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...
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.
Joint Tensor Feature Analysis For Visual Object Recognition.
Wong, Wai Keung; Lai, Zhihui; Xu, Yong; Wen, Jiajun; Ho, Chu Po
2015-11-01
Tensor-based object recognition has been widely studied in the past several years. This paper focuses on the issue of joint feature selection from the tensor data and proposes a novel method called joint tensor feature analysis (JTFA) for tensor feature extraction and recognition. In order to obtain a set of jointly sparse projections for tensor feature extraction, we define the modified within-class tensor scatter value and the modified between-class tensor scatter value for regression. The k-mode optimization technique and the L(2,1)-norm jointly sparse regression are combined together to compute the optimal solutions. The convergent analysis, computational complexity analysis and the essence of the proposed method/model are also presented. It is interesting to show that the proposed method is very similar to singular value decomposition on the scatter matrix but with sparsity constraint on the right singular value matrix or eigen-decomposition on the scatter matrix with sparse manner. Experimental results on some tensor datasets indicate that JTFA outperforms some well-known tensor feature extraction and selection algorithms.
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.
Tensor harmonic analysis on homogenous space
International Nuclear Information System (INIS)
Wrobel, G.
1997-01-01
The Hilbert space of tensor functions on a homogenous space with the compact stability group is considered. The functions are decomposed onto a sum of tensor plane waves (defined in the text), components of which are transformed by irreducible representations of the appropriate transformation group. The orthogonality relation and the completeness relation for tensor plane waves are found. The decomposition constitutes a unitary transformation, which allows to obtain the Parseval equality. The Fourier components can be calculated by means of the Fourier transformation, the form of which is given explicitly. (author)
TensorLy: Tensor Learning in Python
Kossaifi, Jean; Panagakis, Yannis; Pantic, Maja
2016-01-01
Tensors are higher-order extensions of matrices. While matrix methods form the cornerstone of machine learning and data analysis, tensor methods have been gaining increasing traction. However, software support for tensor operations is not on the same footing. In order to bridge this gap, we have developed \\emph{TensorLy}, a high-level API for tensor methods and deep tensorized neural networks in Python. TensorLy aims to follow the same standards adopted by the main projects of the Python scie...
Diffusion tensor imaging tensor shape analysis for assessment of regional white matter differences.
Middleton, Dana M; Li, Jonathan Y; Lee, Hui J; Chen, Steven; Dickson, Patricia I; Ellinwood, N Matthew; White, Leonard E; Provenzale, James M
2017-08-01
Purpose The purpose of this study was to investigate a novel tensor shape plot analysis technique of diffusion tensor imaging data as a means to assess microstructural differences in brain tissue. We hypothesized that this technique could distinguish white matter regions with different microstructural compositions. Methods Three normal canines were euthanized at seven weeks old. Their brains were imaged using identical diffusion tensor imaging protocols on a 7T small-animal magnetic resonance imaging system. We examined two white matter regions, the internal capsule and the centrum semiovale, each subdivided into an anterior and posterior region. We placed 100 regions of interest in each of the four brain regions. Eigenvalues for each region of interest triangulated onto tensor shape plots as the weighted average of three shape metrics at the plot's vertices: CS, CL, and CP. Results The distribution of data on the plots for the internal capsule differed markedly from the centrum semiovale data, thus confirming our hypothesis. Furthermore, data for the internal capsule were distributed in a relatively tight cluster, possibly reflecting the compact and parallel nature of its fibers, while data for the centrum semiovale were more widely distributed, consistent with the less compact and often crossing pattern of its fibers. This indicates that the tensor shape plot technique can depict data in similar regions as being alike. Conclusion Tensor shape plots successfully depicted differences in tissue microstructure and reflected the microstructure of individual brain regions. This proof of principle study suggests that if our findings are reproduced in larger samples, including abnormal white matter states, the technique may be useful in assessment of white matter diseases.
Tensor Rank Preserving Discriminant Analysis for Facial Recognition.
Tao, Dapeng; Guo, Yanan; Li, Yaotang; Gao, Xinbo
2017-10-12
Facial recognition, one of the basic topics in computer vision and pattern recognition, has received substantial attention in recent years. However, for those traditional facial recognition algorithms, the facial images are reshaped to a long vector, thereby losing part of the original spatial constraints of each pixel. In this paper, a new tensor-based feature extraction algorithm termed tensor rank preserving discriminant analysis (TRPDA) for facial image recognition is proposed; the proposed method involves two stages: in the first stage, the low-dimensional tensor subspace of the original input tensor samples was obtained; in the second stage, discriminative locality alignment was utilized to obtain the ultimate vector feature representation for subsequent facial recognition. On the one hand, the proposed TRPDA algorithm fully utilizes the natural structure of the input samples, and it applies an optimization criterion that can directly handle the tensor spectral analysis problem, thereby decreasing the computation cost compared those traditional tensor-based feature selection algorithms. On the other hand, the proposed TRPDA algorithm extracts feature by finding a tensor subspace that preserves most of the rank order information of the intra-class input samples. Experiments on the three facial databases are performed here to determine the effectiveness of the proposed TRPDA algorithm.
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.
An introduction to diffusion tensor image analysis.
O'Donnell, Lauren J; Westin, Carl-Fredrik
2011-04-01
Diffusion tensor magnetic resonance imaging (DTI) is a relatively new technology that is popular for imaging the white matter of the brain. This article provides a basic and broad overview of DTI to enable the reader to develop an intuitive understanding of these types of data, and an awareness of their strengths and weaknesses. Copyright © 2011 Elsevier Inc. All rights reserved.
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...
The tensor product in Wadler's analysis of lists
DEFF Research Database (Denmark)
Nielson, Flemming; Nielson, Hanne Riis
1992-01-01
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 Wadler's strictness analysis for lists using the notion of open set. Finally, we illustrate the intimate connection between the case analysis implicit in Wadler's strictness analysis and the precision that the tensor product allows for modelling the inverse cons operation....
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 Wadler's strictness analysis for lists (1987) using the notion of open set. Finally, we illustrate the intimate connection between the case analysis implicit in Wadler's strictness analysis and the precision that the tensor product allows for modelling the inverse cons operation...
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
2018-03-09
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.
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.
Tucker tensor analysis of Matern functions in spatial statistics
Litvinenko, Alexander
2018-04-20
Low-rank Tucker tensor methods in spatial statistics 1. Motivation: improve statistical models 2. Motivation: disadvantages of matrices 3. Tools: Tucker tensor format 4. Tensor approximation of Matern covariance function via FFT 5. Typical statistical operations in Tucker tensor format 6. Numerical experiments
Incremental Tensor Principal Component Analysis for Handwritten Digit Recognition
Directory of Open Access Journals (Sweden)
Chang Liu
2014-01-01
Full Text Available To overcome the shortcomings of traditional dimensionality reduction algorithms, incremental tensor principal component analysis (ITPCA based on updated-SVD technique algorithm is proposed in this paper. This paper proves the relationship between PCA, 2DPCA, MPCA, and the graph embedding framework theoretically and derives the incremental learning procedure to add single sample and multiple samples in detail. The experiments on handwritten digit recognition have demonstrated that ITPCA has achieved better recognition performance than that of vector-based principal component analysis (PCA, incremental principal component analysis (IPCA, and multilinear principal component analysis (MPCA algorithms. At the same time, ITPCA also has lower time and space complexity.
Multivariate analysis of eigenvalues and eigenvectors in tensor based morphometry
Rajagopalan, Vidya; Schwartzman, Armin; Hua, Xue; Leow, Alex; Thompson, Paul; Lepore, Natasha
2015-01-01
We develop a new algorithm to compute voxel-wise shape differences in tensor-based morphometry (TBM). As in standard TBM, we non-linearly register brain T1-weighed MRI data from a patient and control group to a template, and compute the Jacobian of the deformation fields. In standard TBM, the determinants of the Jacobian matrix at each voxel are statistically compared between the two groups. More recently, a multivariate extension of the statistical analysis involving the deformation tensors derived from the Jacobian matrices has been shown to improve statistical detection power.7 However, multivariate methods comprising large numbers of variables are computationally intensive and may be subject to noise. In addition, the anatomical interpretation of results is sometimes difficult. Here instead, we analyze the eigenvalues and the eigenvectors of the Jacobian matrices. Our method is validated on brain MRI data from Alzheimer's patients and healthy elderly controls from the Alzheimer's Disease Neuro Imaging Database.
Visual Tracking via Feature Tensor Multimanifold Discriminate Analysis
Directory of Open Access Journals (Sweden)
Ting-quan Deng
2014-01-01
Full Text Available In the visual tracking scenarios, if there are multiple objects, due to the interference of similar objects, tracking may fail in the progress of occlusion to separation. To address this problem, this paper proposed a visual tracking algorithm with discrimination through multimanifold learning. Color-gradient-based feature tensor was used to describe object appearance for accommodation of partial occlusion. A prior multimanifold tensor dataset is established through the template matching tracking algorithm. For the purpose of discrimination, tensor distance was defined to determine the intramanifold and intermanifold neighborhood relationship in multimanifold space. Then multimanifold discriminate analysis was employed to construct multilinear projection matrices of submanifolds. Finally, object states were obtained by combining with sequence inference. Meanwhile, the multimanifold dataset and manifold learning embedded projection should be updated online. Experiments were conducted on two real visual surveillance sequences to evaluate the proposed algorithm with three state-of-the-art tracking methods qualitatively and quantitatively. Experimental results show that the proposed algorithm can achieve effective and robust effect in multi-similar-object mutual occlusion scenarios.
Tensor algebra and tensor analysis for engineers with applications to continuum mechanics
Itskov, Mikhail
2015-01-01
This is the fourth and revised edition of a well-received book that aims at bridging the gap between the engineering course of tensor algebra on the one side and the mathematical course of classical linear algebra on the other side. In accordance with the contemporary way of scientific publications, a modern absolute tensor notation is preferred throughout. The book provides a comprehensible exposition of the fundamental mathematical concepts of tensor calculus and enriches the presented material with many illustrative examples. In addition, the book also includes advanced chapters dealing with recent developments in the theory of isotropic and anisotropic tensor functions and their applications to continuum mechanics. Hence, this monograph addresses graduate students as well as scientists working in this field. In each chapter numerous exercises are included, allowing for self-study and intense practice. Solutions to the exercises are also provided.
Tucker Tensor analysis of Matern functions in spatial statistics
Litvinenko, Alexander; Keyes, David E.; Khoromskaia, Venera; Khoromskij, Boris N.; Matthies, Hermann G.
2018-01-01
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
Global sensitivity analysis using low-rank tensor approximations
International Nuclear Information System (INIS)
Konakli, Katerina; Sudret, Bruno
2016-01-01
In the context of global sensitivity analysis, the Sobol' indices constitute a powerful tool for assessing the relative significance of the uncertain input parameters of a model. We herein introduce a novel approach for evaluating these indices at low computational cost, by post-processing the coefficients of polynomial meta-models belonging to the class of low-rank tensor approximations. Meta-models of this class can be particularly efficient in representing responses of high-dimensional models, because the number of unknowns in their general functional form grows only linearly with the input dimension. The proposed approach is validated in example applications, where the Sobol' indices derived from the meta-model coefficients are compared to reference indices, the latter obtained by exact analytical solutions or Monte-Carlo simulation with extremely large samples. Moreover, low-rank tensor approximations are confronted to the popular polynomial chaos expansion meta-models in case studies that involve analytical rank-one functions and finite-element models pertinent to structural mechanics and heat conduction. In the examined applications, indices based on the novel approach tend to converge faster to the reference solution with increasing size of the experimental design used to build the meta-model. - Highlights: • A new method is proposed for global sensitivity analysis of high-dimensional models. • Low-rank tensor approximations (LRA) are used as a meta-modeling technique. • Analytical formulas for the Sobol' indices in terms of LRA coefficients are derived. • The accuracy and efficiency of the approach is illustrated in application examples. • LRA-based indices are compared to indices based on polynomial chaos expansions.
Source-Type Identification Analysis Using Regional Seismic Moment Tensors
Chiang, A.; Dreger, D. S.; Ford, S. R.; Walter, W. R.
2012-12-01
Waveform inversion to determine the seismic moment tensor is a standard approach in determining the source mechanism of natural and manmade seismicity, and may be used to identify, or discriminate different types of seismic sources. The successful applications of the regional moment tensor method at the Nevada Test Site (NTS) and the 2006 and 2009 North Korean nuclear tests (Ford et al., 2009a, 2009b, 2010) show that the method is robust and capable for source-type discrimination at regional distances. The well-separated populations of explosions, earthquakes and collapses on a Hudson et al., (1989) source-type diagram enables source-type discrimination; however the question remains whether or not the separation of events is universal in other regions, where we have limited station coverage and knowledge of Earth structure. Ford et al., (2012) have shown that combining regional waveform data and P-wave first motions removes the CLVD-isotropic tradeoff and uniquely discriminating the 2009 North Korean test as an explosion. Therefore, including additional constraints from regional and teleseismic P-wave first motions enables source-type discrimination at regions with limited station coverage. We present moment tensor analysis of earthquakes and explosions (M6) from Lop Nor and Semipalatinsk test sites for station paths crossing Kazakhstan and Western China. We also present analyses of smaller events from industrial sites. In these sparse coverage situations we combine regional long-period waveforms, and high-frequency P-wave polarity from the same stations, as well as from teleseismic arrays to constrain the source type. Discrimination capability with respect to velocity model and station coverage is examined, and additionally we investigate the velocity model dependence of vanishing free-surface traction effects on seismic moment tensor inversion of shallow sources and recovery of explosive scalar moment. Our synthetic data tests indicate that biases in scalar
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
FADTTS: functional analysis of diffusion tensor tract statistics.
Zhu, Hongtu; Kong, Linglong; Li, Runze; Styner, Martin; Gerig, Guido; Lin, Weili; Gilmore, John H
2011-06-01
The aim of this paper is to present a functional analysis of a diffusion tensor tract statistics (FADTTS) pipeline for delineating the association between multiple diffusion properties along major white matter fiber bundles with a set of covariates of interest, such as age, diagnostic status and gender, and the structure of the variability of these white matter tract properties in various diffusion tensor imaging studies. The FADTTS integrates five statistical tools: (i) a multivariate varying coefficient model for allowing the varying coefficient functions in terms of arc length to characterize the varying associations between fiber bundle diffusion properties and a set of covariates, (ii) a weighted least squares estimation of the varying coefficient functions, (iii) a functional principal component analysis to delineate the structure of the variability in fiber bundle diffusion properties, (iv) a global test statistic to test hypotheses of interest, and (v) a simultaneous confidence band to quantify the uncertainty in the estimated coefficient functions. Simulated data are used to evaluate the finite sample performance of FADTTS. We apply FADTTS to investigate the development of white matter diffusivities along the splenium of the corpus callosum tract and the right internal capsule tract in a clinical study of neurodevelopment. FADTTS can be used to facilitate the understanding of normal brain development, the neural bases of neuropsychiatric disorders, and the joint effects of environmental and genetic factors on white matter fiber bundles. The advantages of FADTTS compared with the other existing approaches are that they are capable of modeling the structured inter-subject variability, testing the joint effects, and constructing their simultaneous confidence bands. However, FADTTS is not crucial for estimation and reduces to the functional analysis method for the single measure. Copyright © 2011 Elsevier Inc. All rights reserved.
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.
Diffusion tensor analysis of corpus callosum in progressive supranuclear palsy
International Nuclear Information System (INIS)
Ito, Shoichi; Makino, Takahiro; Shirai, Wakako; Hattori, Takamichi
2008-01-01
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
General tensor discriminant analysis and gabor features for gait recognition.
Tao, Dacheng; Li, Xuelong; Wu, Xindong; Maybank, Stephen J
2007-10-01
The traditional image representations are not suited to conventional classification methods, such as the linear discriminant analysis (LDA), because of the under sample problem (USP): the dimensionality of the feature space is much higher than the number of training samples. Motivated by the successes of the two dimensional LDA (2DLDA) for face recognition, we develop a general tensor discriminant analysis (GTDA) as a preprocessing step for LDA. The benefits of GTDA compared with existing preprocessing methods, e.g., principal component analysis (PCA) and 2DLDA, include 1) the USP is reduced in subsequent classification by, for example, LDA; 2) the discriminative information in the training tensors is preserved; and 3) GTDA provides stable recognition rates because the alternating projection optimization algorithm to obtain a solution of GTDA converges, while that of 2DLDA does not. We use human gait recognition to validate the proposed GTDA. The averaged gait images are utilized for gait representation. Given the popularity of Gabor function based image decompositions for image understanding and object recognition, we develop three different Gabor function based image representations: 1) the GaborD representation is the sum of Gabor filter responses over directions, 2) GaborS is the sum of Gabor filter responses over scales, and 3) GaborSD is the sum of Gabor filter responses over scales and directions. The GaborD, GaborS and GaborSD representations are applied to the problem of recognizing people from their averaged gait images.A large number of experiments were carried out to evaluate the effectiveness (recognition rate) of gait recognition based on first obtaining a Gabor, GaborD, GaborS or GaborSD image representation, then using GDTA to extract features and finally using LDA for classification. The proposed methods achieved good performance for gait recognition based on image sequences from the USF HumanID Database. Experimental comparisons are made with nine
Fisher statistics for analysis of diffusion tensor directional information.
Hutchinson, Elizabeth B; Rutecki, Paul A; Alexander, Andrew L; Sutula, Thomas P
2012-04-30
A statistical approach is presented for the quantitative analysis of diffusion tensor imaging (DTI) directional information using Fisher statistics, which were originally developed for the analysis of vectors in the field of paleomagnetism. In this framework, descriptive and inferential statistics have been formulated based on the Fisher probability density function, a spherical analogue of the normal distribution. The Fisher approach was evaluated for investigation of rat brain DTI maps to characterize tissue orientation in the corpus callosum, fornix, and hilus of the dorsal hippocampal dentate gyrus, and to compare directional properties in these regions following status epilepticus (SE) or traumatic brain injury (TBI) with values in healthy brains. Direction vectors were determined for each region of interest (ROI) for each brain sample and Fisher statistics were applied to calculate the mean direction vector and variance parameters in the corpus callosum, fornix, and dentate gyrus of normal rats and rats that experienced TBI or SE. Hypothesis testing was performed by calculation of Watson's F-statistic and associated p-value giving the likelihood that grouped observations were from the same directional distribution. In the fornix and midline corpus callosum, no directional differences were detected between groups, however in the hilus, significant (pstatistical comparison of tissue structural orientation. Copyright © 2012 Elsevier B.V. All rights reserved.
Tensor eigenvalues and their applications
Qi, Liqun; Chen, Yannan
2018-01-01
This book offers an introduction to applications prompted by tensor analysis, especially by the spectral tensor theory developed in recent years. It covers applications of tensor eigenvalues in multilinear systems, exponential data fitting, tensor complementarity problems, and tensor eigenvalue complementarity problems. It also addresses higher-order diffusion tensor imaging, third-order symmetric and traceless tensors in liquid crystals, piezoelectric tensors, strong ellipticity for elasticity tensors, and higher-order tensors in quantum physics. This book is a valuable reference resource for researchers and graduate students who are interested in applications of tensor eigenvalues.
Voxel-based analysis of the diffusion tensor
International Nuclear Information System (INIS)
Abe, Osamu; Takao, Hidemasa; Gonoi, Wataru; Sasaki, Hiroki; Murakami, Mizuho; Ohtomo, Kuni; Kabasawa, Hiroyuki; Kawaguchi, Hiroshi; Goto, Masami; Yamada, Haruyasu; Yamasue, Hidenori; Kasai, Kiyoto; Aoki, Shigeki
2010-01-01
Diffusion tensor imaging (DTI) has provided important insights into the neurobiological basis for normal development and aging and various disease processes in the central nervous system. The aim of this article is to review the current protocols for DTI acquisition and preprocessing and statistical testing for a voxelwise analysis of DTI, focused on statistical parametric mapping (SPM) and tract-based spatial statistics (TBSS). We tested the effects of distortion correction induced by gradient nonlinearity on fractional anisotropy (FA) maps or FA skeletons processed via two SPM-based methods (coregistration and FA template methods), or TBSS-based method, respectively. With two SPM-based methods, we found similar results in some points (e.g., significant FA elevation for uncorrected images in anterior-dominant white matter and for corrected images in bilateral middle cerebellar peduncles) and different results in other points (e.g., significantly larger FA for corrected images with coregistration method, but significantly smaller with FA template method in bilateral internal capsules, extending to corona radiata, and semioval centers). In contrast, there was no area with significant difference between uncorrected and corrected FA skeletons with TBSS-based method. The discrepancy among these results was not explained in full, but possible explanations were misregistration and smoothing for the SPM-based methods and insensitivity to FA changes outside the local centers of white matter bundles for TBSS-based method. (orig.)
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.
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-...
Parallel Flux Tensor Analysis for Efficient Moving Object Detection
2011-07-01
sensing and layered sensor fusion. Such agile sensor networks need to be further en- hanced to minimize overall power consumption under the constraint of...but also higher power consumption . The speed-up of the multicore flux tensor implementation ranged from a factor of 11 to 20 for the smaller SD video...1107. [7] S. Ali and M. Shah, “ COCOA - Tracking in aerial imagery,” in SPIE Airborne Intelligence, Surveillance, Reconnaissance (ISR) Systems and
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....... In addition, it is demonstrated that each corresponding tensor is formally determined by device structures, which allows for a synthesized study of device combinations more systematically. For implementing numerical methods, the practical significance of the tensor model is it simplifies the derivation...... details compared with series-based approaches by hiding the underlying multi-fold summation and index operation. The integrity of the proposed methodology is validated by investigating the classical intensity modulated system. Furthermore, to give an application model of the tensor formalism, we make...
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.
Population Based Analysis of Directional Information in Serial Deformation Tensor Morphometry
Studholme, Colin; Cardenas, Valerie
2012-01-01
Deformation morphometry provides a sensitive approach to detecting and mapping subtle volume changes in the brain. Population based analyses of this data have been used successfully to detect characteristic changes in different neurodegenerative conditions. However, most studies have been limited to statistical mapping of the scalar volume change at each point in the brain, by evaluating the determinant of the Jacobian of the deformation field. In this paper we describe an approach to spatial normalisation and analysis of the full deformation tensor. The approach employs a spatial relocation and reorientation of tensors of each subject. Using the assumption of small changes, we use a linear modeling of effects of clinical variables on each deformation tensor component across a population. We illustrate the use of this approach by examining the pattern of significance and orientation of the volume change effects in recovery from alcohol abuse. Results show new local structure which was not apparent in the analysis of scalar volume changes. PMID:18044583
3D structure tensor analysis of light microscopy data for validating diffusion MRI.
Khan, Ahmad Raza; Cornea, Anda; Leigland, Lindsey A; Kohama, Steven G; Jespersen, Sune Nørhøj; Kroenke, Christopher D
2015-05-01
Diffusion magnetic resonance imaging (d-MRI) is a powerful non-invasive and non-destructive technique for characterizing brain tissue on the microscopic scale. However, the lack of validation of d-MRI by independent experimental means poses an obstacle to accurate interpretation of data acquired using this method. Recently, structure tensor analysis has been applied to light microscopy images, and this technique holds promise to be a powerful validation strategy for d-MRI. Advantages of this approach include its similarity to d-MRI in terms of averaging the effects of a large number of cellular structures, and its simplicity, which enables it to be implemented in a high-throughput manner. However, a drawback of previous implementations of this technique arises from it being restricted to 2D. As a result, structure tensor analyses have been limited to tissue sectioned in a direction orthogonal to the direction of interest. Here we describe the analytical framework for extending structure tensor analysis to 3D, and utilize the results to analyze serial image "stacks" acquired with confocal microscopy of rhesus macaque hippocampal tissue. Implementation of 3D structure tensor procedures requires removal of sources of anisotropy introduced in tissue preparation and confocal imaging. This is accomplished with image processing steps to mitigate the effects of anisotropic tissue shrinkage, and the effects of anisotropy in the point spread function (PSF). In order to address the latter confound, we describe procedures for measuring the dependence of PSF anisotropy on distance from the microscope objective within tissue. Prior to microscopy, ex vivo d-MRI measurements performed on the hippocampal tissue revealed three regions of tissue with mutually orthogonal directions of least restricted diffusion that correspond to CA1, alveus and inferior longitudinal fasciculus. We demonstrate the ability of 3D structure tensor analysis to identify structure tensor orientations that
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
Tensor decompositions for the analysis of atomic resolution electron energy loss spectra
Energy Technology Data Exchange (ETDEWEB)
Spiegelberg, Jakob; Rusz, Ján [Department of Physics and Astronomy, Uppsala University, Box 516, S-751 20 Uppsala (Sweden); Pelckmans, Kristiaan [Department of Information Technology, Uppsala University, Box 337, S-751 05 Uppsala (Sweden)
2017-04-15
A selection of tensor decomposition techniques is presented for the detection of weak signals in electron energy loss spectroscopy (EELS) data. The focus of the analysis lies on the correct representation of the simulated spatial structure. An analysis scheme for EEL spectra combining two-dimensional and n-way decomposition methods is proposed. In particular, the performance of robust principal component analysis (ROBPCA), Tucker Decompositions using orthogonality constraints (Multilinear Singular Value Decomposition (MLSVD)) and Tucker decomposition without imposed constraints, canonical polyadic decomposition (CPD) and block term decompositions (BTD) on synthetic as well as experimental data is examined. - Highlights: • A scheme for compression and analysis of EELS or EDX data is proposed. • Several tensor decomposition techniques are presented for BSS on hyperspectral data. • Robust PCA and MLSVD are discussed for denoising of raw data.
Li, Jonathan Y; Middleton, Dana M; Chen, Steven; White, Leonard; Ellinwood, N Matthew; Dickson, Patricia; Vite, Charles; Bradbury, Allison; Provenzale, James M
2017-08-01
Purpose We describe a novel technique for measuring diffusion tensor imaging metrics in the canine brain. We hypothesized that a standard method for region of interest placement could be developed that is highly reproducible, with less than 10% difference in measurements between raters. Methods Two sets of canine brains (three seven-week-old full-brains and two 17-week-old single hemispheres) were scanned ex-vivo on a 7T small-animal magnetic resonance imaging system. Strict region of interest placement criteria were developed and then used by two raters to independently measure diffusion tensor imaging metrics within four different white-matter regions within each specimen. Average values of fractional anisotropy, radial diffusivity, and the three eigenvalues (λ1, λ2, and λ3) within each region in each specimen overall and within each individual image slice were compared between raters by calculating the percentage difference between raters for each metric. Results The mean percentage difference between raters for all diffusion tensor imaging metrics when pooled by each region and specimen was 1.44% (range: 0.01-5.17%). The mean percentage difference between raters for all diffusion tensor imaging metrics when compared by individual image slice was 2.23% (range: 0.75-4.58%) per hemisphere. Conclusion Our results indicate that the technique described is highly reproducible, even when applied to canine specimens of differing age, morphology, and image resolution. We propose this technique for future studies of diffusion tensor imaging analysis in canine brains and for cross-sectional and longitudinal studies of canine brain models of human central nervous system disease.
Tensor Deflation for CANDECOMP/PARAFAC - Part II: Initialization and Error Analysis
Czech Academy of Sciences Publication Activity Database
Phan, A. H.; Tichavský, Petr; Cichocki, A.
2015-01-01
Roč. 63, č. 22 (2015), s. 5939-5950 ISSN 1053-587X R&D Projects: GA ČR(CZ) GA14-13713S Institutional support: RVO:67985556 Keywords : Canonical polyadic decomposition * tensor deflation * performance analysis Subject RIV: BB - Applied Statistics, Operational Research Impact factor: 2.624, year: 2015 http://library.utia.cas.cz/separaty/2015/SI/tichavsky-0448266.pdf
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.)
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
Virtual Reality Presentation of Moment Tensor Analysis by SiGMA
International Nuclear Information System (INIS)
Ohtsu, Masayasu; Shigeishi, Mitsuhiro
2003-01-01
Nucleation of a crack is readily defected by acoustic emission (AE) method. One powerful technique for AE waveform analysis has been developed as SiGMh (Simplified Greens functions for Moment tensor Analysis), as crack kinematics of locations, types and orientations are quantitatively determined. Because these kinematical outcomes are obtained as three-dimensional (3-D) locations and vectors, 3-D visualization is definitely desirable. To this end, the visualization system has been developed by using VRML (Virtual Reality Modeling Language). As an application, failure protest of a reinforced concrete beam is discussed
International Nuclear Information System (INIS)
Szubiakowski, Jacek P.
2014-01-01
The subject of this paper is studies of the deterministic identifiability of molecular parameters, such as rotational diffusion tensor components and orientation of electronic transition moments, resulting from the time-resolved fluorescence anisotropy experiment. In the most general case considered, a pair of perpendicularly polarized emissions enables the unique determination of all the rotational diffusion tensor's principal components. The influence of the tensor's symmetry and the associated degeneration of its eigenvalues on the identifiability of the electronic transitions moments is systematically investigated. The analysis reveals that independently of the rotational diffusion tensor's symmetry, the transition moments involved in photoselection and emission processes cannot be uniquely identified without a priori information about their mutual orientation or their orientation with respect to the principal axes of the tensor. Moreover, it is shown that increasing the symmetry of the rotational diffusion tensor deteriorates the degree of the transition moments identifiability. To obtain these results analytically, a novel approach to solve bilinear system of equations for Markov parameters is applied. The effect of the additional information, obtained from fluorescence measurements for different molecular mobilities, to improve the identifiability at various levels of analysis is shown. The effectiveness and reliability of the target analysis method for experimental determination of the molecular parameters is also discussed
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.
ELATE: an open-source online application for analysis and visualization of elastic tensors
International Nuclear Information System (INIS)
Gaillac, Romain; Coudert, François-Xavier; Pullumbi, Pluton
2016-01-01
We report on the implementation of a tool for the analysis of second-order elastic stiffness tensors, provided with both an open-source Python module and a standalone online application allowing the visualization of anisotropic mechanical properties. After describing the software features, how we compute the conventional elastic constants and how we represent them graphically, we explain our technical choices for the implementation. In particular, we focus on why a Python module is used to generate the HTML web page with embedded Javascript for dynamical plots. (paper)
Böbel, A.; Knapek, C. A.; Räth, C.
2018-05-01
Experiments of the recrystallization processes in two-dimensional complex plasmas are analyzed to rigorously test a recently developed scale-free phase transition theory. The "fractal-domain-structure" (FDS) theory is based on the kinetic theory of Frenkel. It assumes the formation of homogeneous domains, separated by defect lines, during crystallization and a fractal relationship between domain area and boundary length. For the defect number fraction and system energy a scale-free power-law relation is predicted. The long-range scaling behavior of the bond-order correlation function shows clearly that the complex plasma phase transitions are not of the Kosterlitz, Thouless, Halperin, Nelson, and Young type. Previous preliminary results obtained by counting the number of dislocations and applying a bond-order metric for structural analysis are reproduced. These findings are supplemented by extending the use of the bond-order metric to measure the defect number fraction and furthermore applying state-of-the-art analysis methods, allowing a systematic testing of the FDS theory with unprecedented scrutiny: A morphological analysis of lattice structure is performed via Minkowski tensor methods. Minkowski tensors form a complete family of additive, motion covariant and continuous morphological measures that are sensitive to nonlinear properties. The FDS theory is rigorously confirmed and predictions of the theory are reproduced extremely well. The predicted scale-free power-law relation between defect fraction number and system energy is verified for one more order of magnitude at high energies compared to the inherently discontinuous bond-order metric. It is found that the fractal relation between crystalline domain area and circumference is independent of the experiment, the particular Minkowski tensor method, and the particular choice of parameters. Thus, the fractal relationship seems to be inherent to two-dimensional phase transitions in complex plasmas. Minkowski
Double polarized neutron-proton scattering and nucleon-nucleon tensor force: An alternative analysis
International Nuclear Information System (INIS)
Tornow, W.; Gould, C.R.; Haase, D.G.; Walston, J.R.; Raichle, B.W.
2002-01-01
Previous neutron-proton total cross-section difference measurements Δσ L and Δσ T between E n =7.43 and 17.1 MeV have been analyzed in a new way that reduces experimental systematic uncertainties. The results obtained for the 3 S 1 - 3 D 1 mixing parameter ε 1 are very similar to the published values, substantiating the previous conclusion that the nucleon-nucleon tensor force at low energies is stronger than predicted by the Nijmegen partial-wave analysis and, therefore, by all the recent high-precision nucleon-nucleon potential models as well
Tensor Based Representation and Analysis of Diffusion-Weighted Magnetic Resonance Images
Barmpoutis, Angelos
2009-01-01
Cartesian tensor bases have been widely used to model spherical functions. In medical imaging, tensors of various orders can approximate the diffusivity function at each voxel of a diffusion-weighted MRI data set. This approximation produces tensor-valued datasets that contain information about the underlying local structure of the scanned tissue.…
Tensor surgery and tensor rank
M. Christandl (Matthias); J. Zuiddam (Jeroen)
2018-01-01
textabstractWe introduce a method for transforming low-order tensors into higher-order tensors and apply it to tensors defined by graphs and hypergraphs. The transformation proceeds according to a surgery-like procedure that splits vertices, creates and absorbs virtual edges and inserts new vertices
Tensor surgery and tensor rank
M. Christandl (Matthias); J. Zuiddam (Jeroen)
2016-01-01
textabstractWe introduce a method for transforming low-order tensors into higher-order tensors and apply it to tensors defined by graphs and hypergraphs. The transformation proceeds according to a surgery-like procedure that splits vertices, creates and absorbs virtual edges and inserts new
Diffusion tensor analysis with nuclear magnetic resonance in human central nervous system
International Nuclear Information System (INIS)
Nakayama, Naoki
1998-01-01
Nuclear magnetic resonance has been used to measure the diffusivity of water molecules. In central nervous system, anisotropic diffusion, which is characterized by apparent diffusion tensor D app ξ , is thought to be related to neuronal fiber tract orientation. For precise observation of anisotropic diffusion, it is needed to determine the diagonal and off-diagonal elements of D app ξ . Once D app ξ is estimated from a series of diffusion weighted images, a tissue's orthotropic principal axes and diffusivity of each direction are determined from eigenvalues and eigenvectors of D app ξ . There are several methods to represent anisotropic diffusion with D app ξ . Examples are diffusion ellipsoids constructed in each voxel depicting both these principal axes and the mean diffusion length in these directions, trace invariant values and its mapping image, largest eigenvalue, and ratio of largest eigenvalue to the other eigenvalue. In this study, the author investigated practical procedure to analyze diffusion tensor D app ξ using both of spin-echo end echo-planer diffusion weighted imagings with 3-tesla magnetic resonance machine in human brain. The ellipsoid representation provided particularly useful information about microanatomy including neuronal fiber tract orientation and molecular mobility reflective of microstructure. Furthermore, in the lesion of Wallerian degeneration, the loss of anisotropy of local apparent diffusion was observed. It is suggested that the function of axons can be observed via degree of anisotropy of apparent diffusion. Consequently, diffusion tensor analysis is expected to be a powerful, noninvasive method capable of quantitative and functional evaluation of the central nervous system. (author)
Top-down approach in protein RDC data analysis: de novo estimation of the alignment tensor
International Nuclear Information System (INIS)
Chen Kang; Tjandra, Nico
2007-01-01
In solution NMR spectroscopy the residual dipolar coupling (RDC) is invaluable in improving both the precision and accuracy of NMR structures during their structural refinement. The RDC also provides a potential to determine protein structure de novo. These procedures are only effective when an accurate estimate of the alignment tensor has already been made. Here we present a top-down approach, starting from the secondary structure elements and finishing at the residue level, for RDC data analysis in order to obtain a better estimate of the alignment tensor. Using only the RDCs from N-H bonds of residues in α-helices and CA-CO bonds in β-strands, we are able to determine the offset and the approximate amplitude of the RDC modulation-curve for each secondary structure element, which are subsequently used as targets for global minimization. The alignment order parameters and the orientation of the major principal axis of individual helix or strand, with respect to the alignment frame, can be determined in each of the eight quadrants of a sphere. The following minimization against RDC of all residues within the helix or strand segment can be carried out with fixed alignment order parameters to improve the accuracy of the orientation. For a helical protein Bax, the three components A xx , A yy and A zz , of the alignment order can be determined with this method in average to within 2.3% deviation from the values calculated with the available atomic coordinates. Similarly for β-sheet protein Ubiquitin they agree in average to within 8.5%. The larger discrepancy in β-strand parameters comes from both the diversity of the β-sheet structure and the lower precision of CA-CO RDCs. This top-down approach is a robust method for alignment tensor estimation and also holds a promise for providing a protein topological fold using limited sets of RDCs
Voxel-based analysis of diffusion tensor indices in the brain in patients with Parkinson's disease
International Nuclear Information System (INIS)
Zhang Kaiyuan; Yu Chunshui; Zhang Yujin; Wu Xiaoli; Zhu Chaozhe; Chan Piu; Li Kuncheng
2011-01-01
Purpose: To investigate the abnormal diffusion in cerebral white matter and its relationship with the olfactory dysfunction in patients with Parkinson's disease (PD) through diffusion tensor imaging (DTI). Materials and methods: Diffusion tensor imaging of the cerebrum was performed in 25 patients with Parkinson's disease and 25 control subjects matched for age and sex. Differences in fractional anisotropy (FA) and mean diffusivity (MD) between these two groups were studied by voxel-based analysis of the DTI data. Correlations between diffusion indices and the olfactory function in PD patients were evaluated using the multiple regression model after controlling for the duration of the disease, Unified Parkinson's Disease Rating Sale (UPDRS), and age. Results: The damaged white and gray matter showed decreased FA or increased MD, localized bilaterally in the cerebellar and orbitofrontal cortex. In addition, in PD patients there was a positive correlation between FA values in the white matter of the left cerebellum and the thresholds of olfactory identification (TOI) and a negative correlation between MD values in the white matter of right cerebellum and the TOI. Conclusion: In patients with PD, there was disruption in the cerebellar white matter which may play an important role in the olfactory dysfunction in patients with Parkinson's disease.
International Nuclear Information System (INIS)
Ramos, Tomas; Rubilar, Guillermo F.; Obukhov, Yuri N.
2011-01-01
Highlights: → The definition of the momentum of light inside matter is studied. → Fully relativistic analysis of the dielectric 'Einstein box' thought experiment. → Minkowski, Abraham and the total energy-momentum tensors are derived in detail. → Some assumptions hidden in the usual Einstein box argument are identified. → The Abraham momentum is not uniquely selected as the momentum of light in this case. - Abstract: We analyse the 'Einstein box' thought experiment and the definition of the momentum of light inside matter. We stress the importance of the total energy-momentum tensor of the closed system (electromagnetic field plus material medium) and derive in detail the relativistic expressions for the Abraham and Minkowski momenta, together with the corresponding balance equations for an isotropic and homogeneous medium. We identify some assumptions hidden in the Einstein box argument, which make it weaker than it is usually recognized. In particular, we show that the Abraham momentum is not uniquely selected as the momentum of light in this case.
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
2014-06-01
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. 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. 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, χ(2) (3) = 38.907, p tensor and linear tensor. These metrics might be clinically applied for diagnosis, follow-up, and the study of other neurological diseases.
MR diffusion tensor analysis of schizophrenic brain using statistical parametric mapping
International Nuclear Information System (INIS)
Yamada, Haruyasu; Abe, Osamu; Kasai, Kiyoto
2005-01-01
The purpose of this study is to investigate diffusion anisotropy in the schizophrenic brain by voxel-based analysis of diffusion tensor imaging (DTI), using statistical parametric mapping (SPM). We studied 33 patients with schizophrenia diagnosed by diagnostic and statistical manual of mental disorders (DSM)-IV criteria and 42 matched controls. The data was obtained with a 1.5 T MRI system. We used single-shot spin-echo planar sequences (repetition time/echo time (TR/TE)=5000/102 ms, 5 mm slice thickness and 1.5 mm gap, field of view (FOV)=21 x 21 cm 2 , number of excitation (NEX)=4, 128 x 128 pixel matrix) for diffusion tensor acquisition. Diffusion gradients (b-value of 500 or 1000 s/mm 2 ) were applied on two axes simultaneously. Diffusion properties were measured along 6 non-linear directions. The structural distortion induced by the large diffusion gradients was corrected, based on each T 2 -weighted echo-planar image (b=0 s/mm 2 ). The fractional anisotropy (FA) maps were generated on a voxel-by-voxel basis. T 2 -weighted echo-planar images were then segmented into gray matter, white matter, and cerebrospinal fluid, using SPM (Wellcome Department of Imaging, University College London, UK). All apparent diffusion coefficient (ADC) and FA maps in native space were transformed to the stereotactic space by registering each of the images to the same template image. The normalized data was smoothed and analyzed using SPM. The significant FA decrease in the patient group was found in the uncinate fasciculus, parahippocampal white matter, anterior cingulum and other areas (corrected p<0.05). No significant increased region was noted. Our results may reflect reduced diffusion anisotropy of the white matter pathway of the limbic system as shown by the decreased FA. Manual region-of-interest analysis is usually more sensitive than voxel-based analysis, but it is subjective and difficult to set with anatomical reproducibility. Voxel-based analysis of the diffusion tensor
Multiscale analysis of the invariants of the velocity gradient tensor in isotropic turbulence
Danish, Mohammad; Meneveau, Charles
2018-04-01
Knowledge of local flow-topology, the patterns of streamlines around a moving fluid element as described by the velocity-gradient tensor, is useful for developing insights into turbulence processes, such as energy cascade, material element deformation, or scalar mixing. Much has been learned in the recent past about flow topology at the smallest (viscous) scales of turbulence. However, less is known at larger scales, for instance, at the inertial scales of turbulence. In this work, we present a detailed study on the scale dependence of various quantities of interest, such as the population fraction of different types of flow-topologies, the joint probability distribution of the second and third invariants of the velocity gradient tensor, and the geometrical alignment of vorticity with strain-rate eigenvectors. We perform the analysis on a simulation dataset of isotropic turbulence at Reλ=433 . While quantities appear close to scale invariant in the inertial range, we observe a "bump" in several quantities at length scales between the inertial and viscous ranges. For instance, the population fraction of unstable node-saddle-saddle flow topology shows an increase when reducing the scale from the inertial entering the viscous range. A similar bump is observed for the vorticity-strain-rate alignment. In order to document possible dynamical causes for the different trends in the viscous and inertial ranges, we examine the probability fluxes appearing in the Fokker-Plank equation governing the velocity gradient invariants. Specifically, we aim to understand whether the differences observed between the viscous and inertial range statistics are due to effects caused by pressure, subgrid-scale, or viscous stresses or various combinations of these terms. To decompose the flow into small and large scales, we mainly use a spectrally compact non-negative filter with good spatial localization properties (Eyink-Aluie filter). The analysis shows that when going from the inertial
Glioma grade assessment by using histogram analysis of diffusion tensor imaging-derived maps
International Nuclear Information System (INIS)
Jakab, Andras; Berenyi, Ervin; Molnar, Peter; Emri, Miklos
2011-01-01
Current endeavors in neuro-oncology include morphological validation of imaging methods by histology, including molecular and immunohistochemical techniques. Diffusion tensor imaging (DTI) is an up-to-date methodology of intracranial diagnostics that has gained importance in studies of neoplasia. Our aim was to assess the feasibility of discriminant analysis applied to histograms of preoperative diffusion tensor imaging-derived images for the prediction of glioma grade validated by histomorphology. Tumors of 40 consecutive patients included 13 grade II astrocytomas, seven oligoastrocytomas, six grade II oligodendrogliomas, three grade III oligoastrocytomas, and 11 glioblastoma multiformes. Preoperative DTI data comprised: unweighted (B 0 ) images, fractional anisotropy, longitudinal and radial diffusivity maps, directionally averaged diffusion-weighted imaging, and trace images. Sampling consisted of generating histograms for gross tumor volumes; 25 histogram bins per scalar map were calculated. The histogram bins that allowed the most precise determination of low-grade (LG) or high-grade (HG) classification were selected by multivariate discriminant analysis. Accuracy of the model was defined by the success rate of the leave-one-out cross-validation. Statistical descriptors of voxel value distribution did not differ between LG and HG tumors and did not allow classification. The histogram model had 88.5% specificity and 85.7% sensitivity in the separation of LG and HG gliomas; specificity was improved when cases with oligodendroglial components were omitted. Constructing histograms of preoperative radiological images over the tumor volume allows representation of the grade and enables discrimination of LG and HG gliomas which has been confirmed by histopathology. (orig.)
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.
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.
Performance of unscented Kalman filter tractography in edema: Analysis of the two-tensor model
Directory of Open Access Journals (Sweden)
Ruizhi Liao
2017-01-01
Overall, the main contribution of this study is to provide insight into how UKF tractography can work, using a two-tensor model, to begin to address the challenge of fiber tract reconstruction in edematous regions near brain tumors.
Histogram Analysis of Diffusion Tensor Imaging Parameters in Pediatric Cerebellar Tumors.
Wagner, Matthias W; Narayan, Anand K; Bosemani, Thangamadhan; Huisman, Thierry A G M; Poretti, Andrea
2016-05-01
Apparent diffusion coefficient (ADC) values have been shown to assist in differentiating cerebellar pilocytic astrocytomas and medulloblastomas. Previous studies have applied only ADC measurements and calculated the mean/median values. Here we investigated the value of diffusion tensor imaging (DTI) histogram characteristics of the entire tumor for differentiation of cerebellar pilocytic astrocytomas and medulloblastomas. Presurgical DTI data were analyzed with a region of interest (ROI) approach to include the entire tumor. For each tumor, histogram-derived metrics including the 25th percentile, 75th percentile, and skewness were calculated for fractional anisotropy (FA) and mean (MD), axial (AD), and radial (RD) diffusivity. The histogram metrics were used as primary predictors of interest in a logistic regression model. Statistical significance levels were set at p histogram skewness showed statistically significant differences for MD between low- and high-grade tumors (P = .008). The 25th percentile for MD yields the best results for the presurgical differentiation between pediatric cerebellar pilocytic astrocytomas and medulloblastomas. The analysis of other DTI metrics does not provide additional diagnostic value. Our study confirms the diagnostic value of the quantitative histogram analysis of DTI data in pediatric neuro-oncology. Copyright © 2015 by the American Society of Neuroimaging.
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.
Multi-template tensor-based morphometry: application to analysis of Alzheimer's disease.
Koikkalainen, Juha; Lötjönen, Jyrki; Thurfjell, Lennart; Rueckert, Daniel; Waldemar, Gunhild; Soininen, Hilkka
2011-06-01
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, multiple registrations, it can be assumed that the registration errors are averaged and eventually compensated. Four different methods are proposed for multi-template TBM. The methods were evaluated using magnetic resonance (MR) images of healthy controls, patients with stable or progressive mild cognitive impairment (MCI), and patients with Alzheimer's disease (AD) from the ADNI database (N=772). The performance of TBM features in classifying images was evaluated both quantitatively and qualitatively. Classification results show that the multi-template methods are statistically significantly better than the single-template method. The overall classification accuracy was 86.0% for the classification of control and AD subjects, and 72.1% for the classification of stable and progressive MCI subjects. The statistical group-level difference maps produced using multi-template TBM were smoother, formed larger continuous regions, and had larger t-values than the maps obtained with single-template TBM. Copyright © 2011 Elsevier Inc. All rights reserved.
Integrative analysis of many weighted co-expression networks using tensor computation.
Directory of Open Access Journals (Sweden)
Wenyuan Li
2011-06-01
Full Text Available The rapid accumulation of biological networks poses new challenges and calls for powerful integrative analysis tools. Most existing methods capable of simultaneously analyzing a large number of networks were primarily designed for unweighted networks, and cannot easily be extended to weighted networks. However, it is known that transforming weighted into unweighted networks by dichotomizing the edges of weighted networks with a threshold generally leads to information loss. We have developed a novel, tensor-based computational framework for mining recurrent heavy subgraphs in a large set of massive weighted networks. Specifically, we formulate the recurrent heavy subgraph identification problem as a heavy 3D subtensor discovery problem with sparse constraints. We describe an effective approach to solving this problem by designing a multi-stage, convex relaxation protocol, and a non-uniform edge sampling technique. We applied our method to 130 co-expression networks, and identified 11,394 recurrent heavy subgraphs, grouped into 2,810 families. We demonstrated that the identified subgraphs represent meaningful biological modules by validating against a large set of compiled biological knowledge bases. We also showed that the likelihood for a heavy subgraph to be meaningful increases significantly with its recurrence in multiple networks, highlighting the importance of the integrative approach to biological network analysis. Moreover, our approach based on weighted graphs detects many patterns that would be overlooked using unweighted graphs. In addition, we identified a large number of modules that occur predominately under specific phenotypes. This analysis resulted in a genome-wide mapping of gene network modules onto the phenome. Finally, by comparing module activities across many datasets, we discovered high-order dynamic cooperativeness in protein complex networks and transcriptional regulatory networks.
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.
International Nuclear Information System (INIS)
Yang, Xu; Cao, Ding; Liang, Xiumei; Zhao, Jiannong
2017-01-01
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 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.)
Energy Technology Data Exchange (ETDEWEB)
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.)
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
Vector-Tensor and Vector-Vector Decay Amplitude Analysis of B0→φK*0
International Nuclear Information System (INIS)
Aubert, B.; Bona, M.; Boutigny, D.; Couderc, F.; Karyotakis, Y.; Lees, J. P.; Poireau, V.; Tisserand, V.; Zghiche, A.; Grauges, E.; Palano, A.; Chen, J. C.; Qi, N. D.; Rong, G.; Wang, P.; Zhu, Y. S.; Eigen, G.; Ofte, I.; Stugu, B.; Abrams, G. S.
2007-01-01
We perform an amplitude analysis of the decays B 0 →φK 2 * (1430) 0 , φK * (892) 0 , and φ(Kπ) S-wave 0 with a sample of about 384x10 6 BB 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 -0.069 +0.061 ±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
Marami, Bahram; Mohseni Salehi, Seyed Sadegh; Afacan, Onur; Scherrer, Benoit; Rollins, Caitlin K; Yang, Edward; Estroff, Judy A; Warfield, Simon K; Gholipour, Ali
2017-08-01
Diffusion weighted magnetic resonance imaging, or DWI, is one of the most promising tools for the analysis of neural microstructure and the structural connectome of the human brain. The application of DWI to map early development of the human connectome in-utero, however, is challenged by intermittent fetal and maternal motion that disrupts the spatial correspondence of data acquired in the relatively long DWI acquisitions. Fetuses move continuously during DWI scans. Reliable and accurate analysis of the fetal brain structural connectome requires careful compensation of motion effects and robust reconstruction to avoid introducing bias based on the degree of fetal motion. In this paper we introduce a novel robust algorithm to reconstruct in-vivo diffusion-tensor MRI (DTI) of the moving fetal brain and show its effect on structural connectivity analysis. The proposed algorithm involves multiple steps of image registration incorporating a dynamic registration-based motion tracking algorithm to restore the spatial correspondence of DWI data at the slice level and reconstruct DTI of the fetal brain in the standard (atlas) coordinate space. A weighted linear least squares approach is adapted to remove the effect of intra-slice motion and reconstruct DTI from motion-corrected data. The proposed algorithm was tested on data obtained from 21 healthy fetuses scanned in-utero at 22-38 weeks gestation. Significantly higher fractional anisotropy values in fiber-rich regions, and the analysis of whole-brain tractography and group structural connectivity, showed the efficacy of the proposed method compared to the analyses based on original data and previously proposed methods. The results of this study show that slice-level motion correction and robust reconstruction is necessary for reliable in-vivo structural connectivity analysis of the fetal brain. Connectivity analysis based on graph theoretic measures show high degree of modularity and clustering, and short average
The 'gravitating' tensor in the dualistic theory
International Nuclear Information System (INIS)
Mahanta, M.N.
1989-01-01
The exact microscopic system of Einstein-type field equations of the dualistic gravitation theory is investigated as well as an analysis of the modified energy-momentum tensor or so called 'gravitating' tensor is presented
Jiang, Liang; Xiao, Chao-Yong; Xu, Quan; Sun, Jun; Chen, Huiyou; Chen, Yu-Chen; Yin, Xindao
2017-01-01
Purpose: It is critical and difficult to accurately discriminate between high- and low-grade gliomas preoperatively. This study aimed to ascertain the role of several scalar measures in distinguishing high-grade from low-grade gliomas, especially the axial diffusivity (AD), radial diffusivity (RD), planar tensor (Cp), spherical tensor (Cs), and linear tensor (Cl) derived from diffusion tensor imaging (DTI). Materials and Methods: Fifty-three patients with pathologically confirmed brain gliomas (21 low-grade and 32 high-grade) were included. Contrast-enhanced T1-weighted images and DTI were performed in all patients. The AD, RD, Cp, Cs, and Cl values in the tumor zone, peritumoral edema zone, white matter (WM) adjacent to edema and contralateral normal-appearing white matter (NAWM) were calculated. The DTI parameters and tumor grades were statistically analyzed, and receiver operating characteristic (ROC) curve analysis was also performed. Results: The DTI metrics in the affected hemisphere showed significant differences from those in the NAWM, except for the AD values in the tumor zone and the RD values in WM adjacent to edema in the low-grade groups, as well as the Cp values in WM adjacent to edema in the high-grade groups. AD in the tumor zone as well as Cs and Cl in WM adjacent to edema revealed significant differences between the low- and high-grade gliomas. The areas under the curve (Az) of all three metrics were greater than 0.5 in distinguishing low-grade from high-grade gliomas by ROC curve analysis, and the best DTI metric was Cs in WM adjacent to edema (Az: 0.692). Conclusion: AD in the tumor zone as well as Cs and Cl in WM adjacent to edema will provide additional information to better classify gliomas and can be used as non-invasive reliable biomarkers in glioma grading.
Link prediction via generalized coupled tensor factorisation
DEFF Research Database (Denmark)
Ermiş, Beyza; Evrim, Acar Ataman; Taylan Cemgil, A.
2012-01-01
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....
Top-spin analysis of new scalar and tensor interactions in e e ...
Indian Academy of Sciences (India)
Abstract. The top polarization at the International Linear Collider (ILC) with transverse beam polarization is utilized in the + - → t t ¯ process to probe interactions of the scalar and tensor type beyond the Standard Model and to disentangle their individual contributions. Confidence level limits of 90% are presented on the ...
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.
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.
Mock, A.; Korlacki, R.; Knight, S.; Schubert, M.
2018-04-01
We determine the frequency dependence of the four independent Cartesian tensor elements of the dielectric function for monoclinic symmetry Y2SiO5 using generalized spectroscopic ellipsometry from 40-1200 cm-1. Three different crystal cuts, each perpendicular to a principle axis, are investigated. We apply our recently described augmentation of lattice anharmonicity onto the eigendielectric displacement vector summation approach [A. Mock et al., Phys. Rev. B 95, 165202 (2017), 10.1103/PhysRevB.95.165202], and we present and demonstrate the application of an eigendielectric displacement loss vector summation approach with anharmonic broadening. We obtain an excellent match between all measured and model-calculated dielectric function tensor elements and all dielectric loss function tensor elements. We obtain 23 Au and 22 Bu symmetry long-wavelength active transverse and longitudinal optical mode parameters including their eigenvector orientation within the monoclinic lattice. We perform density functional theory calculations and obtain 23 Au symmetry and 22 Bu transverse and longitudinal optical mode parameters and their orientation within the monoclinic lattice. We compare our results from ellipsometry and density functional theory and find excellent agreement. We also determine the static and above reststrahlen spectral range dielectric tensor values and find a recently derived generalization of the Lyddane-Sachs-Teller relation for polar phonons in monoclinic symmetry materials satisfied [M. Schubert, Phys Rev. Lett. 117, 215502 (2016), 10.1103/PhysRevLett.117.215502].
Voxel-based morphometry and voxel-based diffusion tensor analysis in amyotrophic lateral sclerosis
International Nuclear Information System (INIS)
Chen Zhiye; Ma Lin; Lou Xin; Wang Yan
2010-01-01
Objective: To evaluate gray matter volume, white matter volume and FA value changes in amyatrophic lateral sclerosis (ALS) patients by voxel-based morphometry (VBM) and voxel-based diffusion tensor analysis (VBDTA). Methods: Thirty-nine definite or probable ALS patients diagnosed by El Escorial standard and 39 healthy controls were recruited and underwent conventional MR scans and the neuropsychological evaluation. The 3D FSPGR T 1 WI and DTI data were collected on GE Medical 3.0 T MRI system. The 3DT 1 structural images were normalized, segmented and smoothed, and then VBM analysis was performed. DTI data were acquired from 76 healthy controls, and FA map template was made. FA maps generated from the DTI data of ALS patients and healthy controls were normalized to the FA map template for voxel-based analysis. ANCOVA was applied, controlling with age and total intracranial volume for VBM and age for VBDDTA. A statistical threshold of P<0.01 (uncorrected) and cluster level of more than continuous 20 voxels determined significance. Results: Statistical results showed no significant difference in the global volumes of gray matter and white matter, total intracranial volumes and gray matter fraction between ALS patients and healthy controls, but the white matter fraction of ALS patients (0.29 ± 0.02) was significantly less than that of healthy controls (0.30 ± 0.02) statistically (P=0.003). There was significant reduction of gray matter volumes in bilateral superior frontal gyri and precentral gyri, right middle frontal gyrus, right middle and inferior temporal gyrus, left superior occipital gyrus and cuneus and left insula in ALS patients when compared with healthy controls; and the regional reduction of white matter volumes in ALS patients mainly located in genu of corpus callosum, bilateral medial frontal gyri, paracentral lobule and insula, right superior and middle frontal gyrus and left postcentral gyrus. VBDTA showed decrease in FA values in bilateral
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
Wu, Bofeng; Huang, Chao-Guang
2018-04-01
The 1 /r expansion in the distance to the source is applied to the linearized f (R ) gravity, and its multipole expansion in the radiation field with irreducible Cartesian tensors is presented. Then, the energy, momentum, and angular momentum in the gravitational waves are provided for linearized f (R ) gravity. All of these results have two parts, which are associated with the tensor part and the scalar part in the multipole expansion of linearized f (R ) gravity, respectively. The former is the same as that in General Relativity, and the latter, as the correction to the result in General Relativity, is caused by the massive scalar degree of freedom and plays an important role in distinguishing General Relativity and f (R ) gravity.
Using Matrix and Tensor Factorizations for the Single-Trial Analysis of Population Spike Trains.
Directory of Open Access Journals (Sweden)
Arno Onken
2016-11-01
Full Text Available Advances in neuronal recording techniques are leading to ever larger numbers of simultaneously monitored neurons. This poses the important analytical challenge of how to capture compactly all sensory information that neural population codes carry in their spatial dimension (differences in stimulus tuning across neurons at different locations, in their temporal dimension (temporal neural response variations, or in their combination (temporally coordinated neural population firing. Here we investigate the utility of tensor factorizations of population spike trains along space and time. These factorizations decompose a dataset of single-trial population spike trains into spatial firing patterns (combinations of neurons firing together, temporal firing patterns (temporal activation of these groups of neurons and trial-dependent activation coefficients (strength of recruitment of such neural patterns on each trial. We validated various factorization methods on simulated data and on populations of ganglion cells simultaneously recorded in the salamander retina. We found that single-trial tensor space-by-time decompositions provided low-dimensional data-robust representations of spike trains that capture efficiently both their spatial and temporal information about sensory stimuli. Tensor decompositions with orthogonality constraints were the most efficient in extracting sensory information, whereas non-negative tensor decompositions worked well even on non-independent and overlapping spike patterns, and retrieved informative firing patterns expressed by the same population in response to novel stimuli. Our method showed that populations of retinal ganglion cells carried information in their spike timing on the ten-milliseconds-scale about spatial details of natural images. This information could not be recovered from the spike counts of these cells. First-spike latencies carried the majority of information provided by the whole spike train about fine
Ichinose, G. A.; Ford, S. R.; Chiang, A.; Walter, W. R.; Dreger, D. S.
2017-12-01
The Democratic People's Republic of Korea (DPRK) conducted its sixth announced nuclear test on 3 September 2017, 03:30:00 with a magnitude of 6.1 (IDC mb). At 03:38:27, there was an aftershock of magnitude 4.1 (IDC mb). Moment tensor analysis using regional long-period surface waves was performed to identify the source type of these two events. The first event was an explosive isotropic source with total seismic moment magnitude of Mw 5.34 (Mo=1.16e+17 Nm) with strong 66% isotropic component (eigenvalues: 1.30e+17, 0.75e+17, 0.44e+17 Nm). The second event was a closing crack source with an Mw 4.64 (Mo=1.04e+17 Nm) also with a strong 68% isotropic component (eigenvalues: -4.82e+16, -5.33e+16, -10.93e+16 Nm). We used the same stations within 360-1140 km for inversion of both events (stations: IC.MDJ, IC.BJT, IC.HIA) and predict the long-period displacements at KG.TJN and IU.INCN. We used a 1-D velocity model appropriate for active tectonic regions and band pass the data between periods of 20 and 100 sec. Waveform time-shifts were incorporated from previous event-station pairs to account for velocity model inadequacies. Both DPRK events source-types plot within the population of other NNSS nuclear and western US collapse events (Ford et al., 2009) on the fundamental lune (Tape and Tape, 2012). The DPRK collapse event is similar to the hole collapse 0h21m26s after the 5 September 1982 Atrisco shot at NNSS (Springer et al., 2002; DOE NV-209). The DPRK collapse could be explained by a complete or partial apical cavity collapse. The estimated collapse volume is 122000-277000 m3 and crack radius is 30-40 m given the seismic moment, elastic moduli for granite and a closing crack model (Mueller, 2001). In comparison to Denny and Johnson (1994) cavity-yield scaling in granite, the cavity radius ranges from 40 to 60 m given an explosion yield range of 140-400 kT. This collapse event is noteworthy because large aftershocks are rare in nuclear testing and even more rare are
Energy Technology Data Exchange (ETDEWEB)
Wang, Zhi-Gang; Yan, Ze-Hui [North China Electric Power University, Department of Physics, Baoding (China)
2018-01-15
In this article, we construct the axialvector-diquark-axialvector-antidiquark type currents to interpolate the scalar, axialvector, vector, tensor doubly charmed tetraquark states, and study them with QCD sum rules systematically by carrying out the operator product expansion up to the vacuum condensates of dimension 10 in a consistent way, the predicted masses can be confronted with the experimental data in the future. We can search for those doubly charmed tetraquark states in the Okubo-Zweig-Iizuka super-allowed strong decays to the charmed-meson pairs. (orig.)
Voxel-based analysis of diffusion tensor indices in the brain in patients with Parkinson's disease
Energy Technology Data Exchange (ETDEWEB)
Zhang Kaiyuan, E-mail: kaiyuanzhang@yahoo.cn [Department of Radiology, Xuanwu Hospital, Capital Medical University, Beijing 100053 (China); Key Laboratory of Neurodegenerative Diseases, Capital Medical University, Ministry of Education (China); Yu Chunshui, E-mail: chunshuiyu826@yahoo.com.cn [Department of Radiology, Xuanwu Hospital, Capital Medical University, Beijing 100053 (China); Key Laboratory of Neurodegenerative Diseases, Capital Medical University, Ministry of Education (China); Zhang Yujin, E-mail: zyjinjin@gmail.com [State Key Laboratory of Cognitive Neurosciences and Learning, Beijing Normal University, Beijing 100875 (China); Wu Xiaoli, E-mail: wendy2006315@126.com [Key Laboratory of Neurodegenerative Diseases, Capital Medical University, Ministry of Education (China) and Department of Neurology, Xuanwu Hospital, Capital Medical University, Beijing 100053 (China); Zhu Chaozhe, E-mail: czzhu@bnu.edu.cn [State Key Laboratory of Cognitive Neurosciences and Learning, Beijing Normal University, Beijing 100875 (China); Chan Piu, E-mail: pbchan@bjsap.org [Key Laboratory of Neurodegenerative Diseases, Capital Medical University, Ministry of Education (China); Department of Neurology, Xuanwu Hospital, Capital Medical University, Beijing 100053 (China); Li Kuncheng, E-mail: likuncheng1955@yahoo.com.cn [Department of Radiology, Xuanwu Hospital, Capital Medical University, Beijing 100053 (China); Key Laboratory of Neurodegenerative Diseases, Capital Medical University, Ministry of Education (China)
2011-02-15
Purpose: To investigate the abnormal diffusion in cerebral white matter and its relationship with the olfactory dysfunction in patients with Parkinson's disease (PD) through diffusion tensor imaging (DTI). Materials and methods: Diffusion tensor imaging of the cerebrum was performed in 25 patients with Parkinson's disease and 25 control subjects matched for age and sex. Differences in fractional anisotropy (FA) and mean diffusivity (MD) between these two groups were studied by voxel-based analysis of the DTI data. Correlations between diffusion indices and the olfactory function in PD patients were evaluated using the multiple regression model after controlling for the duration of the disease, Unified Parkinson's Disease Rating Sale (UPDRS), and age. Results: The damaged white and gray matter showed decreased FA or increased MD, localized bilaterally in the cerebellar and orbitofrontal cortex. In addition, in PD patients there was a positive correlation between FA values in the white matter of the left cerebellum and the thresholds of olfactory identification (TOI) and a negative correlation between MD values in the white matter of right cerebellum and the TOI. Conclusion: In patients with PD, there was disruption in the cerebellar white matter which may play an important role in the olfactory dysfunction in patients with Parkinson's disease.
Tensor Transpose and Its Properties
Pan, Ran
2014-01-01
Tensor transpose is a higher order generalization of matrix transpose. In this paper, we use permutations and symmetry group to define? the tensor transpose. Then we discuss the classification and composition of tensor transposes. Properties of tensor transpose are studied in relation to tensor multiplication, tensor eigenvalues, tensor decompositions and tensor rank.
Jafari, Azadeh; Deville, Michel O.; Fiétier, Nicolas
2008-09-01
This study discusses the capability of the constitutive laws for the matrix logarithm of the conformation tensor (LCT model) within the framework of the spectral elements method. The high Weissenberg number problems (HWNP) usually produce a lack of convergence of the numerical algorithms. Even though the question whether the HWNP is a purely numerical problem or rather a breakdown of the constitutive law of the model has remained somewhat of a mystery, it has been recognized that the selection of an appropriate constitutive equation constitutes a very crucial step although implementing a suitable numerical technique is still important for successful discrete modeling of non-Newtonian flows. The LCT model formulation of the viscoelastic equations originally suggested by Fattal and Kupferman is applied for 2-dimensional (2D) FENE-CR model. The Planar Poiseuille flow is considered as a benchmark problem to test this representation at high Weissenberg number. The numerical results are compared with numerical solution of the standard constitutive equation.
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
2018-04-01
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.
Ding, Zi'ang
2016-01-01
Both vector and tensor fields are important mathematical tools used to describe the physics of many phenomena in science and engineering. Effective vector and tensor field visualization techniques are therefore needed to interpret and analyze the corresponding data and achieve new insight into the considered problem. This dissertation is concerned with the extraction of important structural properties from vector and tensor datasets. Specifically, we present a unified approach for the charact...
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....
Taoka, Toshiaki; Masutani, Yoshitaka; Kawai, Hisashi; Nakane, Toshiki; Matsuoka, Kiwamu; Yasuno, Fumihiko; Kishimoto, Toshifumi; Naganawa, Shinji
2017-01-01
Purpose: The activity of the glymphatic system is impaired in animal models of Alzheimer’s disease (AD). We evaluated the activity of the human glymphatic system in cases of AD with a diffusion-based technique called diffusion tensor image analysis along the perivascular space (DTI-ALPS). Materials and methods: Diffusion tensor images were acquired to calculate diffusivities in the x, y, and z axes of the plane of the lateral ventricle body in 31 patients. We evaluated the diffusivity along t...
Energy Technology Data Exchange (ETDEWEB)
Yasmin, Hasina; Abe, Osamu; Nakata, Yasuhiro; Hayashi, Naoto; Masutani, Yoshitaka; Goto, Masami; Ohtomo, Kuni [University of Tokyo, Department of Radiology, Bunkyo-ku, Tokyo (Japan); Aoki, Shigeki [Juntendo University, Department of Radiology, Bunkyo-ku, Tokyo (Japan)
2009-12-15
To date, very scant data is available regarding normal diffusion properties of white matter (WM) fibers. The present study aimed to initiate the establishment of a database of normal diffusion tensor metrics of cerebral WM fibers, including the uncinate fasciculus (UF), posterior cingulum (PC), fornix, and corticospinal tract (CST) for healthy adults using tract-specific analysis by diffusion tensor tractography (DTT). We also attempted to clarify whether age and laterality exerted any effects on this study group. DTT of WM fibers were generated for 100 healthy subjects, then mean diffusivity (MD) and fractional anisotropy (FA) of the tracts were measured. Pearson correlation analysis was used to evaluate age relationships. Paired t testing was used to compare hemispheric asymmetry. Interobserver correlation tests were also performed. Our results showed FA values for UF (right, 0.42 {+-} 0.03; left, 0.40{+-}0.03), PC (0.51 {+-} 0.06, 0.52 {+-} 0.06), fornix (0.37 {+-} 0.06, 0.38 {+-} 0.06), CST (0.70 {+-} 0.06, 0.69 {+-} 0.07), and MD values for UF (0.81 {+-} 0.03, 0.82 {+-} 0.04), PC (0.72 {+-} 0.03, 0.72 {+-} 0.04), fornix (1.86 {+-} 0.32, 1.94 {+-} 0.37), and CST (0.72 {+-} 0.03, 0.74 {+-} 0.04). We identified a significant positive correlation between age and MD in the right UF and bilateral fornices, and a negative correlation between age and FA in bilateral fornices. Hemispheric asymmetry was observed in FA of UF (right > left) and MD of CST (left > right). The results constitute a normative dataset for diffusion parameters of four WM tracts that can be used to identify, characterize, and establish the significance of changes in diseases affecting specific tracts. (orig.)
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...
Tensor rank is not multiplicative under the tensor product
M. Christandl (Matthias); A. K. Jensen (Asger Kjærulff); J. Zuiddam (Jeroen)
2018-01-01
textabstractThe 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
Tensor rank is not multiplicative under the tensor product
M. Christandl (Matthias); A. K. Jensen (Asger Kjærulff); J. Zuiddam (Jeroen)
2017-01-01
textabstractThe tensor rank of a tensor is the smallest number r such that the tensor 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 (not to be confused with the "tensor Kronecker product" used in
Black hole perturbations in vector-tensor theories: the odd-mode analysis
Kase, Ryotaro; Minamitsuji, Masato; Tsujikawa, Shinji; Zhang, Ying-li
2018-02-01
In generalized Proca theories with vector-field derivative couplings, a bunch of hairy black hole solutions have been derived on a static and spherically symmetric background. In this paper, we formulate the odd-parity black hole perturbations in generalized Proca theories by expanding the corresponding action up to second order and investigate whether or not black holes with vector hair suffer ghost or Laplacian instabilities. We show that the models with cubic couplings G3(X), where X=‑AμAμ/2 with a vector field Aμ, do not provide any additional stability condition as in General Relativity. On the other hand, the exact charged stealth Schwarzschild solution with a nonvanishing longitudinal vector component A1, which originates from the coupling to the Einstein tensor GμνAμ Aν equivalent to the quartic coupling G4(X) containing a linear function of X, is unstable in the vicinity of the event horizon. The same instability problem also persists for hairy black holes arising from general quartic power-law couplings G4(X) ⊃ β4 Xn with the nonvanishing A1, while the other branch with A1=0 can be consistent with conditions for the absence of ghost and Laplacian instabilities. We also discuss the case of other exact and numerical black hole solutions associated with intrinsic vector-field derivative couplings and show that there exists a wide range of parameter spaces in which the solutions suffer neither ghost nor Laplacian instabilities against odd-parity perturbations.
First order augmentation to tensor voting for boundary inference and multiscale analysis in 3D.
Tong, Wai-Shun; Tang, Chi-Keung; Mordohai, Philippos; Medioni, Gérard
2004-05-01
Most computer vision applications require the reliable detection of boundaries. In the presence of outliers, missing data, orientation discontinuities, and occlusion, this problem is particularly challenging. We propose to address it by complementing the tensor voting framework, which was limited to second order properties, with first order representation and voting. First order voting fields and a mechanism to vote for 3D surface and volume boundaries and curve endpoints in 3D are defined. Boundary inference is also useful for a second difficult problem in grouping, namely, automatic scale selection. We propose an algorithm that automatically infers the smallest scale that can preserve the finest details. Our algorithm then proceeds with progressively larger scales to ensure continuity where it has not been achieved. Therefore, the proposed approach does not oversmooth features or delay the handling of boundaries and discontinuities until model misfit occurs. The interaction of smooth features, boundaries, and outliers is accommodated by the unified representation, making possible the perceptual organization of data in curves, surfaces, volumes, and their boundaries simultaneously. We present results on a variety of data sets to show the efficacy of the improved formalism.
Energy Technology Data Exchange (ETDEWEB)
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.)
International Nuclear Information System (INIS)
Aldhafeeri, Faten M.; Mackenzie, Ian; Kay, Tony; Alghamdi, Jamaan; Sluming, Vanessa
2012-01-01
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.)
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.
Sparse alignment for robust tensor learning.
Lai, Zhihui; Wong, Wai Keung; Xu, Yong; Zhao, Cairong; Sun, Mingming
2014-10-01
Multilinear/tensor extensions of manifold learning based algorithms have been widely used in computer vision and pattern recognition. This paper first provides a systematic analysis of the multilinear extensions for the most popular methods by using alignment techniques, thereby obtaining a general tensor alignment framework. From this framework, it is easy to show that the manifold learning based tensor learning methods are intrinsically different from the alignment techniques. Based on the alignment framework, a robust tensor learning method called sparse tensor alignment (STA) is then proposed for unsupervised tensor feature extraction. Different from the existing tensor learning methods, L1- and L2-norms are introduced to enhance the robustness in the alignment step of the STA. The advantage of the proposed technique is that the difficulty in selecting the size of the local neighborhood can be avoided in the manifold learning based tensor feature extraction algorithms. Although STA is an unsupervised learning method, the sparsity encodes the discriminative information in the alignment step and provides the robustness of STA. Extensive experiments on the well-known image databases as well as action and hand gesture databases by encoding object images as tensors demonstrate that the proposed STA algorithm gives the most competitive performance when compared with the tensor-based unsupervised learning methods.
Brugger, Peter; Katul, Gabriel G.; De Roo, Frederik; Kröniger, Konstantin; Rotenberg, Eyal; Rohatyn, Shani; Mauder, Matthias
2018-05-01
Anisotropy in the turbulent stress tensor, which forms the basis of invariant analysis, is conducted using velocity time series measurements collected in the canopy sublayer (CSL) and the atmospheric surface layer (ASL). The goal is to assess how thermal stratification and surface roughness conditions simultaneously distort the scalewise relaxation towards isotropic state from large to small scales when referenced to homogeneous turbulence. To achieve this goal, conventional invariant analysis is extended to allow scalewise information about relaxation to isotropy in physical (instead of Fourier) space to be incorporated. The proposed analysis shows that the CSL is more isotropic than its ASL counterpart at large, intermediate, and small (or inertial) scales irrespective of the thermal stratification. Moreover, the small (or inertial) scale anisotropy is more prevalent in the ASL when compared to the CSL, a finding that cannot be fully explained by the intensity of the mean velocity gradient acting on all scales. Implications to the validity of scalewise Rotta and Lumley models for return to isotropy as well as advantages to using barycentric instead of anisotropy invariant maps for such scalewise analysis are discussed.
On improving the efficiency of tensor voting
Moreno, Rodrigo; Garcia, Miguel Angel; Puig, Domenec; Pizarro, Luis; Burgeth, Bernhard; Weickert, Joachim
2011-01-01
This paper proposes two alternative formulations to reduce the high computational complexity of tensor voting, a robust perceptual grouping technique used to extract salient information from noisy data. The first scheme consists of numerical approximations of the votes, which have been derived from an in-depth analysis of the plate and ball voting processes. The second scheme simplifies the formulation while keeping the same perceptual meaning of the original tensor voting: The stick tensor v...
Newlander, Shawn M; Chu, Alan; Sinha, Usha S; Lu, Po H; Bartzokis, George
2014-02-01
To identify regional differences in apparent diffusion coefficient (ADC) and fractional anisotropy (FA) using customized preprocessing before voxel-based analysis (VBA) in 14 normal subjects with the specific genes that decrease (apolipoprotein [APO] E ε2) and that increase (APOE ε4) the risk of Alzheimer's disease. Diffusion tensor images (DTI) acquired at 1.5 Tesla were denoised with a total variation tensor regularization algorithm before affine and nonlinear registration to generate a common reference frame for the image volumes of all subjects. Anisotropic and isotropic smoothing with varying kernel sizes was applied to the aligned data before VBA to determine regional differences between cohorts segregated by allele status. VBA on the denoised tensor data identified regions of reduced FA in APOE ε4 compared with the APOE ε2 healthy older carriers. The most consistent results were obtained using the denoised tensor and anisotropic smoothing before statistical testing. In contrast, isotropic smoothing identified regional differences for small filter sizes alone, emphasizing that this method introduces bias in FA values for higher kernel sizes. Voxel-based DTI analysis can be performed on low signal to noise ratio images to detect subtle regional differences in cohorts using the proposed preprocessing techniques. Copyright © 2013 Wiley Periodicals, Inc.
Tensor rank is not multiplicative under the tensor product
Christandl, Matthias; Jensen, Asger Kjærulff; Zuiddam, Jeroen
2017-01-01
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 between restrictions and degenerations. A result of our study is that tensor rank is not in general multiplicative under the tensor product. This answers a question of Draisma and Saptharishi. Specif...
Tensor gauge condition and tensor field decomposition
Zhu, Ben-Chao; Chen, Xiang-Song
2015-10-01
We discuss various proposals of separating a tensor field into pure-gauge and gauge-invariant components. Such tensor field decomposition is intimately related to the effort of identifying the real gravitational degrees of freedom out of the metric tensor in Einstein’s general relativity. We show that as for a vector field, the tensor field decomposition has exact correspondence to and can be derived from the gauge-fixing approach. The complication for the tensor field, however, is that there are infinitely many complete gauge conditions in contrast to the uniqueness of Coulomb gauge for a vector field. The cause of such complication, as we reveal, is the emergence of a peculiar gauge-invariant pure-gauge construction for any gauge field of spin ≥ 2. We make an extensive exploration of the complete tensor gauge conditions and their corresponding tensor field decompositions, regarding mathematical structures, equations of motion for the fields and nonlinear properties. Apparently, no single choice is superior in all aspects, due to an awkward fact that no gauge-fixing can reduce a tensor field to be purely dynamical (i.e. transverse and traceless), as can the Coulomb gauge in a vector case.
Tensor structure for Nori motives
Barbieri-Viale, Luca; Huber, Annette; Prest, Mike
2018-01-01
We construct a tensor product on Freyd's universal abelian category attached to an additive tensor category or a tensor quiver and establish a universal property. This is used to give an alternative construction for the tensor product on Nori motives.
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.
Vitolo, Enrico; Tatu, Mona Karina; Pignolo, Claudia; Cauda, Franco; Costa, Tommaso; Ando', Agata; Zennaro, Alessandro
2017-12-30
Voxel-based morphometry (VBM) and diffusion tensor imaging (DTI) are the most implemented methodologies to detect alterations of both gray and white matter (WM). However, the role of WM in mental disorders is still not well defined. We aimed at clarifying the role of WM disruption in schizophrenia and at identifying the most frequently involved brain networks. A systematic literature search was conducted to identify VBM and DTI studies focusing on WM alterations in patients with schizophrenia compared to control subjects. We selected studies reporting the coordinates of WM reductions and we performed the anatomical likelihood estimation (ALE). Moreover, we labeled the WM bundles with an anatomical atlas and compared VBM and DTI ALE-scores of each significant WM tract. A total of 59 studies were eligible for the meta-analysis. WM alterations were reported in 31 and 34 foci with VBM and DTI methods, respectively. The most occurred WM bundles in both VBM and DTI studies and largely involved in schizophrenia were long projection fibers, callosal and commissural fibers, part of motor descending fibers, and fronto-temporal-limbic pathways. The meta-analysis showed a widespread WM disruption in schizophrenia involving specific cerebral circuits instead of well-defined regions. Copyright © 2017 Elsevier B.V. All rights reserved.
Directory of Open Access Journals (Sweden)
Takuya Ishida
2017-06-01
Full Text Available Background: Little is known regarding interhemispheric functional connectivity (FC abnormalities via the corpus callosum in subjects with bipolar disorder (BD, which might be a key pathophysiological basis of emotional processing alterations in BD. Methods: We performed tract-based spatial statistics (TBSS using diffusion tensor imaging (DTI in 24 healthy control (HC and 22 BD subjects. Next, we analyzed the neural networks with independent component analysis (ICA in 32HC and 25 BD subjects using resting-state functional magnetic resonance imaging. Results: In TBSS analysis, we found reduced fractional anisotropy (FA in the corpus callosum of BD subjects. In ICA, functional within-connectivity was reduced in two clusters in the sensorimotor network (SMN (right and left primary somatosensory areas of BD subjects compared with HCs. FC between the two clusters and FA values in the corpus callosum of BD subjects was significantly correlated. Further, the functional within-connectivity was related to Young Mania Rating Scale (YMRS total scores in the right premotor area in the SMN of BD subjects. Limitations: Almost all of our BD subjects were taking several medications which could be a confounding factor. Conclusions: Our findings suggest that interhemispheric FC dysfunction in the SMN is associated with the impaired nerve fibers in the corpus callosum, which could be one of pathophysiological bases of emotion processing dysregulation in BD patients. Keywords: Neuroscience, Medical imaging, Psychiatry
Directory of Open Access Journals (Sweden)
Didier G. Leibovici
2010-10-01
Full Text Available The purpose of this paper is to describe the R package {PTAk and how the spatio-temporal context can be taken into account in the analyses. Essentially PTAk( is a multiway multidimensional method to decompose a multi-entries data-array, seen mathematically as a tensor of any order. This PTAk-modes method proposes a way of generalizing SVD (singular value decomposition, as well as some other well known methods included in the R package, such as PARAFAC or CANDECOMP and the PCAn-modes or Tucker-n model. The example datasets cover different domains with various spatio-temporal characteristics and issues: (i~medical imaging in neuropsychology with a functional MRI (magnetic resonance imaging study, (ii~pharmaceutical research with a pharmacodynamic study with EEG (electro-encephaloegraphic data for a central nervous system (CNS drug, and (iii~geographical information system (GIS with a climatic dataset that characterizes arid and semi-arid variations. All the methods implemented in the R package PTAk also support non-identity metrics, as well as penalizations during the optimization process. As a result of these flexibilities, together with pre-processing facilities, PTAk constitutes a framework for devising extensions of multidimensional methods such ascorrespondence analysis, discriminant analysis, and multidimensional scaling, also enabling spatio-temporal constraints.
Energy Technology Data Exchange (ETDEWEB)
Hohmann, Manuel [Physikalisches Institut, Universitaet Tartu (Estonia)
2016-07-01
Tensor harmonics are a useful mathematical tool for finding solutions to differential equations which transform under a particular representation of the rotation group SO(3). In order to make use of this tool also in the setting of Finsler geometry, where the objects of relevance are d-tensors instead of tensors, we construct a set of d-tensor harmonics for both SO(3) and SO(4) symmetries and show how these can be used for calculations in Finsler geometry and gravity.
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.
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.
Pastura, Giuseppe; Doering, Thomas; Gasparetto, Emerson Leandro; Mattos, Paulo; Araújo, Alexandra Prüfer
2016-06-01
Abnormalities in the white matter microstructure of the attentional system have been implicated in the aetiology of attention deficit hyperactivity disorder (ADHD). Diffusion tensor imaging (DTI) is a promising magnetic resonance imaging (MRI) technology that has increasingly been used in studies of white matter microstructure in the brain. The main objective of this work was to perform an exploratory analysis of white matter tracts in a sample of children with ADHD versus typically developing children (TDC). For this purpose, 13 drug-naive children with ADHD of both genders underwent MRI using DTI acquisition methodology and tract-based spatial statistics. The results were compared to those of a sample of 14 age- and gender-matched TDC. Lower fractional anisotropy was observed in the splenium of the corpus callosum, right superior longitudinal fasciculus, bilateral retrolenticular part of the internal capsule, bilateral inferior fronto-occipital fasciculus, left external capsule and posterior thalamic radiation (including right optic radiation). We conclude that white matter tracts in attentional and motor control systems exhibited signs of abnormal microstructure in this sample of drug-naive children with ADHD.
International Nuclear Information System (INIS)
Beig, Robert; Krammer, Werner
2004-01-01
For a conformally flat 3-space, we derive a family of linear second-order partial differential operators which sends vectors into trace-free, symmetric 2-tensors. These maps, which are parametrized by conformal Killing vectors on the 3-space, are such that the divergence of the resulting tensor field depends only on the divergence of the original vector field. In particular, these maps send source-free electric fields into TT tensors. Moreover, if the original vector field is the Coulomb field on R 3 {0}, the resulting tensor fields on R 3 {0} are nothing but the family of TT tensors originally written by Bowen and York
Tensor methods for parameter estimation and bifurcation analysis of stochastic reaction networks
Czech Academy of Sciences Publication Activity Database
Liao, S.; Vejchodský, Tomáš; Erban, R.
2015-01-01
Roč. 12, č. 108 (2015), s. 20150233 ISSN 1742-5689 EU Projects: European Commission(XE) 328008 - STOCHDETBIOMODEL Institutional support: RVO:67985840 Keywords : gene regulatory networks * stochastic modelling * parametric analysis Subject RIV: BA - General Mathematics Impact factor: 3.818, year: 2015 http://rsif.royalsocietypublishing.org/content/12/108/20150233
International Nuclear Information System (INIS)
Kurki, Timo; Himanen, Leena; Vuorinen, Elina; Myllyniemi, Anna; Saarenketo, Anna-Riitta; Kauko, Tommi; Brandstack, Nina; Tenovuo, Olli
2014-01-01
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.)
Energy Technology Data Exchange (ETDEWEB)
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.)
Efficient Tensor Strategy for Recommendation
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Aboagye Emelia Opoku
2017-07-01
Full Text Available The era of big data has witnessed the explosion of tensor datasets, and large scale Probabilistic Tensor Factorization (PTF analysis is important to accommodate such increasing trend of data. Sparsity, and Cold-Start are some of the inherent problems of recommender systems in the era of big data. This paper proposes a novel Sentiment-Based Probabilistic Tensor Analysis technique senti-PTF to address the problems. The propose framework first applies a Natural Language Processing technique to perform sentiment analysis taking advantage of the huge sums of textual data generated available from the social media which are predominantly left untouched. Although some current studies do employ review texts, many of them do not consider how sentiments in reviews influence recommendation algorithm for prediction. There is therefore this big data text analytics gap whose modeling is computationally expensive. From our experiments, our novel machine learning sentiment-based tensor analysis is computationally less expensive, and addresses the cold-start problem, for optimal recommendation prediction.
Seely, Jeffrey S; Kaufman, Matthew T; Ryu, Stephen I; Shenoy, Krishna V; Cunningham, John P; Churchland, Mark M
2016-11-01
Cortical firing rates frequently display elaborate and heterogeneous temporal structure. One often wishes to compute quantitative summaries of such structure-a basic example is the frequency spectrum-and compare with model-based predictions. The advent of large-scale population recordings affords the opportunity to do so in new ways, with the hope of distinguishing between potential explanations for why responses vary with time. We introduce a method that assesses a basic but previously unexplored form of population-level structure: when data contain responses across multiple neurons, conditions, and times, they are naturally expressed as a third-order tensor. We examined tensor structure for multiple datasets from primary visual cortex (V1) and primary motor cortex (M1). All V1 datasets were 'simplest' (there were relatively few degrees of freedom) along the neuron mode, while all M1 datasets were simplest along the condition mode. These differences could not be inferred from surface-level response features. Formal considerations suggest why tensor structure might differ across modes. For idealized linear models, structure is simplest across the neuron mode when responses reflect external variables, and simplest across the condition mode when responses reflect population dynamics. This same pattern was present for existing models that seek to explain motor cortex responses. Critically, only dynamical models displayed tensor structure that agreed with the empirical M1 data. These results illustrate that tensor structure is a basic feature of the data. For M1 the tensor structure was compatible with only a subset of existing models.
Directory of Open Access Journals (Sweden)
Jeffrey S Seely
2016-11-01
Full Text Available Cortical firing rates frequently display elaborate and heterogeneous temporal structure. One often wishes to compute quantitative summaries of such structure-a basic example is the frequency spectrum-and compare with model-based predictions. The advent of large-scale population recordings affords the opportunity to do so in new ways, with the hope of distinguishing between potential explanations for why responses vary with time. We introduce a method that assesses a basic but previously unexplored form of population-level structure: when data contain responses across multiple neurons, conditions, and times, they are naturally expressed as a third-order tensor. We examined tensor structure for multiple datasets from primary visual cortex (V1 and primary motor cortex (M1. All V1 datasets were 'simplest' (there were relatively few degrees of freedom along the neuron mode, while all M1 datasets were simplest along the condition mode. These differences could not be inferred from surface-level response features. Formal considerations suggest why tensor structure might differ across modes. For idealized linear models, structure is simplest across the neuron mode when responses reflect external variables, and simplest across the condition mode when responses reflect population dynamics. This same pattern was present for existing models that seek to explain motor cortex responses. Critically, only dynamical models displayed tensor structure that agreed with the empirical M1 data. These results illustrate that tensor structure is a basic feature of the data. For M1 the tensor structure was compatible with only a subset of existing models.
New analysis of ηπ tensor resonances measured at the COMPASS experiment
Jackura, A.; Fernández-Ramírez, C.; Mikhasenko, M.; Pilloni, A.; Mathieu, V.; Nys, J.; Pauk, V.; Szczepaniak, A. P.; Fox, G.; JPAC Collaboration
2018-04-01
We present a new amplitude analysis of the ηπ D-wave in the reaction π- p → ηπ- 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 a2 (1320) and the excited a2‧ (1700), and perform a comprehensive analysis of their pole positions. For the mass and width of the a2 we find M = (1307 ± 1 ± 6) MeV and Γ = (112 ± 1 ± 8) MeV, and for the excited state a2‧ we obtain M = (1720 ± 10 ± 60) MeV and Γ = (280 ± 10 ± 70) MeV, respectively.
Meintjes, E M; Narr, K L; van der Kouwe, A J W; Molteno, C D; Pirnia, T; Gutman, B; Woods, R P; Thompson, P M; Jacobson, J L; Jacobson, S W
2014-01-01
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.
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.
Categorical Tensor Network States
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Jacob D. Biamonte
2011-12-01
Full Text Available We examine the use of string diagrams and the mathematics of category theory in the description of quantum states by tensor networks. This approach lead to a unification of several ideas, as well as several results and methods that have not previously appeared in either side of the literature. Our approach enabled the development of a tensor network framework allowing a solution to the quantum decomposition problem which has several appealing features. Specifically, given an n-body quantum state |ψ〉, we present a new and general method to factor |ψ〉 into a tensor network of clearly defined building blocks. We use the solution to expose a previously unknown and large class of quantum states which we prove can be sampled efficiently and exactly. This general framework of categorical tensor network states, where a combination of generic and algebraically defined tensors appear, enhances the theory of tensor network states.
Ye, Yusen; Gao, Lin; Zhang, Shihua
2017-01-01
Transcription factors play a key role in transcriptional regulation of genes and determination of cellular identity through combinatorial interactions. However, current studies about combinatorial regulation is deficient due to lack of experimental data in the same cellular environment and extensive existence of data noise. Here, we adopt a Bayesian CANDECOMP/PARAFAC (CP) factorization approach (BCPF) to integrate multiple datasets in a network paradigm for determining precise TF interaction landscapes. In our first application, we apply BCPF to integrate three networks built based on diverse datasets of multiple cell lines from ENCODE respectively to predict a global and precise TF interaction network. This network gives 38 novel TF interactions with distinct biological functions. In our second application, we apply BCPF to seven types of cell type TF regulatory networks and predict seven cell lineage TF interaction networks, respectively. By further exploring the dynamics and modularity of them, we find cell lineage-specific hub TFs participate in cell type or lineage-specific regulation by interacting with non-specific TFs. Furthermore, we illustrate the biological function of hub TFs by taking those of cancer lineage and blood lineage as examples. Taken together, our integrative analysis can reveal more precise and extensive description about human TF combinatorial interactions. PMID:29033978
Diffusion Tensor MR Imaging Evaluation of Callosal Abnormalities in Schizophrenia: A Meta-Analysis.
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Chuanjun Zhuo
Full Text Available Widespread white matter (WM abnormalities have been found in patients with schizophrenia. Corpus callosum (CC is the key area that connects the left and right brain hemispheres. However, the results of studies considering different subregions of the CC as regions of interest in patients with schizophrenia have been inconsistent. To obtain a more consistent evaluation of the diffusion characteristics change of the corpus callosum (CC related to schizophrenia. A meta-analysis involving fractional anisotropy (FA values in the CC of 729 schizophrenic subjects and 682 healthy controls from 22 studies was conducted. Overall FA values in the CC of the schizophrenic group were less than that of the healthy control group [weighted mean difference (WMD = -0.021,P< 0.001]. So were the FA values in the genus region (WMD = -0.019, P< 0.001 and the splenium region (WMD = -0.020, P< 0.001 of the CC respectively. The FA reduction was also significant in subjects with chronic schizophrenia (WMD = -0.032, P< 0.001 and first-episode schizophrenia (WMD = -0.014, P = 0.001. In present study, we demonstrated an overall FA decrease in the CC of schizophrenic patients. In the two subgroup analyses of the genu vs splenium region and chronic vs first-episode schizophrenia, the decrease of all groups was significant. Further studies with more homogenous populations and standardized DTI protocols are needed to confirm and extend these findings.
International Nuclear Information System (INIS)
Yasmin, Hasina; Nakata, Yasuhiro; Abe, Osamu; Masutani, Yoshitaka; Ohtomo, Kuni; Aoki, Shigeki; Sato, Noriko; Nemoto, Kiyotaka; Arima, Kunimasa; Furuta, Nobuo; Uno, Masatake; Hirai, Shigeo
2008-01-01
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 0.93 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.)
Linear Invariant Tensor Interpolation Applied to Cardiac Diffusion Tensor MRI
Gahm, Jin Kyu; Wisniewski, Nicholas; Kindlmann, Gordon; Kung, Geoffrey L.; Klug, William S.; Garfinkel, Alan; Ennis, Daniel B.
2015-01-01
Purpose Various methods exist for interpolating diffusion tensor fields, but none of them linearly interpolate tensor shape attributes. Linear interpolation is expected not to introduce spurious changes in tensor shape. Methods Herein we define a new linear invariant (LI) tensor interpolation method that linearly interpolates components of tensor shape (tensor invariants) and recapitulates the interpolated tensor from the linearly interpolated tensor invariants and the eigenvectors of a linearly interpolated tensor. The LI tensor interpolation method is compared to the Euclidean (EU), affine-invariant Riemannian (AI), log-Euclidean (LE) and geodesic-loxodrome (GL) interpolation methods using both a synthetic tensor field and three experimentally measured cardiac DT-MRI datasets. Results EU, AI, and LE introduce significant microstructural bias, which can be avoided through the use of GL or LI. Conclusion GL introduces the least microstructural bias, but LI tensor interpolation performs very similarly and at substantially reduced computational cost. PMID:23286085
Feature Surfaces in Symmetric Tensor Fields Based on Eigenvalue Manifold.
Palacios, Jonathan; Yeh, Harry; Wang, Wenping; Zhang, Yue; Laramee, Robert S; Sharma, Ritesh; Schultz, Thomas; Zhang, Eugene
2016-03-01
Three-dimensional symmetric tensor fields have a wide range of applications in solid and fluid mechanics. Recent advances in the (topological) analysis of 3D symmetric tensor fields focus on degenerate tensors which form curves. In this paper, we introduce a number of feature surfaces, such as neutral surfaces and traceless surfaces, into tensor field analysis, based on the notion of eigenvalue manifold. Neutral surfaces are the boundary between linear tensors and planar tensors, and the traceless surfaces are the boundary between tensors of positive traces and those of negative traces. Degenerate curves, neutral surfaces, and traceless surfaces together form a partition of the eigenvalue manifold, which provides a more complete tensor field analysis than degenerate curves alone. We also extract and visualize the isosurfaces of tensor modes, tensor isotropy, and tensor magnitude, which we have found useful for domain applications in fluid and solid mechanics. Extracting neutral and traceless surfaces using the Marching Tetrahedra method can cause the loss of geometric and topological details, which can lead to false physical interpretation. To robustly extract neutral surfaces and traceless surfaces, we develop a polynomial description of them which enables us to borrow techniques from algebraic surface extraction, a topic well-researched by the computer-aided design (CAD) community as well as the algebraic geometry community. In addition, we adapt the surface extraction technique, called A-patches, to improve the speed of finding degenerate curves. Finally, we apply our analysis to data from solid and fluid mechanics as well as scalar field analysis.
Mean template for tensor-based morphometry using deformation tensors.
Leporé, Natasha; Brun, Caroline; Pennec, Xavier; Chou, Yi-Yu; Lopez, Oscar L; Aizenstein, Howard J; Becker, James T; Toga, Arthur W; Thompson, Paul M
2007-01-01
Tensor-based morphometry (TBM) studies anatomical differences between brain images statistically, to identify regions that differ between groups, over time, or correlate with cognitive or clinical measures. Using a nonlinear registration algorithm, all images are mapped to a common space, and statistics are most commonly performed on the Jacobian determinant (local expansion factor) of the deformation fields. In, it was shown that the detection sensitivity of the standard TBM approach could be increased by using the full deformation tensors in a multivariate statistical analysis. Here we set out to improve the common space itself, by choosing the shape that minimizes a natural metric on the deformation tensors from that space to the population of control subjects. This method avoids statistical bias and should ease nonlinear registration of new subjects data to a template that is 'closest' to all subjects' anatomies. As deformation tensors are symmetric positive-definite matrices and do not form a vector space, all computations are performed in the log-Euclidean framework. The control brain B that is already the closest to 'average' is found. A gradient descent algorithm is then used to perform the minimization that iteratively deforms this template and obtains the mean shape. We apply our method to map the profile of anatomical differences in a dataset of 26 HIV/AIDS patients and 14 controls, via a log-Euclidean Hotelling's T2 test on the deformation tensors. These results are compared to the ones found using the 'best' control, B. Statistics on both shapes are evaluated using cumulative distribution functions of the p-values in maps of inter-group differences.
International Nuclear Information System (INIS)
Wit, B. de; Rocek, M.
1982-01-01
We construct a conformally invariant theory of the N = 1 supersymmetric tensor gauge multiplet and discuss the situation in N = 2. We show that our results give rise to the recently proposed variant of Poincare supergravity, and provide the complete tensor calculus for the theory. Finally, we argue that this theory cannot be quantized sensibly. (orig.)
Time integration of tensor trains
Lubich, Christian; Oseledets, Ivan; Vandereycken, Bart
2014-01-01
A robust and efficient time integrator for dynamical tensor approximation in the tensor train or matrix product state format is presented. The method is based on splitting the projector onto the tangent space of the tensor manifold. The algorithm can be used for updating time-dependent tensors in the given data-sparse tensor train / matrix product state format and for computing an approximate solution to high-dimensional tensor differential equations within this data-sparse format. The formul...
International Nuclear Information System (INIS)
Kawamo, Michiaki; Abe, Takumi; Izumiyama, Hitoshi
2008-01-01
In patients with brain hemorrhage, the entire visualized pyramidal tract was established as an area of interest (ROI). Its Fractional Anisotropy (FA) value was determined by diffusion tensor analysis (DTA), and its relationship to motor function at the onset and three months later was investigated. In 30 patients with brain hemorrhage accompanying paralysis, MRI was performed during the subacute phase (6-14 days after onset). In addition, using a workstation, DTA was performed in order to visualize the pyramidal tract. The FA of the ROI was measured on the affected and unaffected sides, and as previously reported, the ratio of FA in the affected and unaffected sides was calculated. Subsequently, we examined the relationship between the FA ratio and motor function prognosis. Motor function prognosis was assessed based on the sum of the Brunnstrom stage at the onset and three months later. A strong correlation coefficient existed between the FA ratio of the entire pyramidal tract and the sum of the Brunnstrom stage three months after onset (0.74, p<0.001), and prognosis of motor function tended to improve in patients with FA ratios of 0.95 or higher. Patients with mild paralysis were identified in order to ascertain the degree of improvement in paralysis, and a significant correlation between the FA ratio of the entire pyramidal tract and the degree of improvement in the Brunnstrom stage was observed (correlation coefficient 0.77, p<0.001). When compared to putamen hemorrhage, the FA ratio affected the prognosis of paralysis more in thalamic hemorrhage. The results suggest that in patients with an FA ratio of 1.0, the recovery rate of paralysis three months after onset is markedly high. In brain hemorrhage patients, a reduction in the FA ratio of the entire pyramidal tract was correlated with the functional prognosis of motor paralysis, and in thalamic hemorrhage, it may be possible to predict motor function based on FA ratios. Hence, the DTA of the pyramidal tract
On the skew-symmetric character of the couple-stress tensor
Hadjesfandiari, Ali R.
2013-01-01
In this paper, the skew-symmetric character of the couple-stress tensor is established as the result of arguments from tensor analysis. Consequently, the couple-stress pseudo-tensor has a true vectorial character. The fundamental step in this development is that the isotropic couple-stress tensor cannot exist.
Thaler, Avner; Artzi, Moran; Mirelman, Anat; Jacob, Yael; Helmich, Rick C; van Nuenen, Bart F L; Gurevich, Tanya; Orr-Urtreger, Avi; Marder, Karen; Bressman, Susan; Bloem, Bastiaan R; Hendler, Talma; Giladi, Nir; Ben Bashat, Dafna
2014-05-01
Patients with Parkinson's disease have reduced gray matter volume and fractional anisotropy in both cortical and sub-cortical structures, yet changes in the pre-motor phase of the disease are unknown. A comprehensive imaging study using voxel-based morphometry and diffusion tensor imaging tract-based spatial statistics analysis was performed on 64 Ashkenazi Jewish asymptomatic first degree relatives of patients with Parkinson's disease (30 mutation carriers), who carry the G2019S mutation in the leucine-rich repeat kinase 2 (LRRK2) gene. No between-group differences in gray matter volume could be noted in either whole-brain or volume-of-interest analysis. Diffusion tensor imaging analysis did not identify group differences in white matter areas, and volume-of-interest analysis identified no differences in diffusivity parameters in Parkinson's disease-related structures. G2019S carriers do not manifest changes in gray matter volume or diffusivity parameters in Parkinson's disease-related structures prior to the appearance of motor symptoms. © 2014 International Parkinson and Movement Disorder Society.
On improving the efficiency of tensor voting.
Moreno, Rodrigo; Garcia, Miguel Angel; Puig, Domenec; Pizarro, Luis; Burgeth, Bernhard; Weickert, Joachim
2011-11-01
This paper proposes two alternative formulations to reduce the high computational complexity of tensor voting, a robust perceptual grouping technique used to extract salient information from noisy data. The first scheme consists of numerical approximations of the votes, which have been derived from an in-depth analysis of the plate and ball voting processes. The second scheme simplifies the formulation while keeping the same perceptual meaning of the original tensor voting: The stick tensor voting and the stick component of the plate tensor voting must reinforce surfaceness, the plate components of both the plate and ball tensor voting must boost curveness, whereas junctionness must be strengthened by the ball component of the ball tensor voting. Two new parameters have been proposed for the second formulation in order to control the potentially conflictive influence of the stick component of the plate vote and the ball component of the ball vote. Results show that the proposed formulations can be used in applications where efficiency is an issue since they have a complexity of order O(1). Moreover, the second proposed formulation has been shown to be more appropriate than the original tensor voting for estimating saliencies by appropriately setting the two new parameters.
Tensor spherical harmonics and tensor multipoles. II. Minkowski space
International Nuclear Information System (INIS)
Daumens, M.; Minnaert, P.
1976-01-01
The bases of tensor spherical harmonics and of tensor multipoles discussed in the preceding paper are generalized in the Hilbert space of Minkowski tensor fields. The transformation properties of the tensor multipoles under Lorentz transformation lead to the notion of irreducible tensor multipoles. We show that the usual 4-vector multipoles are themselves irreducible, and we build the irreducible tensor multipoles of the second order. We also give their relations with the symmetric tensor multipoles defined by Zerilli for application to the gravitational radiation
Lu, Shikun; Zhang, Hao; Li, Xihai; Li, Yihong; Niu, Chao; Yang, Xiaoyun; Liu, Daizhi
2018-03-01
Combining analyses of spatial and temporal characteristics of the ionosphere is of great significance for scientific research and engineering applications. Tensor decomposition is performed to explore the temporal-longitudinal-latitudinal characteristics in the ionosphere. Three-dimensional tensors are established based on the time series of ionospheric vertical total electron content maps obtained from the Centre for Orbit Determination in Europe. To obtain large-scale characteristics of the ionosphere, rank-1 decomposition is used to obtain U^{(1)}, U^{(2)}, and U^{(3)}, which are the resulting vectors for the time, longitude, and latitude modes, respectively. Our initial finding is that the correspondence between the frequency spectrum of U^{(1)} and solar variation indicates that rank-1 decomposition primarily describes large-scale temporal variations in the global ionosphere caused by the Sun. Furthermore, the time lags between the maxima of the ionospheric U^{(2)} and solar irradiation range from 1 to 3.7 h without seasonal dependence. The differences in time lags may indicate different interactions between processes in the magnetosphere-ionosphere-thermosphere system. Based on the dataset displayed in the geomagnetic coordinates, the position of the barycenter of U^{(3)} provides evidence for north-south asymmetry (NSA) in the large-scale ionospheric variations. The daily variation in such asymmetry indicates the influences of solar ionization. The diurnal geomagnetic coordinate variations in U^{(3)} show that the large-scale EIA (equatorial ionization anomaly) variations during the day and night have similar characteristics. Considering the influences of geomagnetic disturbance on ionospheric behavior, we select the geomagnetic quiet GIMs to construct the ionospheric tensor. The results indicate that the geomagnetic disturbances have little effect on large-scale ionospheric characteristics.
Dynamical analysis for a scalar-tensor model with Gauss-Bonnet and non-minimal couplings
Energy Technology Data Exchange (ETDEWEB)
Granda, L.N.; Jimenez, D.F. [Universidad del Valle, Departamento de Fisica, Cali (Colombia)
2017-10-15
We study the autonomous system for a scalar-tensor model of dark energy with Gauss-Bonnet and non-minimal couplings. The critical points describe important stable asymptotic scenarios including quintessence, phantom and de Sitter attractor solutions. Two functional forms for the coupling functions and the scalar potential are considered: power-law and exponential functions of the scalar field. For the exponential functions the existence of stable quintessence, phantom or de Sitter solutions, allows for an asymptotic behavior where the effective Newtonian coupling becomes constant. The phantom solutions could be realized without appealing to ghost degrees of freedom. Transient inflationary and radiation-dominated phases can also be described. (orig.)
Lepore, N; Brun, C; Chou, Y Y; Chiang, M C; Dutton, R A; Hayashi, K M; Luders, E; Lopez, O L; Aizenstein, H J; Toga, A W; Becker, J T; Thompson, P M
2008-01-01
This paper investigates the performance of a new multivariate method for tensor-based morphometry (TBM). Statistics on Riemannian manifolds are developed that exploit the full information in deformation tensor fields. In TBM, multiple brain images are warped to a common neuroanatomical template via 3-D nonlinear registration; the resulting deformation fields are analyzed statistically to identify group differences in anatomy. Rather than study the Jacobian determinant (volume expansion factor) of these deformations, as is common, we retain the full deformation tensors and apply a manifold version of Hotelling's $T(2) test to them, in a Log-Euclidean domain. In 2-D and 3-D magnetic resonance imaging (MRI) data from 26 HIV/AIDS patients and 14 matched healthy subjects, we compared multivariate tensor analysis versus univariate tests of simpler tensor-derived indices: the Jacobian determinant, the trace, geodesic anisotropy, and eigenvalues of the deformation tensor, and the angle of rotation of its eigenvectors. We detected consistent, but more extensive patterns of structural abnormalities, with multivariate tests on the full tensor manifold. Their improved power was established by analyzing cumulative p-value plots using false discovery rate (FDR) methods, appropriately controlling for false positives. This increased detection sensitivity may empower drug trials and large-scale studies of disease that use tensor-based morphometry.
Directory of Open Access Journals (Sweden)
Dan Yang
2017-04-01
Full Text Available To solve the problem of multi-fault blind source separation (BSS in the case that the observed signals are under-determined, a novel approach for single channel blind source separation (SCBSS based on the improved tensor-based singular spectrum analysis (TSSA is proposed. As the most natural representation of high-dimensional data, tensor can preserve the intrinsic structure of the data to the maximum extent. Thus, TSSA method can be employed to extract the multi-fault features from the measured single-channel vibration signal. However, SCBSS based on TSSA still has some limitations, mainly including unsatisfactory convergence of TSSA in many cases and the number of source signals is hard to accurately estimate. Therefore, the improved TSSA algorithm based on canonical decomposition and parallel factors (CANDECOMP/PARAFAC weighted optimization, namely CP-WOPT, is proposed in this paper. CP-WOPT algorithm is applied to process the factor matrix using a first-order optimization approach instead of the original least square method in TSSA, so as to improve the convergence of this algorithm. In order to accurately estimate the number of the source signals in BSS, EMD-SVD-BIC (empirical mode decomposition—singular value decomposition—Bayesian information criterion method, instead of the SVD in the conventional TSSA, is introduced. To validate the proposed method, we applied it to the analysis of the numerical simulation signal and the multi-fault rolling bearing signals.
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
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...... of polynomial equations of small degree in non-generic cases. We propose a new algorithm for symmetric tensor decomposition, based on this characterization and on linear algebra computations with Hankel matrices. The impact of this contribution is two-fold. First it permits an efficient computation...... of the decomposition of any tensor of sub-generic rank, as opposed to widely used iterative algorithms with unproved global convergence (e.g. Alternate Least Squares or gradient descents). Second, it gives tools for understanding uniqueness conditions and for detecting the rank....
International Nuclear Information System (INIS)
Scheunert, M.
1982-10-01
We develop a graded tensor calculus corresponding to arbitrary Abelian groups of degrees and arbitrary commutation factors. The standard basic constructions and definitions like tensor products, spaces of multilinear mappings, contractions, symmetrization, symmetric algebra, as well as the transpose, adjoint, and trace of a linear mapping, are generalized to the graded case and a multitude of canonical isomorphisms is presented. Moreover, the graded versions of the classical Lie algebras are introduced and some of their basic properties are described. (orig.)
Unsupervised Tensor Mining for Big Data Practitioners.
Papalexakis, Evangelos E; Faloutsos, Christos
2016-09-01
Multiaspect data are ubiquitous in modern Big Data applications. For instance, different aspects of a social network are the different types of communication between people, the time stamp of each interaction, and the location associated to each individual. How can we jointly model all those aspects and leverage the additional information that they introduce to our analysis? Tensors, which are multidimensional extensions of matrices, are a principled and mathematically sound way of modeling such multiaspect data. In this article, our goal is to popularize tensors and tensor decompositions to Big Data practitioners by demonstrating their effectiveness, outlining challenges that pertain to their application in Big Data scenarios, and presenting our recent work that tackles those challenges. We view this work as a step toward a fully automated, unsupervised tensor mining tool that can be easily and broadly adopted by practitioners in academia and industry.
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.
Lazzeretti, Paolo
2018-04-01
It is shown that nonsymmetric second-rank current density tensors, related to the current densities induced by magnetic fields and nuclear magnetic dipole moments, are fundamental properties of a molecule. Together with magnetizability, nuclear magnetic shielding, and nuclear spin-spin coupling, they completely characterize its response to magnetic perturbations. Gauge invariance, resolution into isotropic, deviatoric, and antisymmetric parts, and contributions of current density tensors to magnetic properties are discussed. The components of the second-rank tensor properties are rationalized via relationships explicitly connecting them to the direction of the induced current density vectors and to the components of the current density tensors. The contribution of the deviatoric part to the average value of magnetizability, nuclear shielding, and nuclear spin-spin coupling, uniquely determined by the antisymmetric part of current density tensors, vanishes identically. The physical meaning of isotropic and anisotropic invariants of current density tensors has been investigated, and the connection between anisotropy magnitude and electron delocalization has been discussed.
A Review of Tensors and Tensor Signal Processing
Cammoun, L.; Castaño-Moraga, C. A.; Muñoz-Moreno, E.; Sosa-Cabrera, D.; Acar, B.; Rodriguez-Florido, M. A.; Brun, A.; Knutsson, H.; Thiran, J. P.
Tensors have been broadly used in mathematics and physics, since they are a generalization of scalars or vectors and allow to represent more complex properties. In this chapter we present an overview of some tensor applications, especially those focused on the image processing field. From a mathematical point of view, a lot of work has been developed about tensor calculus, which obviously is more complex than scalar or vectorial calculus. Moreover, tensors can represent the metric of a vector space, which is very useful in the field of differential geometry. In physics, tensors have been used to describe several magnitudes, such as the strain or stress of materials. In solid mechanics, tensors are used to define the generalized Hooke’s law, where a fourth order tensor relates the strain and stress tensors. In fluid dynamics, the velocity gradient tensor provides information about the vorticity and the strain of the fluids. Also an electromagnetic tensor is defined, that simplifies the notation of the Maxwell equations. But tensors are not constrained to physics and mathematics. They have been used, for instance, in medical imaging, where we can highlight two applications: the diffusion tensor image, which represents how molecules diffuse inside the tissues and is broadly used for brain imaging; and the tensorial elastography, which computes the strain and vorticity tensor to analyze the tissues properties. Tensors have also been used in computer vision to provide information about the local structure or to define anisotropic image filters.
Taoka, Toshiaki; Masutani, Yoshitaka; Kawai, Hisashi; Nakane, Toshiki; Matsuoka, Kiwamu; Yasuno, Fumihiko; Kishimoto, Toshifumi; Naganawa, Shinji
2017-04-01
The activity of the glymphatic system is impaired in animal models of Alzheimer's disease (AD). We evaluated the activity of the human glymphatic system in cases of AD with a diffusion-based technique called diffusion tensor image analysis along the perivascular space (DTI-ALPS). Diffusion tensor images were acquired to calculate diffusivities in the x, y, and z axes of the plane of the lateral ventricle body in 31 patients. We evaluated the diffusivity along the perivascular spaces as well as projection fibers and association fibers separately, to acquire an index for diffusivity along the perivascular space (ALPS-index) and correlated them with the mini mental state examinations (MMSE) score. We found a significant negative correlation between diffusivity along the projection fibers and association fibers. We also observed a significant positive correlation between diffusivity along perivascular spaces shown as ALPS-index and the MMSE score, indicating lower water diffusivity along the perivascular space in relation to AD severity. Activity of the glymphatic system may be evaluated with diffusion images. Lower diffusivity along the perivascular space on DTI-APLS seems to reflect impairment of the glymphatic system. This method may be useful for evaluating the activity of the glymphatic system.
Tensor spaces and exterior algebra
Yokonuma, Takeo
1992-01-01
This book explains, as clearly as possible, tensors and such related topics as tensor products of vector spaces, tensor algebras, and exterior algebras. You will appreciate Yokonuma's lucid and methodical treatment of the subject. This book is useful in undergraduate and graduate courses in multilinear algebra. Tensor Spaces and Exterior Algebra begins with basic notions associated with tensors. To facilitate understanding of the definitions, Yokonuma often presents two or more different ways of describing one object. Next, the properties and applications of tensors are developed, including the classical definition of tensors and the description of relative tensors. Also discussed are the algebraic foundations of tensor calculus and applications of exterior algebra to determinants and to geometry. This book closes with an examination of algebraic systems with bilinear multiplication. In particular, Yokonuma discusses the theory of replicas of Chevalley and several properties of Lie algebras deduced from them.
Wei, Liang-Feng; Wang, Shou-Sen; Zheng, Zhao-Cong; Tian, Jun; Xue, Liang
2017-05-01
Diffusion tensor imaging (DTI) shows great advantage in the diagnosis of brain diseases, including cervical spinal cord (CSC) disease. This study aims to obtain the normal values of the DTI parameters for a healthy population and to establish a baseline for CSC disease diagnosis using DTI. A total of 36 healthy adults were subjected to magnetic resonance imaging (MRI) for the entire CSC using the Siemens 3.0 T MR System. Sagittal DTI acquisition was carried out with a single-shot spin-echo echo-planar imaging (EPI) sequence along 12 non-collinear directions. Fractional anisotropy (FA) and apparent diffusion coefficient (ADC) values were determined at different cervical levels using a region of interest (ROI) method, following which they were correlated with parameters, like age and sex. Further, diffusion tensor tracking (DTT) was carried out to reconstruct the white matter fiber bundles of the CSC. The full and complete fiber bundle structure of a normal CSC was confirmed in both the T2-weighted and DTI images. The FA and ADC values were significantly negatively correlated with each other and showed strongly negative and positive correlations with age, respectively, but not with sex. Additionally, there was no significant difference between the FA and the ADC values at different cervical levels. The DTI technique can act as an important supplement to the conventional MRI technique for CSC observation. Moreover, the FA and ADC values can be used as sensitive parameters in the DTI study on the CSC by taking the effects of age into consideration.
Generalized dielectric permittivity tensor
International Nuclear Information System (INIS)
Borzdov, G.N.; Barkovskii, L.M.; Fedorov, F.I.
1986-01-01
The authors deal with the question of what is to be done with the formalism of the electrodynamics of dispersive media based on the introduction of dielectric-permittivity tensors for purely harmonic fields when Voigt waves and waves of more general form exist. An attempt is made to broaden and generalize the formalism to take into account dispersion of waves of the given type. In dispersive media, the polarization, magnetization, and conduction current-density vectors of point and time are determined by the values of the electromagnetic field vectors in the vicinity of this point (spatial dispersion) in the preceding instants of time (time dispersion). The dielectric-permittivity tensor and other tensors of electrodynamic parameters of the medium are introduced in terms of a set of evolution operators and not the set of harmonic function. It is noted that a magnetic-permeability tensor and an elastic-modulus tensor may be introduced for an acoustic field in dispersive anisotropic media with coupling equations of general form
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.
Kronecker-Basis-Representation Based Tensor Sparsity and Its Applications to Tensor Recovery.
Xie, Qi; Zhao, Qian; Meng, Deyu; Xu, Zongben
2017-08-02
It is well known that the sparsity/low-rank of a vector/matrix can be rationally measured by nonzero-entries-number ($l_0$ norm)/nonzero- singular-values-number (rank), respectively. However, data from real applications are often generated by the interaction of multiple factors, which obviously cannot be sufficiently represented by a vector/matrix, while a high order tensor is expected to provide more faithful representation to deliver the intrinsic structure underlying such data ensembles. Unlike the vector/matrix case, constructing a rational high order sparsity measure for tensor is a relatively harder task. To this aim, in this paper we propose a measure for tensor sparsity, called Kronecker-basis-representation based tensor sparsity measure (KBR briefly), which encodes both sparsity insights delivered by Tucker and CANDECOMP/PARAFAC (CP) low-rank decompositions for a general tensor. Then we study the KBR regularization minimization (KBRM) problem, and design an effective ADMM algorithm for solving it, where each involved parameter can be updated with closed-form equations. Such an efficient solver makes it possible to extend KBR to various tasks like tensor completion and tensor robust principal component analysis. A series of experiments, including multispectral image (MSI) denoising, MSI completion and background subtraction, substantiate the superiority of the proposed methods beyond state-of-the-arts.
Killing tensors and conformal Killing tensors from conformal Killing vectors
International Nuclear Information System (INIS)
Rani, Raffaele; Edgar, S Brian; Barnes, Alan
2003-01-01
Koutras has proposed some methods to construct reducible proper conformal Killing tensors and Killing tensors (which are, in general, irreducible) when a pair of orthogonal conformal Killing vectors exist in a given space. We give the completely general result demonstrating that this severe restriction of orthogonality is unnecessary. In addition, we correct and extend some results concerning Killing tensors constructed from a single conformal Killing vector. A number of examples demonstrate that it is possible to construct a much larger class of reducible proper conformal Killing tensors and Killing tensors than permitted by the Koutras algorithms. In particular, by showing that all conformal Killing tensors are reducible in conformally flat spaces, we have a method of constructing all conformal Killing tensors, and hence all the Killing tensors (which will in general be irreducible) of conformally flat spaces using their conformal Killing vectors
Energy Technology Data Exchange (ETDEWEB)
Chatzistavrakidis, Athanasios [Van Swinderen Institute for Particle Physics and Gravity, University of Groningen,Nijenborgh 4, 9747 AG Groningen (Netherlands); Khoo, Fech Scen [Department of Physics and Earth Sciences, Jacobs University Bremen,Campus Ring 1, 28759 Bremen (Germany); Roest, Diederik [Van Swinderen Institute for Particle Physics and Gravity, University of Groningen,Nijenborgh 4, 9747 AG Groningen (Netherlands); Schupp, Peter [Department of Physics and Earth Sciences, Jacobs University Bremen,Campus Ring 1, 28759 Bremen (Germany)
2017-03-13
The particular structure of Galileon interactions allows for higher-derivative terms while retaining second order field equations for scalar fields and Abelian p-forms. In this work we introduce an index-free formulation of these interactions in terms of two sets of Grassmannian variables. We employ this to construct Galileon interactions for mixed-symmetry tensor fields and coupled systems thereof. We argue that these tensors are the natural generalization of scalars with Galileon symmetry, similar to p-forms and scalars with a shift-symmetry. The simplest case corresponds to linearised gravity with Lovelock invariants, relating the Galileon symmetry to diffeomorphisms. Finally, we examine the coupling of a mixed-symmetry tensor to gravity, and demonstrate in an explicit example that the inclusion of appropriate counterterms retains second order field equations.
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...
International Nuclear Information System (INIS)
Ito, Kenji; Masutani, Yoshitaka; Suzuki, Yuichi; Ino, Kenji; Kunimatsu, Akira; Ohtomo, Kuni; Kamagata, Koji; Yasmin, Hasina; Aoki, Shigeki
2013-01-01
Tract-specific analysis (TSA) measures diffusion parameters along a specific fiber that has been extracted by fiber tracking using manual regions of interest (ROIs), but TSA is limited by its requirement for manual operation, poor reproducibility, and high time consumption. We aimed to develop a fully automated extraction method for the cingulum bundle (CB) and to apply the method to TSA in neurobehavioral disorders such as Parkinson's disease (PD). We introduce the voxel classification (VC) and auto diffusion tensor fiber-tracking (AFT) methods of extraction. The VC method directly extracts the CB, skipping the fiber-tracking step, whereas the AFT method uses fiber tracking from automatically selected ROIs. We compared the results of VC and AFT to those obtained by manual diffusion tensor fiber tracking (MFT) performed by 3 operators. We quantified the Jaccard similarity index among the 3 methods in data from 20 subjects (10 normal controls [NC] and 10 patients with Parkinson's disease dementia [PDD]). We used all 3 extraction methods (VC, AFT, and MFT) to calculate the fractional anisotropy (FA) values of the anterior and posterior CB for 15 NC subjects, 15 with PD, and 15 with PDD. The Jaccard index between results of AFT and MFT, 0.72, was similar to the inter-operator Jaccard index of MFT. However, the Jaccard indices between VC and MFT and between VC and AFT were lower. Consequently, the VC method classified among 3 different groups (NC, PD, and PDD), whereas the others classified only 2 different groups (NC, PD or PDD). For TSA in Parkinson's disease, the VC method can be more useful than the AFT and MFT methods for extracting the CB. In addition, the results of patient data analysis suggest that a reduction of FA in the posterior CB may represent a useful biological index for monitoring PD and PDD. (author)
International Nuclear Information System (INIS)
Liu Xiang; Tian Wei; Li Lilin; Kolar, Balasubramanya; Qiu Xing; Chen, Feng; Dogra, Vikram S.
2012-01-01
Purpose: Hyperintensity along the ipsilateral cortical spinal tract (CST) on a diffusion weighted imaging (DWI) has been reported to may be associated with motor disability after brain infarction and can be misdiagnosed as a new infarction. However, the underlying patho-physiology related to this finding is not clear. The goal of our study was to analyze the diffusion tensor imaging (DTI) changes in patients with this hyperintensity. Materials and methods: Eight patients (50 ± 10 years) who exhibited hyperintensity on DWI along ipsilateral CST from 3 to 21 days after stroke onset were reviewed as positive group, including 5 patients with serial DTI examinations. Twelve patients without hyperintensity during the matched examination time were classified as reference group. The apparent diffusion coefficient (ADC), fractional anisotropy (FA), and eigenvalues and their ratios (ipsilateral/contralateral value) in cerebral peduncle were measured, their correlation with motor function scale at eight months after stroke onset were evaluated. Results: The serial examinations showed that hyperintensity could eventually disappear. Both the ipsilateral ADC and FA values were significantly decreased (p < 0.05) compared to the contralateral side. The ipsilateral FA significantly correlated with motor function scale in both groups (r = 0.875, 0.738; p = 0.004, 0.006 respectively). Conclusions: The hyperintensity on DWI is a transient pathological process of Wallerian degeneration after ischemic stroke, its diffusion characteristics include concurrent significant decrease of ipsilateral ADC and FA. The ipsilateral FA value has the potential to predict neurological motor function outcome in such patients.
International Nuclear Information System (INIS)
Alsing, Paul M; McDonald, Jonathan R; Miller, Warner A
2011-01-01
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.
Alsing, Paul M.; McDonald, Jonathan R.; Miller, Warner A.
2011-08-01
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 Poincarè 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.
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 s...
The evolution of tensor polarization
International Nuclear Information System (INIS)
Huang, H.; Lee, S.Y.; Ratner, L.
1993-01-01
By using the equation of motion for the vector polarization, the spin transfer matrix for spin tensor polarization, the spin transfer matrix for spin tensor polarization is derived. The evolution equation for the tensor polarization is studied in the presence of an isolate spin resonance and in the presence of a spin rotor, or snake
Tensor Calculus: Unlearning Vector Calculus
Lee, Wha-Suck; Engelbrecht, Johann; Moller, Rita
2018-01-01
Tensor calculus is critical in the study of the vector calculus of the surface of a body. Indeed, tensor calculus is a natural step-up for vector calculus. This paper presents some pitfalls of a traditional course in vector calculus in transitioning to tensor calculus. We show how a deeper emphasis on traditional topics such as the Jacobian can…
Diffusion tensor image registration using hybrid connectivity and tensor features.
Wang, Qian; Yap, Pew-Thian; Wu, Guorong; Shen, Dinggang
2014-07-01
Most existing diffusion tensor imaging (DTI) registration methods estimate structural correspondences based on voxelwise matching of tensors. The rich connectivity information that is given by DTI, however, is often neglected. In this article, we propose to integrate complementary information given by connectivity features and tensor features for improved registration accuracy. To utilize connectivity information, we place multiple anchors representing different brain anatomies in the image space, and define the connectivity features for each voxel as the geodesic distances from all anchors to the voxel under consideration. The geodesic distance, which is computed in relation to the tensor field, encapsulates information of brain connectivity. We also extract tensor features for every voxel to reflect the local statistics of tensors in its neighborhood. We then combine both connectivity features and tensor features for registration of tensor images. From the images, landmarks are selected automatically and their correspondences are determined based on their connectivity and tensor feature vectors. The deformation field that deforms one tensor image to the other is iteratively estimated and optimized according to the landmarks and their associated correspondences. Experimental results show that, by using connectivity features and tensor features simultaneously, registration accuracy is increased substantially compared with the cases using either type of features alone. Copyright © 2013 Wiley Periodicals, Inc.
Wang, Xiandi; Wang, Hongli; Sun, Chi; Zhou, Shuyi; Meng, Tao; Lv, Feizhou; Ma, Xiaosheng; Xia, Xinlei; Jiang, Jianyuan
2018-04-26
Previous studies have indicated that decreased fractional anisotropy (FA) values on diffusion tensor imaging (DTI) are well correlated with the symptoms of nerve root compression. The aim of our study is to determine primary radiological parameters associated with decreased FA values in patients with lumbar spinal stenosis involving single L5 nerve root. Patients confirmed with single L5 nerve root compression by transforaminal nerve root blocks were included in this study. FA values of L5 nerve roots on both symptomatic and asymptomatic side were obtained. Conventional radiological parameters, such as disc height, degenerative scoliosis, dural sac cross-sectional area (DSCSA), foraminal height (FH), hypertrophic facet joint degeneration (HFJD), sagittal rotation (SR), sedimentation sign, sagittal translation and traction spur were measured. Correlation and regression analyses were performed between the radiological parameters and FA values of the symptomatic L5 nerve roots. A predictive regression equation was established. Twenty-one patients were included in this study. FA values were significantly lower at the symptomatic side comparing to the asymptomatic side (0.263 ± 0.069 vs. 0.334 ± 0.080, P = 0.038). DSCSA, FH, HFJD, and SR were significantly correlated with the decreased FA values, with r = 0.518, 0.443, 0.472 and - 0.910, respectively (P values, and the regression equation is FA = - 0.012 × SR + 0.002 × DSCSA. DSCSA and SR were primary contributors to decreased FA values in LSS patients involving single L5 nerve root, indicating that central canal decompression and segmental stability should be the first considerations in preoperative planning of these patients. These slides can be retrieved under Electronic Supplementary Material.
A Gradient Based Iterative Solutions for Sylvester Tensor Equations
Directory of Open Access Journals (Sweden)
Zhen Chen
2013-01-01
proposed by Ding and Chen, 2005, and by using tensor arithmetic concepts, an iterative algorithm and its modification are established to solve the Sylvester tensor equation. Convergence analysis indicates that the iterative solutions always converge to the exact solution for arbitrary initial value. Finally, some examples are provided to show that the proposed algorithms are effective.
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.
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.
Diffusion tensor smoothing through weighted Karcher means
Carmichael, Owen; Chen, Jun; Paul, Debashis; Peng, Jie
2014-01-01
Diffusion tensor magnetic resonance imaging (MRI) quantifies the spatial distribution of water Diffusion at each voxel on a regular grid of locations in a biological specimen by Diffusion tensors– 3 × 3 positive definite matrices. Removal of noise from DTI is an important problem due to the high scientific relevance of DTI and relatively low signal to noise ratio it provides. Leading approaches to this problem amount to estimation of weighted Karcher means of Diffusion tensors within spatial neighborhoods, under various metrics imposed on the space of tensors. However, it is unclear how the behavior of these estimators varies with the magnitude of DTI sensor noise (the noise resulting from the thermal e!ects of MRI scanning) as well as the geometric structure of the underlying Diffusion tensor neighborhoods. In this paper, we combine theoretical analysis, empirical analysis of simulated DTI data, and empirical analysis of real DTI scans to compare the noise removal performance of three kernel-based DTI smoothers that are based on Euclidean, log-Euclidean, and affine-invariant metrics. The results suggest, contrary to conventional wisdom, that imposing a simplistic Euclidean metric may in fact provide comparable or superior noise removal, especially in relatively unstructured regions and/or in the presence of moderate to high levels of sensor noise. On the contrary, log-Euclidean and affine-invariant metrics may lead to better noise removal in highly structured anatomical regions, especially when the sensor noise is of low magnitude. These findings emphasize the importance of considering the interplay of sensor noise magnitude and tensor field geometric structure when assessing Diffusion tensor smoothing options. They also point to the necessity for continued development of smoothing methods that perform well across a large range of scenarios. PMID:25419264
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.)
The geomagnetic field gradient tensor
DEFF Research Database (Denmark)
Kotsiaros, Stavros; Olsen, Nils
2012-01-01
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...... tensor elements. Furthermore, in current free regions the magnetic gradient tensor becomes symmetric, further reducing the number of independent elements to five. In that case B is a Laplacian potential field and the gradient tensor can be expressed in series of spherical harmonics. We present properties...... 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...
International Nuclear Information System (INIS)
Abraham-shrauner, B.
1975-01-01
The development of solar wind shock models with tensor plasma pressure and the comparison of some of the shock models with the satellite data from Pioneer 6 through Pioneer 9 are reported. Theoretically, difficulties were found in non-turbulent fluid shock models for tensor pressure plasmas. For microscopic shock theories nonlinear growth caused by plasma instabilities was frequently not clearly demonstrated to lead to the formation of a shock. As a result no clear choice for a shock model for the bow shock or interplanetary tensor pressure shocks emerged
Andreev, Pavel A.
2017-02-01
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 for 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.
Federated Tensor Factorization for Computational Phenotyping
Kim, Yejin; Sun, Jimeng; Yu, Hwanjo; Jiang, Xiaoqian
2017-01-01
Tensor factorization models offer an effective approach to convert massive electronic health records into meaningful clinical concepts (phenotypes) for data analysis. These models need a large amount of diverse samples to avoid population bias. An open challenge is how to derive phenotypes jointly across multiple hospitals, in which direct patient-level data sharing is not possible (e.g., due to institutional policies). In this paper, we developed a novel solution to enable federated tensor factorization for computational phenotyping without sharing patient-level data. We developed secure data harmonization and federated computation procedures based on alternating direction method of multipliers (ADMM). Using this method, the multiple hospitals iteratively update tensors and transfer secure summarized information to a central server, and the server aggregates the information to generate phenotypes. We demonstrated with real medical datasets that our method resembles the centralized training model (based on combined datasets) in terms of accuracy and phenotypes discovery while respecting privacy. PMID:29071165
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...
Oehr, Lucy; Anderson, Jacqueline
2017-11-01
To undertake a systematic review and meta-analysis of the relationship between microstructural damage and cognitive function after hospitalized mixed-mechanism (HMM) mild traumatic brain injury (mTBI). PsycInfo, EMBASE, and MEDLINE were used to find relevant empirical articles published between January 2002 and January 2016. Studies that examined the specific relationship between diffusion tensor imaging (DTI) and cognitive test performance were included. The final sample comprised previously medically and psychiatrically healthy adults with HMM mTBI. Specific data were extracted including mTBI definitional criteria, descriptive statistics, outcome measures, and specific results of associations between DTI metrics and cognitive test performance. Of the 248 original articles retrieved and reviewed, 8 studies met all inclusion criteria and were included in the meta-analysis. The meta-analysis revealed statistically significant associations between reduced white matter integrity and poor performance on measures of attention (fractional anisotropy [FA]: d=.413, Pmemory (FA: d=.347, Pattention, memory, and executive function. These findings provide an avenue for future research to examine the causal relationship between mTBI-related neuropathology and cognitive dysfunction. Furthermore, they have important implications for clinical management of patients with mTBI because they provide a more comprehensive understanding of factors that are associated with cognitive dysfunction after mTBI. Copyright © 2017 American Congress of Rehabilitation Medicine. Published by Elsevier Inc. All rights reserved.
International Nuclear Information System (INIS)
Littlejohn, R.G.
1982-01-01
The Hamiltonian structures discovered by Morrison and Greene for various fluid equations were obtained by guessing a Hamiltonian and a suitable Poisson bracket formula, expressed in terms of noncanonical (but physical) coordinates. In general, such a procedure for obtaining a Hamiltonian system does not produce a Hamiltonian phase space in the usual sense (a symplectic manifold), but rather a family of symplectic manifolds. To state the matter in terms of a system with a finite number of degrees of freedom, the family of symplectic manifolds is parametrized by a set of Casimir functions, which are characterized by having vanishing Poisson brackets with all other functions. The number of independent Casimir functions is the corank of the Poisson tensor J/sup ij/, the components of which are the Poisson brackets of the coordinates among themselves. Thus, these Casimir functions exist only when the Poisson tensor is singular
Dillon, Joshua V.; Langmore, Ian; Tran, Dustin; Brevdo, Eugene; Vasudevan, Srinivas; Moore, Dave; Patton, Brian; Alemi, Alex; Hoffman, Matt; Saurous, Rif A.
2017-01-01
The TensorFlow Distributions library implements a vision of probability theory adapted to the modern deep-learning paradigm of end-to-end differentiable computation. Building on two basic abstractions, it offers flexible building blocks for probabilistic computation. Distributions provide fast, numerically stable methods for generating samples and computing statistics, e.g., log density. Bijectors provide composable volume-tracking transformations with automatic caching. Together these enable...
The tensor distribution function.
Leow, A D; Zhu, S; Zhan, L; McMahon, K; de Zubicaray, G I; Meredith, M; Wright, M J; Toga, A W; Thompson, P M
2009-01-01
Diffusion weighted magnetic resonance imaging is a powerful tool that can be employed to study white matter microstructure by examining the 3D displacement profile of water molecules in brain tissue. By applying diffusion-sensitized gradients along a minimum of six directions, second-order tensors (represented by three-by-three positive definite matrices) can be computed to model dominant diffusion processes. However, conventional DTI is not sufficient to resolve more complicated white matter configurations, e.g., crossing fiber tracts. Recently, a number of high-angular resolution schemes with more than six gradient directions have been employed to address this issue. In this article, we introduce the tensor distribution function (TDF), a probability function defined on the space of symmetric positive definite matrices. Using the calculus of variations, we solve the TDF that optimally describes the observed data. Here, fiber crossing is modeled as an ensemble of Gaussian diffusion processes with weights specified by the TDF. Once this optimal TDF is determined, the orientation distribution function (ODF) can easily be computed by analytic integration of the resulting displacement probability function. Moreover, a tensor orientation distribution function (TOD) may also be derived from the TDF, allowing for the estimation of principal fiber directions and their corresponding eigenvalues.
Tensors, differential forms, and variational principles
Lovelock, David
1989-01-01
Incisive, self-contained account of tensor analysis and the calculus of exterior differential forms, interaction between the concept of invariance and the calculus of variations. Emphasis is on analytical techniques, with large number of problems, from routine manipulative exercises to technically difficult assignments.
Tensor Permutation Matrices in Finite Dimensions
Christian, Rakotonirina
2005-01-01
We have generalised the properties with the tensor product, of one 4x4 matrix which is a permutation matrix, and we call a tensor commutation matrix. Tensor commutation matrices can be constructed with or without calculus. A formula allows us to construct a tensor permutation matrix, which is a generalisation of tensor commutation matrix, has been established. The expression of an element of a tensor commutation matrix has been generalised in the case of any element of a tensor permutation ma...
Kaufman, Jason A; Ahrens, Eric T; Laidlaw, David H; Zhang, Song; Allman, John M
2005-11-01
This report presents initial results of a multimodal analysis of tissue volume and microstructure in the brain of an aye-aye (Daubentonia madagascariensis). The left hemisphere of an aye-aye brain was scanned using T2-weighted structural magnetic resonance imaging (MRI) and diffusion-tensor imaging (DTI) prior to histological processing and staining for Nissl substance and myelinated fibers. The objectives of the experiment were to estimate the volume of gross brain regions for comparison with published data on other prosimians and to validate DTI data on fiber anisotropy with histological measurements of fiber spread. Measurements of brain structure volumes in the specimen are consistent with those reported in the literature: the aye-aye has a very large brain for its body size, a reduced volume of visual structures (V1 and LGN), and an increased volume of the olfactory lobe. This trade-off between visual and olfactory reliance is likely a reflection of the nocturnal extractive foraging behavior practiced by Daubentonia. Additionally, frontal cortex volume is large in the aye-aye, a feature that may also be related to its complex foraging behavior and sensorimotor demands. Analysis of DTI data in the anterior cingulum bundle demonstrates a strong correlation between fiber spread as measured from histological sections and fiber spread as measured from DTI. These results represent the first quantitative comparison of DTI data and fiber-stained histology in the brain. (c) 2005 Wiley-Liss, Inc.
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.
International Nuclear Information System (INIS)
Qin, Yuan-Yuan; Li, Mu-Wei; Oishi, Kenichi; Zhang, Shun; Zhang, Yan; Zhao, Ling-Yun; Zhu, Wen-Zhen; Lei, Hao
2013-01-01
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). 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 feasibility of applying whole-brain analysis methods to the investigation of an AD mouse model. (orig.)
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.
Tang, Xiaoying; Qin, Yuanyuan; Zhu, Wenzhen; Miller, Michael I
2017-04-01
In this article, we present a unified statistical pipeline for analyzing the white matter (WM) tracts morphometry and microstructural integrity, both globally and locally within the same WM tract, from diffusion tensor imaging. Morphometry is quantified globally by the volumetric measurement and locally by the vertexwise surface areas. Meanwhile, microstructural integrity is quantified globally by the mean fractional anisotropy (FA) and trace values within the specific WM tract and locally by the FA and trace values defined at each vertex of its bounding surface. The proposed pipeline consists of four steps: (1) fully automated segmentation of WM tracts in a multi-contrast multi-atlas framework; (2) generation of the smooth surface representations for the WM tracts of interest; (3) common template surface generation on which the localized morphometric and microstructural statistics are defined and a variety of statistical analyses can be conducted; (4) multiple comparison correction to determine the significance of the statistical analysis results. Detailed herein, this pipeline has been applied to the corpus callosum in Alzheimer's disease (AD) with significantly decreased FA values and increased trace values, both globally and locally, being detected in patients with AD when compared to normal aging populations. A subdivision of the corpus callosum in both hemispheres revealed that the AD pathology primarily affects the body and splenium of the corpus callosum. Validation analyses and two multiple comparison correction strategies are provided. Hum Brain Mapp 38:1875-1893, 2017. © 2017 Wiley Periodicals, Inc. © 2017 Wiley Periodicals, Inc.
Tensor Train Neighborhood Preserving Embedding
Wang, Wenqi; Aggarwal, Vaneet; Aeron, Shuchin
2018-05-01
In this paper, we propose a Tensor Train Neighborhood Preserving Embedding (TTNPE) to embed multi-dimensional tensor data into low dimensional tensor subspace. Novel approaches to solve the optimization problem in TTNPE are proposed. For this embedding, we evaluate novel trade-off gain among classification, computation, and dimensionality reduction (storage) for supervised learning. It is shown that compared to the state-of-the-arts tensor embedding methods, TTNPE achieves superior trade-off in classification, computation, and dimensionality reduction in MNIST handwritten digits and Weizmann face datasets.
Notes on super Killing tensors
Energy Technology Data Exchange (ETDEWEB)
Howe, P.S. [Department of Mathematics, King’s College London,The Strand, London WC2R 2LS (United Kingdom); Lindström, University [Department of Physics and Astronomy, Theoretical Physics, Uppsala University,SE-751 20 Uppsala (Sweden); Theoretical Physics, Imperial College London,Prince Consort Road, London SW7 2AZ (United Kingdom)
2016-03-14
The notion of a Killing tensor is generalised to a superspace setting. Conserved quantities associated with these are defined for superparticles and Poisson brackets are used to define a supersymmetric version of the even Schouten-Nijenhuis bracket. Superconformal Killing tensors in flat superspaces are studied for spacetime dimensions 3,4,5,6 and 10. These tensors are also presented in analytic superspaces and super-twistor spaces for 3,4 and 6 dimensions. Algebraic structures associated with superconformal Killing tensors are also briefly discussed.
International Nuclear Information System (INIS)
Levashov, V. A.
2016-01-01
It is possible to associate with every atom or molecule in a liquid its own atomic stress tensor. These atomic stress tensors can be used to describe liquids’ structures and to investigate the connection between structural and dynamic properties. In particular, atomic stresses allow to address atomic scale correlations relevant to the Green-Kubo expression for viscosity. Previously correlations between the atomic stresses of different atoms were studied using the Cartesian representation of the stress tensors or the representation based on spherical harmonics. In this paper we address structural correlations in a 3D model binary liquid using the eigenvalues and eigenvectors of the atomic stress tensors. This approach allows to interpret correlations relevant to the Green-Kubo expression for viscosity in a simple geometric way. On decrease of temperature the changes in the relevant stress correlation function between different atoms are significantly more pronounced than the changes in the pair density function. We demonstrate that this behaviour originates from the orientational correlations between the eigenvectors of the atomic stress tensors. We also found correlations between the eigenvalues of the same atomic stress tensor. For the studied system, with purely repulsive interactions between the particles, the eigenvalues of every atomic stress tensor are positive and they can be ordered: λ 1 ≥ λ 2 ≥ λ 3 ≥ 0. We found that, for the particles of a given type, the probability distributions of the ratios (λ 2 /λ 1 ) and (λ 3 /λ 2 ) are essentially identical to each other in the liquids state. We also found that λ 2 tends to be equal to the geometric average of λ 1 and λ 3 . In our view, correlations between the eigenvalues may represent “the Poisson ratio effect” at the atomic scale.
Energy Technology Data Exchange (ETDEWEB)
Levashov, V. A. [Technological Design Institute of Scientific Instrument Engineering, Novosibirsk 630058 (Russian Federation)
2016-03-07
It is possible to associate with every atom or molecule in a liquid its own atomic stress tensor. These atomic stress tensors can be used to describe liquids’ structures and to investigate the connection between structural and dynamic properties. In particular, atomic stresses allow to address atomic scale correlations relevant to the Green-Kubo expression for viscosity. Previously correlations between the atomic stresses of different atoms were studied using the Cartesian representation of the stress tensors or the representation based on spherical harmonics. In this paper we address structural correlations in a 3D model binary liquid using the eigenvalues and eigenvectors of the atomic stress tensors. This approach allows to interpret correlations relevant to the Green-Kubo expression for viscosity in a simple geometric way. On decrease of temperature the changes in the relevant stress correlation function between different atoms are significantly more pronounced than the changes in the pair density function. We demonstrate that this behaviour originates from the orientational correlations between the eigenvectors of the atomic stress tensors. We also found correlations between the eigenvalues of the same atomic stress tensor. For the studied system, with purely repulsive interactions between the particles, the eigenvalues of every atomic stress tensor are positive and they can be ordered: λ{sub 1} ≥ λ{sub 2} ≥ λ{sub 3} ≥ 0. We found that, for the particles of a given type, the probability distributions of the ratios (λ{sub 2}/λ{sub 1}) and (λ{sub 3}/λ{sub 2}) are essentially identical to each other in the liquids state. We also found that λ{sub 2} tends to be equal to the geometric average of λ{sub 1} and λ{sub 3}. In our view, correlations between the eigenvalues may represent “the Poisson ratio effect” at the atomic scale.
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.
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], pFourier 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 for noninvasive detection of microstructural alterations in the hippocampus proper. These alterations may be potential imaging markers for epileptogenesis
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.)
Dark energy in scalar-tensor theories
International Nuclear Information System (INIS)
Moeller, J.
2007-12-01
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 σ-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.)
Typesafe Abstractions for Tensor Operations
Chen, Tongfei
2017-01-01
We propose a typesafe abstraction to tensors (i.e. multidimensional arrays) exploiting the type-level programming capabilities of Scala through heterogeneous lists (HList), and showcase typesafe abstractions of common tensor operations and various neural layers such as convolution or recurrent neural networks. This abstraction could lay the foundation of future typesafe deep learning frameworks that runs on Scala/JVM.
Indicial tensor manipulation on MACSYMA
International Nuclear Information System (INIS)
Bogen, R.A.; Pavelle, R.
1977-01-01
A new computational tool for physical calculations is described. It is the first computer system capable of performing indicial tensor calculus (as opposed to component tensor calculus). It is now operational on the symbolic manipulation system MACSYMA. The authors outline the capabilities of the system and describe some of the physical problems considered as well as others being examined at this time. (Auth.)
Killing-Yano tensors and Nambu mechanics
International Nuclear Information System (INIS)
Baleanu, D.
1998-01-01
Killing-Yano tensors were introduced in 1952 by Kentaro-Yano from mathematical point of view. The physical interpretation of Killing-Yano tensors of rank higher than two was unclear. We found that all Killing-Yano tensors η i 1 i 2 . .. i n with covariant derivative zero are Nambu tensors. We found that in the case of flat space case all Killing-Yano tensors are Nambu tensors. In the case of Taub-NUT and Kerr-Newmann metric Killing-Yano tensors of order two generate Nambu tensors of rank 3
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
Directory of Open Access Journals (Sweden)
Rui Jiang
Full Text Available Differentiation of high-grade gliomas and solitary brain metastases is an important clinical issue because the treatment strategies differ greatly. Our study aimed to investigate the potential value of diffusion tensor imaging (DTI in differentiating high-grade gliomas from brain metastases using a meta-analytic approach.We searched Pubmed, Embase and the Cochrane Library for relevant articles published in English. Studies that both investigated high-grade gliomas and brain metastases using DTI were included. Random effect model was used to compare fractional anisotropy (FA and mean diffusivity (MD values in the two tumor entities.Nine studies were included into the meta-analysis. In the peritumoral region, compared with brain metastases, high-grade gliomas had a significant increase of FA (SMD = 0.47; 95% CI, 0.22-0.71; P<0.01 and a significant decrease of MD (SMD = -1.49; 95% CI, -1.91 to -1.06; P<0.01. However, in the intratumoral area, no significant change in FA (SMD = 0.16; 95% CI, -0.49 to 0.82; P = 0.73 or MD (SMD = 0.34; 95% CI, -0.91 to 1.60; P = 0.59 was detected between gliomas and metastases.High-grade gliomas may be distinguished from brain metastases by comparing the peritumoral FA and MD values. DTI appears to be a promising tool in diagnosing solitary intracranial lesions.
International Nuclear Information System (INIS)
Fujiwara, Shunrou; Nishimoto, Hideaki; Ogasawara, Kuniaki; Beppu, Takaaki; Sanjo, Katsumi; Koeda, Atsuhiko; Mori, Kiyoshi; Kudo, Kohsuke; Sasaki, Makoto
2012-01-01
The present study aimed to detect the main regions of cerebral white matter (CWM) showing damage in the subacute phase for CO-poisoned patients with chronic neurological symptoms using voxel-based analysis (VBA) with diffusion tensor imaging (DTI). Subjects comprised 22 adult CO-poisoned patients and 16 age-matched healthy volunteers as controls. Patients were classified into patients with transient acute symptoms only (group A) and patients with chronic neurological symptoms (group S). In all patients, DTI covering the whole brain was performed with a 3.0-T magnetic resonance imaging system at 2 weeks after CO exposure. As procedures for VBA, all fractional anisotropy (FA) maps obtained from DTI were spatially normalized, and FA values for all voxels in the whole CWM on normalized FA maps were statistically compared among the two patient groups and controls. Voxels with significant differences in FA were detected at various regions in comparisons between groups S and A and between group S and controls. In these comparisons, more voxels were detected in deep CWM, including the centrum semiovale, than in other regions. A few voxels were detected between group A and controls. Absolute FA values in the centrum semiovale were significantly lower in group S than in group A or controls. VBA demonstrated that CO-poisoned patients with chronic neurological symptoms had already suffered damage to various CWM regions in the subacute phase. In these regions, the centrum semiovale was suggested to be the main region damaged in the subacute phase after CO inhalation. (orig.)
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
Clerx, L.; Visser, P.J.; Verhey, F.; Aalten, P.
2012-01-01
The aim of the present study is to evaluate the diagnostic value of diffusion tensor imaging (DTI) for early Alzheimer's disease (AD) in comparison to widely accepted medial temporal lobe (MTL) atrophy measurements. A systematic literature research was performed into DTI and MTL atrophy in AD and
MATLAB tensor classes for fast algorithm prototyping.
Energy Technology Data Exchange (ETDEWEB)
Bader, Brett William; Kolda, Tamara Gibson (Sandia National Laboratories, Livermore, CA)
2004-10-01
Tensors (also known as mutidimensional arrays or N-way arrays) are used in a variety of applications ranging from chemometrics to psychometrics. We describe four MATLAB classes for tensor manipulations that can be used for fast algorithm prototyping. The tensor class extends the functionality of MATLAB's multidimensional arrays by supporting additional operations such as tensor multiplication. The tensor as matrix class supports the 'matricization' of a tensor, i.e., the conversion of a tensor to a matrix (and vice versa), a commonly used operation in many algorithms. Two additional classes represent tensors stored in decomposed formats: cp tensor and tucker tensor. We descibe all of these classes and then demonstrate their use by showing how to implement several tensor algorithms that have appeared in the literature.
Efficient tensor completion for color image and video recovery: Low-rank tensor train
Bengua, Johann A.; Phien, Ho N.; Tuan, Hoang D.; Do, Minh N.
2016-01-01
This paper proposes a novel approach to tensor completion, which recovers missing entries of data represented by tensors. The approach is based on the tensor train (TT) rank, which is able to capture hidden information from tensors thanks to its definition from a well-balanced matricization scheme. Accordingly, new optimization formulations for tensor completion are proposed as well as two new algorithms for their solution. The first one called simple low-rank tensor completion via tensor tra...
Random SU(2) invariant tensors
Li, Youning; Han, Muxin; Ruan, Dong; Zeng, Bei
2018-04-01
SU(2) invariant tensors are states in the (local) SU(2) tensor product representation but invariant under the global group action. They are of importance in the study of loop quantum gravity. A random tensor is an ensemble of tensor states. An average over the ensemble is carried out when computing any physical quantities. The random tensor exhibits a phenomenon known as ‘concentration of measure’, which states that for any bipartition the average value of entanglement entropy of its reduced density matrix is asymptotically the maximal possible as the local dimensions go to infinity. We show that this phenomenon is also true when the average is over the SU(2) invariant subspace instead of the entire space for rank-n tensors in general. It is shown in our earlier work Li et al (2017 New J. Phys. 19 063029) that the subleading correction of the entanglement entropy has a mild logarithmic divergence when n = 4. In this paper, we show that for n > 4 the subleading correction is not divergent but a finite number. In some special situation, the number could be even smaller than 1/2, which is the subleading correction of random state over the entire Hilbert space of tensors.
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.)
International Nuclear Information System (INIS)
Li Yadi; Feng Xiaoyuan; He Huijin; Ding Ding; Tang Weijun; Zhao Qianhua
2011-01-01
Objective: To evaluate the microstructural integrity of white matter (WM) in patients with amnestic mild cognitive impairment (aMCI) and mild Alzheimer's disease (AD) using voxel-based analysis (VBA), and investigate the relationship between WM abnormalities and gray matter (GM) atrophy. Methods: Thirty-three cases with aMCI, 32 cases with mild AD and 31 normal aging volunteers as control subjects were scanned on a 3.0 T MR system using diffusion tensor imaging (DTI) and three-dimensional spoiled gradient-recalled (3DSPGR) sequences. Fractional anisotropy (FA) maps and morphological images were preprocessed by SPM5 and voxel-based comparisons between the 2 patient groups and the control group were performed by t test. Results: Relative to the control group, patients with aMCI showed significantly reduced FA value in bilateral frontal, temporal and left occipital WM, left anterior part of cingulum, left inferior parietal lobule, and the WM adjacent to the triangular part of the right lateral ventricle (k ≥ 20 voxels). In mild AD, significantly reduced FA value was found in bilateral hippocampal, inferior parietal lobular, frontal, temporal, and occipital WM, bilateral corpus callosum, anterior part of cingulums, the WM adjacent to the triangular part of the bilateral lateral ventricles, left temporal stem, left thalamus, right precuneus (k ≥ 20 voxels). Significantly reduced GM volume was found in left hippocampus, parahippocampal gyrus, lingual gyrus and superior temporal gyrus, bilateral insulae and middle temporal gyri in aMCI group when compared with control group (k ≥ 50 voxels). In mild AD, significantly reduced GM volume was found in bilateral hippocampi, parahippocampal gyri, amygdalae, thalami, temporal, parietal, frontal, occipital cortex (k ≥ 50 voxels). The pattern of areas with reduced FA differs from that of the GM volumetric reduction. No areas with significantly reduced FA was detected in aMCI compared with mild AD. There was no significant
Tensor Product of Polygonal Cell Complexes
Chien, Yu-Yen
2017-01-01
We introduce the tensor product of polygonal cell complexes, which interacts nicely with the tensor product of link graphs of complexes. We also develop the unique factorization property of polygonal cell complexes with respect to the tensor product, and study the symmetries of tensor products of polygonal cell complexes.
The Einstein tensor characterizing some Riemann spaces
International Nuclear Information System (INIS)
Rahman, M.S.
1993-07-01
A formal definition of the Einstein tensor is given. Mention is made of how this tensor plays a role of expressing certain conditions in a precise form. The cases of reducing the Einstein tensor to a zero tensor are studied on its merit. A lucid account of results, formulated as theorems, on Einstein symmetric and Einstein recurrent spaces is then presented. (author). 5 refs
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.
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.
Tensor Completion Algorithms in Big Data Analytics
Song, Qingquan; Ge, Hancheng; Caverlee, James; Hu, Xia
2017-01-01
Tensor completion is a problem of filling the missing or unobserved entries of partially observed tensors. Due to the multidimensional character of tensors in describing complex datasets, tensor completion algorithms and their applications have received wide attention and achievement in areas like data mining, computer vision, signal processing, and neuroscience. In this survey, we provide a modern overview of recent advances in tensor completion algorithms from the perspective of big data an...
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.
Physical and Geometric Interpretations of the Riemann Tensor, Ricci Tensor, and Scalar Curvature
Loveridge, Lee C.
2004-01-01
Various interpretations of the Riemann Curvature Tensor, Ricci Tensor, and Scalar Curvature are described. Also, the physical meanings of the Einstein Tensor and Einstein's Equations are discussed. Finally a derivation of Newtonian Gravity from Einstein's Equations is given.
Thermodynamical inequivalence of quantum stress-energy and spin tensors
International Nuclear Information System (INIS)
Becattini, F.; Tinti, L.
2011-01-01
It is shown that different couples of stress-energy and spin tensors of quantum-relativistic fields, which would be otherwise equivalent, are in fact inequivalent if the second law of thermodynamics is taken into account. The proof of the inequivalence is based on the analysis of a macroscopic system at full thermodynamical equilibrium with a macroscopic total angular momentum and a specific instance is given for the free Dirac field, for which we show that the canonical and Belinfante stress-energy tensors are not equivalent. For this particular case, we show that the difference between the predicted angular momentum densities for a rotating system at full thermodynamical equilibrium is a quantum effect, persisting in the nonrelativistic limit, corresponding to a polarization of particles of the order of (ℎ/2π)ω/KT (ω being the angular velocity) and could in principle be measured experimentally. This result implies that specific stress-energy and spin tensors are physically meaningful even in the absence of gravitational coupling and raises the issue of finding the thermodynamically right (or the right class of) tensors. We argue that the maximization of the thermodynamic potential theoretically allows us to discriminate between two different couples, yet for the present we are unable to provide a theoretical method to single out the best couple of tensors in a given quantum field theory. The existence of a nonvanishing spin tensor would have major consequences in hydrodynamics, gravity and cosmology.
Inference of segmented color and texture description by tensor voting.
Jia, Jiaya; Tang, Chi-Keung
2004-06-01
A robust synthesis method is proposed to automatically infer missing color and texture information from a damaged 2D image by (N)D tensor voting (N > 3). The same approach is generalized to range and 3D data in the presence of occlusion, missing data and noise. Our method translates texture information into an adaptive (N)D tensor, followed by a voting process that infers noniteratively the optimal color values in the (N)D texture space. A two-step method is proposed. First, we perform segmentation based on insufficient geometry, color, and texture information in the input, and extrapolate partitioning boundaries by either 2D or 3D tensor voting to generate a complete segmentation for the input. Missing colors are synthesized using (N)D tensor voting in each segment. Different feature scales in the input are automatically adapted by our tensor scale analysis. Results on a variety of difficult inputs demonstrate the effectiveness of our tensor voting approach.
The tensor rank of tensor product of two three-qubit W states is eight
Chen, Lin; Friedland, Shmuel
2017-01-01
We show that the tensor rank of tensor product of two three-qubit W states is not less than eight. Combining this result with the recent result of M. Christandl, A. K. Jensen, and J. Zuiddam that the tensor rank of tensor product of two three-qubit W states is at most eight, we deduce that the tensor rank of tensor product of two three-qubit W states is eight. We also construct the upper bound of the tensor rank of tensor product of many three-qubit W states.
X-ray strain tensor imaging: FEM simulation and experiments with a micro-CT.
Kim, Jae G; Park, So E; Lee, Soo Y
2014-01-01
In tissue elasticity imaging, measuring the strain tensor components is necessary to solve the inverse problem. However, it is impractical to measure all the tensor components in ultrasound or MRI elastography because of their anisotropic spatial resolution. The objective of this study is to compute 3D strain tensor maps from the 3D CT images of a tissue-mimicking phantom. We took 3D micro-CT images of the phantom twice with applying two different mechanical compressions to it. Applying the 3D image correlation technique to the CT images under different compression, we computed 3D displacement vectors and strain tensors at every pixel. To evaluate the accuracy of the strain tensor maps, we made a 3D FEM model of the phantom, and we computed strain tensor maps through FEM simulation. Experimentally obtained strain tensor maps showed similar patterns to the FEM-simulated ones in visual inspection. The correlation between the strain tensor maps obtained from the experiment and the FEM simulation ranges from 0.03 to 0.93. Even though the strain tensor maps suffer from high level noise, we expect the x-ray strain tensor imaging may find some biomedical applications such as malignant tissue characterization and stress analysis inside the tissues.
Spectral Tensor-Train Decomposition
DEFF Research Database (Denmark)
Bigoni, Daniele; Engsig-Karup, Allan Peter; Marzouk, Youssef M.
2016-01-01
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...... adaptive Smolyak approach. The method is also used to approximate the solution of an elliptic PDE with random input data. The open source software and examples presented in this work are available online (http://pypi.python.org/pypi/TensorToolbox/)....
Confinement through tensor gauge fields
International Nuclear Information System (INIS)
Salam, A.; Strathdee, J.
1977-12-01
Using the 0(3,2)-symmetric de Sitter solution of Einstein's equation describing a strongly interacting tensor field it is shown that hadronic bags confining quarks can be represented as de Sitter ''micro-universes'' with radii given 1/R 2 =lambdak 2 /6. Here k 2 and lambda are the strong coupling and the ''cosmological'' constant which apear in the Einstein equation used. Surprisingly the energy spectrum for the two-body hadronic states is the same as that for a harmonic oscillator potential, though the wave functions are completely different. The Einstein equation can be extended to include colour for the tensor fields
Tensor product of quantum logics
Pulmannová, Sylvia
1985-01-01
A quantum logic is the couple (L,M) where L is an orthomodular σ-lattice and M is a strong set of states on L. The Jauch-Piron property in the σ-form is also supposed for any state of M. A ``tensor product'' of quantum logics is defined. This definition is compared with the definition of a free orthodistributive product of orthomodular σ-lattices. The existence and uniqueness of the tensor product in special cases of Hilbert space quantum logics and one quantum and one classical logic are studied.
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.
International Nuclear Information System (INIS)
Tachibana, Yasuhiko; Obata, Takayuki; Yoshida, Mariko; Hori, Masaaki; Kamagata, Koji; Suzuki, Michimasa; Fukunaga, Issei; Kamiya, Kouhei; Aoki, Shigeki; Yokoyama, Kazumasa; Hattori, Nobutaka; Inoue, Tomio
2015-01-01
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 -3 mm 2 /s) in comparison to control (0.100 x 10 -3 mm 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.)
Energy Technology Data Exchange (ETDEWEB)
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.)
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...
Reciprocal mass tensor : a general form
International Nuclear Information System (INIS)
Roy, C.L.
1978-01-01
Using the results of earlier treatment of wave packets, a general form of reciprocal mass tensor has been obtained. The elements of this tensor are seen to be dependent on momentum as well as space coordinates of the particle under consideration. The conditions under which the tensor would reduce to the usual space-independent form, are discussed and the impact of the space-dependence of this tensor on the motion of Bloch electrons, is examined. (author)
A new deteriorated energy-momentum tensor
International Nuclear Information System (INIS)
Duff, M.J.
1982-01-01
The stress-tensor of a scalar field theory is not unique because of the possibility of adding an 'improvement term'. In supersymmetric field theories the stress-tensor will appear in a super-current multiplet along with the sypersymmetry current. The general question of the supercurrent multiplet for arbitrary deteriorated stress tensors and their relationship to supercurrent multiplets for models with gauge antisymmetric tensors is answered for various models of N = 1, 2 and 4 supersymmetry. (U.K.)
Tensor-based spatiotemporal saliency detection
Dou, Hao; Li, Bin; Deng, Qianqian; Zhang, LiRui; Pan, Zhihong; Tian, Jinwen
2018-03-01
This paper proposes an effective tensor-based spatiotemporal saliency computation model for saliency detection in videos. First, we construct the tensor representation of video frames. Then, the spatiotemporal saliency can be directly computed by the tensor distance between different tensors, which can preserve the complete temporal and spatial structure information of object in the spatiotemporal domain. Experimental results demonstrate that our method can achieve encouraging performance in comparison with the state-of-the-art methods.
Akkerman, Erik M.
2010-01-01
Both in diffusion tensor imaging (DTI) and in generalized diffusion tensor imaging (GDTI) the relation between the diffusion tensor and the measured apparent diffusion coefficients is given by a tensorial equation, which needs to be inverted in order to solve the diffusion tensor. The traditional
Weyl tensors for asymmetric complex curvatures
International Nuclear Information System (INIS)
Oliveira, C.G.
Considering a second rank Hermitian field tensor and a general Hermitian connection the associated complex curvature tensor is constructed. The Weyl tensor that corresponds to this complex curvature is determined. The formalism is applied to the Weyl unitary field theory and to the Moffat gravitational theory. (Author) [pt
Spherical Tensor Calculus for Local Adaptive Filtering
Reisert, Marco; Burkhardt, Hans
In 3D image processing tensors play an important role. While rank-1 and rank-2 tensors are well understood and commonly used, higher rank tensors are rare. This is probably due to their cumbersome rotation behavior which prevents a computationally efficient use. In this chapter we want to introduce the notion of a spherical tensor which is based on the irreducible representations of the 3D rotation group. In fact, any ordinary cartesian tensor can be decomposed into a sum of spherical tensors, while each spherical tensor has a quite simple rotation behavior. We introduce so called tensorial harmonics that provide an orthogonal basis for spherical tensor fields of any rank. It is just a generalization of the well known spherical harmonics. Additionally we propose a spherical derivative which connects spherical tensor fields of different degree by differentiation. Based on the proposed theory we present two applications. We propose an efficient algorithm for dense tensor voting in 3D, which makes use of tensorial harmonics decomposition of the tensor-valued voting field. In this way it is possible to perform tensor voting by linear-combinations of convolutions in an efficient way. Secondly, we propose an anisotropic smoothing filter that uses a local shape and orientation adaptive filter kernel which can be computed efficiently by the use spherical derivatives.
TENSOR DECOMPOSITIONS AND SPARSE LOG-LINEAR MODELS
Johndrow, James E.; Bhattacharya, Anirban; Dunson, David B.
2017-01-01
Contingency table analysis routinely relies on log-linear models, with latent structure analysis providing a common alternative. Latent structure models lead to a reduced rank tensor factorization of the probability mass function for multivariate categorical data, while log-linear models achieve dimensionality reduction through sparsity. Little is known about the relationship between these notions of dimensionality reduction in the two paradigms. We derive several results relating the support of a log-linear model to nonnegative ranks of the associated probability tensor. Motivated by these findings, we propose a new collapsed Tucker class of tensor decompositions, which bridge existing PARAFAC and Tucker decompositions, providing a more flexible framework for parsimoniously characterizing multivariate categorical data. Taking a Bayesian approach to inference, we illustrate empirical advantages of the new decompositions. PMID:29332971
A new Weyl-like tensor of geometric origin
Vishwakarma, Ram Gopal
2018-04-01
A set of new tensors of purely geometric origin have been investigated, which form a hierarchy. A tensor of a lower rank plays the role of the potential for the tensor of one rank higher. The tensors have interesting mathematical and physical properties. The highest rank tensor of the hierarchy possesses all the geometrical properties of the Weyl tensor.
A locally convergent Jacobi iteration for the tensor singular value problem
Shekhawat, Hanumant Singh; Weiland, Siep
2018-01-01
Multi-linear functionals or tensors are useful in study and analysis multi-dimensional signal and system. Tensor approximation, which has various applications in signal processing and system theory, can be achieved by generalizing the notion of singular values and singular vectors of matrices to
Comparison of Magnetic Susceptibility Tensor and Diffusion Tensor of the Brain.
Li, Wei; Liu, Chunlei
2013-10-01
Susceptibility tensor imaging (STI) provides a novel approach for noninvasive assessment of the white matter pathways of the brain. Using mouse brain ex vivo , we compared STI with diffusion tensor imaging (DTI), in terms of tensor values, principal tensor values, anisotropy values, and tensor orientations. Despite the completely different biophysical underpinnings, magnetic susceptibility tensors and diffusion tensors show many similarities in the tensor and principal tensor images, for example, the tensors perpendicular to the fiber direction have the highest gray-white matter contrast, and the largest principal tensor is along the fiber direction. Comparison to DTI fractional anisotropy, the susceptibility anisotropy provides much higher sensitivity to the chemical composition of the white matter, especially myelin. The high sensitivity can be further enhanced with the perfusion of ProHance, a gadolinium-based contrast agent. Regarding the tensor orientations, the direction of the largest principal susceptibility tensor agrees with that of diffusion tensors in major white matter fiber bundles. The STI fiber tractography can reconstruct the fiber pathways for the whole corpus callosum and for white matter fiber bundles that are in close contact but in different orientations. There are some differences between susceptibility and diffusion tensor orientations, which are likely due to the limitations in the current STI reconstruction. With the development of more accurate reconstruction methods, STI holds the promise for probing the white matter micro-architectures with more anatomical details and higher chemical sensitivity.
Tensor voting for robust color edge detection
Moreno, Rodrigo; García, Miguel Ángel; Puig, Domenec
2014-01-01
The final publication is available at Springer via http://dx.doi.org/10.1007/978-94-007-7584-8_9 This chapter proposes two robust color edge detection methods based on tensor voting. The first method is a direct adaptation of the classical tensor voting to color images where tensors are initialized with either the gradient or the local color structure tensor. The second method is based on an extension of tensor voting in which the encoding and voting processes are specifically tailored to ...
The Physical Interpretation of the Lanczos Tensor
Roberts, Mark D.
1999-01-01
The field equations of general relativity can be written as first order differential equations in the Weyl tensor, the Weyl tensor in turn can be written as a first order differential equation in a three index tensor called the Lanczos tensor. The Lanczos tensor plays a similar role in general relativity to that of the vector potential in electro-magnetic theory. The Aharonov-Bohm effect shows that when quantum mechanics is applied to electro-magnetic theory the vector potential is dynamicall...
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...
Diffusion tensor MR microscopy of tissues with low diffusional anisotropy.
Bajd, Franci; Mattea, Carlos; Stapf, Siegfried; Sersa, Igor
2016-06-01
Diffusion tensor imaging exploits preferential diffusional motion of water molecules residing within tissue compartments for assessment of tissue structural anisotropy. However, instrumentation and post-processing errors play an important role in determination of diffusion tensor elements. In the study, several experimental factors affecting accuracy of diffusion tensor determination were analyzed. Effects of signal-to-noise ratio and configuration of the applied diffusion-sensitizing gradients on fractional anisotropy bias were analyzed by means of numerical simulations. In addition, diffusion tensor magnetic resonance microscopy experiments were performed on a tap water phantom and bovine articular cartilage-on-bone samples to verify the simulation results. In both, the simulations and the experiments, the multivariate linear regression of the diffusion-tensor analysis yielded overestimated fractional anisotropy with low SNRs and with low numbers of applied diffusion-sensitizing gradients. An increase of the apparent fractional anisotropy due to unfavorable experimental conditions can be overcome by applying a larger number of diffusion sensitizing gradients with small values of the condition number of the transformation matrix. This is in particular relevant in magnetic resonance microscopy, where imaging gradients are high and the signal-to-noise ratio is low.
Tensor perturbations during inflation in a spatially closed Universe
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Bonga, Béatrice; Gupt, Brajesh; Yokomizo, Nelson, E-mail: bpb165@psu.edu, E-mail: bgupt@gravity.psu.edu, E-mail: yokomizo@gravity.psu.edu [Institute for Gravitation and the Cosmos and Physics Department, The Pennsylvania State University, 104 Lavey Lab, University Park, PA 16802 (United States)
2017-05-01
In a recent paper [1], we studied the evolution of the background geometry and scalar perturbations in an inflationary, spatially closed Friedmann-Lemaȋtre-Robertson-Walker (FLRW) model having constant positive spatial curvature and spatial topology S{sup 3}. Due to the spatial curvature, the early phase of slow-roll inflation is modified, leading to suppression of power in the scalar power spectrum at large angular scales. In this paper, we extend the analysis to include tensor perturbations. We find that, similarly to the scalar perturbations, the tensor power spectrum also shows suppression for long wavelength modes. The correction to the tensor spectrum is limited to the very long wavelength modes, therefore the resulting observable CMB B-mode polarization spectrum remains practically the same as in the standard scenario with flat spatial sections. However, since both the tensor and scalar power spectra are modified, there are scale dependent corrections to the tensor-to-scalar ratio that leads to violation of the standard slow-roll consistency relation.
Nonperturbative loop quantization of scalar-tensor theories of gravity
International Nuclear Information System (INIS)
Zhang Xiangdong; Ma Yongge
2011-01-01
The Hamiltonian formulation of scalar-tensor theories of gravity is derived from their Lagrangian formulation by Hamiltonian analysis. The Hamiltonian formalism marks off two sectors of the theories by the coupling parameter ω(φ). In the sector of ω(φ)=-(3/2), the feasible theories are restricted and a new primary constraint generating conformal transformations of spacetime is obtained, while in the other sector of ω(φ)≠-(3/2), the canonical structure and constraint algebra of the theories are similar to those of general relativity coupled with a scalar field. By canonical transformations, we further obtain the connection-dynamical formalism of the scalar-tensor theories with real su(2) connections as configuration variables in both sectors. This formalism enables us to extend the scheme of nonperturbative loop quantum gravity to the scalar-tensor theories. The quantum kinematical framework for the scalar-tensor theories is rigorously constructed. Both the Hamiltonian constraint operator and master constraint operator are well defined and proposed to represent quantum dynamics. Thus the loop quantum gravity method is also valid for general scalar-tensor theories.
Simultaneous tensor decomposition and completion using factor priors.
Chen, Yi-Lei; Hsu, Chiou-Ting; Liao, Hong-Yuan Mark
2014-03-01
The success of research on matrix completion is evident in a variety of real-world applications. Tensor completion, which is a high-order extension of matrix completion, has also generated a great deal of research interest in recent years. Given a tensor with incomplete entries, existing methods use either factorization or completion schemes to recover the missing parts. However, as the number of missing entries increases, factorization schemes may overfit the model because of incorrectly predefined ranks, while completion schemes may fail to interpret the model factors. In this paper, we introduce a novel concept: complete the missing entries and simultaneously capture the underlying model structure. To this end, we propose a method called simultaneous tensor decomposition and completion (STDC) that combines a rank minimization technique with Tucker model decomposition. Moreover, as the model structure is implicitly included in the Tucker model, we use factor priors, which are usually known a priori in real-world tensor objects, to characterize the underlying joint-manifold drawn from the model factors. By exploiting this auxiliary information, our method leverages two classic schemes and accurately estimates the model factors and missing entries. We conducted experiments to empirically verify the convergence of our algorithm on synthetic data and evaluate its effectiveness on various kinds of real-world data. The results demonstrate the efficacy of the proposed method and its potential usage in tensor-based applications. It also outperforms state-of-the-art methods on multilinear model analysis and visual data completion tasks.
Robust estimation of adaptive tensors of curvature by tensor voting.
Tong, Wai-Shun; Tang, Chi-Keung
2005-03-01
Although curvature estimation from a given mesh or regularly sampled point set is a well-studied problem, it is still challenging when the input consists of a cloud of unstructured points corrupted by misalignment error and outlier noise. Such input is ubiquitous in computer vision. In this paper, we propose a three-pass tensor voting algorithm to robustly estimate curvature tensors, from which accurate principal curvatures and directions can be calculated. Our quantitative estimation is an improvement over the previous two-pass algorithm, where only qualitative curvature estimation (sign of Gaussian curvature) is performed. To overcome misalignment errors, our improved method automatically corrects input point locations at subvoxel precision, which also rejects outliers that are uncorrectable. To adapt to different scales locally, we define the RadiusHit of a curvature tensor to quantify estimation accuracy and applicability. Our curvature estimation algorithm has been proven with detailed quantitative experiments, performing better in a variety of standard error metrics (percentage error in curvature magnitudes, absolute angle difference in curvature direction) in the presence of a large amount of misalignment noise.
Antisymmetric tensor generalizations of affine vector fields.
Houri, Tsuyoshi; Morisawa, Yoshiyuki; Tomoda, Kentaro
2016-02-01
Tensor generalizations of affine vector fields called symmetric and antisymmetric affine tensor fields are discussed as symmetry of spacetimes. We review the properties of the symmetric ones, which have been studied in earlier works, and investigate the properties of the antisymmetric ones, which are the main theme in this paper. It is shown that antisymmetric affine tensor fields are closely related to one-lower-rank antisymmetric tensor fields which are parallelly transported along geodesics. It is also shown that the number of linear independent rank- p antisymmetric affine tensor fields in n -dimensions is bounded by ( n + 1)!/ p !( n - p )!. We also derive the integrability conditions for antisymmetric affine tensor fields. Using the integrability conditions, we discuss the existence of antisymmetric affine tensor fields on various spacetimes.
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
Mesh Denoising based on Normal Voting Tensor and Binary Optimization.
Yadav, Sunil Kumar; Reitebuch, Ulrich; Polthier, Konrad
2017-08-17
This paper presents a two-stage mesh denoising algorithm. Unlike other traditional averaging approaches, our approach uses an element-based normal voting tensor to compute smooth surfaces. By introducing a binary optimization on the proposed tensor together with a local binary neighborhood concept, our algorithm better retains sharp features and produces smoother umbilical regions than previous approaches. On top of that, we provide a stochastic analysis on the different kinds of noise based on the average edge length. The quantitative results demonstrate that the performance of our method is better compared to state-of-the-art smoothing approaches.
Extended vector-tensor theories
Energy Technology Data Exchange (ETDEWEB)
Kimura, Rampei; Naruko, Atsushi; Yoshida, Daisuke, E-mail: rampei@th.phys.titech.ac.jp, E-mail: naruko@th.phys.titech.ac.jp, E-mail: yoshida@th.phys.titech.ac.jp [Department of Physics, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, Tokyo 152-8551 (Japan)
2017-01-01
Recently, several extensions of massive vector theory in curved space-time have been proposed in many literatures. In this paper, we consider the most general vector-tensor theories that contain up to two derivatives with respect to metric and vector field. By imposing a degeneracy condition of the Lagrangian in the context of ADM decomposition of space-time to eliminate an unwanted mode, we construct a new class of massive vector theories where five degrees of freedom can propagate, corresponding to three for massive vector modes and two for massless tensor modes. We find that the generalized Proca and the beyond generalized Proca theories up to the quartic Lagrangian, which should be included in this formulation, are degenerate theories even in curved space-time. Finally, introducing new metric and vector field transformations, we investigate the properties of thus obtained theories under such transformations.
Scalar-tensor linear inflation
Energy Technology Data Exchange (ETDEWEB)
Artymowski, Michał [Institute of Physics, Jagiellonian University, Łojasiewicza 11, 30-348 Kraków (Poland); Racioppi, Antonio, E-mail: Michal.Artymowski@uj.edu.pl, E-mail: Antonio.Racioppi@kbfi.ee [National Institute of Chemical Physics and Biophysics, Rävala 10, 10143 Tallinn (Estonia)
2017-04-01
We investigate two approaches to non-minimally coupled gravity theories which present linear inflation as attractor solution: a) the scalar-tensor theory approach, where we look for a scalar-tensor theory that would restore results of linear inflation in the strong coupling limit for a non-minimal coupling to gravity of the form of f (φ) R /2; b) the particle physics approach, where we motivate the form of the Jordan frame potential by loop corrections to the inflaton field. In both cases the Jordan frame potentials are modifications of the induced gravity inflationary scenario, but instead of the Starobinsky attractor they lead to linear inflation in the strong coupling limit.
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.
An efficient method for tensor voting using steerable filters
Franken, E.M.; Almsick, van M.A.; Rongen, P.M.J.; Florack, L.M.J.; Haar Romenij, ter B.M.; Leonardis, A.; Bischof, H; Pinz, A.
2006-01-01
In many image analysis applications there is a need to extract curves in noisy images. To achieve a more robust extraction, one can exploit correlations of oriented features over a spatial context in the image. Tensor voting is an existing technique to extract features in this way. In this paper, we
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
Energy Technology Data Exchange (ETDEWEB)
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].
Transposes, L-Eigenvalues and Invariants of Third Order Tensors
Qi, Liqun
2017-01-01
Third order tensors have wide applications in mechanics, physics and engineering. The most famous and useful third order tensor is the piezoelectric tensor, which plays a key role in the piezoelectric effect, first discovered by Curie brothers. On the other hand, the Levi-Civita tensor is famous in tensor calculus. In this paper, we study third order tensors and (third order) hypermatrices systematically, by regarding a third order tensor as a linear operator which transforms a second order t...
International Nuclear Information System (INIS)
Sijens, Paul E.; Irwan, Roy; Potze, Jan Hendrik; Oudkerk, Matthijs; Mostert, Jop P.; Keyser, Jacques de
2005-01-01
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 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.)
Teh, Irvin; McClymont, Darryl; Zdora, Marie-Christine; Whittington, Hannah J; Davidoiu, Valentina; Lee, Jack; Lygate, Craig A; Rau, Christoph; Zanette, Irene; Schneider, Jürgen E
2017-03-10
Diffusion tensor imaging (DTI) is widely used to assess tissue microstructure non-invasively. Cardiac DTI enables inference of cell and sheetlet orientations, which are altered under pathological conditions. However, DTI is affected by many factors, therefore robust validation is critical. Existing histological validation is intrinsically flawed, since it requires further tissue processing leading to sample distortion, is routinely limited in field-of-view and requires reconstruction of three-dimensional volumes from two-dimensional images. In contrast, synchrotron radiation imaging (SRI) data enables imaging of the heart in 3D without further preparation following DTI. The objective of the study was to validate DTI measurements based on structure tensor analysis of SRI data. One isolated, fixed rat heart was imaged ex vivo with DTI and X-ray phase contrast SRI, and reconstructed at 100 μm and 3.6 μm isotropic resolution respectively. Structure tensors were determined from the SRI data and registered to the DTI data. Excellent agreement in helix angles (HA) and transverse angles (TA) was observed between the DTI and structure tensor synchrotron radiation imaging (STSRI) data, where HA DTI-STSRI = -1.4° ± 23.2° and TA DTI-STSRI = -1.4° ± 35.0° (mean ± 1.96 standard deviation across all voxels in the left ventricle). STSRI confirmed that the primary eigenvector of the diffusion tensor corresponds with the cardiomyocyte long-axis across the whole myocardium. We have used STSRI as a novel and high-resolution gold standard for the validation of DTI, allowing like-with-like comparison of three-dimensional tissue structures in the same intact heart free of distortion. This represents a critical step forward in independently verifying the structural basis and informing the interpretation of cardiac DTI data, thereby supporting the further development and adoption of DTI in structure-based electro-mechanical modelling and routine clinical
Applications of tensor functions in creep mechanics
International Nuclear Information System (INIS)
Betten, J.
1991-01-01
Within this contribution a short survey is given of some recent advances in the mathematical modelling of materials behaviour under creep conditions. The mechanical behaviour of anisotropic solids requires a suitable mathematical modelling. The properties of tensor functions with several argument tensors constitute a rational basis for a consistent mathematical modelling of complex material behaviour. This paper presents certain principles, methods, and recent successfull applications of tensor functions in solid mechanics. The rules for specifying irreducible sets of tensor invariants and tensor generators for material tensors of rank two and four are also discussed. Furthermore, it is very important that the scalar coefficients in constitutive and evolutional equations are determined as functions of the integrity basis and experimental data. It is explained in detail that these coefficients can be determined by using tensorial interpolation methods. Some examples for practical use are discussed. (orig./RHM)
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...... of seams, including voxels in which the deformation is extensive. Backward mapping, however, cannot reorient tensors in the template space because information about the directional orientation of fiber tracts is contained in the original, unwarped imaging space only, and backward mapping alone cannot...... transfer that information to the template space. To combine the advantages of forward and backward mapping, we propose a novel method for the spatial normalization of diffusion tensor (DT) fields that uses a bijection (a bidirectional mapping with one-to-one correspondences between image spaces) to warp DT...
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
.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...... an all-at-once optimization approach called CMTF-OPT (CMTF-OPTimization), which is a gradient-based optimization approach for joint analysis of matrices and higher-order tensors. We also extend the algorithm to handle coupled incomplete data sets. Using numerical experiments, we demonstrate...
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.
Schrimpf, Martin
2016-01-01
Google's Machine Learning framework TensorFlow was open-sourced in November 2015 [1] and has since built a growing community around it. TensorFlow is supposed to be flexible for research purposes while also allowing its models to be deployed productively. This work is aimed towards people with experience in Machine Learning considering whether they should use TensorFlow in their environment. Several aspects of the framework important for such a decision are examined, such as the heterogenity,...
Efficient Low Rank Tensor Ring Completion
Wang, Wenqi; Aggarwal, Vaneet; Aeron, Shuchin
2017-01-01
Using the matrix product state (MPS) representation of the recently proposed tensor ring decompositions, in this paper we propose a tensor completion algorithm, which is an alternating minimization algorithm that alternates over the factors in the MPS representation. This development is motivated in part by the success of matrix completion algorithms that alternate over the (low-rank) factors. In this paper, we propose a spectral initialization for the tensor ring completion algorithm and ana...
The Riemann-Lovelock Curvature Tensor
Kastor, David
2012-01-01
In order to study the properties of Lovelock gravity theories in low dimensions, we define the kth-order Riemann-Lovelock tensor as a certain quantity having a total 4k-indices, which is kth-order in the Riemann curvature tensor and shares its basic algebraic and differential properties. We show that the kth-order Riemann-Lovelock tensor is determined by its traces in dimensions 2k \\le D
The 1/ N Expansion of Tensor Models with Two Symmetric Tensors
Gurau, Razvan
2018-06-01
It is well known that tensor models for a tensor with no symmetry admit a 1/ N expansion dominated by melonic graphs. This result relies crucially on identifying jackets, which are globally defined ribbon graphs embedded in the tensor graph. In contrast, no result of this kind has so far been established for symmetric tensors because global jackets do not exist. In this paper we introduce a new approach to the 1/ N expansion in tensor models adapted to symmetric tensors. In particular we do not use any global structure like the jackets. We prove that, for any rank D, a tensor model with two symmetric tensors and interactions the complete graph K D+1 admits a 1/ N expansion dominated by melonic graphs.
Dictionary-Based Tensor Canonical Polyadic Decomposition
Cohen, Jeremy Emile; Gillis, Nicolas
2018-04-01
To ensure interpretability of extracted sources in tensor decomposition, we introduce in this paper a dictionary-based tensor canonical polyadic decomposition which enforces one factor to belong exactly to a known dictionary. A new formulation of sparse coding is proposed which enables high dimensional tensors dictionary-based canonical polyadic decomposition. The benefits of using a dictionary in tensor decomposition models are explored both in terms of parameter identifiability and estimation accuracy. Performances of the proposed algorithms are evaluated on the decomposition of simulated data and the unmixing of hyperspectral images.
Bayesian regularization of diffusion tensor images
DEFF Research Database (Denmark)
Frandsen, Jesper; Hobolth, Asger; Østergaard, Leif
2007-01-01
Diffusion tensor imaging (DTI) is a powerful tool in the study of the course of nerve fibre bundles in the human brain. Using DTI, the local fibre orientation in each image voxel can be described by a diffusion tensor which is constructed from local measurements of diffusion coefficients along...... several directions. The measured diffusion coefficients and thereby the diffusion tensors are subject to noise, leading to possibly flawed representations of the three dimensional fibre bundles. In this paper we develop a Bayesian procedure for regularizing the diffusion tensor field, fully utilizing...
A RENORMALIZATION PROCEDURE FOR TENSOR MODELS AND SCALAR-TENSOR THEORIES OF GRAVITY
SASAKURA, NAOKI
2010-01-01
Tensor models are more-index generalizations of the so-called matrix models, and provide models of quantum gravity with the idea that spaces and general relativity are emergent phenomena. In this paper, a renormalization procedure for the tensor models whose dynamical variable is a totally symmetric real three-tensor is discussed. It is proven that configurations with certain Gaussian forms are the attractors of the three-tensor under the renormalization procedure. Since these Gaussian config...
An optimization approach for fitting canonical tensor decompositions.
Energy Technology Data Exchange (ETDEWEB)
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.
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.
Dirac tensor with heavy photon
Energy Technology Data Exchange (ETDEWEB)
Bytev, V.V.; Kuraev, E.A. [Joint Institute of Nuclear Research, Moscow (Russian Federation). Bogoliubov Lab. of Theoretical Physics; Scherbakova, E.S. [Hamburg Univ. (Germany). 1. Inst. fuer Theoretische Physik
2012-01-15
For the large-angles hard photon emission by initial leptons in process of high energy annihilation of e{sup +}e{sup -} {yields} to hadrons the Dirac tensor is obtained, taking into account the lowest order radiative corrections. The case of large-angles emission of two hard photons by initial leptons is considered. This result is being completed by the kinematics case of collinear hard photons emission as well as soft virtual and real photons and can be used for construction of Monte-Carlo generators. (orig.)
The Scalar, Vector and Tensor Fields in Theory of Elasticity and Plasticity
Directory of Open Access Journals (Sweden)
František FOJTÍK
2014-06-01
Full Text Available This article is devoted to an analysis of scalar, vector and tensor fields, which occur in the loaded and deformed bodies. The aim of this article is to clarify and simplify the creation of an understandable idea of some elementary concepts and quantities in field theories, such as, for example equiscalar levels, scalar field gradient, Hamilton operator, divergence, rotation and gradient of vector or tensor and others. Applications of those mathematical terms are shown in simple elasticity and plasticity tasks. We hope that content of our article might help technicians to make their studies of necessary mathematical chapters of vector and tensor analysis and field theories easier.
Image denoising using non linear diffusion tensors
International Nuclear Information System (INIS)
Benzarti, F.; Amiri, H.
2011-01-01
Image denoising is an important pre-processing step for many image analysis and computer vision system. It refers to the task of recovering a good estimate of the true image from a degraded observation without altering and changing useful structure in the image such as discontinuities and edges. In this paper, we propose a new approach for image denoising based on the combination of two non linear diffusion tensors. One allows diffusion along the orientation of greatest coherences, while the other allows diffusion along orthogonal directions. The idea is to track perfectly the local geometry of the degraded image and applying anisotropic diffusion mainly along the preferred structure direction. To illustrate the effective performance of our model, we present some experimental results on a test and real photographic color images.
Diffusion tensor in electron swarm transport
International Nuclear Information System (INIS)
Makabe, T.; Mori, T.
1983-01-01
Expression for the diffusion tensor of the electron (or light ion) swarm is presented from the higher-order expansion of the velocity distribution in the Boltzmann equation in hydrodynamic stage. Derived diffusion coefficients for the transverse and longitudinal directions include the additional terms representative of the curvature effect under the action of an electric field with the usual-two-term expressions. Numerical analysis is given for the electron swarm in model gases having the momentum transfer cross section Qsub(m)(epsilon)=Q 0 epsilon sup(beta) (β=0, 1/2, 1) using the present theory. As the result, appreciable degree of discrepancy appears between the transverse diffusion coefficient defined here and the conventional expression with increasing of β in Qsub(m). (Author)
3D reconstruction of tensors and vectors
International Nuclear Information System (INIS)
Defrise, Michel; Gullberg, Grant T.
2005-01-01
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
Raman scattering tensors of tyrosine.
Tsuboi, M; Ezaki, Y; Aida, M; Suzuki, M; Yimit, A; Ushizawa, K; Ueda, T
1998-01-01
Polarized Raman scattering measurements have been made of a single crystal of L-tyrosine by the use of a Raman microscope with the 488.0-nm exciting beam from an argon ion laser. The L-tyrosine crystal belongs to the space group P2(1)2(1)2(1) (orthorhombic), and Raman scattering intensities corresponding to the aa, bb, cc, ab and ac components of the crystal Raman tensor have been determined for each prominent Raman band. A similar set of measurements has been made of L-tyrosine-d4, in which four hydrogen atoms on the benzene ring are replaced by deuterium atoms. The effects of NH3-->ND3 and OH-->OD on the Raman spectrum have also been examined. In addition, depolarization ratios of some bands of L-tyrosine in aqueous solutions of pH 13 and pH 1 were examined. For comparison with these experimental results, on the other hand, ab initio molecular orbital calculations have been made of the normal modes of vibration and their associated polarizability oscillations of the L-tyrosine molecule. On the basis of these experimental data and by referring to the results of the calculations, discussions have been presented on the Raman tensors associated to some Raman bands, including those at 829 cm-1 (benzene ring breathing), 642 cm-1 (benzene ring deformation), and 432 cm-1 (C alpha-C beta-C gamma bending).
Algebraic classification of the Weyl tensor in higher dimensions based on its 'superenergy' tensor
International Nuclear Information System (INIS)
Senovilla, Jose M M
2010-01-01
The algebraic classification of the Weyl tensor in the arbitrary dimension n is recovered by means of the principal directions of its 'superenergy' tensor. This point of view can be helpful in order to compute the Weyl aligned null directions explicitly, and permits one to obtain the algebraic type of the Weyl tensor by computing the principal eigenvalue of rank-2 symmetric future tensors. The algebraic types compatible with states of intrinsic gravitational radiation can then be explored. The underlying ideas are general, so that a classification of arbitrary tensors in the general dimension can be achieved. (fast track communication)
Gravitational Metric Tensor Exterior to Rotating Homogeneous ...
African Journals Online (AJOL)
The covariant and contravariant metric tensors exterior to a homogeneous spherical body rotating uniformly about a common φ axis with constant angular velocity ω is constructed. The constructed metric tensors in this gravitational field have seven non-zero distinct components.The Lagrangian for this gravitational field is ...
Tensor Network Quantum Virtual Machine (TNQVM)
Energy Technology Data Exchange (ETDEWEB)
2016-11-18
There is a lack of state-of-the-art quantum computing simulation software that scales on heterogeneous systems like Titan. Tensor Network Quantum Virtual Machine (TNQVM) provides a quantum simulator that leverages a distributed network of GPUs to simulate quantum circuits in a manner that leverages recent results from tensor network theory.
Tensor product varieties and crystals. GL case
Malkin, Anton
2001-01-01
The role of Spaltenstein varieties in the tensor product for GL is explained. In particular a direct (non-combinatorial) proof of the fact that the number of irreducible components of a Spaltenstein variety is equal to a Littlewood-Richardson coefficient (i.e. certain tensor product multiplicity) is obtained.
Differential invariants for higher-rank tensors. A progress report
International Nuclear Information System (INIS)
Tapial, V.
2004-07-01
We outline the construction of differential invariants for higher-rank tensors. In section 2 we outline the general method for the construction of differential invariants. A first result is that the simplest tensor differential invariant contains derivatives of the same order as the rank of the tensor. In section 3 we review the construction for the first-rank tensors (vectors) and second-rank tensors (metrics). In section 4 we outline the same construction for higher-rank tensors. (author)
Beyond Low Rank: A Data-Adaptive Tensor Completion Method
Zhang, Lei; Wei, Wei; Shi, Qinfeng; Shen, Chunhua; Hengel, Anton van den; Zhang, Yanning
2017-01-01
Low rank tensor representation underpins much of recent progress in tensor completion. In real applications, however, this approach is confronted with two challenging problems, namely (1) tensor rank determination; (2) handling real tensor data which only approximately fulfils the low-rank requirement. To address these two issues, we develop a data-adaptive tensor completion model which explicitly represents both the low-rank and non-low-rank structures in a latent tensor. Representing the no...
Unique characterization of the Bel-Robinson tensor
International Nuclear Information System (INIS)
Bergqvist, G; Lankinen, P
2004-01-01
We prove that a completely symmetric and trace-free rank-4 tensor is, up to sign, a Bel-Robinson-type tensor, i.e., the superenergy tensor of a tensor with the same algebraic symmetries as the Weyl tensor, if and only if it satisfies a certain quadratic identity. This may be seen as the first Rainich theory result for rank-4 tensors
Tensor completion and low-n-rank tensor recovery via convex optimization
International Nuclear Information System (INIS)
Gandy, Silvia; Yamada, Isao; Recht, Benjamin
2011-01-01
In this paper we consider sparsity on a tensor level, as given by the n-rank of a tensor. In an important sparse-vector approximation problem (compressed sensing) and the low-rank matrix recovery problem, using a convex relaxation technique proved to be a valuable solution strategy. Here, we will adapt these techniques to the tensor setting. We use the n-rank of a tensor as a sparsity measure and consider the low-n-rank tensor recovery problem, i.e. the problem of finding the tensor of the lowest n-rank that fulfills some linear constraints. We introduce a tractable convex relaxation of the n-rank and propose efficient algorithms to solve the low-n-rank tensor recovery problem numerically. The algorithms are based on the Douglas–Rachford splitting technique and its dual variant, the alternating direction method of multipliers
Weyl curvature tensor in static spherical sources
International Nuclear Information System (INIS)
Ponce de Leon, J.
1988-01-01
The role of the Weyl curvature tensor in static sources of the Schwarzschild field is studied. It is shown that in general the contribution from the Weyl curvature tensor (the ''purely gravitational field energy'') to the mass-energy inside the body may be positive, negative, or zero. It is proved that a positive (negative) contribution from the Weyl tensor tends to increase (decrease) the effective gravitational mass, the red-shift (from a point in the sphere to infinity), as well as the gravitational force which acts on a constituent matter element of a body. It is also proved that the contribution from the Weyl tensor always is negative in sources with surface gravitational potential larger than (4/9. It is pointed out that large negative contributions from the Weyl tensor could give rise to the phenomenon of gravitational repulsion. A simple example which illustrates the results is discussed
A recursive reduction of tensor Feynman integrals
International Nuclear Information System (INIS)
Diakonidis, T.; Riemann, T.; Tausk, J.B.; Fleischer, J.
2009-07-01
We perform a recursive reduction of one-loop n-point rank R tensor Feynman integrals [in short: (n,R)-integrals] for n≤6 with R≤n by representing (n,R)-integrals in terms of (n,R-1)- and (n-1,R-1)-integrals. We use the known representation of tensor integrals in terms of scalar integrals in higher dimension, which are then reduced by recurrence relations to integrals in generic dimension. With a systematic application of metric tensor representations in terms of chords, and by decomposing and recombining these representations, we find the recursive reduction for the tensors. The procedure represents a compact, sequential algorithm for numerical evaluations of tensor Feynman integrals appearing in next-to-leading order contributions to massless and massive three- and four-particle production at LHC and ILC, as well as at meson factories. (orig.)
On Lovelock analogs of the Riemann tensor
Camanho, Xián O.; Dadhich, Naresh
2016-03-01
It is possible to define an analog of the Riemann tensor for Nth order Lovelock gravity, its characterizing property being that the trace of its Bianchi derivative yields the corresponding analog of the Einstein tensor. Interestingly there exist two parallel but distinct such analogs and the main purpose of this note is to reconcile both formulations. In addition we will introduce a simple tensor identity and use it to show that any pure Lovelock vacuum in odd d=2N+1 dimensions is Lovelock flat, i.e. any vacuum solution of the theory has vanishing Lovelock-Riemann tensor. Further, in the presence of cosmological constant it is the Lovelock-Weyl tensor that vanishes.
Energy-momentum tensor and definition of particle states for Robertson-Walker space-time
International Nuclear Information System (INIS)
Brown, M.R.; Dutton, C.R.
1978-01-01
A new regularization scheme is developed for calculating expectation values of the energy-momentum tensor of a quantized scalar field in Robertson-Walker space-times. Using this regularized stress tensor we consider a definition for the vacuum state of the scalar field on any initial hypersurface. Asymptotic methods are developed to investigate the structure of both the divergent and finite terms of the stress tensor when evaluated in this state. The conformal anomaly is discussed in the context of this model. It does not naturally enter into the analysis and we argue that its inclusion is unnecessary
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...... deviations compared to conventional vector observations at almost all latitudes. Analytical and numerical analysis of the spectral properties of the gradient tensor shows that specific combinations of the East-West and North-South gradients have almost identical signal content to the radial gradient...
A Tensor Statistical Model for Quantifying Dynamic Functional Connectivity.
Zhu, Yingying; Zhu, Xiaofeng; Kim, Minjeong; Yan, Jin; Wu, Guorong
2017-06-01
Functional connectivity (FC) has been widely investigated in many imaging-based neuroscience and clinical studies. Since functional Magnetic Resonance Image (MRI) signal is just an indirect reflection of brain activity, it is difficult to accurately quantify the FC strength only based on signal correlation. To address this limitation, we propose a learning-based tensor model to derive high sensitivity and specificity connectome biomarkers at the individual level from resting-state fMRI images. First, we propose a learning-based approach to estimate the intrinsic functional connectivity. In addition to the low level region-to-region signal correlation, latent module-to-module connection is also estimated and used to provide high level heuristics for measuring connectivity strength. Furthermore, sparsity constraint is employed to automatically remove the spurious connections, thus alleviating the issue of searching for optimal threshold. Second, we integrate our learning-based approach with the sliding-window technique to further reveal the dynamics of functional connectivity. Specifically, we stack the functional connectivity matrix within each sliding window and form a 3D tensor where the third dimension denotes for time. Then we obtain dynamic functional connectivity (dFC) for each individual subject by simultaneously estimating the within-sliding-window functional connectivity and characterizing the across-sliding-window temporal dynamics. Third, in order to enhance the robustness of the connectome patterns extracted from dFC, we extend the individual-based 3D tensors to a population-based 4D tensor (with the fourth dimension stands for the training subjects) and learn the statistics of connectome patterns via 4D tensor analysis. Since our 4D tensor model jointly (1) optimizes dFC for each training subject and (2) captures the principle connectome patterns, our statistical model gains more statistical power of representing new subject than current state
Efficient Tensor Completion for Color Image and Video Recovery: Low-Rank Tensor Train.
Bengua, Johann A; Phien, Ho N; Tuan, Hoang Duong; Do, Minh N
2017-05-01
This paper proposes a novel approach to tensor completion, which recovers missing entries of data represented by tensors. The approach is based on the tensor train (TT) rank, which is able to capture hidden information from tensors thanks to its definition from a well-balanced matricization scheme. Accordingly, new optimization formulations for tensor completion are proposed as well as two new algorithms for their solution. The first one called simple low-rank tensor completion via TT (SiLRTC-TT) is intimately related to minimizing a nuclear norm based on TT rank. The second one is from a multilinear matrix factorization model to approximate the TT rank of a tensor, and is called tensor completion by parallel matrix factorization via TT (TMac-TT). A tensor augmentation scheme of transforming a low-order tensor to higher orders is also proposed to enhance the effectiveness of SiLRTC-TT and TMac-TT. Simulation results for color image and video recovery show the clear advantage of our method over all other methods.
Tensor network method for reversible classical computation
Yang, Zhi-Cheng; Kourtis, Stefanos; Chamon, Claudio; Mucciolo, Eduardo R.; Ruckenstein, Andrei E.
2018-03-01
We develop a tensor network technique that can solve universal reversible classical computational problems, formulated as vertex models on a square lattice [Nat. Commun. 8, 15303 (2017), 10.1038/ncomms15303]. By encoding the truth table of each vertex constraint in a tensor, the total number of solutions compatible with partial inputs and outputs at the boundary can be represented as the full contraction of a tensor network. We introduce an iterative compression-decimation (ICD) scheme that performs this contraction efficiently. The ICD algorithm first propagates local constraints to longer ranges via repeated contraction-decomposition sweeps over all lattice bonds, thus achieving compression on a given length scale. It then decimates the lattice via coarse-graining tensor contractions. Repeated iterations of these two steps gradually collapse the tensor network and ultimately yield the exact tensor trace for large systems, without the need for manual control of tensor dimensions. Our protocol allows us to obtain the exact number of solutions for computations where a naive enumeration would take astronomically long times.
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.
Conformal field theories and tensor categories. Proceedings
International Nuclear Information System (INIS)
Bai, Chengming; Fuchs, Juergen; Huang, Yi-Zhi; Kong, Liang; Runkel, Ingo; Schweigert, Christoph
2014-01-01
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.
Tensor Fields for Use in Fractional-Order Viscoelasticity
Freed, Alan D.; Diethelm, Kai
2003-01-01
To be able to construct viscoelastic material models from fractional0order differentegral equations that are applicable for 3D finite-strain analysis requires definitions for fractional derivatives and integrals for symmetric tensor fields, like stress and strain. We define these fields in the body manifold. We then map them ito spatial fields expressed in terms of an Eulerian or Lagrangian reference frame where most analysts prefer to solve boundary problems.
Local transformations of units in scalar-tensor cosmology
International Nuclear Information System (INIS)
Catena, R.; Pietroni, M.; Scarabello, L.; Padua Univ.
2006-10-01
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.)
Abelian gauge theories with tensor gauge fields
International Nuclear Information System (INIS)
Kapuscik, E.
1984-01-01
Gauge fields of arbitrary tensor type are introduced. In curved space-time the gravitational field serves as a bridge joining different gauge fields. The theory of second order tensor gauge field is developed on the basis of close analogy to Maxwell electrodynamics. The notion of tensor current is introduced and an experimental test of its detection is proposed. The main result consists in a coupled set of field equations representing a generalization of Maxwell theory in which the Einstein equivalence principle is not satisfied. (author)
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...
Scalable Tensor Factorizations with Missing Data
DEFF Research Database (Denmark)
Acar, Evrim; Dunlavy, Daniel M.; Kolda, Tamara G.
2010-01-01
of missing data, many important data sets will be discarded or improperly analyzed. Therefore, we need a robust and scalable approach for factorizing multi-way arrays (i.e., tensors) in the presence of missing data. We focus on one of the most well-known tensor factorizations, CANDECOMP/PARAFAC (CP...... 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...
Surface tensor estimation from linear sections
DEFF Research Database (Denmark)
Kousholt, Astrid; Kiderlen, Markus; Hug, Daniel
From Crofton's formula for Minkowski tensors we derive stereological estimators of translation invariant surface tensors of convex bodies in the n-dimensional Euclidean space. The estimators are based on one-dimensional linear sections. In a design based setting we suggest three types of estimators....... These are based on isotropic uniform random lines, vertical sections, and non-isotropic random lines, respectively. Further, we derive estimators of the specific surface tensors associated with a stationary process of convex particles in the model based setting....
Surface tensor estimation from linear sections
DEFF Research Database (Denmark)
Kousholt, Astrid; Kiderlen, Markus; Hug, Daniel
2015-01-01
From Crofton’s formula for Minkowski tensors we derive stereological estimators of translation invariant surface tensors of convex bodies in the n-dimensional Euclidean space. The estimators are based on one-dimensional linear sections. In a design based setting we suggest three types of estimators....... These are based on isotropic uniform random lines, vertical sections, and non-isotropic random lines, respectively. Further, we derive estimators of the specific surface tensors associated with a stationary process of convex particles in the model based setting....
Tensor products of higher almost split sequences
Pasquali, Andrea
2015-01-01
We investigate how the higher almost split sequences over a tensor product of algebras are related to those over each factor. Herschend and Iyama gave a precise criterion for when the tensor product of an $n$-representation finite algebra and an $m$-representation finite algebra is $(n+m)$-representation finite. In this case we give a complete description of the higher almost split sequences over the tensor product by expressing every higher almost split sequence as the mapping cone of a suit...
Scalable tensor factorizations for incomplete data
DEFF Research Database (Denmark)
Acar, Evrim; Dunlavy, Daniel M.; KOlda, Tamara G.
2011-01-01
to factorize data sets with missing values with the goal of capturing the underlying latent structure of the data and possibly reconstructing missing values (i.e., tensor completion). We focus on one of the most well-known tensor factorizations that captures multi-linear structure, CANDECOMP/PARAFAC (CP...... 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...
Directory of Open Access Journals (Sweden)
Ruili Li
2015-12-01
Conclusion: Multiple cerebral white matter fiber tracts are damaged in HIV-infected patients without cognitive impairment. Quantitative analysis of DTI using TBSS is valuable in evaluating changes of HIV-associated white matter microstructures.
Stefanou, Maria-Ioanna; Lumsden, Daniel E; Ashmore, Jonathan; Ashkan, Keyoumars; Lin, Jean-Pierre; Charles-Edwards, Geoffrey
2016-10-01
Non-invasive measures of corticospinal tract (CST) integrity may help to guide clinical interventions, particularly in children and young people (CAYP) with motor disorders. We compared diffusion tensor imaging (DTI) metrics extracted from the CST generated by tensor and non-tensor based tractography algorithms. For a group of 25 CAYP undergoing clinical evaluation, the CST was reconstructed using (1) deterministic tensor-based tractography algorithm, (2) probabilistic tensor-based, and (3) constrained spherical deconvolution (CSD)-derived tractography algorithms. Choice of tractography algorithm significantly altered the results of tracking. Larger tracts were consistently defined with CSD, with differences in FA but not MD values for tracts to the pre- or post-central gyrus. Differences between deterministic and probabilistic tensor-based algorithms were minimal. Non-tensor reconstructed tracts appeared to be more anatomically representative. Examining metrics along the tract, difference in FA values appeared to be greatest in voxels with predominantly single-fibre orientations. Less pronounced differences were seen outwith of these regions. With an increasing interest in the applications of tractography analysis at all stages of movement disorder surgery, it is important that clinicians remain alert to the consequences of choice of tractography algorithm on subsequently generated tracts, including differences in volumes, anatomical reconstruction, and DTI metrics, the latter of which will have global as well as more regional effects. Tract-wide analysis of DTI based metrics is of limited utility, and a more segmental approach to analysis may be appropriate, particularly if disruption to a focal region of a white matter pathway is anticipated.
General projective relativity and the vector-tensor gravitational field
International Nuclear Information System (INIS)
Arcidiacono, G.
1986-01-01
In the general projective relativity, the induced 4-dimensional metric is symmetric in three cases, and we obtain the vector-tensor, the scalar-tensor, and the scalar-vector-tensor theories of gravitation. In this work we examine the vector-tensor theory, similar to the Veblen's theory, but with a different physical interpretation
TensorFlow Agents: Efficient Batched Reinforcement Learning in TensorFlow
Hafner, Danijar; Davidson, James; Vanhoucke, Vincent
2017-01-01
We introduce TensorFlow Agents, an efficient infrastructure paradigm for building parallel reinforcement learning algorithms in TensorFlow. We simulate multiple environments in parallel, and group them to perform the neural network computation on a batch rather than individual observations. This allows the TensorFlow execution engine to parallelize computation, without the need for manual synchronization. Environments are stepped in separate Python processes to progress them in parallel witho...
Reconstruction of convex bodies from surface tensors
DEFF Research Database (Denmark)
Kousholt, Astrid; Kiderlen, Markus
. The output of the reconstruction algorithm is a polytope P, where the surface tensors of P and K are identical up to rank s. We establish a stability result based on a generalization of Wirtinger’s inequality that shows that for large s, two convex bodies are close in shape when they have identical surface...... that are translates of each other. An algorithm for reconstructing an unknown convex body in R 2 from its surface tensors up to a certain rank is presented. Using the reconstruction algorithm, the shape of an unknown convex body can be approximated when only a finite number s of surface tensors are available...... tensors up to rank s. This is used to establish consistency of the developed reconstruction algorithm....
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...... of surface tensors are available for reconstruction, we recommend to use certain values of the surface tensors, namely harmonic intrinsic volumes instead of the surface tensors evaluated at the standard basis. The second algorithm we present is based on harmonic intrinsic volumes 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 on measurements subject to noise is established under certain assumptions on the noise...
Energy-momentum tensor in scalar QED
International Nuclear Information System (INIS)
Joglekar, S.D.; Misra, A.
1988-01-01
We consider the renormalization of the energy-momentum tensor in scalar quantum electrodynamics. We show the need for adding an improvement term to the conventional energy-momentum tensor. We consider two possible forms for the improvement term: (i) one in which the improvement coefficient is a finite function of bare parameters of the theory (so that the energy-momentum tensor can be obtained from an action that is a finite function of bare quantities); (ii) one in which the improvement coefficient is a finite quantity, i.e., a finite function of renormalized parameters. We establish a negative result; viz., neither form leads to a finite energy-momentum tensor to O(e 2 λ/sup n/). .AE
Potentials for transverse trace-free tensors
International Nuclear Information System (INIS)
Conboye, Rory; Murchadha, Niall Ó
2014-01-01
In constructing and understanding initial conditions in the 3 + 1 formalism for numerical relativity, the transverse and trace-free (TT) part of the extrinsic curvature plays a key role. We know that TT tensors possess two degrees of freedom per space point. However, finding an expression for a TT tensor depending on only two scalar functions is a non-trivial task. Assuming either axial or translational symmetry, expressions depending on two scalar potentials alone are derived here for all TT tensors in flat 3-space. In a more general spatial slice, only one of these potentials is found, the same potential given in (Baker and Puzio 1999 Phys. Rev. D 59 044030) and (Dain 2001 Phys. Rev. D 64 124002), with the remaining equations reduced to a partial differential equation, depending on boundary conditions for a solution. As an exercise, we also derive the potentials which give the Bowen-York curvature tensor in flat space. (paper)
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.
Loop optimization for tensor network renormalization
Yang, Shuo; Gu, Zheng-Cheng; Wen, Xiao-Gang
We introduce a tensor renormalization group scheme for coarse-graining a two-dimensional tensor network, which can be successfully applied to both classical and quantum systems on and off criticality. The key idea of our scheme is to deform a 2D tensor network into small loops and then optimize tensors on each loop. In this way we remove short-range entanglement at each iteration step, and significantly improve the accuracy and stability of the renormalization flow. We demonstrate our algorithm in the classical Ising model and a frustrated 2D quantum model. NSF Grant No. DMR-1005541 and NSFC 11274192, BMO Financial Group, John Templeton Foundation, Government of Canada through Industry Canada, Province of Ontario through the Ministry of Economic Development & Innovation.
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.
Algebraic classification of the conformal tensor
International Nuclear Information System (INIS)
Ares de Parga, Gonzalo; Chavoya, O.; Lopez B, J.L.; Ovando Z, Gerardo
1989-01-01
Starting from the Petrov matrix method, we deduce a new algorithm (adaptable to computers), within the Newman-Penrose formalism, to obtain the algebraic type of the Weyl tensor in general relativity. (author)
Effects of tensor forces in nuclei
International Nuclear Information System (INIS)
Tanihata, Isao
2013-01-01
Recent studies of nuclei far from the stability line have revealed drastic changes in nuclear orbitals and reported the appearance of new magic numbers and the disappearance of magic numbers observed at the stability line. One of the important reasons for such changes is considered to be because of the effect of tensor forces on nuclear structure. Although the role of tensor forces in binding very light nuclei such as deuterons and 4 He has been known, direct experimental evidence for the effect on nuclear structure is scarce. In this paper, I review known effects of tensor forces in nuclei and then discuss the recently raised question of s–p wave mixing in a halo nucleus of 11 Li. Following these reviews, the development of a new experiment to see the high-momentum components due to the tensor forces is discussed and some of the new data are presented. (paper)
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.
Yiu, Chang-li; Wilde, Carroll O.
Vector analysis is viewed to play a key role in many branches of engineering and the physical sciences. This unit is geared towards deriving identities and establishing "machinery" to make derivations a routine task. It is noted that the module is not an applications unit, but has as its primary objective the goal of providing science,…
Geometric decomposition of the conformation tensor in viscoelastic turbulence
Hameduddin, Ismail; Meneveau, Charles; Zaki, Tamer A.; Gayme, Dennice F.
2018-05-01
This work introduces a mathematical approach to analysing the polymer dynamics in turbulent viscoelastic flows that uses a new geometric decomposition of the conformation tensor, along with associated scalar measures of the polymer fluctuations. The approach circumvents an inherent difficulty in traditional Reynolds decompositions of the conformation tensor: the fluctuating tensor fields are not positive-definite and so do not retain the physical meaning of the tensor. The geometric decomposition of the conformation tensor yields both mean and fluctuating tensor fields that are positive-definite. The fluctuating tensor in the present decomposition has a clear physical interpretation as a polymer deformation relative to the mean configuration. Scalar measures of this fluctuating conformation tensor are developed based on the non-Euclidean geometry of the set of positive-definite tensors. Drag-reduced viscoelastic turbulent channel flow is then used an example case study. The conformation tensor field, obtained using direct numerical simulations, is analysed using the proposed framework.
MULTISCALE TENSOR ANISOTROPIC FILTERING OF FLUORESCENCE MICROSCOPY FOR DENOISING MICROVASCULATURE.
Prasath, V B S; Pelapur, R; Glinskii, O V; Glinsky, V V; Huxley, V H; Palaniappan, K
2015-04-01
Fluorescence microscopy images are contaminated by noise and improving image quality without blurring vascular structures by filtering is an important step in automatic image analysis. The application of interest here is to automatically extract the structural components of the microvascular system with accuracy from images acquired by fluorescence microscopy. A robust denoising process is necessary in order to extract accurate vascular morphology information. For this purpose, we propose a multiscale tensor with anisotropic diffusion model which progressively and adaptively updates the amount of smoothing while preserving vessel boundaries accurately. Based on a coherency enhancing flow with planar confidence measure and fused 3D structure information, our method integrates multiple scales for microvasculature preservation and noise removal membrane structures. Experimental results on simulated synthetic images and epifluorescence images show the advantage of our improvement over other related diffusion filters. We further show that the proposed multiscale integration approach improves denoising accuracy of different tensor diffusion methods to obtain better microvasculature segmentation.
Estimation of Uncertainties of Full Moment Tensors
2017-10-06
For our moment tensor inversions, we use the ‘cut-and-paste’ ( CAP ) code of Zhu and Helmberger (1996) and Zhu and Ben-Zion (2013), with some...modifications. For the misfit function we use an L1 norm Silwal and Tape (2016), and we incorporate the number of misfitting polarities into the waveform... norm of the eigenvalue triple provides the magnitude of the moment tensor, leaving two free parameters to define the source type. In the same year
Superconformal tensor calculus in five dimensions
International Nuclear Information System (INIS)
Fujita, Tomoyuki; Ohashi, Keisuke
2001-01-01
We present a full superconformal tensor calculus in five spacetime dimensions in which the Weyl multiplet has 32 Bose plus 32 Fermi degrees of freedom. It is derived using dimensional reduction from the 6D superconformal tensor calculus. We present two types of 32+32 Weyl multiplets, a vector multiplet, linear multiplet, hypermultiplet and nonlinear multiplet. Their superconformal transformation laws and the embedding and invariant action formulas are given. (author)
Goldsborough, Peter
2016-01-01
Deep learning is a branch of artificial intelligence employing deep neural network architectures that has significantly advanced the state-of-the-art in computer vision, speech recognition, natural language processing and other domains. In November 2015, Google released $\\textit{TensorFlow}$, an open source deep learning software library for defining, training and deploying machine learning models. In this paper, we review TensorFlow and put it in context of modern deep learning concepts and ...
Geometrical foundations of tensor calculus and relativity
Schuller , Frédéric; Lorent , Vincent
2006-01-01
Manifolds, particularly space curves: basic notions 1 The first groundform, the covariant metric tensor 11 The second groundform, Meusnier's theorem 19 Transformation groups in the plane 28 Co- and contravariant components for a special affine transformation in the plane 29 Surface vectors 32 Elements of tensor calculus 36 Generalization of the first groundform to the space 46 The covariant (absolute) derivation 57 Examples from elasticity theory 61 Geodesic lines 63 Main curvatur...
Diffusion tensor MRI: clinical applications
International Nuclear Information System (INIS)
Meli, Francisco; Romero, Carlos; Carpintiero, Silvina; Salvatico, Rosana; Lambre, Hector; Vila, Jose
2005-01-01
Purpose: To evaluate the usefulness of diffusion-tensor imaging (DTI) on different neurological diseases, and to know if this technique shows additional information than conventional Magnetic Resonance Imaging (MRI). Materials and method: Eight patients, with neurological diseases (five patients with brain tumors, one with multiple sclerosis (MS), one with variant Creutzfeldt-Jakob disease (vCJD) and the other with delayed CO intoxication were evaluated. A MR scanner of 1.5 T was used and conventional sequences and DTI with twenty-five directions were done. Quantitative maps were gotten, where the fractional anisotropy (FA) through regions of interest (ROIs) in specific anatomic area were quantified (i.e.: internal and external capsules, frontal and temporal bundles, corpus fibers). Results: In the patients with brain tumors, there was a decrease of FA on intra and peritumoral fibers. Some of them had a disruption in their pattern. In patients with MS and CO intoxication, partial interruption along white matter bundles was demonstrated. However, a 'mismatch' between the findings of FLAIR, Diffusion-weighted images (DWI) and DTI, in the case of CO intoxication, was seen. Conclusions: DTI gave more information compared to conventional sequences about ultrastructural brain tissue in almost all the diseases above mentioned. Therefore, there is a work in progress about DTI acquisition, to evaluate a new technique, called tractography. (author)
Multivariate tensor-based brain anatomical surface morphometry via holomorphic one-forms.
Wang, Yalin; Chan, Tony F; Toga, Arthur W; Thompson, Paul M
2009-01-01
Here we introduce multivariate tensor-based surface morphometry using holomorphic one-forms to study brain anatomy. We computed new statistics from the Riemannian metric tensors that retain the full information in the deformation tensor fields. We introduce two different holomorphic one-forms that induce different surface conformal parameterizations. We applied this framework to 3D MRI data to analyze hippocampal surface morphometry in Alzheimer's Disease (AD; 26 subjects), lateral ventricular surface morphometry in HIV/AIDS (19 subjects) and cortical surface morphometry in Williams Syndrome (WS; 80 subjects). Experimental results demonstrated that our method powerfully detected brain surface abnormalities. Multivariate statistics on the local tensors outperformed other TBM methods including analysis of the Jacobian determinant, the largest eigenvalue, or the pair of eigenvalues, of the surface Jacobian matrix.
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...
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.
On the concircular curvature tensor of Riemannian manifolds
International Nuclear Information System (INIS)
Rahman, M.S.; Lal, S.
1990-06-01
Definition of the concircular curvature tensor, Z hijk , along with Z-tensor, Z ij , is given and some properties of Z hijk are described. Tensors identical with Z hijk are shown. A necessary and sufficient condition that a Riemannian V n has zero Z-tensor is found. A number of theorems on concircular symmetric space, concircular recurrent space (Z n -space) and Z n -space with zero Z-tensor are deduced. (author). 6 refs
(Ln-bar, g)-spaces. Special tensor fields
International Nuclear Information System (INIS)
Manoff, S.; Dimitrov, B.
1998-01-01
The Kronecker tensor field, the contraction tensor field, as well as the multi-Kronecker and multi-contraction tensor fields are determined and the action of the covariant differential operator, the Lie differential operator, the curvature operator, and the deviation operator on these tensor fields is established. The commutation relations between the operators Sym and Asym and the covariant and Lie differential operators are considered acting on symmetric and antisymmetric tensor fields over (L n bar, g)-spaces
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.)
Two-photon couplings of 1 = 0 scalars and tensors from analysis of new γγ → ππ data
International Nuclear Information System (INIS)
Morgan, D.; Pennington, M.R.
1989-11-01
New data on γγ→π + π - and π 0 π 0 admit an amplitude analysis whereby two-photon couplings of the I = 0 scalars and of the f 2 (1270) can be extracted in a much more model independent way than hitherto. Alternative trial forms respecting known properties at low energies and of final state interactions are fitted to the data. The ensuing resonance couplings span a much wider range than is commonly supposed. The best fits correspond to solutions with a relatively large S-wave coupling (∼ 8keV) through the f 2 -region. All fits have an S* coupling of about 1/2 keV. (author)
Marin Quintero, Maider J.
2013-01-01
The structure tensor for vector valued images is most often defined as the average of the scalar structure tensors in each band. The problem with this definition is the assumption that all bands provide the same amount of edge information giving them the same weights. As a result non-edge pixels can be reinforced and edges can be weakened…
Tunable Tensor Voting Improves Grouping of Membrane-Bound Macromolecules
Energy Technology Data Exchange (ETDEWEB)
Loss, Leandro A.; Bebis, George; Parvin, Bahram
2009-04-15
Membrane-bound macromolecules are responsible for structural support and mediation of cell-cell adhesion in tissues. Quantitative analysis of these macromolecules provides morphological indices for damage or loss of tissue, for example as a result of exogenous stimuli. From an optical point of view, a membrane signal may have nonuniform intensity around the cell boundary, be punctate or diffused, and may even be perceptual at certain locations along the boundary. In this paper, a method for the detection and grouping of punctate, diffuse curvilinear signals is proposed. Our work builds upon the tensor voting and the iterative voting frameworks to propose an efficient method to detect and refine perceptually interesting curvilinear structures in images. The novelty of our method lies on the idea of iteratively tuning the tensor voting fields, which allows the concentration of the votes only over areas of interest. We validate the utility of our system with synthetic and annotated real data. The effectiveness of the tunable tensor voting is demonstrated on complex phenotypic signals that are representative of membrane-bound macromolecular structures.
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.
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.
Killing-Yano tensors, rank-2 Killing tensors, and conserved quantities in higher dimensions
Energy Technology Data Exchange (ETDEWEB)
Krtous, Pavel [Institute of Theoretical Physics, Charles University, V Holesovickach 2, Prague (Czech Republic); Kubiznak, David [Institute of Theoretical Physics, Charles University, V Holesovickach 2, Prague (Czech Republic); Page, Don N. [Theoretical Physics Institute, University of Alberta, Edmonton T6G 2G7, Alberta (Canada); Frolov, Valeri P. [Theoretical Physics Institute, University of Alberta, Edmonton T6G 2G7, Alberta (Canada)
2007-02-15
From the metric and one Killing-Yano tensor of rank D-2 in any D-dimensional spacetime with such a principal Killing-Yano tensor, we show how to generate k = [(D+1)/2] Killing-Yano tensors, of rank D-2j for all 0 {<=} j {<=} k-1, and k rank-2 Killing tensors, giving k constants of geodesic motion that are in involution. For the example of the Kerr-NUT-AdS spacetime (hep-th/0604125) with its principal Killing-Yano tensor (gr-qc/0610144), these constants and the constants from the k Killing vectors give D independent constants in involution, making the geodesic motion completely integrable (hep-th/0611083). The constants of motion are also related to the constants recently obtained in the separation of the Hamilton-Jacobi and Klein-Gordon equations (hep-th/0611245)
Killing-Yano tensors, rank-2 Killing tensors, and conserved quantities in higher dimensions
International Nuclear Information System (INIS)
Krtous, Pavel; Kubiznak, David; Page, Don N.; Frolov, Valeri P.
2007-01-01
From the metric and one Killing-Yano tensor of rank D-2 in any D-dimensional spacetime with such a principal Killing-Yano tensor, we show how to generate k = [(D+1)/2] Killing-Yano tensors, of rank D-2j for all 0 ≤ j ≤ k-1, and k rank-2 Killing tensors, giving k constants of geodesic motion that are in involution. For the example of the Kerr-NUT-AdS spacetime (hep-th/0604125) with its principal Killing-Yano tensor (gr-qc/0610144), these constants and the constants from the k Killing vectors give D independent constants in involution, making the geodesic motion completely integrable (hep-th/0611083). The constants of motion are also related to the constants recently obtained in the separation of the Hamilton-Jacobi and Klein-Gordon equations (hep-th/0611245)
Eigenvector of gravity gradient tensor for estimating fault dips considering fault type
Kusumoto, Shigekazu
2017-12-01
The dips of boundaries in faults and caldera walls play an important role in understanding their formation mechanisms. The fault dip is a particularly important parameter in numerical simulations for hazard map creation as the fault dip affects estimations of the area of disaster occurrence. In this study, I introduce a technique for estimating the fault dip using the eigenvector of the observed or calculated gravity gradient tensor on a profile and investigating its properties through numerical simulations. From numerical simulations, it was found that the maximum eigenvector of the tensor points to the high-density causative body, and the dip of the maximum eigenvector closely follows the dip of the normal fault. It was also found that the minimum eigenvector of the tensor points to the low-density causative body and that the dip of the minimum eigenvector closely follows the dip of the reverse fault. It was shown that the eigenvector of the gravity gradient tensor for estimating fault dips is determined by fault type. As an application of this technique, I estimated the dip of the Kurehayama Fault located in Toyama, Japan, and obtained a result that corresponded to conventional fault dip estimations by geology and geomorphology. Because the gravity gradient tensor is required for this analysis, I present a technique that estimates the gravity gradient tensor from the gravity anomaly on a profile.
TensorCalculator: exploring the evolution of mechanical stress in the CCMV capsid
Kononova, Olga; Maksudov, Farkhad; Marx, Kenneth A.; Barsegov, Valeri
2018-01-01
A new computational methodology for the accurate numerical calculation of the Cauchy stress tensor, stress invariants, principal stress components, von Mises and Tresca tensors is developed. The methodology is based on the atomic stress approach which permits the calculation of stress tensors, widely used in continuum mechanics modeling of materials properties, using the output from the MD simulations of discrete atomic and C_α -based coarse-grained structural models of biological particles. The methodology mapped into the software package TensorCalculator was successfully applied to the empty cowpea chlorotic mottle virus (CCMV) shell to explore the evolution of mechanical stress in this mechanically-tested specific example of a soft virus capsid. We found an inhomogeneous stress distribution in various portions of the CCMV structure and stress transfer from one portion of the virus structure to another, which also points to the importance of entropic effects, often ignored in finite element analysis and elastic network modeling. We formulate a criterion for elastic deformation using the first principal stress components. Furthermore, we show that von Mises and Tresca stress tensors can be used to predict the onset of a viral capsid’s mechanical failure, which leads to total structural collapse. TensorCalculator can be used to study stress evolution and dynamics of defects in viral capsids and other large-size protein assemblies.
Gordon, Christopher P.; Yamamoto, Keishi; Searles, Keith; Shirase, Satoru
2018-01-01
Metal alkylidenes, which are key organometallic intermediates in reactions such as olefination or alkene and alkane metathesis, are typically generated from metal dialkyl compounds [M](CH2R)2 that show distinctively deshielded chemical shifts for their α-carbons. Experimental solid-state NMR measurements combined with DFT/ZORA calculations and a chemical shift tensor analysis reveal that this remarkable deshielding originates from an empty metal d-orbital oriented in the M–Cα–Cα′ plane, interacting with the Cα p-orbital lying in the same plane. This π-type interaction inscribes some alkylidene character into Cα that favors alkylidene generation via α-H abstraction. The extent of the deshielding and the anisotropy of the alkyl chemical shift tensors distinguishes [M](CH2R)2 compounds that form alkylidenes from those that do not, relating the reactivity to molecular orbitals of the respective molecules. The α-carbon chemical shifts and tensor orientations thus predict the reactivity of metal alkyl compounds towards alkylidene generation. PMID:29675237
Susceptibility tensor imaging (STI) of the brain.
Li, Wei; Liu, Chunlei; Duong, Timothy Q; van Zijl, Peter C M; Li, Xu
2017-04-01
Susceptibility tensor imaging (STI) is a recently developed MRI technique that allows quantitative determination of orientation-independent magnetic susceptibility parameters from the dependence of gradient echo signal phase on the orientation of biological tissues with respect to the main magnetic field. By modeling the magnetic susceptibility of each voxel as a symmetric rank-2 tensor, individual magnetic susceptibility tensor elements as well as the mean magnetic susceptibility and magnetic susceptibility anisotropy can be determined for brain tissues that would still show orientation dependence after conventional scalar-based quantitative susceptibility mapping to remove such dependence. Similar to diffusion tensor imaging, STI allows mapping of brain white matter fiber orientations and reconstruction of 3D white matter pathways using the principal eigenvectors of the susceptibility tensor. In contrast to diffusion anisotropy, the main determinant factor of the susceptibility anisotropy in brain white matter is myelin. Another unique feature of the susceptibility anisotropy of white matter is its sensitivity to gadolinium-based contrast agents. Mechanistically, MRI-observed susceptibility anisotropy is mainly attributed to the highly ordered lipid molecules in the myelin sheath. STI provides a consistent interpretation of the dependence of phase and susceptibility on orientation at multiple scales. This article reviews the key experimental findings and physical theories that led to the development of STI, its practical implementations, and its applications for brain research. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd.
Susceptibility Tensor Imaging (STI) of the Brain
Li, Wei; Liu, Chunlei; Duong, Timothy Q.; van Zijl, Peter C.M.; Li, Xu
2016-01-01
Susceptibility tensor imaging (STI) is a recently developed MRI technique that allows quantitative determination of orientation-independent magnetic susceptibility parameters from the dependence of gradient echo signal phase on the orientation of biological tissues with respect to the main magnetic field. By modeling the magnetic susceptibility of each voxel as a symmetric rank-2 tensor, individual magnetic susceptibility tensor elements as well as the mean magnetic susceptibility (MMS) and magnetic susceptibility anisotropy (MSA) can be determined for brain tissues that would still show orientation dependence after conventional scalar-based quantitative susceptibility mapping (QSM) to remove such dependence. Similar to diffusion tensor imaging (DTI), STI allows mapping of brain white matter fiber orientations and reconstruction of 3D white matter pathways using the principal eigenvectors of the susceptibility tensor. In contrast to diffusion anisotropy, the main determinant factor of susceptibility anisotropy in brain white matter is myelin. Another unique feature of susceptibility anisotropy of white matter is its sensitivity to gadolinium-based contrast agents. Mechanistically, MRI-observed susceptibility anisotropy is mainly attributed to the highly ordered lipid molecules in myelin sheath. STI provides a consistent interpretation of the dependence of phase and susceptibility on orientation at multiple scales. This article reviews the key experimental findings and physical theories that led to the development of STI, its practical implementations, and its applications for brain research. PMID:27120169
Off-shell N = 2 tensor supermultiplets
International Nuclear Information System (INIS)
Wit, Bernard de; Saueressig, Frank
2006-01-01
A multiplet calculus is presented for an arbitrary number n of N = 2 tensor supermultiplets. For rigid supersymmetry the known couplings are reproduced. In the superconformal case the target spaces parametrized by the scalar fields are cones over (3n-1)-dimensional spaces encoded in homogeneous SU(2) invariant potentials, subject to certain constraints. The coupling to conformal supergravity enables the derivation of a large class of supergravity Lagrangians with vector and tensor multiplets and hypermultiplets. Dualizing the tensor fields into scalars leads to hypermultiplets with hyperkaehler or quaternion-Kaehler target spaces with at least n abelian isometries. It is demonstrated how to use the calculus for the construction of Lagrangians containing higher-derivative couplings of tensor multiplets. For the application of the c-map between vector and tensor supermultiplets to Lagrangians with higher-order derivatives, an off-shell version of this map is proposed. Various other implications of the results are discussed. As an example an elegant derivation of the classification of 4-dimensional quaternion-Kaehler manifolds with two commuting isometries is given
Stress-tensor OPE in N=2 superconformal theories
International Nuclear Information System (INIS)
Liendo, Pedro; Ramírez, Israel; Seo, Jihye
2016-01-01
We carry out a detailed superspace analysis of the OPE of two N=2 stress-tensor multiplets. Knowledge of the multiplets appearing in the expansion, together with the two-dimensional chiral algebra description of N=2 SCFTs, imply an analytic bound on the central charge c. This bound is valid for any N=2 SCFT regardless of its matter content and flavor symmetries, and is saturated by the simplest Argyres-Douglas fixed point. We also present a partial conformal block analysis for the scalar superconformal primary of the multiplet.
Stress-tensor OPE in N=2 superconformal theories
International Nuclear Information System (INIS)
Liendo, Pedro; Ramirez, Israel; Univ. Tecnica Federico Santa Maria, Valparaiso; Seo, Jihye
2015-11-01
We carry out a detailed superspace analysis of the OPE of two N=2 stress-tensor multiplets. Knowledge of the multiplets appearing in the expansion, together with the two-dimensional chiral algebra description of N=2 SCFTs, imply an analytic bound on the central charge c. This bound is valid for any N=2 SCFT regardless of its matter content and flavor symmetries, and is saturated by the simplest Argyres-Douglas fixed point. We also present a partial conformal block analysis for the scalar superconformal primary of the multiplet.
International Nuclear Information System (INIS)
Huf, P A; Carminati, J
2015-01-01
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. (paper)
Energy-momentum tensor in the fermion-pairing model
International Nuclear Information System (INIS)
Kawati, S.; Miyata, H.
1980-01-01
The symmetric energy-momentum tensor for the self-interacting fermion theory (psi-barpsi) 2 is expressed in terms of the collective mode within the Hartree approximation. The divergent part of the energy-momentum tensor for the fermion theory induces an effective energy-momentum tensor for the collective mode, and this effective energy-momentum tensor automatically has the Callan-Coleman-Jackiw improved form. The renormalized energy-momentum tensor is structurally equivalent to the Callan-Coleman-Jackiw improved tensor for the Yukawa theory
(Ln-bar, g)-spaces. Ordinary and tensor differentials
International Nuclear Information System (INIS)
Manoff, S.; Dimitrov, B.
1998-01-01
Different types of differentials as special cases of differential operators acting on tensor fields over (L n bar, g)-spaces are considered. The ordinary differential, the covariant differential as a special case of the covariant differential operator, and the Lie differential as a special case of the Lie differential operator are investigated. The tensor differential and its special types (Covariant tensor differential, and Lie tensor differential) are determined and their properties are discussed. Covariant symmetric and antisymmetric (external) tensor differentials, Lie symmetric, and Lie antisymmetric (external) tensor differentials are determined and considered over (L n bar, g)-spaces
Savardekar, Amey R; Patra, Devi P; Thakur, Jai D; Narayan, Vinayak; Mohammed, Nasser; Bollam, Papireddy; Nanda, Anil
2018-03-01
OBJECTIVE Total tumor excision with the preservation of neurological function and quality of life is the goal of modern-day vestibular schwannoma (VS) surgery. Postoperative facial nerve (FN) paralysis is a devastating complication of VS surgery. Determining the course of the FN in relation to a VS preoperatively is invaluable to the neurosurgeon and is likely to enhance surgical safety with respect to FN function. Diffusion tensor imaging-fiber tracking (DTI-FT) technology is slowly gaining traction as a viable tool for preoperative FN visualization in patients with VS. METHODS A systematic review of the literature in the PubMed, Cochrane Library, and Web of Science databases was performed in accordance with Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) guidelines, and those studies that preoperatively localized the FN in relation to a VS using the DTI-FT technique and verified those preoperative FN tracking results by using microscopic observation and electrophysiological monitoring during microsurgery were included. A pooled analysis of studies was performed to calculate the surgical concordance rate (accuracy) of DTI-FT technology for FN localization. RESULTS Fourteen studies included 234 VS patients (male/female ratio 1:1.4, age range 17-75 years) who had undergone preoperative DTI-FT for FN identification. The mean tumor size among the studies ranged from 29 to 41.3 mm. Preoperative DTI-FT could not visualize the FN tract in 8 patients (3.4%) and its findings could not be verified in 3 patients (1.2%), were verified but discordant in 18 patients (7.6%), and were verified and concordant in 205 patients (87.1%). CONCLUSIONS Preoperative DTI-FT for FN identification is a useful adjunct in the surgical planning for large VSs (> 2.5 cm). A pooled analysis showed that DTI-FT successfully identifies the complete FN course in 96.6% of VSs (226 of 234 cases) and that FN identification by DTI-FT is accurate in 90.6% of cases (205 of 226
Exploring extra dimensions through inflationary tensor modes
Im, Sang Hui; Nilles, Hans Peter; Trautner, Andreas
2018-03-01
Predictions of inflationary schemes can be influenced by the presence of extra dimensions. This could be of particular relevance for the spectrum of gravitational waves in models where the extra dimensions provide a brane-world solution to the hierarchy problem. Apart from models of large as well as exponentially warped extra dimensions, we analyze the size of tensor modes in the Linear Dilaton scheme recently revived in the discussion of the "clockwork mechanism". The results are model dependent, significantly enhanced tensor modes on one side and a suppression on the other. In some cases we are led to a scheme of "remote inflation", where the expansion is driven by energies at a hidden brane. In all cases where tensor modes are enhanced, the requirement of perturbativity of gravity leads to a stringent upper limit on the allowed Hubble rate during inflation.
On an uninterpretated tensor in Dirac's theory
International Nuclear Information System (INIS)
Costa de Beauregard, O.
1989-01-01
Franz, in 1935, deduced systematically from the Dirac equation 10 tensorial equations, 5 with a mechanical interpretation, 5 with an electromagnetic interpretation, which are also consequences of Kemmer's formalism for spins 1 and 0; Durand, in 1944, operating similarly with the second order Dirac equation, obtained, 10 equations, 5 of which expressing the divergences of the Gordon type tensors. Of these equations, together with the tensors they imply, some are easily interpreted by reference to the classical theories, some other remain uniterpreted. Recently (1988) we proposed a theory of the coupling between Einstein's gravity field and the 5 Franz mechanical equations, yielding as a bonus the complete interpretation of the 5 Franz mechanical equations. This is an incitation to reexamine the 5 electromagnetic equations. We show here that two of these, together with one of the Durand equations, implying the same tensor, remain uninterpreted. This is proposed as a challenge to the reader's sagacity [fr
The Riemann-Lovelock curvature tensor
International Nuclear Information System (INIS)
Kastor, David
2012-01-01
In order to study the properties of Lovelock gravity theories in low dimensions, we define the kth-order Riemann-Lovelock tensor as a certain quantity having a total 4k-indices, which is kth order in the Riemann curvature tensor and shares its basic algebraic and differential properties. We show that the kth-order Riemann-Lovelock tensor is determined by its traces in dimensions 2k ≤ D < 4k. In D = 2k + 1 this identity implies that all solutions of pure kth-order Lovelock gravity are 'Riemann-Lovelock' flat. It is verified that the static, spherically symmetric solutions of these theories, which are missing solid angle spacetimes, indeed satisfy this flatness property. This generalizes results from Einstein gravity in D = 3, which corresponds to the k = 1 case. We speculate about some possible further consequences of Riemann-Lovelock curvature. (paper)
Magnetotelluric impedance tensor analysis for identification of ...
Indian Academy of Sciences (India)
G Pavan Kumar
2017-07-18
Jul 18, 2017 ... The transverse geo-electric strike coincides with the prominent clustering of .... Unrotated apparent resistivity and phase curves for four sites along the profile. ..... The Bhuj earthquake: Tomographic evidence for fluids at.
Aspects of the Antisymmetric Tensor Field
Lahiri, Amitabha
1991-02-01
With the possible exception of gravitation, fundamental interactions are generally described by theories of point particles interacting via massless gauge fields. Since the advent of string theories the picture of physical interaction has changed to accommodate one in which extended objects interact with each other. The generalization of the gauge theories to extended objects leads to theories of antisymmetric tensor fields. At scales corresponding to present-day laboratory experiments one expects to see only point particles, their interactions modified by the presence of antisymmetric tensor fields in the theory. Therefore, in order to establish the validity of any theory with antisymmetric tensor fields one needs to look for manifestations of these fields at low energies. The principal problem of gauge theories is the failure to provide a suitable explanation for the generation of masses for the fields in the theory. While there is a known mechanism (spontaneous symmetry breaking) for generating masses for both the matter fields and the gauge fields, the lack of experimental evidence in support of an elementary scalar field suggests that one look for alternative ways of generating masses for the fields. The interaction of gauge fields with an antisymmetric tensor field seems to be an attractive way of doing so, especially since all indications point to the possibility that there will be no remnant degrees of freedom. On the other hand the interaction of such a field with black holes suggest an independent way of verifying the existence of such fields. In this dissertation the origins of the antisymmetric tensor field are discussed in terms of string theory. The interaction of black holes with such a field is discussed next. The last chapter discusses the effects of an antisymmetric tensor field on quantum electrodynamics when the fields are minimally coupled.
Tensor hypercontraction. II. Least-squares renormalization
Parrish, Robert M.; Hohenstein, Edward G.; Martínez, Todd J.; Sherrill, C. David
2012-12-01
The least-squares tensor hypercontraction (LS-THC) representation for the electron repulsion integral (ERI) tensor is presented. Recently, we developed the generic tensor hypercontraction (THC) ansatz, which represents the fourth-order ERI tensor as a product of five second-order tensors [E. G. Hohenstein, R. M. Parrish, and T. J. Martínez, J. Chem. Phys. 137, 044103 (2012)], 10.1063/1.4732310. Our initial algorithm for the generation of the THC factors involved a two-sided invocation of overlap-metric density fitting, followed by a PARAFAC decomposition, and is denoted PARAFAC tensor hypercontraction (PF-THC). LS-THC supersedes PF-THC by producing the THC factors through a least-squares renormalization of a spatial quadrature over the otherwise singular 1/r12 operator. Remarkably, an analytical and simple formula for the LS-THC factors exists. Using this formula, the factors may be generated with O(N^5) effort if exact integrals are decomposed, or O(N^4) effort if the decomposition is applied to density-fitted integrals, using any choice of density fitting metric. The accuracy of LS-THC is explored for a range of systems using both conventional and density-fitted integrals in the context of MP2. The grid fitting error is found to be negligible even for extremely sparse spatial quadrature grids. For the case of density-fitted integrals, the additional error incurred by the grid fitting step is generally markedly smaller than the underlying Coulomb-metric density fitting error. The present results, coupled with our previously published factorizations of MP2 and MP3, provide an efficient, robust O(N^4) approach to both methods. Moreover, LS-THC is generally applicable to many other methods in quantum chemistry.
Diffusion tensor imaging in spinal cord compression
International Nuclear Information System (INIS)
Wang, Wei; Qin, Wen; Hao, Nanxin; Wang, Yibin; Zong, Genlin
2012-01-01
Background Although diffusion tensor imaging has been successfully applied in brain research for decades, several main difficulties have hindered its extended utilization in spinal cord imaging. Purpose To assess the feasibility and clinical value of diffusion tensor imaging and tractography for evaluating chronic spinal cord compression. Material and Methods Single-shot spin-echo echo-planar DT sequences were scanned in 42 spinal cord compression patients and 49 healthy volunteers. The mean values of the apparent diffusion coefficient and fractional anisotropy were measured in region of interest at the cervical and lower thoracic spinal cord. The patients were divided into two groups according to the high signal on T2WI (the SCC-HI group and the SCC-nHI group for with or without high signal). A one-way ANOVA was used. Diffusion tensor tractography was used to visualize the morphological features of normal and impaired white matter. Results There were no statistically significant differences in the apparent diffusion coefficient and fractional anisotropy values between the different spinal cord segments of the normal subjects. All of the patients in the SCC-HI group had increased apparent diffusion coefficient values and decreased fractional anisotropy values at the lesion level compared to the normal controls. However, there were no statistically significant diffusion index differences between the SCC-nHI group and the normal controls. In the diffusion tensor imaging maps, the normal spinal cord sections were depicted as fiber tracts that were color-encoded to a cephalocaudal orientation. The diffusion tensor images were compressed to different degrees in all of the patients. Conclusion Diffusion tensor imaging and tractography are promising methods for visualizing spinal cord tracts and can provide additional information in clinical studies in spinal cord compression
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...
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...
Tensor modes in pure natural inflation
Nomura, Yasunori; Yamazaki, Masahito
2018-05-01
We study tensor modes in pure natural inflation [1], a recently-proposed inflationary model in which an axionic inflaton couples to pure Yang-Mills gauge fields. We find that the tensor-to-scalar ratio r is naturally bounded from below. This bound originates from the finiteness of the number of metastable branches of vacua in pure Yang-Mills theories. Details of the model can be probed by future cosmic microwave background experiments and improved lattice gauge theory calculations of the θ-angle dependence of the vacuum energy.
White matter injury in newborns with congenital heart disease: a diffusion tensor imaging study.
Mulkey, Sarah B; Ou, Xiawei; Ramakrishnaiah, Raghu H; Glasier, Charles M; Swearingen, Christopher J; Melguizo, Maria S; Yap, Vivien L; Schmitz, Michael L; Bhutta, Adnan T
2014-09-01
Brain injury is observed on cranial magnetic resonance imaging preoperatively in up to 50% of newborns with congenital heart disease. Newer imaging techniques such as diffusion tensor imaging provide sensitive measures of the white matter integrity. The objective of this study was to evaluate the diffusion tensor imaging analysis technique of tract-based spatial statistics in newborns with congenital heart disease. Term newborns with congenital heart disease who would require surgery at less than 1 month of age were prospectively enrolled (n = 19). Infants underwent preoperative and postoperative brain magnetic resonance imaging with diffusion tensor imaging. Tract-based spatial statistics, an objective whole-brain diffusion tensor imaging analysis technique, was used to determine differences in white matter fractional anisotropy between infant groups. Term control infants were also compared with congenital heart disease infants. Postmenstrual age was equivalent between congenital heart disease infant groups and between congenital heart disease and control infants. Ten infants had preoperative brain injury, either infarct or white matter injury, by conventional brain magnetic resonance imaging. The technique of tract-based spatial statistics showed significantly lower fractional anisotropy (P tensor imaging analysis technique that may have better sensitivity in detecting white matter injury compared with conventional brain magnetic resonance imaging in term newborns with congenital heart disease. Copyright © 2014 Elsevier Inc. All rights reserved.
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.
Tensor completion for PDEs with uncertain coefficients and Bayesian Update
Litvinenko, Alexander
2017-01-01
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.
Concatenated image completion via tensor augmentation and completion
Bengua, Johann A.; Tuan, Hoang D.; Phien, Ho N.; Do, Minh N.
2016-01-01
This paper proposes a novel framework called concatenated image completion via tensor augmentation and completion (ICTAC), which recovers missing entries of color images with high accuracy. Typical images are second- or third-order tensors (2D/3D) depending if they are grayscale or color, hence tensor completion algorithms are ideal for their recovery. The proposed framework performs image completion by concatenating copies of a single image that has missing entries into a third-order tensor,...
Tensor polarization in pion-deuteron elastic scattering
International Nuclear Information System (INIS)
Holt, R.J.; Freeman, W.S.; Geesaman, D.F.
1985-01-01
During this year the analysis of measurements of t 20 in π-d elastic scattering was completed and a final summary manuscript was prepared for publication. The results consists of angular distributions of the deuteron tensor polarization in π-d elastic scattering at pion energies of 140, 180, 220 and 256 MeV. Theoretical calculations in which the effects of pion absorption on the elastic channel are small reproduce the data. No rapid angular or energy dependence was found near a pion energy of 134 MeV, where another experiment at SIN has suggested the existence of dibaryon resonances
Norm of the Riemannian Curvature Tensor
Indian Academy of Sciences (India)
We consider the Riemannian functional R p ( g ) = ∫ M | R ( g ) | p d v g defined on the space of Riemannian metrics with unit volume on a closed smooth manifold where R ( g ) and d v g denote the corresponding Riemannian curvature tensor and volume form and p ∈ ( 0 , ∞ ) . First we prove that the Riemannian metrics ...
Abelian tensor models on the lattice
Chaudhuri, Soumyadeep; Giraldo-Rivera, Victor I.; Joseph, Anosh; Loganayagam, R.; Yoon, Junggi
2018-04-01
We consider a chain of Abelian Klebanov-Tarnopolsky fermionic tensor models coupled through quartic nearest-neighbor interactions. We characterize the gauge-singlet spectrum for small chains (L =2 ,3 ,4 ,5 ) and observe that the spectral statistics exhibits strong evidence in favor of quasi-many-body localization.
Tensor squeezed limits and the Higuchi bound
Energy Technology Data Exchange (ETDEWEB)
Bordin, Lorenzo [SISSA, via Bonomea 265, 34136, Trieste (Italy); Creminelli, Paolo [Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11, 34151, Trieste (Italy); Mirbabayi, Mehrdad [Institute for Advanced Study, Princeton, NJ 08540 (United States); Noreña, Jorge, E-mail: lbordin@sissa.it, E-mail: creminel@ictp.it, E-mail: mehrdadm@ias.edu, E-mail: jorge.norena@pucv.cl [Instituto de Física, Pontificia Universidad Católica de Valparaíso, Avenida Universidad 330, Curauma, Valparaíso (Chile)
2016-09-01
We point out that tensor consistency relations—i.e. the behavior of primordial correlation functions in the limit a tensor mode has a small momentum—are more universal than scalar consistency relations. They hold in the presence of multiple scalar fields and as long as anisotropies are diluted exponentially fast. When de Sitter isometries are approximately respected during inflation this is guaranteed by the Higuchi bound, which forbids the existence of light particles with spin: de Sitter space can support scalar hair but no curly hair. We discuss two indirect ways to look for the violation of tensor consistency relations in observations, as a signature of models in which inflation is not a strong isotropic attractor, such as solid inflation: (a) graviton exchange contribution to the scalar four-point function; (b) quadrupolar anisotropy of the scalar power spectrum due to super-horizon tensor modes. This anisotropy has a well-defined statistics which can be distinguished from cases in which the background has a privileged direction.
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.
Higher-order tensors in diffusion imaging
Schultz, T.; Fuster, A.; Ghosh, A.; Deriche, R.; Florack, L.M.J.; Lim, L.H.; Westin, C.-F.; Vilanova, A.; Burgeth, B.
2014-01-01
Diffusion imaging is a noninvasive tool for probing the microstructure of fibrous nerve and muscle tissue. Higher-order tensors provide a powerful mathematical language to model and analyze the large and complex data that is generated by its modern variants such as High Angular Resolution Diffusion
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.
Curvature tensor copies in affine geometry
International Nuclear Information System (INIS)
Srivastava, P.P.
1981-01-01
The sets of space-time and spin-connections which give rise to the same curvature tensor are constructed. The corresponding geometries are compared. Results are illustrated by an explicit calculation and comment on the copies in Einstein-Cartan and Weyl-Cartan geometries. (Author) [pt
Positivity of linear maps under tensor powers
Energy Technology Data Exchange (ETDEWEB)
Müller-Hermes, Alexander, E-mail: muellerh@ma.tum.de; Wolf, Michael M., E-mail: m.wolf@tum.de [Zentrum Mathematik, Technische Universität München, 85748 Garching (Germany); Reeb, David, E-mail: reeb.qit@gmail.com [Zentrum Mathematik, Technische Universität München, 85748 Garching (Germany); Institute for Theoretical Physics, Leibniz Universität Hannover, 30167 Hannover (Germany)
2016-01-15
We investigate linear maps between matrix algebras that remain positive under tensor powers, i.e., under tensoring with n copies of themselves. Completely positive and completely co-positive maps are trivial examples of this kind. We show that for every n ∈ ℕ, there exist non-trivial maps with this property and that for two-dimensional Hilbert spaces there is no non-trivial map for which this holds for all n. For higher dimensions, we reduce the existence question of such non-trivial “tensor-stable positive maps” to a one-parameter family of maps and show that an affirmative answer would imply the existence of non-positive partial transpose bound entanglement. As an application, we show that any tensor-stable positive map that is not completely positive yields an upper bound on the quantum channel capacity, which for the transposition map gives the well-known cb-norm bound. We, furthermore, show that the latter is an upper bound even for the local operations and classical communications-assisted quantum capacity, and that moreover it is a strong converse rate for this task.
Primordial tensor modes from quantum corrected inflation
DEFF Research Database (Denmark)
Joergensen, Jakob; Sannino, Francesco; Svendsen, Ole
2014-01-01
. Finally we confront these theories with the Planck and BICEP2 data. We demonstrate that the discovery of primordial tensor modes by BICEP2 require the presence of sizable quantum departures from the $\\phi^4$-Inflaton model for the non-minimally coupled scenario which we parametrize and quantify. We...
From stochastic completion fields to tensor voting
Almsick, van M.A.; Duits, R.; Franken, E.M.; Haar Romenij, ter B.M.; Olsen, O.F.; Florack, L.M.J.; Kuijper, A.
2005-01-01
Several image processing algorithms imitate the lateral interaction of neurons in the visual striate cortex V1 to account for the correlations along contours and lines. Here we focus on two methodologies: tensor voting by Guy and Medioni, and stochastic completion fields by Mumford, Williams and
Positivity of linear maps under tensor powers
International Nuclear Information System (INIS)
Müller-Hermes, Alexander; Wolf, Michael M.; Reeb, David
2016-01-01
We investigate linear maps between matrix algebras that remain positive under tensor powers, i.e., under tensoring with n copies of themselves. Completely positive and completely co-positive maps are trivial examples of this kind. We show that for every n ∈ ℕ, there exist non-trivial maps with this property and that for two-dimensional Hilbert spaces there is no non-trivial map for which this holds for all n. For higher dimensions, we reduce the existence question of such non-trivial “tensor-stable positive maps” to a one-parameter family of maps and show that an affirmative answer would imply the existence of non-positive partial transpose bound entanglement. As an application, we show that any tensor-stable positive map that is not completely positive yields an upper bound on the quantum channel capacity, which for the transposition map gives the well-known cb-norm bound. We, furthermore, show that the latter is an upper bound even for the local operations and classical communications-assisted quantum capacity, and that moreover it is a strong converse rate for this task
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.
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...
Tensor operators in R-matrix approach
International Nuclear Information System (INIS)
Bytsko, A.G.; Rossijskaya Akademiya Nauk, St. Petersburg
1995-12-01
The definitions and some properties (e.g. the Wigner-Eckart theorem, the fusion procedure) of covariant and contravariant q-tensor operators for quasitriangular quantum Lie algebras are formulated in the R-matrix language. The case of U q (sl(n)) (in particular, for n=2) is discussed in more detail. (orig.)
Baust, Maximilian; Weinmann, Andreas; Wieczorek, Matthias; Lasser, Tobias; Storath, Martin; Navab, Nassir
2016-08-01
In this paper, we consider combined TV denoising and diffusion tensor fitting in DTI using the affine-invariant Riemannian metric on the space of diffusion tensors. Instead of first fitting the diffusion tensors, and then denoising them, we define a suitable TV type energy functional which incorporates the measured DWIs (using an inverse problem setup) and which measures the nearness of neighboring tensors in the manifold. To approach this functional, we propose generalized forward- backward splitting algorithms which combine an explicit and several implicit steps performed on a decomposition of the functional. We validate the performance of the derived algorithms on synthetic and real DTI data. In particular, we work on real 3D data. To our knowledge, the present paper describes the first approach to TV regularization in a combined manifold and inverse problem setup.
The nonabelian tensor square of a bieberbach group with ...
African Journals Online (AJOL)
The main objective of this paper is to compute the nonabelian tensor square of one Bieberbach group with elementary abelian 2-group point group of dimension three by using the computational method of the nonabelian tensor square for polycyclic groups. The finding of the computation showed that the nonabelian tensor ...
[An Improved Spectral Quaternion Interpolation Method of Diffusion Tensor Imaging].
Xu, Yonghong; Gao, Shangce; Hao, Xiaofei
2016-04-01
Diffusion tensor imaging(DTI)is a rapid development technology in recent years of magnetic resonance imaging.The diffusion tensor interpolation is a very important procedure in DTI image processing.The traditional spectral quaternion interpolation method revises the direction of the interpolation tensor and can preserve tensors anisotropy,but the method does not revise the size of tensors.The present study puts forward an improved spectral quaternion interpolation method on the basis of traditional spectral quaternion interpolation.Firstly,we decomposed diffusion tensors with the direction of tensors being represented by quaternion.Then we revised the size and direction of the tensor respectively according to different situations.Finally,we acquired the tensor of interpolation point by calculating the weighted average.We compared the improved method with the spectral quaternion method and the Log-Euclidean method by the simulation data and the real data.The results showed that the improved method could not only keep the monotonicity of the fractional anisotropy(FA)and the determinant of tensors,but also preserve the tensor anisotropy at the same time.In conclusion,the improved method provides a kind of important interpolation method for diffusion tensor image processing.
Tensor based structure estimation in multi-channel images
DEFF Research Database (Denmark)
Schou, Jesper; Dierking, Wolfgang; Skriver, Henning
2000-01-01
. In the second part tensors are used for representing the structure information. This approach has the advantage, that tensors can be averaged either spatially or by applying several images, and the resulting tensor provides information of the average strength as well as orientation of the structure...
Relativistic particles with spin and antisymmetric tensor fields
International Nuclear Information System (INIS)
Sandoval Junior, L.
1990-09-01
A study is made on antisymmetric tensor fields particularly on second order tensor field as far as his equivalence to other fields and quantization through the path integral are concerned. Also, a particle model is studied which has been recently proposed and reveals to be equivalent to antisymmetric tensor fields of any order. (L.C.J.A.)
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.
Lepore, Natasha; Brun, Caroline; Chou, Yi-Yu; Chiang, Ming-Chang; Dutton, Rebecca A.; Hayashi, Kiralee M.; Luders, Eileen; Lopez, Oscar L.; Aizenstein, Howard J.; Toga, Arthur W.; Becker, James T.; Thompson, Paul M.
2008-01-01
This paper investigates the performance of a new multivariate method for tensor-based morphometry (TBM). Statistics on Riemannian manifolds are developed that exploit the full information in deformation tensor fields. In TBM, multiple brain images are warped to a common neuroanatomical template via 3-D nonlinear registration; the resulting deformation fields are analyzed statistically to identify group differences in anatomy. Rather than study the Jacobian determinant (volume expansion factor...
Massless and massive quanta resulting from a mediumlike metric tensor
International Nuclear Information System (INIS)
Soln, J.
1985-01-01
A simple model of the ''primordial'' scalar field theory is presented in which the metric tensor is a generalization of the metric tensor from electrodynamics in a medium. The radiation signal corresponding to the scalar field propagates with a velocity that is generally less than c. This signal can be associated simultaneously with imaginary and real effective (momentum-dependent) masses. The requirement that the imaginary effective mass vanishes, which we take to be the prerequisite for the vacuumlike signal propagation, leads to the ''spontaneous'' splitting of the metric tensor into two distinct metric tensors: one metric tensor gives rise to masslesslike radiation and the other to a massive particle. (author)
Locally extracting scalar, vector and tensor modes in cosmological perturbation theory
International Nuclear Information System (INIS)
Clarkson, Chris; Osano, Bob
2011-01-01
Cosmological perturbation theory relies on the decomposition of perturbations into so-called scalar, vector and tensor modes. This decomposition is non-local and depends on unknowable boundary conditions. The non-locality is particularly important at second and higher order because perturbative modes are sourced by products of lower order modes, which must be integrated over all space in order to isolate each mode. However, given a trace-free rank-2 tensor, a locally defined scalar mode may be trivially derived by taking two divergences, which knocks out the vector and tensor degrees of freedom. A similar local differential operation will return a pure vector mode. This means that scalar and vector degrees of freedom have local descriptions. The corresponding local extraction of the tensor mode is unknown however. We give it here. The operators we define are useful for defining gauge-invariant quantities at second order. We perform much of our analysis using an index-free 'vector-calculus' approach which makes manipulating tensor equations considerably simpler. (papers)
A review of anisotropic conductivity models of brain white matter based on diffusion tensor imaging.
Wu, Zhanxiong; Liu, Yang; Hong, Ming; Yu, Xiaohui
2018-06-01
The conductivity of brain tissues is not only essential for electromagnetic source estimation (ESI), but also a key reflector of the brain functional changes. Different from the other brain tissues, the conductivity of whiter matter (WM) is highly anisotropic and a tensor is needed to describe it. The traditional electrical property imaging methods, such as electrical impedance tomography (EIT) and magnetic resonance electrical impedance tomography (MREIT), usually fail to image the anisotropic conductivity tensor of WM with high spatial resolution. The diffusion tensor imaging (DTI) is a newly developed technique that can fulfill this purpose. This paper reviews the existing anisotropic conductivity models of WM based on the DTI and discusses their advantages and disadvantages, as well as identifies opportunities for future research on this subject. It is crucial to obtain the linear conversion coefficient between the eigenvalues of anisotropic conductivity tensor and diffusion tensor, since they share the same eigenvectors. We conclude that the electrochemical model is suitable for ESI analysis because the conversion coefficient can be directly obtained from the concentration of ions in extracellular liquid and that the volume fraction model is appropriate to study the influence of WM structural changes on electrical conductivity. Graphical abstract ᅟ.
Low Multilinear Rank Approximation of Tensors and Application in Missing Traffic Data
Directory of Open Access Journals (Sweden)
Huachun Tan
2014-02-01
Full Text Available The problem of missing data in multiway arrays (i.e., tensors is common in many fields such as bibliographic data analysis, image processing, and computer vision. We consider the problems of approximating a tensor by another tensor with low multilinear rank in the presence of missing data and possibly reconstructing it (i.e., tensor completion. In this paper, we propose a weighted Tucker model which models only the known elements for capturing the latent structure of the data and reconstructing the missing elements. To treat the nonuniqueness of the proposed weighted Tucker model, a novel gradient descent algorithm based on a Grassmann manifold, which is termed Tucker weighted optimization (Tucker-Wopt, is proposed for guaranteeing the global convergence to a local minimum of the problem. Based on extensive experiments, Tucker-Wopt is shown to successfully reconstruct tensors with noise and up to 95% missing data. Furthermore, the experiments on traffic flow volume data demonstrate the usefulness of our algorithm on real-world application.
Tensor form factor for the D → π(K) transitions with Twisted Mass fermions.
Lubicz, Vittorio; Riggio, Lorenzo; Salerno, Giorgio; Simula, Silvano; Tarantino, Cecilia
2018-03-01
We present a preliminary lattice calculation of the D → π and D → K tensor form factors fT (q2) as a function of the squared 4-momentum transfer q2. ETMC recently computed the vector and scalar form factors f+(q2) and f0(q2) describing D → π(K)lv semileptonic decays analyzing the vector current and the scalar density. The study of the weak tensor current, which is directly related to the tensor form factor, completes the set of hadronic matrix element regulating the transition between these two pseudoscalar mesons within and beyond the Standard Model where a non-zero tensor coupling is possible. Our analysis is based on the gauge configurations produced by the European Twisted Mass Collaboration with Nf = 2 + 1 + 1 flavors of dynamical quarks. We simulated at three different values of the lattice spacing and with pion masses as small as 210 MeV and with the valence heavy quark in the mass range from ≃ 0.7 mc to ≃ 1.2mc. The matrix element of the tensor current are determined for a plethora of kinematical conditions in which parent and child mesons are either moving or at rest. As for the vector and scalar form factors, Lorentz symmetry breaking due to hypercubic effects is clearly observed in the data. We will present preliminary results on the removal of such hypercubic lattice effects.
Diffusion tensor metrics as biomarkers in Alzheimer's disease.
Directory of Open Access Journals (Sweden)
Julio Acosta-Cabronero
Full Text Available Although diffusion tensor imaging has been a major research focus for Alzheimer's disease in recent years, it remains unclear whether it has sufficient stability to have biomarker potential. To date, frequently inconsistent results have been reported, though lack of standardisation in acquisition and analysis make such discrepancies difficult to interpret. There is also, at present, little knowledge of how the biometric properties of diffusion tensor imaging might evolve in the course of Alzheimer's disease.The biomarker question was addressed in this study by adopting a standardised protocol both for the whole brain (tract-based spatial statistics, and for a region of interest: the midline corpus callosum. In order to study the evolution of tensor changes, cross-sectional data from very mild (N = 21 and mild (N = 22 Alzheimer's disease patients were examined as well as a longitudinal cohort (N = 16 that had been rescanned at 12 months.The results revealed that increased axial and mean diffusivity are the first abnormalities to occur and that the first region to develop such significant differences was mesial parietal/splenial white matter; these metrics, however, remained relatively static with advancing disease indicating they are suitable as 'state-specific' markers. In contrast, increased radial diffusivity, and therefore decreased fractional anisotropy-though less detectable early-became increasingly abnormal with disease progression, and, in the splenium of the corpus callosum, correlated significantly with dementia severity; these metrics therefore appear 'stage-specific' and would be ideal for monitoring disease progression. In addition, the cross-sectional and longitudinal analyses showed that the progressive abnormalities in radial diffusivity and fractional anisotropy always occurred in areas that had first shown an increase in axial and mean diffusivity. Given that the former two metrics correlate with dementia severity
Glyph-Based Comparative Visualization for Diffusion Tensor Fields.
Zhang, Changgong; Schultz, Thomas; Lawonn, Kai; Eisemann, Elmar; Vilanova, Anna
2016-01-01
Diffusion Tensor Imaging (DTI) is a magnetic resonance imaging modality that enables the in-vivo reconstruction and visualization of fibrous structures. To inspect the local and individual diffusion tensors, glyph-based visualizations are commonly used since they are able to effectively convey full aspects of the diffusion tensor. For several applications it is necessary to compare tensor fields, e.g., to study the effects of acquisition parameters, or to investigate the influence of pathologies on white matter structures. This comparison is commonly done by extracting scalar information out of the tensor fields and then comparing these scalar fields, which leads to a loss of information. If the glyph representation is kept, simple juxtaposition or superposition can be used. However, neither facilitates the identification and interpretation of the differences between the tensor fields. Inspired by the checkerboard style visualization and the superquadric tensor glyph, we design a new glyph to locally visualize differences between two diffusion tensors by combining juxtaposition and explicit encoding. Because tensor scale, anisotropy type, and orientation are related to anatomical information relevant for DTI applications, we focus on visualizing tensor differences in these three aspects. As demonstrated in a user study, our new glyph design allows users to efficiently and effectively identify the tensor differences. We also apply our new glyphs to investigate the differences between DTI datasets of the human brain in two different contexts using different b-values, and to compare datasets from a healthy and HIV-infected subject.
Tensoral for post-processing users and simulation authors
Dresselhaus, Eliot
1993-01-01
The CTR post-processing effort aims to make turbulence simulations and data more readily and usefully available to the research and industrial communities. The Tensoral language, which provides the foundation for this effort, is introduced here in the form of a user's guide. The Tensoral user's guide is presented in two main sections. Section one acts as a general introduction and guides database users who wish to post-process simulation databases. Section two gives a brief description of how database authors and other advanced users can make simulation codes and/or the databases they generate available to the user community via Tensoral database back ends. The two-part structure of this document conforms to the two-level design structure of the Tensoral language. Tensoral has been designed to be a general computer language for performing tensor calculus and statistics on numerical data. Tensoral's generality allows it to be used for stand-alone native coding of high-level post-processing tasks (as described in section one of this guide). At the same time, Tensoral's specialization to a minute task (namely, to numerical tensor calculus and statistics) allows it to be easily embedded into applications written partly in Tensoral and partly in other computer languages (here, C and Vectoral). Embedded Tensoral, aimed at advanced users for more general coding (e.g. of efficient simulations, for interfacing with pre-existing software, for visualization, etc.), is described in section two of this guide.
Energy-momentum tensor of the electromagnetic field
International Nuclear Information System (INIS)
Horndeski, G.W.; Wainwright, J.
1977-01-01
In this paper we investigate the energy-momentum tensor of the most general second-order vector-tensor theory of gravitation and electromagnetism which has field equations which are (i) derivable from a variational principle, (ii) consistent with the notion of conservation of charge, and (iii) compatible with Maxwell's equations in a flat space. This energy-momentum tensor turns out to be quadratic in the first partial derivatives of the electromagnetic field tensor and depends upon the curvature tensor. The asymptotic behavior of this energy-momentum tensor is examined for solutions to Maxwell's equations in Minkowski space, and it is demonstrated that this energy-momentum tensor predicts regions of negative energy density in the vicinity of point sources
Quantum mechanics of Yano tensors: Dirac equation in curved spacetime
International Nuclear Information System (INIS)
Cariglia, Marco
2004-01-01
In spacetimes admitting Yano tensors, the classical theory of the spinning particle possesses enhanced worldline supersymmetry. Quantum mechanically generators of extra supersymmetries correspond to operators that in the classical limit commute with the Dirac operator and generate conserved quantities. We show that the result is preserved in the full quantum theory, that is, Yano symmetries are not anomalous. This was known for Yano tensors of rank 2, but our main result is to show that it extends to Yano tensors of arbitrary rank. We also describe the conformal Yano equation and show that is invariant under Hodge duality. There is a natural relationship between Yano tensors and supergravity theories. As the simplest possible example, we show that when the spacetime admits a Killing spinor then this generates Yano and conformal Yano tensors. As an application, we construct Yano tensors on maximally symmetric spaces: they are spanned by tensor products of Killing vectors
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...
A Tensor-Based Structural Damage Identification and Severity Assessment
Anaissi, Ali; Makki Alamdari, Mehrisadat; Rakotoarivelo, Thierry; Khoa, Nguyen Lu Dang
2018-01-01
Early damage detection is critical for a large set of global ageing infrastructure. Structural Health Monitoring systems provide a sensor-based quantitative and objective approach to continuously monitor these structures, as opposed to traditional engineering visual inspection. Analysing these sensed data is one of the major Structural Health Monitoring (SHM) challenges. This paper presents a novel algorithm to detect and assess damage in structures such as bridges. This method applies tensor analysis for data fusion and feature extraction, and further uses one-class support vector machine on this feature to detect anomalies, i.e., structural damage. To evaluate this approach, we collected acceleration data from a sensor-based SHM system, which we deployed on a real bridge and on a laboratory specimen. The results show that our tensor method outperforms a state-of-the-art approach using the wavelet energy spectrum of the measured data. In the specimen case, our approach succeeded in detecting 92.5% of induced damage cases, as opposed to 61.1% for the wavelet-based approach. While our method was applied to bridges, its algorithm and computation can be used on other structures or sensor-data analysis problems, which involve large series of correlated data from multiple sensors. PMID:29301314
Thick-walled anisotropic elliptic tube analyzed via curvilinear tensor calculus
Directory of Open Access Journals (Sweden)
Mareš T.
2007-10-01
Full Text Available After a brief introduction into the tensor calculus, the thick-walled anisotropic elliptic tube is analyzed. A procedure of the analysis is described in a stepwise manner. A choice of the appropriate coordinate systems is the first step. The second step consists of the determination of corresponding metric tensors. Then the elasticity tensor of a local orthotropy is transformed into a global computational coordinate system. Next the appropriate Christoffel symbols of the second kind are determined and the total potential energy of the system is expressed. At the end the solution is approximated by a Fourier series and for given geometrical values and loading the numerical results are obtained and graphically represented.It must be said that throughout the calculation the free software only was used and for the numerical operations an old laptop is sufficient. The author regards both the former and the latter as a great advantage of the demonstrated method.
Stress-energy tensor near a charged, rotating, evaporating black hole
International Nuclear Information System (INIS)
Hiscock, W.A.
1977-01-01
The recently developed two-dimensional stress-energy regularization techniques are applied to the two-dimensional analog of the Reissner-Nordstroem family of black-hole metrics. The calculated stress-energy tensor in all cases contains the thermal radiation discovered by Hawking. Implications for the evolution of the interior of a charged black hole are considered. The calculated stress-energy tensor is found to diverge on the inner, Cauchy, horizon. Thus the effect of quantum mechanics is to cause the Cauchy horizon to become singular. The stress-energy tensor is also calculated for the ''most reasonable'' two-dimensional analog of the Kerr-Newman family of black-hole metrics. Although the analysis is not as rigorous as in the Reissner-Nordstroem case, it appears that the correct value for the Hawking radiation also appears in this model
Combining voxel-based morphometry and diffusion tensor imaging to detect age-related brain changes.
Lehmbeck, Jan T; Brassen, Stefanie; Weber-Fahr, Wolfgang; Braus, Dieter F
2006-04-03
The present study combined optimized voxel-based morphometry and diffusion tensor imaging to detect age-related brain changes. We compared grey matter density maps (grey matter voxel-based morphometry) and white matter fractional anisotropy maps (diffusion tensor imaging-voxel-based morphometry) between two groups of 17 younger and 17 older women. Older women exhibited reduced white matter fractional anisotropy as well as decreased grey matter density most prominently in the frontal, limbic, parietal and temporal lobes. A discriminant analysis identified four frontal and limbic grey and white matter areas that separated the two groups most effectively. We conclude that grey matter voxel-based morphometry and diffusion tensor imaging voxel-based morphometry are well suited for the detection of age-related changes and their combination provides high accuracy when detecting the neural correlates of aging.
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.
Determination of 3D magnetic reluctivity tensor of soft magnetic composite material
International Nuclear Information System (INIS)
Guo Youguang; Zhu Jianguo; Lin Zhiwei; Zhong Jinjiang; Lu Haiyan; Wang Shuhong
2007-01-01
Soft magnetic composite (SMC) materials are especially suitable for construction of electrical machines with complex structures and three-dimensional (3D) magnetic fluxes. In the design and optimization of such 3D flux machines, the 3D vector magnetic properties of magnetic materials should be properly determined, modeled, and applied for accurate calculation of the magnetic field distribution, parameters, and performance. This paper presents the measurement of 3D vector magnetic properties and determination of 3D reluctivity tensor of SMC. The reluctivity tensor is a key factor for accurate numerical analysis of magnetic field in a 3D flux SMC motor
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...... coefficients, in particular the bulk viscosity, in the vicinity of a second order phase transition point....
Entanglement entropy from the holographic stress tensor
International Nuclear Information System (INIS)
Bhattacharyya, Arpan; Sinha, Aninda
2013-01-01
We consider entanglement entropy in the context of gauge/gravity duality for conformal field theories in even dimensions. The holographic prescription due to Ryu and Takayanagi (RT) leads to an equation describing how the entangling surface extends into the bulk geometry. We show that setting to zero, the time–time component of the Brown–York stress tensor evaluated on the co-dimension 1 entangling surface, leads to the same equation. By considering a spherical entangling surface as an example, we observe that the Euclidean action methods in AdS/CFT will lead to the RT area functional arising as a counterterm needed to regularize the stress tensor. We present arguments leading to a justification for the minimal area prescription. (paper)
Tensor modes on the string theory landscape
International Nuclear Information System (INIS)
Westphal, Alexander
2012-06-01
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.
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.
International Nuclear Information System (INIS)
Kibler, M.; Grenet, G.
1979-07-01
The SU 2 unit tensor operators tsub(k,α) are studied. In the case where the spinor point group G* coincides with U 1 , then tsub(k α) reduces up to a constant to the Wigner-Racah-Schwinger tensor operator tsub(kqα), an operator which produces an angular momentum state. One first investigates those general properties of tsub(kα) which are independent of their realization. The tsub(kα) in terms of two pairs of boson creation and annihilation operators are realized. This leads to look at the Schwinger calculus relative to one angular momentum of two coupled angular momenta. As a by-product, a procedure is given for producing recursion relationships between SU 2 Wigner coefficients. Finally, some of the properties of the Wigner and Racah operators for an arbitrary compact group and the SU 2 coupling coefficients are studied
Non-orthogonal tensor diagonalization
Czech Academy of Sciences Publication Activity Database
Tichavský, Petr; Phan, A. H.; Cichocki, A.
2017-01-01
Roč. 138, č. 1 (2017), s. 313-320 ISSN 0165-1684 R&D Projects: GA ČR(CZ) GA14-13713S; GA ČR GA17-00902S Institutional support: RVO:67985556 Keywords : multilinear models * canonical polyadic decomposition * parallel factor analysis Subject RIV: BB - Applied Statistics, Operational Research OBOR OECD: Statistics and probability Impact factor: 3.110, year: 2016 http://library.utia.cas.cz/separaty/2017/SI/tichavsky-0474387.pdf
Tensor Networks and Quantum Error Correction
Ferris, Andrew J.; Poulin, David
2014-07-01
We establish several relations between quantum error correction (QEC) and tensor network (TN) methods of quantum many-body physics. We exhibit correspondences between well-known families of QEC codes and TNs, and demonstrate a formal equivalence between decoding a QEC code and contracting a TN. We build on this equivalence to propose a new family of quantum codes and decoding algorithms that generalize and improve upon quantum polar codes and successive cancellation decoding in a natural way.
Old tensor mesons in QCD sum rules
International Nuclear Information System (INIS)
Aliev, T.M.; Shifman, M.A.
1981-01-01
Tensor mesons f, A 2 and A 3 are analyzed within the framework of QCD sum rules. The effects of gluon and quark condensate is accounted for phenomenologically. Accurate estimates of meson masses and coupling constants of the lowest-lying states are obtained. It is shown that the masses are reproduced within theoretical uncertainty of about 80 MeV. The coupling of f meson to the corresponding quark current is determined. The results are in good aqreement with experimental data [ru
Energy-momentum-tensor in quantumelectrodynamics
Energy Technology Data Exchange (ETDEWEB)
Schott, T
1974-01-01
This work deals with the operator properties of the energy-momentum-tensor (ET) in the framework of quantum electrodynamics. The principles of construction of the ET are discussed for quantized fields in the Schwinger variation principle. Dealing with the conserved quantities for quantized fields operator problems are coming up in the Coulomb gauge because Dirac- and Maxwellfield do not commute completely. Further on contemporary commutators of the ET components are investigated mutually. Finally non-canonical methods are developed.
Embryo Cell Membranes Reconstruction by Tensor Voting
Michelin , Gaël; Guignard , Léo; Fiuza , Ulla-Maj; Malandain , Grégoire
2014-01-01
International audience; Image-based studies of developing organs or embryos produce a huge quantity of data. To handle such high-throughput experimental protocols, automated computer-assisted methods are highly desirable. This article aims at designing an efficient cell segmentation method from microscopic images. The proposed approach is twofold: first, cell membranes are enhanced or extracted by the means of structure-based filters, and then perceptual grouping (i.e. tensor voting) allows t...
Sasakian manifolds with purely transversal Bach tensor
Ghosh, Amalendu; Sharma, Ramesh
2017-10-01
We show that a (2n + 1)-dimensional Sasakian manifold (M, g) with a purely transversal Bach tensor has constant scalar curvature ≥2 n (2 n +1 ) , equality holding if and only if (M, g) is Einstein. For dimension 3, M is locally isometric to the unit sphere S3. For dimension 5, if in addition (M, g) is complete, then it has positive Ricci curvature and is compact with finite fundamental group π1(M).
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.
Anisotropic diffusion tensor applied to temporal mammograms
DEFF Research Database (Denmark)
Karemore, Gopal; Brandt, Sami; Sporring, Jon
2010-01-01
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...
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 OBOR OECD: Applied mathematics Impact factor: 1.357, year: 2016 http://library.utia.cas.cz/separaty/2017/SI/tichavsky-0468385. pdf
Experimental status of scalar and tensor mesons
International Nuclear Information System (INIS)
Von Dombrowski, S.
1997-01-01
The recent discoveries of a 0 (1450) and f 0 (1370)/f 0 (1500) in antiproton-proton annihilation at rest shed new light on the interpretation of light scalar mesons. The properties of f 0 (1500) match the expectations of a scalar glueball mixed with nearby qq states. New decay modes of the ξ(2230) are reported in radiative J/Ψ decays, pointing also towards a (tensor) glueball nature of this state. Results from different experiments are discussed and compared. (orig.)
Bayesian approach to magnetotelluric tensor decomposition
Czech Academy of Sciences Publication Activity Database
Červ, Václav; Pek, Josef; Menvielle, M.
2010-01-01
Roč. 53, č. 2 (2010), s. 21-32 ISSN 1593-5213 R&D Projects: GA AV ČR IAA200120701; GA ČR GA205/04/0746; GA ČR GA205/07/0292 Institutional research plan: CEZ:AV0Z30120515 Keywords : galvanic distortion * telluric distortion * impedance tensor * basic procedure * inversion * noise Subject RIV: DE - Earth Magnetism, Geodesy, Geography Impact factor: 0.336, year: 2010
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.
Electrical tensor Green functions for cylindrical waveguides
International Nuclear Information System (INIS)
Prijmenko, S.D.; Papkovich, V.G.; Khizhnyak, N.A.
1988-01-01
Formation of electrical tensor Green functions for cylindrical waveguides is considered. Behaviour of these functions in the source region is studied. Cases of electrical tensor Green functions for vector potential G E (r-vector, r'-vector) and electric field G e (r-vector, r'-vector) are analysed. When forming G E (r-vector, r'-vector), its dependence on lateral coordinates is taken into account by means of two-dimensional fundamental vector Hansen functions, several methods are used to take into account the dependence on transverse coordinate. When forming G e (r-vector, r'-vector) we use the fact that G E (r-vector, r'-vector) and G e (r-vector, r'-vector) are the generalized functions. It is shown that G e (r-vector, r'-vector) behaviour in the source region is defined by a singular term, which properties are described by the delta-function. Two variants of solving the problem of defining singular and regular sides of tensor function G E (r-vector, r'-vector) are presented. 23 refs
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.
Liu, Chunlei; Murphy, Nicole E.; Li, Wei
2012-01-01
Diffusion MRI has become an invaluable tool for studying white matter microstructure and brain connectivity. The emergence of quantitative susceptibility mapping and susceptibility tensor imaging (STI) has provided another unique tool for assessing the structure of white matter. In the highly ordered white matter structure, diffusion MRI measures hindered water mobility induced by various tissue and cell membranes, while susceptibility sensitizes to the molecular composition and axonal arrangement. Integrating these two methods may produce new insights into the complex physiology of white matter. In this study, we investigated the relationship between diffusion and magnetic susceptibility in the white matter. Experiments were conducted on phantoms and human brains in vivo. Diffusion properties were quantified with the diffusion tensor model and also with the higher order tensor model based on the cumulant expansion. Frequency shift and susceptibility tensor were measured with quantitative susceptibility mapping and susceptibility tensor imaging. These diffusion and susceptibility quantities were compared and correlated in regions of single fiber bundles and regions of multiple fiber orientations. Relationships were established with similarities and differences identified. It is believed that diffusion MRI and susceptibility MRI provide complementary information of the microstructure of white matter. Together, they allow a more complete assessment of healthy and diseased brains. PMID:23507987
Non-Newtonian stress tensor and thermal conductivity tensor in granular plane shear flow
Alam, Meheboob; Saha, Saikat
2014-11-01
The non-Newtonian stress tensor and the heat flux in the plane shear flow of smooth inelastic disks are analysed from the Grad-level moment equations using the anisotropic Gaussian as a reference. Closed-form expressions for shear viscosity, pressure, first normal stress difference (N1) and the dissipation rate are given as functions of (i) the density or the area fraction (ν), (ii) the restitution coefficient (e), (iii) the dimensionless shear rate (R), (iv) the temperature anisotropy [ η, the difference between the principal eigenvalues of the second moment tensor] and (v) the angle (ϕ) between the principal directions of the shear tensor and the second moment tensor. Particle simulation data for a sheared hard-disk system is compared with theoretical results, with good agreement for p, μ and N1 over a large range of density. In contrast, the predictions from a Navier-Stokes order constitutive model are found to deviate significantly from both the simulation and the moment theory even at moderate values of e. We show that the gradient of the deviatoric part of the kinetic stress drives a heat current and the thermal conductivity is characterized by an anisotropic 2nd rank tensor for which explicit expressions are derived.
Tensor interaction in heavy-ion scattering. Pt. 1
International Nuclear Information System (INIS)
Nishioka, H.; Johnson, R.C.
1985-01-01
The Heidelberg shape-effect model for heavy-ion tensor interactions is reformulated and generalized using the Hooton-Johnson formulation. The generalized semiclassical model (the turning-point model) predicts that the components of the tensor analysing power anti Tsub(2q) have certain relations with each other for each type of tensor interaction (Tsub(R), Tsub(P) and Tsub(L) types). The predicted relations between the anti Tsub(2q) are very simple and have a direct connection with the properties of the tensor interaction at the turning point. The model predictions are satisfied in quantum-mechanical calculations for 7 Li and 23 Na elastic scattering from 58 Ni in the Fresnel-diffraction energy region. As a consequence of this model, it becomes possible to single out effects from a Tsub(P)- or Tsub(L)-type tensor interaction in polarized heavy-ion scattering. The presence of a Tsub(P)-type tensor interaction is suggested by measured anti T 20 /anti T 22 ratios for 7 Li + 58 Ni scattering. In the turning-point model the three types of tensor operator are not independent, and this is found to be true also in a quantum-mechanical calculation. The model also predicts relations between the components of higher-rank tensor analysing power in the presence of a higher-rank tensor interaction. The rank-3 tensor case is discussed in detail. (orig.)
Tensor network decompositions in the presence of a global symmetry
International Nuclear Information System (INIS)
Singh, Sukhwinder; Pfeifer, Robert N. C.; Vidal, Guifre
2010-01-01
Tensor network decompositions offer an efficient description of certain many-body states of a lattice system and are the basis of a wealth of numerical simulation algorithms. We discuss how to incorporate a global symmetry, given by a compact, completely reducible group G, in tensor network decompositions and algorithms. This is achieved by considering tensors that are invariant under the action of the group G. Each symmetric tensor decomposes into two types of tensors: degeneracy tensors, containing all the degrees of freedom, and structural tensors, which only depend on the symmetry group. In numerical calculations, the use of symmetric tensors ensures the preservation of the symmetry, allows selection of a specific symmetry sector, and significantly reduces computational costs. On the other hand, the resulting tensor network can be interpreted as a superposition of exponentially many spin networks. Spin networks are used extensively in loop quantum gravity, where they represent states of quantum geometry. Our work highlights their importance in the context of tensor network algorithms as well, thus setting the stage for cross-fertilization between these two areas of research.
Nonlocal elasticity tensors in dislocation and disclination cores
International Nuclear Information System (INIS)
Taupin, V.; Gbemou, K.; Fressengeas, C.; Capolungo, L.
2017-01-01
We introduced nonlocal elastic constitutive laws for crystals containing defects such as dislocations and disclinations. Additionally, the pointwise elastic moduli tensors adequately reflect the elastic response of defect-free regions by relating stresses to strains and couple-stresses to curvatures, elastic cross-moduli tensors relating strains to couple-stresses and curvatures to stresses within convolution integrals are derived from a nonlocal analysis of strains and curvatures in the defects cores. Sufficient conditions are derived for positive-definiteness of the resulting free energy, and stability of elastic solutions is ensured. The elastic stress/couple stress fields associated with prescribed dislocation/disclination density distributions and solving the momentum and moment of momentum balance equations in periodic media are determined by using a Fast Fourier Transform spectral method. Here, the convoluted cross-moduli bring the following results: (i) Nonlocal stresses and couple stresses oppose their local counterparts in the defects core regions, playing the role of restoring forces and possibly ensuring spatio-temporal stability of the simulated defects, (ii) The couple stress fields are strongly affected by nonlocality. Such effects favor the stability of the simulated grain boundaries and allow investigating their elastic interactions with extrinsic defects, (iii) Driving forces inducing grain growth or refinement derive from the self-stress and couple stress fields of grain boundaries in nanocrystalline configurations.
Cosmological evolution in vector-tensor theories of gravity
International Nuclear Information System (INIS)
Beltran Jimenez, Jose; Maroto, Antonio L.
2009-01-01
We present a detailed study of the cosmological evolution in general vector-tensor theories of gravity without potential terms. We consider the evolution of the vector field throughout the expansion history of the Universe and carry out a classification of models according to the behavior of the vector field in each cosmological epoch. We also analyze the case in which the Universe is dominated by the vector field, performing a complete analysis of the system phase map and identifying those attracting solutions which give rise to accelerated expansion. Moreover, we consider the evolution in a universe filled with a pressureless fluid in addition to the vector field and study the existence of attractors in which we can have a transition from matter domination to vector domination with accelerated expansion so that the vector field may play the role of dark energy. We find that the existence of solutions with late-time accelerated expansion is a generic prediction of vector-tensor theories and that such solutions typically lead to the presence of future singularities. Finally, limits from local gravity tests are used to get constraints on the value of the vector field at small (Solar System) scales.
Effective description of higher-order scalar-tensor theories
Energy Technology Data Exchange (ETDEWEB)
Langlois, David [APC—Astroparticule et Cosmologie, Université Paris Diderot Paris 7, 75013 Paris (France); Mancarella, Michele; Vernizzi, Filippo [Institut de physique théorique, Université Paris Saclay, CEA, CNRS, 91191 Gif-sur-Yvette (France); Noui, Karim, E-mail: langlois@apc.univ-paris7.fr, E-mail: michele.mancarella@cea.fr, E-mail: karim.noui@lmpt.univ-tours.fr, E-mail: filippo.vernizzi@cea.fr [Laboratoire de Mathématiques et Physique Théorique, Université François Rabelais, Parc de Grandmont, 37200 Tours (France)
2017-05-01
Most existing theories of dark energy and/or modified gravity, involving a scalar degree of freedom, can be conveniently described within the framework of the Effective Theory of Dark Energy, based on the unitary gauge where the scalar field is uniform. We extend this effective approach by allowing the Lagrangian in unitary gauge to depend on the time derivative of the lapse function. Although this dependence generically signals the presence of an extra scalar degree of freedom, theories that contain only one propagating scalar degree of freedom, in addition to the usual tensor modes, can be constructed by requiring the initial Lagrangian to be degenerate. Starting from a general quadratic action, we derive the dispersion relations for the linear perturbations around Minkowski and a cosmological background. Our analysis directly applies to the recently introduced Degenerate Higher-Order Scalar-Tensor (DHOST) theories. For these theories, we find that one cannot recover a Poisson-like equation in the static linear regime except for the subclass that includes the Horndeski and so-called 'beyond Horndeski' theories. We also discuss Lorentz-breaking models inspired by Horava gravity.
On the cosmology of scalar-tensor-vector gravity theory
Jamali, Sara; Roshan, Mahmood; Amendola, Luca
2018-01-01
We consider the cosmological consequences of a special scalar-tensor-vector theory of gravity, known as MOG (for MOdified Gravity), proposed to address the dark matter problem. This theory introduces two scalar fields G(x) and μ(x), and one vector field phiα(x), in addition to the metric tensor. We set the corresponding self-interaction potentials to zero, as in the standard form of MOG. Then using the phase space analysis in the flat Friedmann-Robertson-Walker background, we show that the theory possesses a viable sequence of cosmological epochs with acceptable time dependency for the cosmic scale factor. We also investigate MOG's potential as a dark energy model and show that extra fields in MOG cannot provide a late time accelerated expansion. Furthermore, using a dynamical system approach to solve the non-linear field equations numerically, we calculate the angular size of the sound horizon, i.e. θs, in MOG. We find that 8× 10‑3rad<θs<8.2× 10‑3 rad which is way outside the current observational bounds. Finally, we generalize MOG to a modified form called mMOG, and we find that mMOG passes the sound-horizon constraint. However, mMOG also cannot be considered as a dark energy model unless one adds a cosmological constant, and more importantly, the matter dominated era is still slightly different from the standard case.
Relationship between timed 25-foot walk and diffusion tensor imaging in multiple sclerosis.
Klineova, Sylvia; Farber, Rebecca; Saiote, Catarina; Farrell, Colleen; Delman, Bradley N; Tanenbaum, Lawrence N; Friedman, Joshua; Inglese, Matilde; Lublin, Fred D; Krieger, Stephen
2016-01-01
The majority of multiple sclerosis patients experience impaired walking ability, which impacts quality of life. Timed 25-foot walk is commonly used to gauge gait impairment but results can be broadly variable. Objective biological markers that correlate closely with patients' disability are needed. Diffusion tensor imaging, quantifying fiber tract integrity, might provide such information. In this project we analyzed relationships between timed 25-foot walk, conventional and diffusion tensor imaging magnetic resonance imaging markers. A cohort of gait impaired multiple sclerosis patients underwent brain and cervical spinal cord magnetic resonance imaging. Diffusion tensor imaging mean diffusivity and fractional anisotropy were measured on the brain corticospinal tracts and spinal restricted field of vision at C2/3. We analyzed relationships between baseline timed 25-foot walk, conventional and diffusion tensor imaging magnetic resonance imaging markers. Multivariate linear regression analysis showed a statistically significant association between several magnetic resonance imaging and diffusion tensor imaging metrics and timed 25-foot walk: brain mean diffusivity corticospinal tracts (p = 0.004), brain corticospinal tracts axial and radial diffusivity (P = 0.004 and 0.02), grey matter volume (p = 0.05), white matter volume (p = 0.03) and normalized brain volume (P = 0.01). The linear regression model containing mean diffusivity corticospinal tracts and controlled for gait assistance was the best fit model (p = 0.004). Our results suggest an association between diffusion tensor imaging metrics and gait impairment, evidenced by brain mean diffusivity corticospinal tracts and timed 25-foot walk.
Detection of antisymmetric tensor contribution to the magnetic screening of 13C nuclei
International Nuclear Information System (INIS)
Kuhn, W.
1983-01-01
In the present thesis for the first time a practicable way for the detection of antisymmetric contributions to the tensor of the magnetic screening of atomic nuclei is indicated. The detection is based on the relaxation efficiency of the antisymmetric screening. The measurements were performed on the 13 C nuclei of phthalic acid anhydride. Measured were the spin-lattice relaxation times of all 13 C nuclei of the molecule at field strengths between 4.69 T and 11.74 T, this corresponds to 1 H resonance frequencies in the range from 200 MHz to 500 MHz. From this the interaction-specific relaxation rates could be determined without problems. The space-group of the crystal and the molecule geometry were determined by X-ray structure analysis. For the accurate determination of the hydrogen position on a deuterated monocrystal by means of deuterium nuclear resonance measurements the electric field gradient tensors were measured and from the orientation of the main axes of these tensors the bonding angles calculated. On a monocrystal enriched in the C(7) respectively C(8) position with 13 C the symmetric part of the tensor of the magnetic screening of these two nuclei was measured. With these values and the relaxation rates of the 13 C nuclei by an iterative procedure from the equations for the theoretical relaxation rates of all 13 C nuclei of the molecule the main values of the rotation-diffusion tensor could be determined. On the base of the plane molecule geometry from this the tensor element sigmasub(xz)sup(A) could be explicety detected according to an amount of 11.7 ppm. (orig.) [de
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...
Theoretical study of lithium clusters by electronic stress tensor
International Nuclear Information System (INIS)
Ichikawa, Kazuhide; Nozaki, Hiroo; Komazawa, Naoya; Tachibana, Akitomo
2012-01-01
We study the electronic structure of small lithium clusters Li_n (n = 2 ∼ 8) using the electronic stress tensor. We find that the three eigenvalues of the electronic stress tensor of the Li clusters are negative and degenerate, just like the stress tensor of liquid. This leads us to propose that we may characterize a metallic bond in terms of the electronic stress tensor. Our proposal is that in addition to the negativity of the three eigenvalues of the electronic stress tensor, their degeneracy characterizes some aspects of the metallic nature of chemical bonding. To quantify the degree of degeneracy, we use the differential eigenvalues of the electronic stress tensor. By comparing the Li clusters and hydrocarbon molecules, we show that the sign of the largest eigenvalue and the differential eigenvalues could be useful indices to evaluate the metallicity or covalency of a chemical bond.
Radiative corrections in a vector-tensor model
International Nuclear Information System (INIS)
Chishtie, F.; Gagne-Portelance, M.; Hanif, T.; Homayouni, S.; McKeon, D.G.C.
2006-01-01
In a recently proposed model in which a vector non-Abelian gauge field interacts with an antisymmetric tensor field, it has been shown that the tensor field possesses no physical degrees of freedom. This formal demonstration is tested by computing the one-loop contributions of the tensor field to the self-energy of the vector field. It is shown that despite the large number of Feynman diagrams in which the tensor field contributes, the sum of these diagrams vanishes, confirming that it is not physical. Furthermore, if the tensor field were to couple with a spinor field, it is shown at one-loop order that the spinor self-energy is not renormalizable, and hence this coupling must be excluded. In principle though, this tensor field does couple to the gravitational field
Supergravity tensor calculus in 5D from 6D
International Nuclear Information System (INIS)
Kugo, Taichiro; Ohashi, Keisuke
2000-01-01
Supergravity tensor calculus in five spacetime dimensions is derived by dimensional reduction from the d=6 superconformal tensor calculus. In particular, we obtain an off-shell hypermultiplet in 5D from the on-shell hypermultiplet in 6D. Our tensor calculus retains the dilatation gauge symmetry, so that it is a trivial gauge fixing to make the Einstein term canonical in a general matter-Yang-Mills-supergravity coupled system. (author)
Mesh Denoising based on Normal Voting Tensor and Binary Optimization
Yadav, S. K.; Reitebuch, U.; Polthier, K.
2016-01-01
This paper presents a tensor multiplication based smoothing algorithm that follows a two step denoising method. Unlike other traditional averaging approaches, our approach uses an element based normal voting tensor to compute smooth surfaces. By introducing a binary optimization on the proposed tensor together with a local binary neighborhood concept, our algorithm better retains sharp features and produces smoother umbilical regions than previous approaches. On top of that, we provide a stoc...
Comparison of two global digital algorithms for Minkowski tensor estimation
DEFF Research Database (Denmark)
The geometry of real world objects can be described by Minkowski tensors. Algorithms have been suggested to approximate Minkowski tensors if only a binary image of the object is available. This paper presents implementations of two such algorithms. The theoretical convergence properties...... 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....
Properties of the tensor correlation in He isotopes
International Nuclear Information System (INIS)
Myo, Takayuki; Sugimoto, Satoru; Kato, Kiyoshi; Toki, Hiroshi; Ikeda, Kiyomi
2006-01-01
We investigate the roles of the tensor correlation on the structures of 4,5 He. For 4 He, we take the high angular momentum states as much as possible with the 2p2h excitations of the shell model type method to describe the tensor correlation. Three specific configurations are found to be favored for the tensor correlation. This correlation is also important to describe the scattering phenomena of the 4 He+nsystem including the higher partial waves consistently
A General Expression for the Quartic Lovelock Tensor
Briggs, C. C.
1997-01-01
A general expression is given for the quartic Lovelock tensor in terms of the Riemann-Christoffel and Ricci curvature tensors and the Riemann curvature scalar for n-dimensional differentiable manifolds having a general linear connection. In addition, expressions are given (in the appendix) for the coefficient of the quartic Lovelock Lagrangian as well as for lower-order Lovelock tensors and Lovelock Lagrangian coefficients.
Energy-momentum tensor in the quantum field theory
International Nuclear Information System (INIS)
Azakov, S.I.
1977-01-01
An energy-momentum tensor in the scalar field theory is built. The tensor must satisfy the finiteness requirement of the Green function. The Green functions can always be made finite by renormalizations in the S-matrix by introducing counter terms into the Hamiltonian (or Lagrangian) of the interaction. Such a renormalization leads to divergencies in the Green functions. Elimination of these divergencies requires the introduction of new counter terms, which must be taken into account in the energy-momentum tensor
Umehara, Jun; Ikezoe, Tome; Nishishita, Satoru; Nakamura, Masatoshi; Umegaki, Hiroki; Kobayashi, Takuya; Fujita, Kosuke; Ichihashi, Noriaki
2015-12-01
Decreased flexibility of the tensor fasciae latae is one factor that causes iliotibial band syndrome. Stretching has been used to improve flexibility or tightness of the muscle. However, no studies have investigated the effective stretching position for the tensor fasciae latae using an index to quantify muscle elongation in vivo. The aim of this study was to investigate the effects of hip rotation and knee angle on tensor fasciae latae elongation during stretching in vivo using ultrasonic shear wave elastography. Twenty healthy men participated in this study. The shear elastic modulus of the tensor fasciae latae was calculated using ultrasonic shear wave elastography. Stretching was performed at maximal hip adduction and maximal hip extension in 12 different positions with three hip rotation conditions (neutral, internal, and external rotations) and four knee angles (0°, 45°, 90°, and 135°). Two-way analysis of variance showed a significant main effect for knee angle, but not for hip rotation. The post-hoc test for knee angle indicated that the shear elastic modulus at 90° and 135° were significantly greater than those at 0° and 45°. Our results suggest that adding hip rotation to the stretching position with hip adduction and extension may have less effect on tensor fasciae latae elongation, and that stretching at >90° of knee flexion may effectively elongate the tensor fasciae latae. Copyright © 2015 Elsevier Ltd. All rights reserved.
Aojula, Anuriti; Botfield, Hannah; McAllister, James Patterson; Gonzalez, Ana Maria; Abdullah, Osama; Logan, Ann; Sinclair, Alexandra
2016-05-31
In an effort to develop novel treatments for communicating hydrocephalus, we have shown previously that the transforming growth factor-β antagonist, decorin, inhibits subarachnoid fibrosis mediated ventriculomegaly; however decorin's ability to prevent cerebral cytopathology in communicating hydrocephalus has not been fully examined. Furthermore, the capacity for diffusion tensor imaging to act as a proxy measure of cerebral pathology in multiple sclerosis and spinal cord injury has recently been demonstrated. However, the use of diffusion tensor imaging to investigate cytopathological changes in communicating hydrocephalus is yet to occur. Hence, this study aimed to determine whether decorin treatment influences alterations in diffusion tensor imaging parameters and cytopathology in experimental communicating hydrocephalus. Moreover, the study also explored whether diffusion tensor imaging parameters correlate with cellular pathology in communicating hydrocephalus. Accordingly, communicating hydrocephalus was induced by injecting kaolin into the basal cisterns in 3-week old rats followed immediately by 14 days of continuous intraventricular delivery of either human recombinant decorin (n = 5) or vehicle (n = 6). Four rats remained as intact controls and a further four rats served as kaolin only controls. At 14-days post-kaolin, just prior to sacrifice, routine magnetic resonance imaging and magnetic resonance diffusion tensor imaging was conducted and the mean diffusivity, fractional anisotropy, radial and axial diffusivity of seven cerebral regions were assessed by voxel-based analysis in the corpus callosum, periventricular white matter, caudal internal capsule, CA1 hippocampus, and outer and inner parietal cortex. Myelin integrity, gliosis and aquaporin-4 levels were evaluated by post-mortem immunohistochemistry in the CA3 hippocampus and in the caudal brain of the same cerebral structures analysed by diffusion tensor imaging. Decorin significantly
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.
QCD vacuum tensor susceptibility and properties of transversely polarized mesons
International Nuclear Information System (INIS)
Bakulev, A.P.; Mikhajlov, S.V.
1999-01-01
We re-estimate the tensor susceptibility of QCD vacuum, χ, and to this end, we re-estimate the leptonic decay constants for transversely polarized ρ-, ρ'- and b 1 -mesons. The origin of the susceptibility is analyzed using duality between ρ- and b 1 -channels in a 2-point correlator of tensor currents and disagree with [2] on both OPE expansion and the value of QCD vacuum tensor susceptibility. Using our value for the latter we determine new estimations of nucleon tensor charges related to the first moment of the transverse structure functions h 1 of a nucleon
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...
Superconformal tensor calculus and matter couplings in six dimensions
International Nuclear Information System (INIS)
Bergshoeff, E.; Sezgin, E.; van Proeyen, A.
1989-01-01
Using superconformal tensor calculus the authors construct general interactions of N = 2, d = 6 supergravity with a tensor multiplet and a number of scalar, vector and linear multiplets. They start from the superconformal algebra which they realize on a 40 + 40 Weyl multiplet and on several matter multiplets. A special role is played by the tensor multiplet, which cannot be treated as an ordinary matter multiplet, but leads to a second 40 + 40 version of the Weyl multiplet. The authors also obtain a 48 + 48 off-shell formulation of Poincare supergravity coupled to a tensor multiplet
Superconformal tensor calculus and matter couplings in six dimensions
International Nuclear Information System (INIS)
Bergshoeff, E.; Sezgin, E.; Proeyen, A. van
1986-01-01
Using superconformal tensor calculus we construct general interactions of N = 2, d = 6 supergravity with a tensor multiplet and a number of scalar, vector and linear multiplets. We start from the superconformal algebra which we realize on a 40 + 40 Weyl multiplet and on several matter multiplets. A special role is played by the tensor multiplet, which cannot be treated as an ordinary matter multiplet, but leads to a second 40 + 40 version of the Weyl multiplet. We also obtain a 48 + 48 off-shell formulation of Poincare supergravity coupled to a tensor multiplet. (orig.)
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.
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.
Prescribed curvature tensor in locally conformally flat manifolds
Pina, Romildo; Pieterzack, Mauricio
2018-01-01
A global existence theorem for the prescribed curvature tensor problem in locally conformally flat manifolds is proved for a special class of tensors R. Necessary and sufficient conditions for the existence of a metric g ¯ , conformal to Euclidean g, are determined such that R ¯ = R, where R ¯ is the Riemannian curvature tensor of the metric g ¯ . The solution to this problem is given explicitly for special cases of the tensor R, including the case where the metric g ¯ is complete on Rn. Similar problems are considered for locally conformally flat manifolds.
The classification of the Ricci tensor in the general theory of relativity
International Nuclear Information System (INIS)
Cormack, W.J.
1979-10-01
A comprehensive classification of the Ricci tensor in General Relativity using several techniques is given and their connection with existing classification studied under the headings; canonical forms for the Ricci tensor, invariant 2-spaces in the classification of the Ricci tensor, Riemannian curvature and the classification of the Riemann and Ricci tensors, and spinor classifications of the Ricci tensor. (U.K.)
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.
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
A supersymmetric SYK-like tensor model
Energy Technology Data Exchange (ETDEWEB)
Peng, Cheng; Spradlin, Marcus; Volovich, Anastasia [Department of Physics, Brown University,Providence, RI, 02912 (United States)
2017-05-11
We consider a supersymmetric SYK-like model without quenched disorder that is built by coupling two kinds of fermionic N=1 tensor-valued superfields, “quarks” and “mesons”. We prove that the model has a well-defined large-N limit in which the (s)quark 2-point functions are dominated by mesonic “melon” diagrams. We sum these diagrams to obtain the Schwinger-Dyson equations and show that in the IR, the solution agrees with that of the supersymmetric SYK model.
Tensor glueball-meson mixing phenomenology
International Nuclear Information System (INIS)
Burakovsky, L.; Page, P.R.
2000-01-01
The overpopulated isoscalar tensor states are sifted using Schwinger-type mass relations. Two solutions are found: one where the glueball is the f J (2220), and one where the glueball is more distributed, with f 2 (1820) having the largest component. The f 2 (1565) and f J (1710) cannot be accommodated as glueball-(hybrid) meson mixtures in the absence of significant coupling to decay channels. f 2 '(1525)→ππ is in agreement with experiment. The f J (2220) decays neither flavour democratically nor is narrow. (orig.)
Tensor Network Wavefunctions for Topological Phases
Ware, Brayden Alexander
The combination of quantum effects and interactions in quantum many-body systems can result in exotic phases with fundamentally entangled ground state wavefunctions--topological phases. Topological phases come in two types, both of which will be studied in this thesis. In topologically ordered phases, the pattern of entanglement in the ground state wavefunction encodes the statistics of exotic emergent excitations, a universal indicator of a phase that is robust to all types of perturbations. In symmetry protected topological phases, the entanglement instead encodes a universal response of the system to symmetry defects, an indicator that is robust only to perturbations respecting the protecting symmetry. Finding and creating these phases in physical systems is a motivating challenge that tests all aspects--analytical, numerical, and experimental--of our understanding of the quantum many-body problem. Nearly three decades ago, the creation of simple ansatz wavefunctions--such as the Laughlin fractional quantum hall state, the AKLT state, and the resonating valence bond state--spurred analytical understanding of both the role of entanglement in topological physics and physical mechanisms by which it can arise. However, quantitative understanding of the relevant phase diagrams is still challenging. For this purpose, tensor networks provide a toolbox for systematically improving wavefunction ansatz while still capturing the relevant entanglement properties. In this thesis, we use the tools of entanglement and tensor networks to analyze ansatz states for several proposed new phases. In the first part, we study a featureless phase of bosons on the honeycomb lattice and argue that this phase can be topologically protected under any one of several distinct subsets of the crystalline lattice symmetries. We discuss methods of detecting such phases with entanglement and without. In the second part, we consider the problem of constructing fixed-point wavefunctions for
Scalar-tensor cosmology with cosmological constant
International Nuclear Information System (INIS)
Maslanka, K.
1983-01-01
The equations of scalar-tensor theory of gravitation with cosmological constant in the case of homogeneous and isotropic cosmological model can be reduced to dynamical system of three differential equations with unknown functions H=R/R, THETA=phi/phi, S=e/phi. When new variables are introduced the system becomes more symmetrical and cosmological solutions R(t), phi(t), e(t) are found. It is shown that when cosmological constant is introduced large class of solutions which depend also on Dicke-Brans parameter can be obtained. Investigations of these solutions give general limits for cosmological constant and mean density of matter in plane model. (author)
Tensor Decompositions for Learning Latent Variable Models
2012-12-08
and eigenvectors of tensors is generally significantly more complicated than their matrix counterpart (both algebraically [Qi05, CS11, Lim05] and...The reduction First, let W ∈ Rd×k be a linear transformation such that M2(W,W ) = W M2W = I where I is the k × k identity matrix (i.e., W whitens ...approximate the whitening matrix W ∈ Rd×k from second-moment matrix M2 ∈ Rd×d. To do this, one first multiplies M2 by a random matrix R ∈ Rd×k′ for some k′ ≥ k
Electrical conductivity tensor of an irradiated metal
International Nuclear Information System (INIS)
Corciovei, A.; Dumitru, R.D.
1979-01-01
A method to calculate the electrical conductivity tensor of an irradiated metal is presented. The proposed method relies on the use of the Kubo formula, evaluated by a perturbation method. The one electron Hamiltonian is written as a sum of two terms: the Hamiltonian of the conduction electrons moving in a periodic lattice and the perturbation, namely, the scattering potential due to the irradiation defects of the ideal crystal. Then, the lowest order of the conductivity is determined by the lowest order of the Laplace transform of the current. An integral equation is written for this last quantity. (author)
A supersymmetric SYK-like tensor model
International Nuclear Information System (INIS)
Peng, Cheng; Spradlin, Marcus; Volovich, Anastasia
2017-01-01
We consider a supersymmetric SYK-like model without quenched disorder that is built by coupling two kinds of fermionic N=1 tensor-valued superfields, “quarks” and “mesons”. We prove that the model has a well-defined large-N limit in which the (s)quark 2-point functions are dominated by mesonic “melon” diagrams. We sum these diagrams to obtain the Schwinger-Dyson equations and show that in the IR, the solution agrees with that of the supersymmetric SYK model.
Physical states in the canonical tensor model from the perspective of random tensor networks
Energy Technology Data Exchange (ETDEWEB)
Narain, Gaurav [The Institute for Fundamental Study “The Tah Poe Academia Institute”,Naresuan University, Phitsanulok 65000 (Thailand); Sasakura, Naoki [Yukawa Institute for Theoretical Physics,Kyoto University, Kyoto 606-8502 (Japan); Sato, Yuki [National Institute for Theoretical Physics,School of Physics and Centre for Theoretical Physics,University of the Witwartersrand, WITS 2050 (South Africa)
2015-01-07
Tensor models, generalization of matrix models, are studied aiming for quantum gravity in dimensions larger than two. Among them, the canonical tensor model is formulated as a totally constrained system with first-class constraints, the algebra of which resembles the Dirac algebra of general relativity. When quantized, the physical states are defined to be vanished by the quantized constraints. In explicit representations, the constraint equations are a set of partial differential equations for the physical wave-functions, which do not seem straightforward to be solved due to their non-linear character. In this paper, after providing some explicit solutions for N=2,3, we show that certain scale-free integration of partition functions of statistical systems on random networks (or random tensor networks more generally) provides a series of solutions for general N. Then, by generalizing this form, we also obtain various solutions for general N. Moreover, we show that the solutions for the cases with a cosmological constant can be obtained from those with no cosmological constant for increased N. This would imply the interesting possibility that a cosmological constant can always be absorbed into the dynamics and is not an input parameter in the canonical tensor model. We also observe the possibility of symmetry enhancement in N=3, and comment on an extension of Airy function related to the solutions.
Coupling coefficients for tensor product representations of quantum SU(2)
International Nuclear Information System (INIS)
Groenevelt, Wolter
2014-01-01
We study tensor products of infinite dimensional irreducible * -representations (not corepresentations) of the SU(2) quantum group. We obtain (generalized) eigenvectors of certain self-adjoint elements using spectral analysis of Jacobi operators associated to well-known q-hypergeometric orthogonal polynomials. We also compute coupling coefficients between different eigenvectors corresponding to the same eigenvalue. Since the continuous spectrum has multiplicity two, the corresponding coupling coefficients can be considered as 2 × 2-matrix-valued orthogonal functions. We compute explicitly the matrix elements of these functions. The coupling coefficients can be considered as q-analogs of Bessel functions. As a results we obtain several q-integral identities involving q-hypergeometric orthogonal polynomials and q-Bessel-type functions
Coupling coefficients for tensor product representations of quantum SU(2)
Groenevelt, Wolter
2014-10-01
We study tensor products of infinite dimensional irreducible *-representations (not corepresentations) of the SU(2) quantum group. We obtain (generalized) eigenvectors of certain self-adjoint elements using spectral analysis of Jacobi operators associated to well-known q-hypergeometric orthogonal polynomials. We also compute coupling coefficients between different eigenvectors corresponding to the same eigenvalue. Since the continuous spectrum has multiplicity two, the corresponding coupling coefficients can be considered as 2 × 2-matrix-valued orthogonal functions. We compute explicitly the matrix elements of these functions. The coupling coefficients can be considered as q-analogs of Bessel functions. As a results we obtain several q-integral identities involving q-hypergeometric orthogonal polynomials and q-Bessel-type functions.
Elastic and inelastic electron scattering on tensor polarized deuteron
International Nuclear Information System (INIS)
Zevakov, S.A.; Barkov, L.M.; Arenkhovel', Kh.
2006-01-01
The components T 20 and T 21 of the tensor analysis capability of the elastic electron scattering on deuteron are measured in the momentum transfer range of 8.4-21.6 fm -2 . The form factors of deuteron G C and G Q are defined in the momentum transfer range where the monopole charge form factor G C turns into zero. The preliminary measuring results of T 20 , T 21 and T 22 of the deuteron photodisintegration reaction in the photon energy range of 25-500 MeV and the proton departure angles equal to 20 deg-40 deg and 75 deg-105 deg are presented. The experimental results are compared with the theoretical predictions [ru
Black holes in vector-tensor theories
Energy Technology Data Exchange (ETDEWEB)
Heisenberg, Lavinia [Institute for Theoretical Studies, ETH Zurich, Clausiusstrasse 47, 8092 Zurich (Switzerland); Kase, Ryotaro; Tsujikawa, Shinji [Department of Physics, Faculty of Science, Tokyo University of Science, 1-3, Kagurazaka, Shinjuku-ku, Tokyo 162-8601 (Japan); Minamitsuji, Masato, E-mail: lavinia.heisenberg@eth-its.ethz.ch, E-mail: r.kase@rs.tus.ac.jp, E-mail: masato.minamitsuji@tecnico.ulisboa.pt, E-mail: shinji@rs.kagu.tus.ac.jp [Centro Multidisciplinar de Astrofisica—CENTRA, Departamento de Fisica, Instituto Superior Tecnico—IST, Universidade de Lisboa—UL, Avenida Rovisco Pais 1, 1049-001 Lisboa (Portugal)
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.
Emergent symmetries in the canonical tensor model
Obster, Dennis; Sasakura, Naoki
2018-04-01
The canonical tensor model (CTM) is a tensor model proposing a classically and quantum mechanically consistent description of gravity, formulated as a first-class constraint system with structural similarities to the ADM formalism of general relativity. The classical CTM produces a general relativistic system in a formal continuum limit, the emergence of which should be explained by the quantum CTM. In this paper we study the symmetry properties of a wave function that exactly solves the quantum constraints of the CTM. We have found that it has strong peaks at configurations invariant under some Lie groups, as predicted by a mechanism described in our previous paper. A surprising result is the preference for configurations invariant not only under Lie groups with positive definite signature, but also with Lorentzian signature. Such symmetries could characterize the global structures of spacetimes, and our results are encouraging towards showing spacetime emergence in the CTM. To verify the asymptotic convergence of the wave function we have also analyzed the asymptotic behavior, which for the most part seems to be well under control.
Quantum chaos and holographic tensor models
Energy Technology Data Exchange (ETDEWEB)
Krishnan, Chethan [Center for High Energy Physics, Indian Institute of Science,Bangalore 560012 (India); Sanyal, Sambuddha [International Center for Theoretical Sciences, Tata Institute of Fundamental Research,Bangalore 560089 (India); Subramanian, P.N. Bala [Center for High Energy Physics, Indian Institute of Science,Bangalore 560012 (India)
2017-03-10
A class of tensor models were recently outlined as potentially calculable examples of holography: their perturbative large-N behavior is similar to the Sachdev-Ye-Kitaev (SYK) model, but they are fully quantum mechanical (in the sense that there is no quenched disorder averaging). These facts make them intriguing tentative models for quantum black holes. In this note, we explicitly diagonalize the simplest non-trivial Gurau-Witten tensor model and study its spectral and late-time properties. We find parallels to (a single sample of) SYK where some of these features were recently attributed to random matrix behavior and quantum chaos. In particular, the spectral form factor exhibits a dip-ramp-plateau structure after a running time average, in qualitative agreement with SYK. But we also observe that even though the spectrum has a unique ground state, it has a huge (quasi-?)degeneracy of intermediate energy states, not seen in SYK. If one ignores the delta function due to the degeneracies however, there is level repulsion in the unfolded spacing distribution hinting chaos. Furthermore, there are gaps in the spectrum. The system also has a spectral mirror symmetry which we trace back to the presence of a unitary operator with which the Hamiltonian anticommutes. We use it to argue that to the extent that the model exhibits random matrix behavior, it is controlled not by the Dyson ensembles, but by the BDI (chiral orthogonal) class in the Altland-Zirnbauer classification.
Stress tensor fluctuations in de Sitter spacetime
Energy Technology Data Exchange (ETDEWEB)
Pérez-Nadal, Guillem; Verdaguer, Enric [Departament de Física Fonamental and Institut de Ciències del Cosmos, Universitat de Barcelona, Av. Diagonal 647, 08028 Barcelona (Spain); Roura, Albert, E-mail: guillem@ffn.ub.es, E-mail: albert.roura@aei.mpg.de, E-mail: enric.verdaguer@ub.edu [Max-Planck-Institut für Gravitationsphysik, Albert-Einstein-Institut, Am Mühlenberg 1, 14476 Golm (Germany)
2010-05-01
The two-point function of the stress tensor operator of a quantum field in de Sitter spacetime is calculated for an arbitrary number of dimensions. We assume the field to be in the Bunch-Davies vacuum, and formulate our calculation in terms of de Sitter-invariant bitensors. Explicit results for free minimally coupled scalar fields with arbitrary mass are provided. We find long-range stress tensor correlations for sufficiently light fields (with mass m much smaller than the Hubble scale H), namely, the two-point function decays at large separations like an inverse power of the physical distance with an exponent proportional to m{sup 2}/H{sup 2}. In contrast, we show that for the massless case it decays at large separations like the fourth power of the physical distance. There is thus a discontinuity in the massless limit. As a byproduct of our work, we present a novel and simple geometric interpretation of de Sitter-invariant bitensors for pairs of points which cannot be connected by geodesics.
Quantum chaos and holographic tensor models
International Nuclear Information System (INIS)
Krishnan, Chethan; Sanyal, Sambuddha; Subramanian, P.N. Bala
2017-01-01
A class of tensor models were recently outlined as potentially calculable examples of holography: their perturbative large-N behavior is similar to the Sachdev-Ye-Kitaev (SYK) model, but they are fully quantum mechanical (in the sense that there is no quenched disorder averaging). These facts make them intriguing tentative models for quantum black holes. In this note, we explicitly diagonalize the simplest non-trivial Gurau-Witten tensor model and study its spectral and late-time properties. We find parallels to (a single sample of) SYK where some of these features were recently attributed to random matrix behavior and quantum chaos. In particular, the spectral form factor exhibits a dip-ramp-plateau structure after a running time average, in qualitative agreement with SYK. But we also observe that even though the spectrum has a unique ground state, it has a huge (quasi-?)degeneracy of intermediate energy states, not seen in SYK. If one ignores the delta function due to the degeneracies however, there is level repulsion in the unfolded spacing distribution hinting chaos. Furthermore, there are gaps in the spectrum. The system also has a spectral mirror symmetry which we trace back to the presence of a unitary operator with which the Hamiltonian anticommutes. We use it to argue that to the extent that the model exhibits random matrix behavior, it is controlled not by the Dyson ensembles, but by the BDI (chiral orthogonal) class in the Altland-Zirnbauer classification.
Constraints on the tensor-to-scalar ratio for non-power-law models
International Nuclear Information System (INIS)
Vázquez, J. Alberto; Bridges, M.; Ma, Yin-Zhe; Hobson, M.P.
2013-01-01
Recent cosmological observations hint at a deviation from the simple power-law form of the primordial spectrum of curvature perturbations. In this paper we show that in the presence of a tensor component, a turn-over in the initial spectrum is preferred by current observations, and hence non-power-law models ought to be considered. For instance, for a power-law parameterisation with both a tensor component and running parameter, current data show a preference for a negative running at more than 2.5σ C.L. As a consequence of this deviation from a power-law, constraints on the tensor-to-scalar ratio r are slightly broader. We also present constraints on the inflationary parameters for a model-independent reconstruction and the Lasenby and Doran (LD) model. In particular, the constraints on the tensor-to-scalar ratio from the LD model are: r LD = 0.11±0.024. In addition to current data, we show expected constraints from Planck-like and CMB-Pol sensitivity experiments by using Markov-Chain-Monte-Carlo sampling chains. For all the models, we have included the Bayesian Evidence to perform a model selection analysis. The Bayes factor, using current observations, shows a strong preference for the LD model over the standard power-law parameterisation, and provides an insight into the accuracy of differentiating models through future surveys
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.
Tensor Minkowski Functionals: first application to the CMB
Energy Technology Data Exchange (ETDEWEB)
Ganesan, Vidhya [Indian Institute of Astrophysics, Koramangala II Block, Bangalore 560 034 (India); Chingangbam, Pravabati, E-mail: vidhya@iiap.res.in, E-mail: prava@iiap.res.in [Indian Institute of Science, C.V. Raman Ave, Bangalore 560 012 (India)
2017-06-01
Tensor Minkowski Functionals (TMFs) are tensor generalizations of the usual Minkowski Functionals which are scalar quantities. We introduce them here for use in cosmological analysis, in particular to analyze the Cosmic Microwave Background (CMB) radiation. They encapsulate information about the shapes of structures and the orientation of distributions of structures. We focus on one of the TMFs, namely W {sub 2}{sup 1,1}, which is the (1,1) rank tensor generalization of the genus. The ratio of the eigenvalues of the average of W {sub 2}{sup 1,1} over all structures, α, encodes the net orientation of the structures; and the average of the ratios of the eigenvalues of W {sub 2}{sup 1,1} for each structure, β, encodes the net intrinsic anisotropy of the structures. We have developed a code that computes W {sub 2}{sup 1,1}, and from it α and β, for a set of structures on the 2-dimensional Euclidean plane. We use it to compute α and β as functions of chosen threshold levels for simulated Gaussian and isotropic CMB temperature and E mode fields. We obtain the value of α to be one for both temperature and E mode, which means that we recover the statistical isotropy of density fluctuations that we input in the simulations. We find that the standard ΛCDM model predicts a charateristic shape of β for temperature and E mode as a function of the threshold, and the average over thresholds is β∼ 0.62 for temperature and β∼ 0.63 for E mode. Accurate measurements of α and β can be used to test the standard model of cosmology and to search for deviations from it. For this purpose we compute α and β for temperature and E mode data of various data sets from PLANCK mission. We compare the values measured from observed data with those obtained from simulations to which instrument beam and noise characteristics of the 44GHz frequency channel have been added (which are provided as part of the PLANCK data release). We find very good agreement of β and α between all
Tensor estimation for double-pulsed diffusional kurtosis imaging.
Shaw, Calvin B; Hui, Edward S; Helpern, Joseph A; Jensen, Jens H
2017-07-01
Double-pulsed diffusional kurtosis imaging (DP-DKI) represents the double diffusion encoding (DDE) MRI signal in terms of six-dimensional (6D) diffusion and kurtosis tensors. Here a method for estimating these tensors from experimental data is described. A standard numerical algorithm for tensor estimation from conventional (i.e. single diffusion encoding) diffusional kurtosis imaging (DKI) data is generalized to DP-DKI. This algorithm is based on a weighted least squares (WLS) fit of the signal model to the data combined with constraints designed to minimize unphysical parameter estimates. The numerical algorithm then takes the form of a quadratic programming problem. The principal change required to adapt the conventional DKI fitting algorithm to DP-DKI is replacing the three-dimensional diffusion and kurtosis tensors with the 6D tensors needed for DP-DKI. In this way, the 6D diffusion and kurtosis tensors for DP-DKI can be conveniently estimated from DDE data by using constrained WLS, providing a practical means for condensing DDE measurements into well-defined mathematical constructs that may be useful for interpreting and applying DDE MRI. Data from healthy volunteers for brain are used to demonstrate the DP-DKI tensor estimation algorithm. In particular, representative parametric maps of selected tensor-derived rotational invariants are presented. Copyright © 2017 John Wiley & Sons, Ltd.
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, ...
A tensor approach to the estimation of hydraulic conductivities in ...
African Journals Online (AJOL)
Based on the field measurements of the physical properties of fractured rocks, the anisotropic properties of hydraulic conductivity (HC) of the fractured rock aquifer can be assessed and presented using a tensor approach called hydraulic conductivity tensor. Three types of HC values, namely point value, axial value and flow ...
Tensor meson dominance and e+e--physics
International Nuclear Information System (INIS)
Genz, H.; Karlsruhe Univ.; Mallik, S.
1983-01-01
The phenomenological status of tensor meson dominance is reported. Some new results concerning hadronic decays of the 2 ++ -meson chi 2 (3.55) and the heavy lepton tau are also included. Considering experimental errors, tensor meson dominance is in agreement with experiment. (author)
Tensor Excitations in Nambu - Jona-Lasinio Model
Chizhov, M V
1996-01-01
It is shown that in the one-flavour NJL model the vector and axial-vector quasiparticles described by the antisymmetric tensor field are generated. These excitations have tensor interactions with quarks in contrast to usual vector ones. Phenomenological applications are discussed.
Tensor Basis Neural Network v. 1.0 (beta)
Energy Technology Data Exchange (ETDEWEB)
2017-03-28
This software package can be used to build, train, and test a neural network machine learning model. The neural network architecture is specifically designed to embed tensor invariance properties by enforcing that the model predictions sit on an invariant tensor basis. This neural network architecture can be used in developing constitutive models for applications such as turbulence modeling, materials science, and electromagnetism.
Energy momentum tensor in local causal perturbation theory
International Nuclear Information System (INIS)
Prange, D.
2001-01-01
We study the energy momentum tensor in the Bogolyubov-Epstein-Glaser approach to perturbation theory. It is found to be locally conserved for a class of theories containing to derivated fields in the interaction. For the massless φ 4 -theory we derive the trace anomaly of the improved tensor. (orig.)
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.
Relativistic interpretation of the nature of the nuclear tensor force
Zong, Yao-Yao; Sun, Bao-Yuan
2018-02-01
The spin-dependent nature of the nuclear tensor force is studied in detail within the relativistic Hartree-Fock approach. The relativistic formalism for the tensor force is supplemented with an additional Lorentz-invariant tensor formalism in the σ-scalar channel, so as to take into account almost fully the nature of the tensor force brought about by the Fock diagrams in realistic nuclei. Specifically, the tensor sum rules are tested for the spin and pseudo-spin partners with and without nodes, to further understand the nature of the tensor force within the relativistic model. It is shown that the interference between the two components of nucleon spinors causes distinct violations of the tensor sum rules in realistic nuclei, mainly due to the opposite signs on the κ quantities of the upper and lower components, as well as the nodal difference. However, the sum rules can be precisely reproduced if the same radial wave functions are taken for the spin/pseudo-spin partners in addition to neglecting the lower/upper components, revealing clearly the nature of the tensor force. Supported by National Natural Science Foundation of China (11375076, 11675065) and the Fundamental Research Funds for the Central Universities (lzujbky-2016-30)
Parity and isospin in pion condensation and tensor binding
International Nuclear Information System (INIS)
Pace, E.; Palumbo, F.
1978-01-01
In infinite nuclear matter with pion condensates or tensor binding both parity and isospin symmetries are broken. Finite nuclei with pion condensates or tensor binding, however, can have definite parity. They cannot have a definite value of isospin, whose average value is of the order of the number of nucleons. (Auth.)
Superspace actions and duality transformations for N=2 tensor multiplets
International Nuclear Information System (INIS)
Galperin, A.; Ivanov, E.; Ogievetsky, V.
1985-01-01
General actions for self-interacting N=2 tensor multiplets are considered in the harmonic superspace approach. All of them are shown to be equivalent, by superfield duality transformations, to some restricted class of the hypermultiplets actions. In particular, the improved tensor multiplet theory is dual to a free hypermultiplet one. Superspace couplings of these improved matter multiplets against conformal supergravity are also constructed
Multiple M2-branes and the embedding tensor
Bergshoeff, Eric A.; de Roo, Mees; Hohm, Olaf
2008-01-01
We show that the Bagger-Lambert theory of multiple M2-branes fits into the general construction of maximally supersymmetric gauge theories using the embedding tensor technique. We apply the embedding tensor technique in order to systematically obtain the consistent gaugings of N = 8 superconformal
Subtracting a best rank-1 approximation may increase tensor rank
Stegeman, Alwin; Comon, Pierre
2010-01-01
It has been shown that a best rank-R approximation of an order-k tensor may not exist when R >= 2 and k >= 3. This poses a serious problem to data analysts using tensor decompositions it has been observed numerically that, generally, this issue cannot be solved by consecutively computing and
Couplings of self-dual tensor multiplet in six dimensions
Bergshoeff, E.; Sezgin, E.; Sokatchev, E.
1996-01-01
The (1, 0) supersymmetry in six dimensions admits a tensor multiplet which contains a second-rank antisymmetric tensor field with a self-dual field strength and a dilaton. We describe the fully supersymmetric coupling of this multiplet to a Yangâ€“Mills multiplet, in the absence of supergravity. The
Superconformal tensor calculus and matter couplings in six dimensions
Bergshoeff, E.; Sezgin, E.; Proeyen, A. Van
1986-01-01
Using superconformal tensor calculus we construct general interactions of N = 2, d = 6 supergravity with a tensor multiplet and a number of scalar, vector and linear multiplets. We start from the superconformal algebra which we realize on a 40+40 Weyl multiplet and on several matter multiplets. A
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
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...