although several methods have been proposed for segmenting MR images, segmenting out breast tissues robustly from surrounding structures in a wide range of anatomical diversity still remains challenging. Therefore, in this paper, we propose a practical and general-purpose approach for segmenting the pectoral muscle boundary based on the structure tensor and deformable model. The segmentation work flow comprises four key steps: preprocessing, detection of the region of interest (ROI) within the breast region, segmenting the pectoral muscle and finally extracting and refining the pectoral muscle boundary. From experimental results we show that the proposed method can segment the pectoral muscle robustly in diverse patient cases. In addition, the proposed method will allow the application of the quantification research for various breast images.
Saturn: a software application of tensor utilities for research in neuroimaging.
Cárdenes, Rubén; Muñoz-Moreno, Emma; Tristan-Vega, Antonio; Martin-Fernandez, Marcos
2010-03-01
We present an advanced software tool designed for visualization and quantitative analysis of Diffusion Tensor Imaging (DTI) called Saturn. The software is specially developed to help clinicians and researchers in neuroimaging, and includes a complete set of visualization capabilities to browse and analyze efficiently DTI data, making this application a powerful tool also for diagnosis purposes. The software includes a robust quantification method for DTI data, using an atlas-based method to automatically obtain equivalent anatomical fiber bundles and regions of interest among different DTI data sets. Consequently, a set of measurements is also implemented to perform robust group studies among subjects affected by neurological disorders and control groups in order to look for significant differences. Finally, a comparison study with five similar DTI applications is presented, showing the advantages offered by this tool. Copyright 2009 Elsevier Ireland Ltd. All rights reserved.
Laser pumping Cs atom magnetometer of theory research based on gradient tensor measuring
Energy Technology Data Exchange (ETDEWEB)
Yang Zhang; Chong Kang; Wang Qingtao; Lei Cheng; Zheng Caiping, E-mail: zhangyang@hrbeu.edu.cn [College of Science, Harbin Engineering University, Harbin 150001 (China)
2011-02-01
At present, due to space exploration, military technology, geological exploration, magnetic navigation, medical diagnosis and biological magnetic fields study of the needs of research and development, the magnetometer is given strong driving force. In this paper, it will discuss the theoretical analysis and system design of laser pumping cesium magnetometer, cesium atomic energy level formed hyperfine structure with the I-J coupling, the hyperfine structure has been further split into Zeeman sublevels for the effects of magnetic field. To use laser pump and RF magnetic field make electrons transition in the hyperfine structure to produce the results of magneto-optical double resonance, and ultimately through the resonant frequency will be able to achieve accurate value of the external magnetic field. On this basis, we further have a discussion about magnetic gradient tensor measuring method. To a large extent, it increases the magnetic field measurement of information.
Space time frequency (STF) code tensor for the characterization of the epileptic preictal stage.
Direito, Bruno; Teixeira, César; Ribeiro, Bernardete; Castelo-Branco, Miguel; Dourado, António
2012-01-01
We evaluate the ability of multiway models to characterize the epileptic preictal period. The understanding of the characteristics of the period prior to the seizure onset is a decisive step towards the development of seizure prediction frameworks. Multiway models of EEG segments already demonstrated that hidden structures may be unveiled using tensor decomposition techniques. We propose a novel approach using a multiway model, Parallel Factor Analysis (PARAFAC), to identify spatial, temporal and spectral signatures of the preictal period. The results obtained, from a dataset of 4 patients, with a total of 30 seizures, suggest that a common structure may be involved in seizure generation. Furthermore, the spatial signature may be related to the ictal onset region and that determined frequency sub-bands may be more relevant in preictal stages.
Directory of Open Access Journals (Sweden)
Xiangguo Zeng
2016-01-01
Full Text Available A common measure of deformation between atomic scale simulations and the continuum framework is provided and the strain tensors for multiscale simulations are defined in this paper. In order to compute the deformation gradient of any atom m, the weight function is proposed to eliminate the different contributions within the neighbor atoms which have different distances to atom m, and the weighted least squares error optimization model is established to seek the optimal coefficients of the weight function and the optimal local deformation gradient of each atom. The optimization model involves more than 9 parameters. To guarantee the reliability of subsequent parameters identification result and lighten the calculation workload of parameters identification, an overall analysis method of parameter sensitivity and an advanced genetic algorithm are also developed.
Spatio-Temporal Video Object Segmentation via Scale-Adaptive 3D Structure Tensor
Directory of Open Access Journals (Sweden)
Hai-Yun Wang
2004-06-01
Full Text Available To address multiple motions and deformable objects' motions encountered in existing region-based approaches, an automatic video object (VO segmentation methodology is proposed in this paper by exploiting the duality of image segmentation and motion estimation such that spatial and temporal information could assist each other to jointly yield much improved segmentation results. The key novelties of our method are (1 scale-adaptive tensor computation, (2 spatial-constrained motion mask generation without invoking dense motion-field computation, (3 rigidity analysis, (4 motion mask generation and selection, and (5 motion-constrained spatial region merging. Experimental results demonstrate that these novelties jointly contribute much more accurate VO segmentation both in spatial and temporal domains.
Diffusion tensor imaging for target volume definition in glioblastoma multiforme
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Berberat, Jatta; Remonda, Luca [Cantonal Hospital, Department of Neuro-radiology, Aarau (Switzerland); McNamara, Jane; Rogers, Susanne [Cantonal Hospital, Department of Radiation Oncology, Aarau (Switzerland); Bodis, Stephan [Cantonal Hospital, Department of Radiation Oncology, Aarau (Switzerland); University Hospital, Department of Radiation Oncology, Zurich (Switzerland)
2014-10-15
Diffusion tensor imaging (DTI) is an MR-based technique that may better detect the peritumoural region than MRI. Our aim was to explore the feasibility of using DTI for target volume delineation in glioblastoma patients. MR tensor tracts and maps of the isotropic (p) and anisotropic (q) components of water diffusion were coregistered with CT in 13 glioblastoma patients. An in-house image processing program was used to analyse water diffusion in each voxel of interest in the region of the tumour. Tumour infiltration was mapped according to validated criteria and contralateral normal brain was used as an internal control. A clinical target volume (CTV) was generated based on the T{sub 1}-weighted image obtained using contrast agent (T{sub 1Gd}), tractography and the infiltration map. This was compared to a conventional T{sub 2}-weighted CTV (T{sub 2}-w CTV). Definition of a diffusion-based CTV that included the adjacent white matter tracts proved highly feasible. A statistically significant difference was detected between the DTI-CTV and T{sub 2}-w CTV volumes (p < 0.005, t = 3.480). As the DTI-CTVs were smaller than the T{sub 2}-w CTVs (tumour plus peritumoural oedema), the pq maps were not simply detecting oedema. Compared to the clinical planning target volume (PTV), the DTI-PTV showed a trend towards volume reduction. These diffusion-based volumes were smaller than conventional volumes, yet still included sites of tumour recurrence. Extending the CTV along the abnormal tensor tracts in order to preserve coverage of the likely routes of dissemination, whilst sparing uninvolved brain, is a rational approach to individualising radiotherapy planning for glioblastoma patients. (orig.) [German] Die Diffusions-Tensor-Bildgebung (DTI) ist eine MR-Technik, die dank der Erfassung des peritumoralen Bereichs eine Verbesserung bezueglich MRI bringt. Unser Ziel war die Pruefung der Machbarkeit der Verwendung der DTI fuer die Zielvolumenabgrenzung fuer Patienten mit
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Min, Zhi Gang; Niu, Chen; Zhang, Qiu Li; Zhang, Ming [Dept. of Radiology, First Affiliated Hospital of Xi' an Jiaotong University, Xi' an (China); Qian, Yu Cheng [Dept. of Medical Imaging, School of Medicine, Jiangsu University, Zhenjiang (China)
2017-09-15
To identify the optimal factors in diffusion tensor imaging for predicting corticospinal tract (CST) injury caused by brain tumors. This prospective study included 33 patients with motor weakness and 64 patients with normal motor function. The movement of the CST, minimum distance between the CST and the tumor, and relative fractional anisotropy (rFA) of the CST on diffusion tensor imaging, were compared between patients with motor weakness and normal function. Logistic regression analysis was used to obtain the optimal factor predicting motor weakness. In patients with motor weakness, the displacement (8.44 ± 6.64 mm) of the CST (p = 0.009), minimum distance (3.98 ± 7.49 mm) between the CST and tumor (p < 0.001), and rFA (0.83 ± 0.11) of the CST (p < 0.001) were significantly different from those of the normal group (4.64 ± 6.65 mm, 14.87 ± 12.04 mm, and 0.98 ± 0.05, respectively) (p = 0.009, p < 0.001, and p < 0.001). The frequencies of patients with the CST passing through the tumor (6%, p = 0.002), CST close to the tumor (23%, p < 0.001), CST close to a malignant tumor (high grade glioma, metastasis, or lymphoma) (19%, p < 0.001), and CST passing through infiltrating edema (19%, p < 0.001) in the motor weakness group, were significantly different from those of the patients with normal motor function (0, 8, 1, and 10%, respectively). Logistic regression analysis showed that decreased rFA and CST close to a malignant tumor were effective variables related to motor weakness. Decreased fractional anisotropy, combined with closeness of a malignant tumor to the CST, is the optimal factor in predicting CST injury caused by a brain tumor.
Frames and bases in tensor products of Hilbert spaces and Hilbert C ...
Indian Academy of Sciences (India)
In this article, we study tensor product of Hilbert *-modules and Hilbert spaces. We show that if is a Hilbert -module and is a Hilbert -module, then tensor product of frames (orthonormal bases) for and produce frames (orthonormal bases) for Hilbert A ⊗ B -module E ⊗ F , and we get more results. For Hilbert ...
Nested Vector-Sensor Array Processing via Tensor Modeling (Briefing Charts)
2014-04-24
algorithm based on HOSVD for a mixture of polarized sources, in EUSIPCO 2013, Marrakech, Marocco, Sep. 2013. CSSIP Lab 12 Applications: Acoustic Vector...CSSIP Lab 15 EM Case II: DOA Estimation Fig. 2: MUSIC spectrum using a ULA (left: tensor-based) and a nested array (middle: matrix- based; right: tensor
Estimation of the magnetic field gradient tensor using the Swarm constellation
DEFF Research Database (Denmark)
Kotsiaros, Stavros; Finlay, Chris; Olsen, Nils
2014-01-01
For the first time, part of the magnetic field gradient tensor is estimated in space by the Swarm mission. We investigate the possibility of a more complete estimation of the gradient tensor exploiting the Swarm constellation. The East-West gradients can be approximated by observations from...
Kiehn, R. M.
1976-01-01
With respect to irreversible, non-homeomorphic maps, contravariant and covariant tensor fields have distinctly natural covariance and transformational behavior. For thermodynamic processes which are non-adiabatic, the fact that the process cannot be represented by a homeomorphic map emphasizes the logical arrow of time, an idea which encompasses a principle of retrodictive determinism for covariant tensor fields.
Page 1 On energy-momentum tensors as sources of spin-2 fields 31 ...
Indian Academy of Sciences (India)
(actually a linearised version of the harmonic co-ordinate condition). With this subsidiary condition, the theory given by eq. (6) is simply the conventional mass- less spin-2 theory with the Belinfante tensor as its source, to first order in the coupling constant: Clxuv = 2kBay + O (k”). (10). The improved energy-momentum tensor ...
A tensor-based dictionary learning approach to tomographic image reconstruction
DEFF Research Database (Denmark)
Soltani, Sara; Kilmer, Misha E.; Hansen, Per Christian
2016-01-01
with sparsity constraints. The reconstruction problem is formulated in a convex optimization framework by looking for a solution with a sparse representation in the tensor dictionary. Numerical results show that our tensor formulation leads to very sparse representations of both the training images...
A simple and accurate technique is described for measuring the uniaxial permittivity tensor of biological materials with a coplanar waveguide transmission-line configuration. Permittivity tensor results are presented for several chicken and beef fresh meat samples at 2.45 GHz....
The space generated by metric and torsion tensors, derivation of Einstein-Hilbert equation
Directory of Open Access Journals (Sweden)
Николай Иванович Яременко
2014-11-01
Full Text Available This paper is devoted to the derivation of field equations in space with the geometric structure generated by metric and torsion tensors. We also study the geometry of the space are generated jointly and agreed by the metric tensor and the torsion tensor. We showed that in such space the structure of the curvature tensor has special features and for this tensor obtained analog Ricci - Jacobi identity; was evaluated gap that occurs at the transition from the original to the image and vice versa, in the case of an infinitely small contours. We have researched the geodesic lines equation. We introduce the tensor π_αβ which is similar to the second fundamental tensor of hypersurfaces Y^n-1, but the structure of this tensor is substantially different from the case of Riemannian spaces with zero torsion. Then we obtained formulas which characterize the change of vectors in accompanying basis relative to this basis itself in the small. Taking into considerations our results about the structure of such space we derived from the variation principle the general field equations (electromagnetic and gravitational.
Bose Operator Expansions of Tensor Operators in the Theory of Magnetism
DEFF Research Database (Denmark)
Lindgård, Per-Anker; Kowalska, A.
1976-01-01
For pt.I see ibid., vol.7, p.1523 (1974). The matching of matrix element method is used to find a new self-consistent Bose operator expansion for tensor operators in spin systems with isotropic exchange interaction plus anisotropy. Tables are given for all tensor operators relevant for cubic...
Schraut, Johannes; Arbuznikov, Alexei V; Schinzel, Sandra; Kaupp, Martin
2011-12-09
Based on broken-symmetry density functional calculations, the (55)Mn hyperfine tensors of a series of exchange-coupled, mixed-valence, dinuclear Mn(III) Mn(IV) complexes have been computed. We go beyond previous quantum chemical work by fully including the effects of local zero-field splitting (ZFS) interactions in the spin projection, following the first-order perturbation formalism of Sage et al. [J. Am. Chem. Soc. 1989, 111, 7239]. This allows the ZFS-induced transfer of hyperfine anisotropy from the Mn(III) site to the Mn(IV) site to be described with full consideration of the orientations of local hyperfine and ZFS tensors. After scaling to correct for systematic deficiencies in the quantum chemically computed local ZFS tensors, good agreement with experimental (55)Mn anisotropies at the Mn(IV) site is obtained. The hyperfine coupling anisotropies on the Mn(III) site depend sensitively on structural distortions for a d(4) ion. The latter are neither fully reproduced by using a DFT-optimized coordination environment nor by using experimental structures. For very small exchange-coupling constants, the perturbation treatment breaks down and a dramatic sensitivity to the scaling of the local ZFS tensors is observed. These results are discussed with respect to ongoing work to elucidate the structure of the oxygen-evolving complex of photosystem II by analysis of the EPR spectra. Copyright © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Characteristics of the ion pressure tensor in the Earth`s magnetosheath: AMPTE/IRM observations
Energy Technology Data Exchange (ETDEWEB)
Lewis, H.R.; Li, X.; Phan, T.D.; Treumann, R.A. [Herzberg Inst. of Astrophysics, Ottawa, Ontario (Canada)]|[Max-Planck-Inst. fuer Extraterrestrische Physik, Garching (Germany)
1994-01-01
AMPTE/IRM satellite data are used to examine characteristics of the ion pressure tensor in the Earth`s magnetosheath. The eigenvalues and principal axes of the pressure tensor are computed, and the directions of the principal axes are compared to the direction of the independently measured magnetic field B. When the pressure tensor is anisotropic, as is usually the case in the magnetosheath, one of its eigenvalues is observed to be distinguishable from the other two, which are about equal to one another. The eigenvector associated with the distinguishable eigenvalue is an axis of symmetry of the pressure tensor. This symmetry axis is generally not parallel to B. New features of the plasma distribution function are revealed by using the actual eigenvalues of the pressure tensors rather than the usual p(perpendicular) and p(parallel) where perpendicular and parallel denote directions to B.
Li, Zhendong; Liu, Wenjian
2016-01-01
Complicated mathematical equations involving tensors with permutation symmetries are frequently encountered in fields such as quantum chemistry, e.g., those in coupled cluster theories and derivatives of wavefunction parameters. In automatic derivations of these equations, a key step is the collection of product terms that can be found identical by using permutation symmetries or relabelling dummy indices. In the present work, we define a canonical form for a general tensor product in the presence of permutation symmetries as a result of the classification of all tensor products from a group theoretical point of view. To make such definition of practical use, we provide an efficient algorithm to compute the canonical form by combining the classical backtrack search for permutation groups and the idea of partitions used in graph isomorphism algorithms. The resulted algorithm can compute canonical forms and generators of the automorphism groups of tensor expressions. Moreover, for tensor products with external ...
Ammari, Habib; Qiu, Lingyun; Santosa, Fadil; Zhang, Wenlong
2017-12-01
In this paper we present a mathematical and numerical framework for a procedure of imaging anisotropic electrical conductivity tensor by integrating magneto-acoutic tomography with data acquired from diffusion tensor imaging. Magneto-acoustic tomography with magnetic induction (MAT-MI) is a hybrid, non-invasive medical imaging technique to produce conductivity images with improved spatial resolution and accuracy. Diffusion tensor imaging (DTI) is also a non-invasive technique for characterizing the diffusion properties of water molecules in tissues. We propose a model for anisotropic conductivity in which the conductivity is proportional to the diffusion tensor. Under this assumption, we propose an optimal control approach for reconstructing the anisotropic electrical conductivity tensor. We prove convergence and Lipschitz type stability of the algorithm and present numerical examples to illustrate its accuracy and feasibility.
Energy Technology Data Exchange (ETDEWEB)
Deverdun, Jérémy [Department of Neuroradiology, Montpellier University Hospital Center, Gui de Chauliac Hospital, Montpellier (France); Laboratoire Charles Coulomb, CNRS UMR 5221 - Université Montpellier II, Montpellier (France); I2FH, Institut d’Imagerie Fonctionnelle Humaine, Hôpital Gui de Chauliac, CHRU de, Montpellier (France); Menjot de Champfleur, Sophie [Department of Neuroradiology, Montpellier University Hospital Center, Gui de Chauliac Hospital, Montpellier (France); Clinique du Parc, Castelnau-le-Lez (France); Cabello-Aguilar, Simon [Department of Neuroradiology, Montpellier University Hospital Center, Gui de Chauliac Hospital, Montpellier (France); I2FH, Institut d’Imagerie Fonctionnelle Humaine, Hôpital Gui de Chauliac, CHRU de, Montpellier (France); Maury, Florence [Department of Neurology, Montpellier University Hospital Center, Gui de Chauliac Hospital, Montpellier (France); Molino, François [Laboratoire Charles Coulomb, CNRS UMR 5221 - Université Montpellier II, Montpellier (France); Institut de Génomique Fonctionnelle, UMR 5203 - INSERM U661 - Université Montpellier II - Université, Montpellier I (France); Charif, Mahmoud [Department of Neurology, Montpellier University Hospital Center, Gui de Chauliac Hospital, Montpellier (France); Leboucq, Nicolas [Department of Neuroradiology, Montpellier University Hospital Center, Gui de Chauliac Hospital, Montpellier (France); Ayrignac, Xavier; Labauge, Pierre [Department of Neurology, Montpellier University Hospital Center, Gui de Chauliac Hospital, Montpellier (France); and others
2014-11-15
Background and Purpose: The etiologic diagnosis of parkinsonian syndromes is of particular importance when considering syndromes of vascular or degenerative origin. The purpose of this study is to find differences in the white-matter architecture between those two groups in elderly patients. Materials and Methods: Thirty-five patients were prospectively included (multiple-system atrophy, n = 5; Parkinson's disease, n = 15; progressive supranuclear palsy, n = 9; vascular parkinsonism, n = 6), with a mean age of 76 years. Patients with multiple-system atrophy, progressive supranuclear palsy and Parkinson's disease were grouped as having parkinsonian syndromes of degenerative origin. Brain MRIs included diffusion tensor imaging. Fractional anisotropy and mean-diffusivity maps were spatially normalized, and group analyses between parkinsonian syndromes of degenerative origin and vascular parkinsonism were performed using a voxel-based approach. Results: Statistical parametric-mapping analysis of diffusion tensor imaging data showed decreased fractional anisotropy value in internal capsules bilaterally in patients with vascular parkinsonism compared to parkinsonian syndromes of degenerative origin (p = 0.001) and showed a lower mean diffusivity in the white matter of the left superior parietal lobule (p = 0.01). Fractional anisotropy values were found decreased in the middle cerebellar peduncles in multiple-system atrophy compared to Parkinson's disease and progressive supranuclear palsy. The mean diffusivity was increased in those regions for these subgroups. Conclusion: Clinically defined vascular parkinsonism was associated with decreased fractional anisotropy in the deep white matter (internal capsules) compared to parkinsonian syndromes of degenerative origin. These findings are consistent with previously published neuropathological data.
Amyotrophic lateral sclerosis: diffusion-tensor and chemical shift MR imaging at 3.0 T.
Wang, Sumei; Poptani, Harish; Woo, John H; Desiderio, Lisa M; Elman, Lauren B; McCluskey, Leo F; Krejza, Jaroslaw; Melhem, Elias R
2006-06-01
To prospectively determine whether diffusion-tensor magnetic resonance (MR) imaging in conjunction with two-dimensional chemical shift imaging can assist in identifying upper motor neuron involvement and whether disease severity and duration can be predicted based on imaging parameters in patients with amyotrophic lateral sclerosis (ALS). Institutional review board approval and informed consent were obtained for this HIPAA-compliant study. Fifteen patients with ALS (12 men, three women; mean age, 57.3 years) with clinical evidence of upper motor neuron involvement and 10 healthy control subjects (five men and five women; mean age, 49.4 years) were studied. Fractional anisotropy (FA) and apparent diffusion coefficient (ADC) were measured from the corticospinal tracts at the level of the internal capsule. Average N-acetylaspartate (NAA)/creatine-phosphocreatine (Cr) and NAA/choline-containing compounds (Cho) ratios were calculated from the precentral gyrus. Student t test, multiple linear regression analysis, and Spearman correlation coefficients were employed to quantify relationships between imaging and clinical parameters. Patients with ALS exhibited significantly reduced FA values and NAA/Cr and NAA/Cho ratios compared with values in control subjects (Psides of the brain. ADC was elevated significantly in the affected side (Pside were even stronger predictors of disease duration. Moderate but statistically significant correlation was found between the FA values for the affected side and the ALS Functional Rating Scale Revised (ALSFRS-R) score (r=0.51, P<.05). The NAA/Cr ratio also correlated with both the ALSFRS-R and upper motor neuron scores (r=0.50 and 0.54, respectively; P<.05). Diffusion-tensor and two-dimensional chemical shift MR imaging spectroscopy can be used to identify upper motor neuron involvement and predict disease duration in patients with ALS. Copyright (c) RSNA, 2006.
Reconstruction of large, irregularly sampled multidimensional images. A tensor-based approach.
Morozov, Oleksii Vyacheslav; Unser, Michael; Hunziker, Patrick
2011-02-01
Many practical applications require the reconstruction of images from irregularly sampled data. The spline formalism offers an attractive framework for solving this problem; the currently available methods, however, are hard to deploy for large-scale interpolation problems in dimensions greater than two (3-D, 3-D+time) because of an exponential increase of their computational cost (curse of dimensionality). Here, we revisit the standard regularized least-squares formulation of the interpolation problem, and propose to perform the reconstruction in a uniform tensor-product B-spline basis as an alternative to the classical solution involving radial basis functions. Our analysis reveals that the underlying multilinear system of equations admits a tensor decomposition with an extreme sparsity of its one dimensional components. We exploit this property for implementing a parallel, memory-efficient system solver. We show that the computational complexity of the proposed algorithm is essentially linear in the number of measurements and that its dependency on the number of dimensions is significantly less than that of the original sparse matrix-based implementation. The net benefit is a substantial reduction in memory requirement and operation count when compared to standard matrix-based algorithms, so that even 4-D problems with millions of samples become computationally feasible on desktop PCs in reasonable time. After validating the proposed algorithm in 3-D and 4-D, we apply it to a concrete imaging problem: the reconstruction of medical ultrasound images (3-D+time) from a large set of irregularly sampled measurements, acquired by a fast rotating ultrasound transducer.
Diurnal microstructural variations in healthy adult brain revealed by diffusion tensor imaging.
Directory of Open Access Journals (Sweden)
Chunxiang Jiang
Full Text Available Biorhythm is a fundamental property of human physiology. Changes in the extracellular space induced by cell swelling in response to the neural activity enable the in vivo characterization of cerebral microstructure by measuring the water diffusivity using diffusion tensor imaging (DTI. To study the diurnal microstructural alterations of human brain, fifteen right-handed healthy adult subjects were recruited for DTI studies in two repeated sessions (8∶30 AM and 8∶30 PM within a 24-hour interval. Fractional anisotropy (FA, apparent diffusion coefficient (ADC, axial (λ// and radial diffusivity (λ⊥ were compared pixel by pixel between the sessions for each subject. Significant increased morning measurements in FA, ADC, λ// and λ⊥ were seen in a wide range of brain areas involving frontal, parietal, temporal and occipital lobes. Prominent evening dominant λ⊥ (18.58% was detected in the right inferior temporal and ventral fusiform gyri. AM-PM variation of λ⊥ was substantially left side hemisphere dominant (p<0.05, while no hemispheric preference was observed for the same analysis for ADC (p = 0.77, λ// (p = 0.08 or FA (p = 0.25. The percentage change of ADC, λ//, λ⊥, and FA were 1.59%, 2.15%, 1.20% and 2.84%, respectively, for brain areas without diurnal diffusivity contrast. Microstructural variations may function as the substrates of the phasic neural activities in correspondence to the environment adaptation in a light-dark cycle. This research provided a baseline for researches in neuroscience, sleep medicine, psychological and psychiatric disorders, and necessitates that diurnal effect should be taken into account in following up studies using diffusion tensor quantities.
Muscle changes detected with diffusion-tensor imaging after long-distance running.
Froeling, Martijn; Oudeman, Jos; Strijkers, Gustav J; Maas, Mario; Drost, Maarten R; Nicolay, Klaas; Nederveen, Aart J
2015-02-01
To develop a protocol for diffusion-tensor imaging (DTI) of the complete upper legs and to demonstrate feasibility of detection of subclinical sports-related muscle changes in athletes after strenuous exercise, which remain undetected by using conventional T2-weighted magnetic resonance (MR) imaging with fat suppression. The research was approved by the institutional ethics committee review board, and the volunteers provided written consent before the study. Five male amateur long-distance runners underwent an MR examination (DTI, T1-weighted MR imaging, and T2-weighted MR imaging with fat suppression) of both upper legs 1 week before, 2 days after, and 3 weeks after they participated in a marathon. The tensor eigenvalues (λ1, λ2, and λ3), the mean diffusivity, and the fractional anisotropy (FA) were derived from the DTI data. Data per muscle from the three time-points were compared by using a two-way mixed-design analysis of variance with a Bonferroni posthoc test. The DTI protocol allowed imaging of both complete upper legs with adequate signal-to-noise ratio and within a 20-minute imaging time. After the marathon, T2-weighted MR imaging revealed grade 1 muscle strains in nine of the 180 investigated muscles. The three eigenvalues, mean diffusivity, and FA were significantly increased (P muscle 2 days after running. Mean diffusivity and eigenvalues λ1 and λ2 were significantly (P muscles 2 days after the marathon. A feasible method for DTI measurements of the upper legs was developed that fully included frequently injured muscles, such as hamstrings, in one single imaging session. This study also revealed changes in DTI parameters that over time were not revealed by qualitative T2-weighted MR imaging with fat suppression. © RSNA, 2014.
Neji, Radhouène; Paragios, Nikolaos; Fleury, Gilles; Thiran, Jean-Philippe; Langs, Georg
2009-01-01
In this paper, we present a kernel-based approach to the clustering of diffusion tensors and fiber tracts. We propose to use a Mercer kernel over the tensor space where both spatial and diffusion information are taken into account. This kernel highlights implicitly the connectivity along fiber tracts. Tensor segmentation is performed using kernel-PCA compounded with a landmark-Isomap embedding and k-means clustering. Based on a soft fiber representation, we extend the tensor kernel to deal wi...
Innovative anisotropic phantoms for calibration of diffusion tensor imaging sequences.
Kłodowski, Krzysztof; Krzyżak, Artur Tadeusz
2016-05-01
The paper describes a novel type of anisotropic phantoms designed for b-matrix spatial distribution diffusion tensor imaging (BSD-DTI). Cubic plate anisotropic phantom, cylinder capillary phantom and water reference phantom are described as a complete set necessary for calibration, validation and normalization of BSD-DTI. An innovative design of the phantoms basing on enclosing the anisotropic cores in glass balls filled with liquid made for the first time possible BSD calibration with usage of echo planar imaging (EPI) sequence. Susceptibility artifacts prone to occur in EPI sequences were visibly reduced in the central region of the phantoms. The phantoms were designed for usage in a clinical scanner's head coil, but can be scaled for other coil or scanner types. The phantoms can be also used for a pre-calibration of imaging of other types of phantoms having more specific applications. Copyright © 2015 Elsevier Inc. All rights reserved.
Tensor RG calculations and quantum simulations near criticality
Meurice, Y; Tsai, Shan-Wen; Unmuth-Yockey, J; Yang, Li-Ping; Zhang, Jin
2016-01-01
We discuss the reformulation of the O(2) model with a chemical potential and the Abelian Higgs model on a 1+1 dimensional space-time lattice using the Tensor Renormalization Group (TRG) method. The TRG allows exact blocking and connects smoothly the classical Lagrangian approach to the quantum Hamiltonian approach. We calculate the entanglement entropy in the superfluid phase of the O(2) model and show that it approximately obeys the logarithmic Calabrese-Cardy scaling obtained from Conformal Field Theory (CFT). We calculate the Polyakov loop in the Abelian Higgs model and discuss the possibility of a deconfinement transition at finite volume. We propose Bose-Hubbard Hamiltonians implementable on optical lattices as quantum simulators for CFT models.
Some remarks on the genesis of scalar-tensor theories
Goenner, Hubert
2012-01-01
Between 1941 and 1962, scalar-tensor theories of gravitation were suggested four times by different scientists in four different countries. The earliest originator, the Swiss mathematician W. Scherrer, was virtually unknown until now whereas the chronologically latest pair gave their names to a multitude of publications on Brans-Dicke theory. P. Jordan, one of the pioneers of quantum mechanics theory, and Y. Thiry, a student of the mathematician A. Lichnerowicz, known by his book on celestial mechanics, complete the quartet. Diverse motivations for and conceptual interpretations of their theories will be discussed as well as relations among them. Also, external factors like language, citation habits, or closeness to the mainstream are considered. It will become clear why Brans-Dicke theory, although structurally a d\\'ej\\`a-vu, superseded all the other approaches.
Quantum-chemical insights from deep tensor neural networks
Schütt, Kristof T.; Arbabzadah, Farhad; Chmiela, Stefan; Müller, Klaus R.; Tkatchenko, Alexandre
2017-01-01
Learning from data has led to paradigm shifts in a multitude of disciplines, including web, text and image search, speech recognition, as well as bioinformatics. Can machine learning enable similar breakthroughs in understanding quantum many-body systems? Here we develop an efficient deep learning approach that enables spatially and chemically resolved insights into quantum-mechanical observables of molecular systems. We unify concepts from many-body Hamiltonians with purpose-designed deep tensor neural networks, which leads to size-extensive and uniformly accurate (1 kcal mol-1) predictions in compositional and configurational chemical space for molecules of intermediate size. As an example of chemical relevance, the model reveals a classification of aromatic rings with respect to their stability. Further applications of our model for predicting atomic energies and local chemical potentials in molecules, reliable isomer energies, and molecules with peculiar electronic structure demonstrate the potential of machine learning for revealing insights into complex quantum-chemical systems.
Schwinger-Fronsdal Theory of Abelian Tensor Gauge Fields
Directory of Open Access Journals (Sweden)
Sebastian Guttenberg
2008-09-01
Full Text Available This review is devoted to the Schwinger and Fronsdal theory of Abelian tensor gauge fields. The theory describes the propagation of free massless gauge bosons of integer helicities and their interaction with external currents. Self-consistency of its equations requires only the traceless part of the current divergence to vanish. The essence of the theory is given by the fact that this weaker current conservation is enough to guarantee the unitarity of the theory. Physically this means that only waves with transverse polarizations are propagating very far from the sources. The question whether such currents exist should be answered by a fully interacting theory. We also suggest an equivalent representation of the corresponding action.
Black hole accretion in scalar-tensor-vector gravity
John, Anslyn J
2016-01-01
We examine the accretion of matter onto a black hole in scalar--tensor--vector gravity (STVG). The gravitational constant is $G=G_{N} (1 + \\alpha)$ where $\\alpha$ is a parameter taken to be constant for static black holes in the theory. The STVG black hole is spherically symmetric and characterised by two event horizons. The matter falling into the black hole obeys the polytrope equation of state and passes through two critical points before entering the outer horizon. We obtain analytical expressions for the mass accretion rate as well as for the outer critical point, critical velocity and critical sound speed. Our results complement existing strong field tests like lensing and orbital motion and could be used in conjunction to determine observational constraints on STVG.
Measurement of Deuteron Tensor Polarization in Elastic Electron Scattering
Energy Technology Data Exchange (ETDEWEB)
Gustafsson, Kenneth K. [Univ. of Maryland, College Park, MD (United States)
2000-01-01
Nuclear physics traces it roots back to the very beginning of the last century. The concept of the nuclear atom was introduced by Rutherford around 1910. The discovery of the neutron Chadwick in 1932 gave us the concept of two nucleons: the proton and the neutron. The Jlab electron accelerator with its intermediate energy high current continuous wave beam combined with the Hall C high resolution electron spectrometer and a deutron recoil polarimeter provided experiment E94018 with the opportunity to study the deuteron electomagnetic structure, in particular to measure the tensor polarization observable t_{20}, at high four momentum transfers than ever before. This dissertation presents results of JLab experiment E94018.
Quantum-Chemical Insights from Deep Tensor Neural Networks
Schütt, Kristof T; Chmiela, Stefan; Müller, Klaus R; Tkatchenko, Alexandre
2016-01-01
Learning from data has led to paradigm shifts in a multitude of disciplines, including web, text, and image search, speech recognition, as well as bioinformatics. Can machine learning enable similar breakthroughs in understanding quantum many-body systems? Here we develop an efficient deep learning approach that enables spatially and chemically resolved insights into quantum-mechanical observables of molecular systems. We unify concepts from many-body Hamiltonians with purpose-designed deep tensor neural networks (DTNN), which leads to size-extensive and uniformly accurate (1 kcal/mol) predictions in compositional and configurational chemical space for molecules of intermediate size. As an example of chemical relevance, the DTNN model reveals a classification of aromatic rings with respect to their stability -- a useful property that is not contained as such in the training dataset. Further applications of DTNN for predicting atomic energies and local chemical potentials in molecules, reliable isomer energies...
Extended Nonnegative Tensor Factorisation Models for Musical Sound Source Separation
Directory of Open Access Journals (Sweden)
Derry FitzGerald
2008-01-01
Full Text Available Recently, shift-invariant tensor factorisation algorithms have been proposed for the purposes of sound source separation of pitched musical instruments. However, in practice, existing algorithms require the use of log-frequency spectrograms to allow shift invariance in frequency which causes problems when attempting to resynthesise the separated sources. Further, it is difficult to impose harmonicity constraints on the recovered basis functions. This paper proposes a new additive synthesis-based approach which allows the use of linear-frequency spectrograms as well as imposing strict harmonic constraints, resulting in an improved model. Further, these additional constraints allow the addition of a source filter model to the factorisation framework, and an extended model which is capable of separating mixtures of pitched and percussive instruments simultaneously.
Renormalized stress-energy tensor for stationary black holes
Levi, Adam
2016-01-01
We continue the presentation of the pragmatic mode-sum regularization (PMR) method for computing the renormalized stress-energy tensor (RSET). We show in detail how to employ the $t$-splitting variant of the method, which was first presented for $\\left\\langle\\phi^{2}\\right\\rangle_{ren}$, to compute the RSET in a stationary, asymptotically-flat background. This variant of the PMR method was recently used to compute the RSET for an evaporating spinning black hole. As an example for regularization, we demonstrate here the computation of the RSET for a minimally-coupled, massless scalar field on Schwarzschild background in all three vacuum states. We discuss future work and possible improvements of the regularization schemes in the PMR method.
Cosmologies in Horndeski's second-order vector-tensor theory
Barrow, John D; Yamamoto, Kei
2012-01-01
Horndeski derived a most general vector-tensor theory in which the vector field respects the gauge symmetry and the resulting dynamical equations are of second order. The action contains only one free parameter, $\\lambda$, that determines the strength of the non-minimal coupling between the gauge field and gravity. We investigate the cosmological consequences of this action and discuss observational constraints. For $\\lambda<0$ we identify singularities where the deceleration parameter diverges within a finite proper time. This effectively rules out any sensible cosmological application of the theory for a negative non-minimal coupling. We also find a range of parameter that gives a viable cosmology and study the phenomenology for this case. Observational constraints on the value of the coupling are rather weak since the interaction is higher-order in space-time curvature.
Emergent gravity from vanishing energy-momentum tensor
Carone, Christopher D.; Erlich, Joshua; Vaman, Diana
2017-03-01
A constraint of vanishing energy-momentum tensor is motivated by a variety of perspectives on quantum gravity. We demonstrate in a concrete example how this constraint leads to a metric-independent theory in which quantum gravity emerges as a nonperturbative artifact of regularization-scale physics. We analyze a scalar theory similar to the Dirac-Born-Infeld (DBI) theory with vanishing gauge fields, with the DBI Lagrangian modulated by a scalar potential. In the limit of a large number of scalars, we explicitly demonstrate the existence of a composite massless spin-2 graviton in the spectrum that couples to matter as in Einstein gravity. We comment on the cosmological constant problem and the generalization to theories with fermions and gauge fields.
Spin-Tensor-Momentum-Coupled Bose-Einstein Condensates
Luo, Xi-Wang; Sun, Kuei; Zhang, Chuanwei
2017-11-01
The recent experimental realization of spin-orbit coupling for ultracold atomic gases provides a powerful platform for exploring many interesting quantum phenomena. In these studies, spin represents the spin vector (spin 1 /2 or spin 1) and orbit represents the linear momentum. Here we propose a scheme to realize a new type of spin-tensor-momentum coupling (STMC) in spin-1 ultracold atomic gases. We study the ground state properties of interacting Bose-Einstein condensates with STMC and find interesting new types of stripe superfluid phases and multicritical points for phase transitions. Furthermore, STMC makes it possible to study quantum states with dynamical stripe orders that display density modulation with a long tunable period and high visibility, paving the way for the direct experimental observation of a new dynamical supersolidlike state. Our scheme for generating STMC can be generalized to other systems and may open the door for exploring novel quantum physics and device applications.
Moment Tensor Solutions for the Amatrice 2016 Seismic Sequence
Salimbeni, S.; Pondrelli, S.
2016-12-01
On August 24, 2016 a ML 6.0 earthquake struck central Italy region, nearly completely destroying some small ancient towns as Amatrice, Accumoli, Arquata and Pescara del Tronto. In the following days thousands of aftershocks have been recorded by the INGV National Seismometric Network, 16 of them with a magnitude greater than 4.0. A Quick RCMT solution has been rapidly computed for all of them and made available on the web. Within a few weeks a definitive RCMT solution is ready for all of them, plus one. For major events (and not only) of the Amatrice seismic sequence, several rapid moment tensor solutions have been produced by various groups, using different methods and dataset. Comparing QRCMTs with other similar products, it is evident a great similarity of focal mechanisms while on the contrary, the Mw have a clear variability. We discuss this difference.
Kaluza-Klein reduction and Bergmann-Wagoner bi-scalar general action of scalar-tensor gravity
Bamba, Kazuharu; Momeni, Davood; Myrzakulov, Ratbay
2014-01-01
We examine the Kaluza-Klein (KK) dimensional reduction from higher-dimensional space-time and the properties of the resultant Bergmann-Wagoner general action of scalar-tensor theories. With the analysis of the perturbations, we also investigate the stability of the anti-de Sitter (AdS) space-time in the $D\\in\\mathcal{N}$-dimensional Einstein gravity with the negative cosmological constant. Furthermore, we derive the conditions for the dimensional reduction to successfully be executed and pres...
Kaluza-Klein reduction and Bergmann-Wagoner bi-scalar general action of scalar-tensor gravity
Bamba, Kazuharu; Momeni, Davood; Myrzakulov, Ratbay
2015-07-01
We examine the Kaluza-Klein (KK) dimensional reduction from higher dimensional space-time and the properties of the resultant Bergmann-Wagoner general action of scalar-tensor theories. With the analysis of the perturbations, we also investigate the stability of the anti-de Sitter (AdS) space-time in the (D ∈ 𝒩)-dimensional Einstein gravity with the negative cosmological constant. Furthermore, we derive the conditions for the dimensional reduction to successfully be executed and present the KK compactification mechanism.
DEFF Research Database (Denmark)
Giménez, Mónica; Miranda, Maria J; Born, A Peter
2008-01-01
Twenty-seven preterm infants were compared to 10 full-term infants at term equivalent age using a voxel-based analysis of diffusion tensor imaging of the brain. Preterm infants exhibited higher fractional anisotropy values, which may suggest accelerated maturation, in the location of the sagittal...... to suggest that the increased intensity of stimulation associated with preterm birth may advance the process of white matter maturation in the human brain. Questions remain about whether these findings reflect acceleration of the process of white matter maturation generally, or localized alterations induced...
Energy Technology Data Exchange (ETDEWEB)
Witalis, E.A.
1965-12-15
Rigorous derivations are given of the basic equations and methods available for the analysis of transverse MHD flow when Hall currents are not suppressed. The gas flow is taken to be incompressible and viscous with uniform tensor conductivity and arbitrary magnetic Reynold's number. The magnetic field is perpendicular to the flow and has variable strength. Analytical solutions can be obtained either in terms of the induced magnetic field or from two types of electric potential. The relevant set of suitable simplifications, restrictive conditions and boundary value considerations for each method is given.
Expectation-Maximization Tensor Factorization for Practical Location Privacy Attacks
Directory of Open Access Journals (Sweden)
Murakami Takao
2017-10-01
Full Text Available Location privacy attacks based on a Markov chain model have been widely studied to de-anonymize or de-obfuscate mobility traces. An adversary can perform various kinds of location privacy attacks using a personalized transition matrix, which is trained for each target user. However, the amount of training data available to the adversary can be very small, since many users do not disclose much location information in their daily lives. In addition, many locations can be missing from the training traces, since many users do not disclose their locations continuously but rather sporadically. In this paper, we show that the Markov chain model can be a threat even in this realistic situation. Specifically, we focus on a training phase (i.e. mobility profile building phase and propose Expectation-Maximization Tensor Factorization (EMTF, which alternates between computing a distribution of missing locations (E-step and computing personalized transition matrices via tensor factorization (M-step. Since the time complexity of EMTF is exponential in the number of missing locations, we propose two approximate learning methods, one of which uses the Viterbi algorithm while the other uses the Forward Filtering Backward Sampling (FFBS algorithm. We apply our learning methods to a de-anonymization attack and a localization attack, and evaluate them using three real datasets. The results show that our learning methods significantly outperform a random guess, even when there is only one training trace composed of 10 locations per user, and each location is missing with probability 80% (i.e. even when users hardly disclose two temporally-continuous locations.
Dentinal tubules revealed with X-ray tensor tomography.
Jud, Christoph; Schaff, Florian; Zanette, Irene; Wolf, Johannes; Fehringer, Andreas; Pfeiffer, Franz
2016-09-01
Dentin is a mineralized material making up most of the tooth bulk. A system of microtubules, so called dentinal tubules, transverses it radially from the pulp chamber to the outside. This highly oriented structure leads to anisotropic mechanical properties directly connected to the tubules orientation and density: the ultimate tensile strength as well as the fracture toughness and the shear strength are largest perpendicular to dentinal tubules. Consequently, the fatigue strength depends on the direction of dentinal tubules, too. However, none of the existing techniques used to investigate teeth provide access to orientation and density of dentinal tubules for an entire specimen in a non-destructive way. In this paper, we measure a third molar human tooth both with conventional micro-CT and X-ray tensor tomography (XTT). While the achievable resolution in micro-CT is too low to directly resolve the dentinal tubules, we provide strong evidence that the direction and density of dentinal tubules can be indirectly measured by XTT, which exploits small-angle X-ray scattering to retrieve a 3D map of scattering tensors. We show that the mean directions of scattering structures correlate to the orientation of dentinal tubules and that the mean effective scattering strength provides an estimation of the relative density of dentinal tubules. Thus, this method could be applied to investigate the connection between tubule orientation and fatigue or tensile properties of teeth for a full sample without cutting one, non-representative peace of tooth out of the full sample. Copyright © 2016 The Academy of Dental Materials. All rights reserved.
Biocomputing: numerical simulation of glioblastoma growth using diffusion tensor imaging
Bondiau, Pierre-Yves; Clatz, Olivier; Sermesant, Maxime; Marcy, Pierre-Yves; Delingette, Herve; Frenay, Marc; Ayache, Nicholas
2008-02-01
Glioblastoma multiforma (GBM) is one of the most aggressive tumors of the central nervous system. It can be represented by two components: a proliferative component with a mass effect on brain structures and an invasive component. GBM has a distinct pattern of spread showing a preferential growth in the white fiber direction for the invasive component. By using the architecture of white matter fibers, we propose a new model to simulate the growth of GBM. This architecture is estimated by diffusion tensor imaging in order to determine the preferred direction for the diffusion component. It is then coupled with a mechanical component. To set up our growth model, we make a brain atlas including brain structures with a distinct response to tumor aggressiveness, white fiber diffusion tensor information and elasticity. In this atlas, we introduce a virtual GBM with a mechanical component coupled with a diffusion component. These two components are complementary, and can be tuned independently. Then, we tune the parameter set of our model with an MRI patient. We have compared simulated growth (initialized with the MRI patient) with observed growth six months later. The average and the odd ratio of image difference between observed and simulated images are computed. Displacements of reference points are compared to those simulated by the model. The results of our simulation have shown a good correlation with tumor growth, as observed on an MRI patient. Different tumor aggressiveness can also be simulated by tuning additional parameters. This work has demonstrated that modeling the complex behavior of brain tumors is feasible and will account for further validation of this new conceptual approach.
A newly discovered muscle: The tensor of the vastus intermedius.
Grob, K; Ackland, T; Kuster, M S; Manestar, M; Filgueira, L
2016-03-01
The quadriceps femoris is traditionally described as a muscle group composed of the rectus femoris and the three vasti. However, clinical experience and investigations of anatomical specimens are not consistent with the textbook description. We have found a second tensor-like muscle between the vastus lateralis (VL) and the vastus intermedius (VI), hereafter named the tensor VI (TVI). The aim of this study was to clarify whether this intervening muscle was a variation of the VL or the VI, or a separate head of the extensor apparatus. Twenty-six cadaveric lower limbs were investigated. The architecture of the quadriceps femoris was examined with special attention to innervation and vascularization patterns. All muscle components were traced from origin to insertion and their affiliations were determined. A TVI was found in all dissections. It was supplied by independent muscular and vascular branches of the femoral nerve and lateral circumflex femoral artery. Further distally, the TVI combined with an aponeurosis merging separately into the quadriceps tendon and inserting on the medial aspect of the patella. Four morphological types of TVI were distinguished: Independent-type (11/26), VI-type (6/26), VL-type (5/26), and Common-type (4/26). This study demonstrated that the quadriceps femoris is architecturally different from previous descriptions: there is an additional muscle belly between the VI and VL, which cannot be clearly assigned to the former or the latter. Distal exposure shows that this muscle belly becomes its own aponeurosis, which continues distally as part of the quadriceps tendon. © 2016 Wiley Periodicals, Inc.
Manninen, Otto; Laitinen, Teemu; Lehtimäki, Kimmo K; Tegelberg, Saara; Lehesjoki, Anna-Elina; Gröhn, Olli; Kopra, Outi
2014-01-01
Unverricht-Lundborg type progressive myoclonus epilepsy (EPM1, OMIM 254800) is an autosomal recessive disorder characterized by onset at the age of 6 to 16 years, incapacitating stimulus-sensitive myoclonus and tonic-clonic epileptic seizures. It is caused by mutations in the gene encoding cystatin B. Previously, widespread white matter changes and atrophy has been detected both in adult EPM1 patients and in 6-month-old cystatin B-deficient mice, a mouse model for the EPM1 disease. In order to elucidate the spatiotemporal dynamics of the brain atrophy and white matter changes in EPM1, we conducted longitudinal in vivo magnetic resonance imaging and ex vivo diffusion tensor imaging accompanied with tract-based spatial statistics analysis to compare volumetric changes and fractional anisotropy in the brains of 1 to 6 months of age cystatin B-deficient and control mice. The results reveal progressive but non-uniform volume loss of the cystatin B-deficient mouse brains, indicating that different neuronal populations possess distinct sensitivity to the damage caused by cystatin B deficiency. The diffusion tensor imaging data reveal early and progressive white matter alterations in cystatin B-deficient mice affecting all major tracts. The results also indicate that the white matter damage in the cystatin B-deficient brain is most likely secondary to glial activation and neurodegenerative events rather than a primary result of CSTB deficiency. The data also show that diffusion tensor imaging combined with TBSS analysis provides a feasible approach not only to follow white matter damage in neurodegenerative mouse models but also to detect fractional anisotropy changes related to normal white matter maturation and reorganisation.
Energy Technology Data Exchange (ETDEWEB)
Delgado Acosta, E.G.; Banda Guzman, V.M.; Kirchbach, M. [UASLP, Instituto de Fisica, San Luis Potosi (Mexico)
2015-03-01
We propose a general method for the description of arbitrary single spin-j states transforming according to (j, 0) + (0, j) carrier spaces of the Lorentz algebra in terms of Lorentz tensors for bosons, and tensor-spinors for fermions, and by means of second-order Lagrangians. The method allows to avoid the cumbersome matrix calculus and higher ∂{sup 2j} order wave equations inherent to the Weinberg-Joos approach. We start with reducible Lorentz tensor (tensor-spinor) representation spaces hosting one sole (j, 0) + (0, j) irreducible sector and design there a representation reduction algorithm based on one of the Casimir invariants of the Lorentz algebra. This algorithm allows us to separate neatly the pure spin-j sector of interest from the rest, while preserving the separate Lorentz and Dirac indexes. However, the Lorentz invariants are momentum independent and do not provide wave equations. Genuine wave equations are obtained by conditioning the Lorentz tensors under consideration to satisfy the Klein-Gordon equation. In so doing, one always ends up with wave equations and associated Lagrangians that are of second order in the momenta. Specifically, a spin-3/2 particle transforming as (3/2, 0) + (0, 3/2) is comfortably described by a second-order Lagrangian in the basis of the totally anti-symmetric Lorentz tensor-spinor of second rank, Ψ {sub [μν]}. Moreover, the particle is shown to propagate causally within an electromagnetic background. In our study of (3/2, 0) + (0, 3/2) as part of Ψ {sub [μν]} we reproduce the electromagnetic multipole moments known from the Weinberg-Joos theory. We also find a Compton differential cross-section that satisfies unitarity in forward direction. The suggested tensor calculus presents itself very computer friendly with respect to the symbolic software FeynCalc. (orig.)
Delgado Acosta, E. G.; Banda Guzmán, V. M.; Kirchbach, M.
2015-03-01
We propose a general method for the description of arbitrary single spin- j states transforming according to ( j, 0) ⊕ (0, j) carrier spaces of the Lorentz algebra in terms of Lorentz tensors for bosons, and tensor-spinors for fermions, and by means of second-order Lagrangians. The method allows to avoid the cumbersome matrix calculus and higher ∂2 j order wave equations inherent to the Weinberg-Joos approach. We start with reducible Lorentz tensor (tensor-spinor) representation spaces hosting one sole ( j, 0) ⊕ (0, j) irreducible sector and design there a representation reduction algorithm based on one of the Casimir invariants of the Lorentz algebra. This algorithm allows us to separate neatly the pure spin- j sector of interest from the rest, while preserving the separate Lorentz and Dirac indexes. However, the Lorentz invariants are momentum independent and do not provide wave equations. Genuine wave equations are obtained by conditioning the Lorentz tensors under consideration to satisfy the Klein-Gordon equation. In so doing, one always ends up with wave equations and associated Lagrangians that are of second order in the momenta. Specifically, a spin-3/2 particle transforming as (3/2, 0) ⊕ (0, 3/2) is comfortably described by a second-order Lagrangian in the basis of the totally anti-symmetric Lorentz tensor-spinor of second rank, Ψ [ μν]. Moreover, the particle is shown to propagate causally within an electromagnetic background. In our study of (3/2, 0) ⊕ (0, 3/2) as part of Ψ [ μν] we reproduce the electromagnetic multipole moments known from the Weinberg-Joos theory. We also find a Compton differential cross-section that satisfies unitarity in forward direction. The suggested tensor calculus presents itself very computer friendly with respect to the symbolic software FeynCalc.
Sugisaki, Kenji; Toyota, Kazuo; Sato, Kazunobu; Shiomi, Daisuke; Takui, Takeji
2017-11-15
Spin-orbit contributions to the zero-field splitting (ZFS) tensor (D SO tensor) of M III (acac) 3 complexes (M = V, Cr, Mn, Fe and Mo; acac = acetylacetonate anion) are evaluated by means of ab initio (a hybrid CASSCF/MRMP2) and DFT (Pederson-Khanna (PK) and natural orbital-based Pederson-Khanna (NOB-PK)) methods, focusing on the behaviour of DFT-based approaches to the D SO tensors against the valence d-electron configurations of the transition metal ions in octahedral coordination. Both the DFT-based approaches reproduce trends in the D tensors. Significantly, the differences between the theoretical and experimental D (D = D ZZ - (D XX + D YY )/2) values are smaller in NOB-PK than in PK, emphasising the usefulness of the natural orbital-based approach to the D tensor calculations of transition metal ion complexes. In the case of d 2 and d 4 electronic configurations, the D SO (NOB-PK) values are considerably underestimated in the absolute magnitude, compared with the experimental ones. The D SO tensor analysis based on the orbital region partitioning technique (ORPT) revealed that the D SO contributions attributed to excitations from the singly occupied region (SOR) to the unoccupied region (UOR) are significantly underestimated in the DFT-based approaches to all the complexes under study. In the case of d 3 and d 5 configurations, the (SOR → UOR) excitations contribute in a nearly isotropic manner, which causes fortuitous error cancellations in the DFT-based D SO values. These results indicate that more efforts to develop DFT frameworks should be directed towards the reproduction of quantitative D SO tensors of transition metal complexes with various electronic configurations and local symmetries around metal ions.
A tensor-based subspace approach for bistatic MIMO radar in spatial colored noise.
Wang, Xianpeng; Wang, Wei; Li, Xin; Wang, Junxiang
2014-02-25
In this paper, a new tensor-based subspace approach is proposed to estimate the direction of departure (DOD) and the direction of arrival (DOA) for bistatic multiple-input multiple-output (MIMO) radar in the presence of spatial colored noise. Firstly, the received signals can be packed into a third-order measurement tensor by exploiting the inherent structure of the matched filter. Then, the measurement tensor can be divided into two sub-tensors, and a cross-covariance tensor is formulated to eliminate the spatial colored noise. Finally, the signal subspace is constructed by utilizing the higher-order singular value decomposition (HOSVD) of the cross-covariance tensor, and the DOD and DOA can be obtained through the estimation of signal parameters via rotational invariance technique (ESPRIT) algorithm, which are paired automatically. Since the multidimensional inherent structure and the cross-covariance tensor technique are used, the proposed method provides better angle estimation performance than Chen's method, the ESPRIT algorithm and the multi-SVD method. Simulation results confirm the effectiveness and the advantage of the proposed method.
A Tensor-Based Subspace Approach for Bistatic MIMO Radar in Spatial Colored Noise
Directory of Open Access Journals (Sweden)
Xianpeng Wang
2014-02-01
Full Text Available In this paper, a new tensor-based subspace approach is proposed to estimate the direction of departure (DOD and the direction of arrival (DOA for bistatic multiple-input multiple-output (MIMO radar in the presence of spatial colored noise. Firstly, the received signals can be packed into a third-order measurement tensor by exploiting the inherent structure of the matched filter. Then, the measurement tensor can be divided into two sub-tensors, and a cross-covariance tensor is formulated to eliminate the spatial colored noise. Finally, the signal subspace is constructed by utilizing the higher-order singular value decomposition (HOSVD of the cross-covariance tensor, and the DOD and DOA can be obtained through the estimation of signal parameters via rotational invariance technique (ESPRIT algorithm, which are paired automatically. Since the multidimensional inherent structure and the cross-covariance tensor technique are used, the proposed method provides better angle estimation performance than Chen’s method, the ESPRIT algorithm and the multi-SVD method. Simulation results confirm the effectiveness and the advantage of the proposed method.
Hartono, Albert; Lu, Qingda; Henretty, Thomas; Krishnamoorthy, Sriram; Zhang, Huaijian; Baumgartner, Gerald; Bernholdt, David E.; Nooijen, Marcel; Pitzer, Russell; Ramanujam, J.; Sadayappan, P.
2009-09-01
Complex tensor contraction expressions arise in accurate electronic structure models in quantum chemistry, such as the coupled cluster method. This paper addresses two complementary aspects of performance optimization of such tensor contraction expressions. Transformations using algebraic properties of commutativity and associativity can be used to significantly decrease the number of arithmetic operations required for evaluation of these expressions. The identification of common subexpressions among a set of tensor contraction expressions can result in a reduction of the total number of operations required to evaluate the tensor contractions. The first part of the paper describes an effective algorithm for operation minimization with common subexpression identification and demonstrates its effectiveness on tensor contraction expressions for coupled cluster equations. The second part of the paper highlights the importance of data layout transformation in the optimization of tensor contraction computations on modern processors. A number of considerations, such as minimization of cache misses and utilization of multimedia vector instructions, are discussed. A library for efficient index permutation of multidimensional tensors is described, and experimental performance data is provided that demonstrates its effectiveness.
Tri-Clustered Tensor Completion for Social-Aware Image Tag Refinement.
Tang, Jinhui; Shu, Xiangbo; Qi, Guo-Jun; Li, Zechao; Wang, Meng; Yan, Shuicheng; Jain, Ramesh
2017-08-01
Social image tag refinement, which aims to improve tag quality by automatically completing the missing tags and rectifying the noise-corrupted ones, is an essential component for social image search. Conventional approaches mainly focus on exploring the visual and tag information, without considering the user information, which often reveals important hints on the (in)correct tags of social images. Towards this end, we propose a novel tri-clustered tensor completion framework to collaboratively explore these three kinds of information to improve the performance of social image tag refinement. Specifically, the inter-relations among users, images and tags are modeled by a tensor, and the intra-relations between users, images and tags are explored by three regularizations respectively. To address the challenges of the super-sparse and large-scale tensor factorization that demands expensive computing and memory cost, we propose a novel tri-clustering method to divide the tensor into a certain number of sub-tensors by simultaneously clustering users, images and tags into a bunch of tri-clusters. And then we investigate two strategies to complete these sub-tensors by considering (in)dependence between the sub-tensors. Experimental results on a real-world social image database demonstrate the superiority of the proposed method compared with the state-of-the-art methods.
Advanced fit of the diffusion kurtosis tensor by directional weighting and regularization.
Kuder, Tristan A; Stieltjes, Bram; Bachert, Peter; Semmler, Wolfhard; Laun, Frederik B
2012-05-01
The diffusional kurtosis is an indicator for diffusion restrictions in biological tissue. It is observed experimentally that the kurtosis is largest for directions perpendicular to the fiber direction in white matter. The directional dependence of the kurtosis can be described by the diffusion kurtosis tensor. Since the intention of diffusion kurtosis imaging is to detect diffusion restrictions, the fit of the kurtosis tensor should be dominated by directions perpendicular to the fibers. In this work, it is shown that the basic approach, which is solving the occurring linear system by a pseudoinverse matrix, may completely fail in this regard if the diffusion is highly anisotropic. This problem is solved by adapting the weights of the fit--and thus emphasizing directions of restricted water motion--using a direct fit of the kurtosis tensor to the measured kurtosis values. Moreover, due to its large number of degrees of freedom, the kurtosis tensor can assume complicated shapes resulting in a fit which is sensitive to noise. This article demonstrates that the quality of the kurtosis tensor calculation can be further improved if the fit is regularized by suppressing too large and too small kurtosis tensor values and thus restricting the possible tensor shapes. Copyright © 2011 Wiley Periodicals, Inc.
A Tensor-Based Subspace Approach for Bistatic MIMO Radar in Spatial Colored Noise
Wang, Xianpeng; Wang, Wei; Li, Xin; Wang, Junxiang
2014-01-01
In this paper, a new tensor-based subspace approach is proposed to estimate the direction of departure (DOD) and the direction of arrival (DOA) for bistatic multiple-input multiple-output (MIMO) radar in the presence of spatial colored noise. Firstly, the received signals can be packed into a third-order measurement tensor by exploiting the inherent structure of the matched filter. Then, the measurement tensor can be divided into two sub-tensors, and a cross-covariance tensor is formulated to eliminate the spatial colored noise. Finally, the signal subspace is constructed by utilizing the higher-order singular value decomposition (HOSVD) of the cross-covariance tensor, and the DOD and DOA can be obtained through the estimation of signal parameters via rotational invariance technique (ESPRIT) algorithm, which are paired automatically. Since the multidimensional inherent structure and the cross-covariance tensor technique are used, the proposed method provides better angle estimation performance than Chen's method, the ESPRIT algorithm and the multi-SVD method. Simulation results confirm the effectiveness and the advantage of the proposed method. PMID:24573313
An efficient tensor transpose algorithm for multicore CPU, Intel Xeon Phi, and NVidia Tesla GPU
Lyakh, Dmitry I.
2015-04-01
An efficient parallel tensor transpose algorithm is suggested for shared-memory computing units, namely, multicore CPU, Intel Xeon Phi, and NVidia GPU. The algorithm operates on dense tensors (multidimensional arrays) and is based on the optimization of cache utilization on x86 CPU and the use of shared memory on NVidia GPU. From the applied side, the ultimate goal is to minimize the overhead encountered in the transformation of tensor contractions into matrix multiplications in computer implementations of advanced methods of quantum many-body theory (e.g., in electronic structure theory and nuclear physics). A particular accent is made on higher-dimensional tensors that typically appear in the so-called multireference correlated methods of electronic structure theory. Depending on tensor dimensionality, the presented optimized algorithms can achieve an order of magnitude speedup on x86 CPUs and 2-3 times speedup on NVidia Tesla K20X GPU with respect to the naïve scattering algorithm (no memory access optimization). The tensor transpose routines developed in this work have been incorporated into a general-purpose tensor algebra library (TAL-SH).
Monitoring the refinement of crystal structures with (15)N solid-state NMR shift tensor data.
Kalakewich, Keyton; Iuliucci, Robbie; Mueller, Karl T; Eloranta, Harriet; Harper, James K
2015-11-21
The (15)N chemical shift tensor is shown to be extremely sensitive to lattice structure and a powerful metric for monitoring density functional theory refinements of crystal structures. These refinements include lattice effects and are applied here to five crystal structures. All structures improve based on a better agreement between experimental and calculated (15)N tensors, with an average improvement of 47.0 ppm. Structural improvement is further indicated by a decrease in forces on the atoms by 2-3 orders of magnitude and a greater similarity in atom positions to neutron diffraction structures. These refinements change bond lengths by more than the diffraction errors including adjustments to X-Y and X-H bonds (X, Y = C, N, and O) of 0.028 ± 0.002 Å and 0.144 ± 0.036 Å, respectively. The acquisition of (15)N tensors at natural abundance is challenging and this limitation is overcome by improved (1)H decoupling in the FIREMAT method. This decoupling dramatically narrows linewidths, improves signal-to-noise by up to 317%, and significantly improves the accuracy of measured tensors. A total of 39 tensors are measured with shifts distributed over a range of more than 400 ppm. Overall, experimental (15)N tensors are at least 5 times more sensitive to crystal structure than (13)C tensors due to nitrogen's greater polarizability and larger range of chemical shifts.
Tensor numerical methods in quantum chemistry: from Hartree-Fock to excitation energies.
Khoromskaia, Venera; Khoromskij, Boris N
2015-12-21
We resume the recent successes of the grid-based tensor numerical methods and discuss their prospects in real-space electronic structure calculations. These methods, based on the low-rank representation of the multidimensional functions and integral operators, first appeared as an accurate tensor calculus for the 3D Hartree potential using 1D complexity operations, and have evolved to entirely grid-based tensor-structured 3D Hartree-Fock eigenvalue solver. It benefits from tensor calculation of the core Hamiltonian and two-electron integrals (TEI) in O(n log n) complexity using the rank-structured approximation of basis functions, electron densities and convolution integral operators all represented on 3D n × n × n Cartesian grids. The algorithm for calculating TEI tensor in a form of the Cholesky decomposition is based on multiple factorizations using algebraic 1D "density fitting" scheme, which yield an almost irreducible number of product basis functions involved in the 3D convolution integrals, depending on a threshold ε > 0. The basis functions are not restricted to separable Gaussians, since the analytical integration is substituted by high-precision tensor-structured numerical quadratures. The tensor approaches to post-Hartree-Fock calculations for the MP2 energy correction and for the Bethe-Salpeter excitation energies, based on using low-rank factorizations and the reduced basis method, were recently introduced. Another direction is towards the tensor-based Hartree-Fock numerical scheme for finite lattices, where one of the numerical challenges is the summation of electrostatic potentials of a large number of nuclei. The 3D grid-based tensor method for calculation of a potential sum on a L × L × L lattice manifests the linear in L computational work, O(L), instead of the usual O(L(3) log L) scaling by the Ewald-type approaches.
Projectors and seed conformal blocks for traceless mixed-symmetry tensors
Costa, Miguel S.; Penedones, João; Trevisani, Emilio
2016-01-01
In this paper we derive the projectors to all irreducible SO(d) representations (traceless mixed-symmetry tensors) that appear in the partial wave decomposition of a conformal correlator of four stress-tensors in d dimensions. These projectors are given in a closed form for arbitrary length $l_1$ of the first row of the Young diagram. The appearance of Gegenbauer polynomials leads directly to recursion relations in $l_1$ for seed conformal blocks. Further results include a differential operator that generates the projectors to traceless mixed-symmetry tensors and the general normalization constant of the shadow operator.
arXiv Tensor to scalar ratio from single field magnetogenesis
Giovannini, Massimo
2017-08-10
The tensor to scalar ratio is affected by the evolution of the large-scale gauge fields potentially amplified during an inflationary stage of expansion. After deriving the exact evolution equations for the scalar and tensor modes of the geometry in the presence of dynamical gauge fields, it is shown that the tensor to scalar ratio is bounded from below by the dominance of the adiabatic contribution and it cannot be smaller than one thousands whenever the magnetogenesis is driven by a single inflaton field.
Bartel, J.; Bencheikh, K.; Meyer, J.
2008-02-01
For a one-body Hamiltonian obtained from the energy-density functional associated with a Skyrme effective interaction, including a tensor force, semiclassical functional densities are derived in the framework of the Extended Thomas-Fermi method, in spherical symmetry, for the kinetic energy and spin-orbit density. The structure of the self-consistent mean-field potentials constructed with such semiclassical functionals is studied. The impact of the tensor force in particular on the spin-orbit form factor clearly indicates the necessity of including such tensor-force terms in the theoretical description of atomic nuclei and their possible influence on the shell structure of exotic nuclei.
A solution for tensor reduction of one-loop N-point functions with N{>=}6
Energy Technology Data Exchange (ETDEWEB)
Fleischer, J. [Bielefeld Univ. (Germany). Fakultaet fuer Physik; Riemann, T. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany)
2011-11-15
Collisions at the LHC produce many-particle final states, and for precise predictions the one-loop N-point corrections are needed. We study here the tensor reduction for Feynman integrals with N{>=}6. A general, recursive solution by Binoth et al. expresses N-point Feynman integrals of rank R in terms of (N-1)-point Feynman integrals of rank (R-1) (for N{>=}6). We show that the coefficients can be obtained analytically from suitable representations of the metric tensor. Contractions of the tensor integrals with external momenta can be efficiently expressed as well. We consider our approach particularly well suited for automatization. (orig.)
Haakma, Wieke; Dik, Pieter; ten Haken, Bennie; Froeling, Martijn; Nievelstein, Rutger A J; Cuppen, Inge; de Jong, Tom P V M; Leemans, Alexander
2014-09-01
It is still largely unknown how neural tube defects in spina bifida affect the nerves at the level of the sacral plexus. Visualizing the sacral plexus in 3 dimensions could improve our anatomical understanding of neurological problems in patients with spina bifida. We investigated anatomical and microstructural properties of the sacral plexus of patients with spina bifida using diffusion tensor imaging and fiber tractography. Ten patients 8 to 16 years old with spina bifida underwent diffusion tensor imaging on a 3 Tesla magnetic resonance imaging system. Anatomical 3-dimensional reconstructions were obtained of the sacral plexus of the 10 patients. Fiber tractography was performed with a diffusion magnetic resonance imaging toolbox to determine fractional anisotropy, and mean, axial and radial diffusivity in the sacral plexus of the patients. Results were compared to 10 healthy controls. Nerves of patients with spina bifida showed asymmetry and disorganization to a large extent compared to those of healthy controls. Especially at the myelomeningocele level it was difficult to find a connection with the cauda equina. Mean, axial and radial diffusivity values at S1-S3 were significantly lower in patients. To our knowledge this 3 Tesla magnetic resonance imaging study showed for the first time sacral plexus asymmetry and disorganization in 10 patients with spina bifida using diffusion tensor imaging and fiber tractography. The observed difference in diffusion values indicates that these methods may be used to identify nerve abnormalities. We expect that this technique could provide a valuable contribution to better analysis and understanding of the problems of patients with spina bifida in the future. Copyright © 2014 American Urological Association Education and Research, Inc. Published by Elsevier Inc. All rights reserved.
Directory of Open Access Journals (Sweden)
Hyeong Jun Tak
2016-01-01
Full Text Available We investigated the radiologic developmental process of the arcuate fasciculus (AF using subcomponent diffusion tensor imaging (DTI analysis in typically developing volunteers. DTI data were acquired from 96 consecutive typically developing children, aged 0-14 years. AF subcomponents, including the posterior, anterior, and direct AF tracts were analyzed. Success rates of analysis (AR and fractional anisotropy (FA values of each subcomponent tract were measured and compared. AR of all subcomponent tracts, except the posterior, showed a significant increase with aging (P < 0.05. Subcomponent tracts had a specific developmental sequence: First, the posterior AF tract, second, the anterior AF tract, and last, the direct AF tract in identical hemispheres. FA values of all subcomponent tracts, except right direct AF tract, showed correlation with subject′s age (P < 0.05. Increased AR and FA values were observed in female subjects in young age (0-2 years group compared with males (P < 0.05. The direct AF tract showed leftward hemispheric asymmetry and this tendency showed greater consolidation in older age (3-14 years groups (P < 0.05. These findings demonstrated the radiologic developmental patterns of the AF from infancy to adolescence using subcomponent DTI analysis. The AF showed a specific developmental sequence, sex difference in younger age, and hemispheric asymmetry in older age.
Brandão, Sofia; Parente, Marco; Silva, Elisabete; Da Roza, Thuane; Mascarenhas, Teresa; Leitão, João; Cunha, João; Natal Jorge, Renato; Nunes, Rita Gouveia
2017-05-01
Biomechanical analysis of pelvic floor dysfunction requires knowledge of certain biomechanical parameters, such as muscle fiber direction, in order to adequately model function. Magnetic resonance (MR) diffusion tensor imaging (DTI) provides an estimate of overall muscle fiber directionality based on the mathematical description of water diffusivity. This work aimed at evaluating the concurrence between pubovisceralis muscle fiber representations obtained from DTI, and the maximum principal stress lines obtained through the finite element method. Seven datasets from axial T2-weighted images were used to build numerical models, and muscle fiber orientation estimated from the DT images. The in-plane projections of the first eigenvector of both vector fields describing muscle fiber orientation were extracted and compared. The directional consistency was evaluated by calculating the angle between the normalized vectors for the entire muscle and also for the right and left insertions, middle portions, and anorectal area. The values varied between 28° ± 6 (right middle portion) and 34° ± 9 (anorectal area), and were higher than the angular precision of the DT estimates, evaluated using wild bootstrapping analysis. Angular dispersion ranged from 17° ± 4 (left middle portion) to 23° ± 5 (anorectal area). Further studies are needed to examine acceptability of these differences when integrating the vectors estimated from DTI in the numerical analysis.
Diffusion Tensor Imaging in Autism Spectrum Disorder: A Review
Travers, BG; Adluru, N; Ennis, C; Tromp, DPM; Destiche, D; Doran, S; Bigler, ED; Lange, N; Lainhart, JE; Alexander, AL
2012-01-01
Lay Abstract White matter tracts are like the “highways” of the brain, allowing for fast and efficient communication among diverse brain regions. The purpose of this paper is to review the results of autism studies that have used Diffusion Tensor Imaging (DTI), which is a neuroimaging method that allows us to examine the structure and integrity of these white matter tracts. From the 48 studies we reviewed, persons with ASD tended to have decreased white matter integrity spanning across many regions of the brain but most consistently in regions such as the corpus callosum (connecting the left and right hemispheres and associated with motor skill and complex information processing), the cingulum bundles (connecting regions along the middle-line of the brain with important frontal projections and associated with executive function), and white matter tracts that pass through the temporal lobe (connecting temporal lobe regions with other brain regions and associated with social functioning). The pattern of results in these studies suggests that the white matter tracts may be atypical in persons with ASD. Additionally, the review suggests that people with ASD may not exhibit the typical left-greater-than-right-brain asymmetry in white matter integrity compared to people with typical development. White matter alterations in persons with ASD are a target of emerging interventions and may help identify the brain basis of individual differences in this population. Scientific Abstract White matter tracts of the brain allow neurons and neuronal networks to communicate and function with high efficiency. The aim of this review is to briefly introduce Diffusion Tensor Imaging (DTI) methods that examine white matter tracts and then to give an overview of the studies that have investigated white matter integrity in the brains of individuals with Autism Spectrum Disorder (ASD). From the 48 studies we reviewed, persons with ASD tended to have decreased fractional anisotropy and
Diffusion tensor imaging of the brainstem in children with achondroplasia.
Bosemani, Thangamadhan; Orman, Gunes; Carson, Kathryn A; Meoded, Avner; Huisman, Thierry A G M; Poretti, Andrea
2014-11-01
The aims of this study were to compare, using diffusion tensor imaging (DTI) of the brainstem, microstructural integrity of the white matter in children with achondroplasia and age-matched participants and to correlate the severity of craniocervical junction (CCJ) narrowing and neurological findings with DTI scalars in children with achondroplasia. This study also aimed to assess the potential role of fibroblast growth factor receptor type 3 on white matter microstructure. Diffusion tensor imaging was performed using a 1.5T magnetic resonance scanner and balanced pairs of diffusion gradients along 20 non-collinear directions. Measurements were obtained from regions of interest, sampled in each pontine corticospinal tract (CST), medial lemniscus, and middle cerebellar peduncle, as well as in the lower brainstem and centrum semiovale, for fractional anisotropy and for mean, axial, and radial diffusivity. In addition, a severity score for achondroplasia was assessed by measuring CCJ narrowing. Eight patients with achondroplasia (seven males, one female; mean age 5y 6mo, range 1y 1mo-15y 1mo) and eight age- and sex-matched comparison participants (mean age 5y 2mo, range 1y 1mo-14y 11mo) were included in this study. Fractional anisotropy was lower and mean diffusivity and radial diffusivity were higher in the lower brainstem of patients with achondroplasia than in age-matched comparison participants. The CST and middle cerebellar peduncle of the participants showed increases in mean, axial, and radial diffusivity. Fractional anisotropy in the lower brainstem was negatively correlated with the degree of CCJ narrowing. No differences in the DTI metrics of the centrum semiovale were observed between the two groups. The reduction in fractional anisotropy and increase in diffusivities in the lower brainstem of participants with achondroplasia may reflect secondary encephalomalacic degeneration and cavitation of the affected white matter tracts as shown by histology. In
Directory of Open Access Journals (Sweden)
Steven M. Nesbit
2006-06-01
Full Text Available This paper discusses the inertia tensors of tennis rackets and their influence on the elbow swing torques in a forehand motion, the loadings transmitted to the elbow from central and eccentric impacts, and the racket acceleration responses from central and eccentric impacts. Inertia tensors of various rackets with similar mass and mass center location were determined by an inertia pendulum and were found to vary considerably in all three orthogonal directions. Tennis swing mechanics and impact analyses were performed using a computer model comprised of a full-body model of a human, a parametric model of the racket, and an impact function. The swing mechanics analysis of a forehand motion determined that inertia values had a moderate linear effect on the pronation-supination elbow torques required to twist the racket, and a minor effect on the flexion-extension and valgus-varus torques. The impact analysis found that mass center inertia values had a considerable effect on the transmitted torques for both longitudinal and latitudinal eccentric impacts and significantly affected all elbow torque components. Racket acceleration responses to central and eccentric impacts were measured experimentally and found to be notably sensitive to impact location and mass center inertia values
Hand-waving and interpretive dance: an introductory course on tensor networks
Bridgeman, Jacob C.; Chubb, Christopher T.
2017-06-01
The curse of dimensionality associated with the Hilbert space of spin systems provides a significant obstruction to the study of condensed matter systems. Tensor networks have proven an important tool in attempting to overcome this difficulty in both the numerical and analytic regimes. These notes form the basis for a seven lecture course, introducing the basics of a range of common tensor networks and algorithms. In particular, we cover: introductory tensor network notation, applications to quantum information, basic properties of matrix product states, a classification of quantum phases using tensor networks, algorithms for finding matrix product states, basic properties of projected entangled pair states, and multiscale entanglement renormalisation ansatz states. The lectures are intended to be generally accessible, although the relevance of many of the examples may be lost on students without a background in many-body physics/quantum information. For each lecture, several problems are given, with worked solutions in an ancillary file.
Energy Technology Data Exchange (ETDEWEB)
Orús, Román, E-mail: roman.orus@uni-mainz.de
2014-10-15
This is a partly non-technical introduction to selected topics on tensor network methods, based on several lectures and introductory seminars given on the subject. It should be a good place for newcomers to get familiarized with some of the key ideas in the field, specially regarding the numerics. After a very general introduction we motivate the concept of tensor network and provide several examples. We then move on to explain some basics about Matrix Product States (MPS) and Projected Entangled Pair States (PEPS). Selected details on some of the associated numerical methods for 1d and 2d quantum lattice systems are also discussed. - Highlights: • A practical introduction to selected aspects of tensor network methods is presented. • We provide analytical examples of MPS and 2d PEPS. • We provide basic aspects on several numerical methods for MPS and 2d PEPS. • We discuss a number of applications of tensor network methods from a broad perspective.
Flat-space holography and stress tensor of Kerr black hole
Energy Technology Data Exchange (ETDEWEB)
Baghchesaraei, Omid, E-mail: omidbaghchesaraei@gmail.com [Department of Physics, Shahid Beheshti University, G.C., Evin, Tehran 19839 (Iran, Islamic Republic of); Fareghbal, Reza, E-mail: r_fareghbal@sbu.ac.ir [Department of Physics, Shahid Beheshti University, G.C., Evin, Tehran 19839 (Iran, Islamic Republic of); Izadi, Yousef, E-mail: yizadi2015@fau.edu [Department of Physics, Florida Atlantic University, Boca Raton, FL 33431 (United States)
2016-09-10
We propose a stress tensor for the Kerr black hole written in the Boyer–Lindquist coordinate. To achieve this, we use the dictionary of the Flat/CCFT correspondence and take the flat-space limit from the quasi-local stress tensor of the four-dimensional Kerr–AdS black hole. The proposed stress tensor yields the correct values for the mass and angular momentum of the Kerr black hole at spatial infinity. We also calculate some components of the energy momentum tensor of the three dimensional CCFT and show that they are consistent with the holographic calculation of the Kerr black hole. The calculation we present in this paper is another confirmation for the Flat/CCFT proposal.
Energy Technology Data Exchange (ETDEWEB)
Peng, Bo; Kowalski, Karol
2017-03-01
In this letter, we introduce the reverse Cuthill-McKee (RCM) algorithm, which is often used for the bandwidth reduction of sparse tensors, to transform the two-electron integral tensors to their block diagonal forms. By further applying the pivoted Cholesky decomposition (CD) on each of the diagonal blocks, we are able to represent the high-dimensional two-electron integral tensors in terms of permutation matrices and low-rank Cholesky vectors. This representation facilitates the low-rank factorization of the high-dimensional tensor contractions that are usually encountered in post-Hartree-Fock calculations. In this letter, we discuss the second-order Møller-Plesset (MP2) method and linear coupled- cluster model with doubles (L-CCD) as two simple examples to demonstrate the efficiency of the RCM-CD technique in representing two-electron integrals in a compact form.
The nonabelian tensor square of a crystallographic group with quaternion point group of order eight
Afiqah Mohammad, Siti; Haniza Sarmin, Nor; Izzati Mat Hassim, Hazzirah
2017-10-01
A crystallographic group is a discrete subgroup of the set of isometries of Euclidean space where the quotient space is compact. A torsion free crystallographic group, or also known as a Bieberbach group has the symmetry structure that will reveal its algebraic properties. One of the algebraic properties is its nonabelian tensor square. The nonabelian tensor square is a special case of the nonabelian tensor product where the product is defined if the two groups act on each other in a compatible way and their action is taken to be conjugation. Meanwhile, Bieberbach group with quaternion point group of order eight is a polycyclic group. In this paper, by using the polycyclic method, the computation of the nonabelian tensor square of this group will be shown.
Energy Technology Data Exchange (ETDEWEB)
Schatz, Martin D. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Kolda, Tamara G. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); van de Geijn, Robert [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
2015-09-01
Large-scale datasets in computational chemistry typically require distributed-memory parallel methods to perform a special operation known as tensor contraction. Tensors are multidimensional arrays, and a tensor contraction is akin to matrix multiplication with special types of permutations. Creating an efficient algorithm and optimized im- plementation in this domain is complex, tedious, and error-prone. To address this, we develop a notation to express data distributions so that we can apply use automated methods to find optimized implementations for tensor contractions. We consider the spin-adapted coupled cluster singles and doubles method from computational chemistry and use our methodology to produce an efficient implementation. Experiments per- formed on the IBM Blue Gene/Q and Cray XC30 demonstrate impact both improved performance and reduced memory consumption.
Tensor decomposition-based sparsity divergence index for hyperspectral anomaly detection.
Zhang, Lili; Zhao, Chunhui
2017-09-01
Recently, some methods exploiting both the spatial and spectral features have drawn increasing attention in hyperspectral anomaly detection (AD) and they perform well. In addition, a tensor decomposition-based (TenB) algorithm treating the hyperspectral dataset as a three-order tensor (two modes for space and one mode for spectra) has been proposed to further improve the performance for AD. In this paper, a method using the sparsity divergence index (SDI) based on tensor decomposition (SDI-TD) is proposed. First, three modes of the hyperspectral dataset are obtained by tensor decomposition. Then, low-rank and sparse matrix decomposition is employed separately along the three modes and three sparse matrices are acquired. Finally, SDIs based on the three sparse matrices along the three modes are obtained, and the final result is generated by using the joint SDI. Experiments tested on the real and synthetic hyperspectral dataset reveal that the proposed SDI-TD performs better than the comparison algorithms.