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 ...
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)
Eckart frame vibration-rotation Hamiltonians: Contravariant metric tensor
International Nuclear Information System (INIS)
Pesonen, Janne
2014-01-01
Eckart frame is a unique embedding in the theory of molecular vibrations and rotations. It is defined by the condition that the Coriolis coupling of the reference structure of the molecule is zero for every choice of the shape coordinates. It is far from trivial to set up Eckart kinetic energy operators (KEOs), when the shape of the molecule is described by curvilinear coordinates. In order to obtain the KEO, one needs to set up the corresponding contravariant metric tensor. Here, I derive explicitly the Eckart frame rotational measuring vectors. Their inner products with themselves give the rotational elements, and their inner products with the vibrational measuring vectors (which, in the absence of constraints, are the mass-weighted gradients of the shape coordinates) give the Coriolis elements of the contravariant metric tensor. The vibrational elements are given as the inner products of the vibrational measuring vectors with themselves, and these elements do not depend on the choice of the body-frame. The present approach has the advantage that it does not depend on any particular choice of the shape coordinates, but it can be used in conjunction with all shape coordinates. Furthermore, it does not involve evaluation of covariant metric tensors, chain rules of derivation, or numerical differentiation, and it can be easily modified if there are constraints on the shape of the molecule. Both the planar and non-planar reference structures are accounted for. The present method is particular suitable for numerical work. Its computational implementation is outlined in an example, where I discuss how to evaluate vibration-rotation energies and eigenfunctions of a general N-atomic molecule, the shape of which is described by a set of local polyspherical coordinates
Four dimensional sigma model coupled to the metric tensor field
International Nuclear Information System (INIS)
Ghika, G.; Visinescu, M.
1980-02-01
We discuss the four dimensional nonlinear sigma model with an internal O(n) invariance coupled to the metric tensor field satisfying Einstein equations. We derive a bound on the coupling constant between the sigma field and the metric tensor using the theory of harmonic maps. A special attention is paid to Einstein spaces and some new explicit solutions of the model are constructed. (author)
Assessment of the Log-Euclidean Metric Performance in Diffusion Tensor Image Segmentation
Directory of Open Access Journals (Sweden)
Mostafa Charmi
2010-06-01
Full Text Available Introduction: Appropriate definition of the distance measure between diffusion tensors has a deep impact on Diffusion Tensor Image (DTI segmentation results. The geodesic metric is the best distance measure since it yields high-quality segmentation results. However, the important problem with the geodesic metric is a high computational cost of the algorithms based on it. The main goal of this paper is to assess the possible substitution of the geodesic metric with the Log-Euclidean one to reduce the computational cost of a statistical surface evolution algorithm. Materials and Methods: We incorporated the Log-Euclidean metric in the statistical surface evolution algorithm framework. To achieve this goal, the statistics and gradients of diffusion tensor images were defined using the Log-Euclidean metric. Numerical implementation of the segmentation algorithm was performed in the MATLAB software using the finite difference techniques. Results: In the statistical surface evolution framework, the Log-Euclidean metric was able to discriminate the torus and helix patterns in synthesis datasets and rat spinal cords in biological phantom datasets from the background better than the Euclidean and J-divergence metrics. In addition, similar results were obtained with the geodesic metric. However, the main advantage of the Log-Euclidean metric over the geodesic metric was the dramatic reduction of computational cost of the segmentation algorithm, at least by 70 times. Discussion and Conclusion: The qualitative and quantitative results have shown that the Log-Euclidean metric is a good substitute for the geodesic metric when using a statistical surface evolution algorithm in DTIs segmentation.
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.
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
a tensor theory of gravitation in a curved metric on a flat background
International Nuclear Information System (INIS)
Drummond, J.E.
1979-01-01
A theory of gravity is proposed using a tensor potential for the field on a flat metric. This potential cannot be isolated by local observations, but some details can be deduced from measurements at a distance. The requirement that the field equations for the tensor potential shall be deducible from an action integral, that the action and field equations are gauge invariant, and, conversely, that the Lagrangian in the action integral can be integrated from the field equations leads to Einstein's field equations. The requirement that the field energy-momentum tensor exists leads to a constraint on the tensor potential. If the constraint is a differential gauge condition, then it can only be the Hilbert condition giving a unique background tensor, metric tensor and tensor potential. For a continuous field inside a solid sphere the metric must be homogeneous in the spatial coordinates, and the associated field energy-momentum tensor has properties consistent with Newtonian dynamics. (author)
On the (1,1)-tensor bundle with Cheeger–Gromoll type metric
Indian Academy of Sciences (India)
The main purpose of the present paper is to construct Riemannian almost product structures on the (1, 1)-tensor bundle equipped with Cheeger–Gromoll type metric over a Riemannian manifold and present some results concerning these structures. Keywords. Almost product structure; Cheeger–Gromoll type metric; metric ...
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.
Srinivasan, K; Thomas, B; Shah, D; Kannath, S K; Menon, G; Sandhyamani, S; Kesavadas, C; Kapilamoorthy, T R
2016-12-01
To quantitatively evaluate the diffusion tensor metrics p, q, L and fractional anisotropy in intracranial epidermoids in comparison with normal white matter in the splenium of the corpus callosum. This retrospective study included 20 consecutive patients referred to our institute. All patients had a magnetic resonance imaging (MRI) study on a 1.5-Tesla MR system. A spin-echo echo-planar DTI sequence with diffusion gradients along 30 non-collinear directions was performed. The eigen values (λ 1 , λ 2 , λ 3 ) were computed for each voxel and, using p: q tensor decomposition, the DTI metrics p, q and L-values and fractional anositropy (FA) were calculated. The region of interest (ROI) (6 pixels each) was placed within the lesion in all the cases and in the splenium of the corpus callosum. The mean FA in the lesion and splenium were 0.50 and 0.88 respectively, with a statistically significant difference between them (Ptensor decomposition, the mean p-value in the epidermoid was 1.55±0.24 and 1.35±0.20 in the splenium; the mean q-values in the epidermoid was 0.67±0.13 and 1.27±0.17 in the splenium; the differences were statistically significant (P=0.01 and <0.01 respectively). The significant difference between p- and q-values in epidermoids compared with the splenium of callosum was probably due to structural and orientation differences in the keratin flakes in epidermoids and white matter bundles in the callosum. However, no significant statistical difference in L-values was noted (P=0.44). DTI metrics p and q have the potential to quantify the diffusion and anisotropy in various tissues thereby gaining information about their internal architecture. The results also suggest that significant differences of DTI metrics p and q between epidermoid and the splenium of the corpus callosum are due to the difference in structural organization within them. Copyright © 2016. Published by Elsevier Masson SAS.
On the energy-momentum tensors for field theories in spaces with affine connection and metric
International Nuclear Information System (INIS)
Manoff, S.
1991-01-01
Generalized covariant Bianchi type identities are obtained and investigated for Lagrangian densities, depending on co- and contravariant tensor fields and their first and second covariant derivatives in spaces with affine connection and metric (L n -space). The notions of canonical, generalized canonical, symmetric and variational energy-momentum tensor are introduced and necessary and sufficient conditions for the existence of the symmetric energy-momentum tensor as a local conserved quantity are obtained. 19 refs.; 1 tab
The metric theory of tensor products (grthendieck's résumé revisited ...
African Journals Online (AJOL)
This paper presents the first of a multi-part series of papers on the metric theory of tensor products according to Grothendieck's “Résumé de la theorie metrique des produits tensoriels topologiques” It contains the basics on tensor norms: a discussion of the special character of the injective and the projective norms, ...
On the generally invariant Lagrangians for the metric field and other tensor fields
International Nuclear Information System (INIS)
Novotny, J.
1978-01-01
The Krupka and Trautman method for the description of all generally invariant functions of the components of geometrical object fields is applied to the invariants of second degree of the metrical field and other tensor fields. The complete system of differential identities fulfilled by the invariants mentioned is found and it is proved that these invariants depend on the tensor quantities only. (author)
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.
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
On the properties of an extended class of metric tensors in relativity
International Nuclear Information System (INIS)
Oliveira, C.G.
1984-01-01
Considering an extended 'metric' tensor which is a function of an internalvector y sup(a) (x), it is possible to determine a spin 1 massless field of gravitational origin. It is shown that this new field vanishes in the linear aproximation for the extended 'metric'. (Author) [pt
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
Black Holes in the Framework of the Metric Tensor Exterior to the Sun and Planets
Directory of Open Access Journals (Sweden)
Chifu E.N.
2011-04-01
Full Text Available The conditions for the Sun and oblate spheroidal planets in the solar system to reduce to black holes is investigated. The metric tensor exterior to oblate spheroidal masses indicates that for the Sun to reduce to a black hole, its mass must condense by a factor of 2 : 32250 10 5 . Using Schwarzschild’s metric, this factor is obtained as 2 : 3649 10 5 . Similar results are obtained for oblate spheroidal planets in the solar system.
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.
Representation of symmetric metric connection via Riemann-Christoffel curvature tensor
International Nuclear Information System (INIS)
Selikhov, A.V.
1989-01-01
Bivector σ-bar μ ν ' which is the Jacoby matrix of the transformation to the Riemanian coordinates is considered in the paper. Basing on the dual nature of σ-bar μ ν ' the representation of metric connection (Christoffel symbols) have been obtained at the Riemanian coordinates via Riemann-Christoffel curvature tensor; the covariant conserved four-momentum in the general theory of relativity have been constructed. 11 refs
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...
International Nuclear Information System (INIS)
Adler, S.L.; Lieberman, J.
1978-01-01
We reanalyze the problem of regularization of the stress-energy tensor for massless vector particles propating in a general background metric, using covariant point separation techniques applied to the Hadamard elementary solution. We correct an error, point out by Wald, in the earlier formulation of Adler, Lieberman, and Ng, and find a stress-energy tensor trace anomaly agreeing with that found by other regularization methods
Improvement of Reliability of Diffusion Tensor Metrics in Thigh Skeletal Muscles.
Keller, Sarah; Chhabra, Avneesh; Ahmed, Shaheen; Kim, Anne C; Chia, Jonathan M; Yamamura, Jin; Wang, Zhiyue J
2018-05-01
Quantitative diffusion tensor imaging (DTI) of skeletal muscles is challenging due to the bias in DTI metrics, such as fractional anisotropy (FA) and mean diffusivity (MD), related to insufficient signal-to-noise ratio (SNR). This study compares the bias of DTI metrics in skeletal muscles via pixel-based and region-of-interest (ROI)-based analysis. DTI of the thigh muscles was conducted on a 3.0-T system in N = 11 volunteers using a fat-suppressed single-shot spin-echo echo planar imaging (SS SE-EPI) sequence with eight repetitions (number of signal averages (NSA) = 4 or 8 for each repeat). The SNR was calculated for different NSAs and estimated for the composite images combining all data (effective NSA = 48) as standard reference. The bias of MD and FA derived by pixel-based and ROI-based quantification were compared at different NSAs. An "intra-ROI diffusion direction dispersion angle (IRDDDA)" was calculated to assess the uniformity of diffusion within the ROI. Using our standard reference image with NSA = 48, the ROI-based and pixel-based measurements agreed for FA and MD. Larger disagreements were observed for the pixel-based quantification at NSA = 4. MD was less sensitive than FA to the noise level. The IRDDDA decreased with higher NSA. At NSA = 4, ROI-based FA showed a lower average bias (0.9% vs. 37.4%) and narrower 95% limits of agreement compared to the pixel-based method. The ROI-based estimation of FA is less prone to bias than the pixel-based estimations when SNR is low. The IRDDDA can be applied as a quantitative quality measure to assess reliability of ROI-based DTI metrics. Copyright © 2018 Elsevier B.V. All rights reserved.
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.
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.
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.
Measures of agreement between computation and experiment:validation metrics.
Energy Technology Data Exchange (ETDEWEB)
Barone, Matthew Franklin; Oberkampf, William Louis
2005-08-01
With the increasing role of computational modeling in engineering design, performance estimation, and safety assessment, improved methods are needed for comparing computational results and experimental measurements. Traditional methods of graphically comparing computational and experimental results, though valuable, are essentially qualitative. Computable measures are needed that can quantitatively compare computational and experimental results over a range of input, or control, variables and sharpen assessment of computational accuracy. This type of measure has been recently referred to as a validation metric. We discuss various features that we believe should be incorporated in a validation metric and also features that should be excluded. We develop a new validation metric that is based on the statistical concept of confidence intervals. Using this fundamental concept, we construct two specific metrics: one that requires interpolation of experimental data and one that requires regression (curve fitting) of experimental data. We apply the metrics to three example problems: thermal decomposition of a polyurethane foam, a turbulent buoyant plume of helium, and compressibility effects on the growth rate of a turbulent free-shear layer. We discuss how the present metrics are easily interpretable for assessing computational model accuracy, as well as the impact of experimental measurement uncertainty on the accuracy assessment.
Computing the Gromov hyperbolicity of a discrete metric space
Fournier, Hervé
2015-01-01
We give exact and approximation algorithms for computing the Gromov hyperbolicity of an n-point discrete metric space. We observe that computing the Gromov hyperbolicity from a fixed base-point reduces to a (max,min) matrix product. Hence, using
Towards Information Security Metrics Framework for Cloud Computing
Muhammad Imran Tariq
2012-01-01
Cloud computing has recently emerged as new computing paradigm which basically aims to provide customized, reliable, dynamic services over the internet. Cost and security are influential issues to deploy cloud computing in large enterprise. Privacy and security are very important issues in terms of user trust and legal compliance. Information Security (IS) metrics are best tool used to measure the efficiency, performance, effectiveness and impact of the security constraints. It is very hard...
Energy Technology Data Exchange (ETDEWEB)
Mueller-Mang, Christina; Mang, Thomas; Fruehwald-Pallamar, Julia; Weber, Michael; Thurnher, Majda M. [Medical University of Vienna, Department of Radiology, Vienna (Austria); Law, Meng [University of Southern California, Los Angeles County Hospital and USC Medical Center, Department of Radiology, Keck School of Medicine, Los Angeles, CA (United States)
2011-08-15
This study was conducted to compare diffusion tensor MR imaging (DTI) metrics of the cervical spinal cord in asymptomatic human immunodeficiency virus (HIV)-positive patients with those measured in healthy volunteers, and to assess whether DTI is a valuable diagnostic tool in the early detection of HIV-associated myelopathy (HIVM). MR imaging of the cervical spinal cord was performed in 20 asymptomatic HIV-positive patients and in 20 healthy volunteers on a 3-T MR scanner. Average fractional anisotropy (FA), mean diffusivity (MD), and major (E1) and minor (E2, E3) eigenvalues were calculated within regions of interest (ROIs) at the C2/3 level (central and bilateral anterior, lateral and posterior white matter). Statistical analysis showed significant differences with regard to mean E3 values between patients and controls (p = 0.045; mixed-model analysis of variance (ANOVA) test). Mean FA was lower, and mean MD, mean E1, and mean E2 were higher in each measured ROI in patients compared to controls, but these differences were not statistically significant. Asymptomatic HIV-positive patients demonstrate only subtle changes in DTI metrics measured in the cervical spinal cord compared to healthy volunteers that currently do not support using DTI as a diagnostic tool for the early detection of HIVM. (orig.)
Woo, John H; Wang, Sumei; Melhem, Elias R; Gee, James C; Cucchiara, Andrew; McCluskey, Leo; Elman, Lauren
2014-01-01
To assess the relationship between clinically assessed Upper Motor Neuron (UMN) disease in Amyotrophic Lateral Sclerosis (ALS) and local diffusion alterations measured in the brain corticospinal tract (CST) by a tractography-driven template-space region-of-interest (ROI) analysis of Diffusion Tensor Imaging (DTI). This cross-sectional study included 34 patients with ALS, on whom DTI was performed. Clinical measures were separately obtained including the Penn UMN Score, a summary metric based upon standard clinical methods. After normalizing all DTI data to a population-specific template, tractography was performed to determine a region-of-interest (ROI) outlining the CST, in which average Mean Diffusivity (MD) and Fractional Anisotropy (FA) were estimated. Linear regression analyses were used to investigate associations of DTI metrics (MD, FA) with clinical measures (Penn UMN Score, ALSFRS-R, duration-of-disease), along with age, sex, handedness, and El Escorial category as covariates. For MD, the regression model was significant (p = 0.02), and the only significant predictors were the Penn UMN Score (p = 0.005) and age (p = 0.03). The FA regression model was also significant (p = 0.02); the only significant predictor was the Penn UMN Score (p = 0.003). Measured by the template-space ROI method, both MD and FA were linearly associated with the Penn UMN Score, supporting the hypothesis that DTI alterations reflect UMN pathology as assessed by the clinical examination.
Hiremath, S B; Muraleedharan, A; Kumar, S; Nagesh, C; Kesavadas, C; Abraham, M; Kapilamoorthy, T R; Thomas, B
2017-04-01
Tumefactive demyelinating lesions with atypical features can mimic high-grade gliomas on conventional imaging sequences. The aim of this study was to assess the role of conventional imaging, DTI metrics ( p:q tensor decomposition), and DSC perfusion in differentiating tumefactive demyelinating lesions and high-grade gliomas. Fourteen patients with tumefactive demyelinating lesions and 21 patients with high-grade gliomas underwent brain MR imaging with conventional, DTI, and DSC perfusion imaging. Imaging sequences were assessed for differentiation of the lesions. DTI metrics in the enhancing areas and perilesional hyperintensity were obtained by ROI analysis, and the relative CBV values in enhancing areas were calculated on DSC perfusion imaging. Conventional imaging sequences had a sensitivity of 80.9% and specificity of 57.1% in differentiating high-grade gliomas ( P = .049) from tumefactive demyelinating lesions. DTI metrics ( p : q tensor decomposition) and DSC perfusion demonstrated a statistically significant difference in the mean values of ADC, the isotropic component of the diffusion tensor, the anisotropic component of the diffusion tensor, the total magnitude of the diffusion tensor, and rCBV among enhancing portions in tumefactive demyelinating lesions and high-grade gliomas ( P ≤ .02), with the highest specificity for ADC, the anisotropic component of the diffusion tensor, and relative CBV (92.9%). Mean fractional anisotropy values showed no significant statistical difference between tumefactive demyelinating lesions and high-grade gliomas. The combination of DTI and DSC parameters improved the diagnostic accuracy (area under the curve = 0.901). Addition of a heterogeneous enhancement pattern to DTI and DSC parameters improved it further (area under the curve = 0.966). The sensitivity increased from 71.4% to 85.7% after the addition of the enhancement pattern. DTI and DSC perfusion add profoundly to conventional imaging in differentiating tumefactive
Computing the Gromov hyperbolicity constant of a discrete metric space
Ismail, Anas
2012-07-01
Although it was invented by Mikhail Gromov, in 1987, to describe some family of groups[1], the notion of Gromov hyperbolicity has many applications and interpretations in different fields. It has applications in Biology, Networking, Graph Theory, and many other areas of research. The Gromov hyperbolicity constant of several families of graphs and geometric spaces has been determined. However, so far, the only known algorithm for calculating the Gromov hyperbolicity constant δ of a discrete metric space is the brute force algorithm with running time O (n4) using the four-point condition. In this thesis, we first introduce an approximation algorithm which calculates a O (log n)-approximation of the hyperbolicity constant δ, based on a layering approach, in time O(n2), where n is the number of points in the metric space. We also calculate the fixed base point hyperbolicity constant δr for a fixed point r using a (max, min)−matrix multiplication algorithm by Duan in time O(n2.688)[2]. We use this result to present a 2-approximation algorithm for calculating the hyper-bolicity constant in time O(n2.688). We also provide an exact algorithm to compute the hyperbolicity constant δ in time O(n3.688) for a discrete metric space. We then present some partial results we obtained for designing some approximation algorithms to compute the hyperbolicity constant δ.
Computing the Gromov hyperbolicity of a discrete metric space
Fournier, Hervé
2015-02-12
We give exact and approximation algorithms for computing the Gromov hyperbolicity of an n-point discrete metric space. We observe that computing the Gromov hyperbolicity from a fixed base-point reduces to a (max,min) matrix product. Hence, using the (max,min) matrix product algorithm by Duan and Pettie, the fixed base-point hyperbolicity can be determined in O(n2.69) time. It follows that the Gromov hyperbolicity can be computed in O(n3.69) time, and a 2-approximation can be found in O(n2.69) time. We also give a (2log2n)-approximation algorithm that runs in O(n2) time, based on a tree-metric embedding by Gromov. We also show that hyperbolicity at a fixed base-point cannot be computed in O(n2.05) time, unless there exists a faster algorithm for (max,min) matrix multiplication than currently known.
Accelerating Neuroimage Registration through Parallel Computation of Similarity Metric.
Directory of Open Access Journals (Sweden)
Yun-Gang Luo
Full Text Available Neuroimage registration is crucial for brain morphometric analysis and treatment efficacy evaluation. However, existing advanced registration algorithms such as FLIRT and ANTs are not efficient enough for clinical use. In this paper, a GPU implementation of FLIRT with the correlation ratio (CR as the similarity metric and a GPU accelerated correlation coefficient (CC calculation for the symmetric diffeomorphic registration of ANTs have been developed. The comparison with their corresponding original tools shows that our accelerated algorithms can greatly outperform the original algorithm in terms of computational efficiency. This paper demonstrates the great potential of applying these registration tools in clinical applications.
International Nuclear Information System (INIS)
Chernyshenko, Dmitri; Fangohr, Hans
2015-01-01
In the finite difference method which is commonly used in computational micromagnetics, the demagnetizing field is usually computed as a convolution of the magnetization vector field with the demagnetizing tensor that describes the magnetostatic field of a cuboidal cell with constant magnetization. An analytical expression for the demagnetizing tensor is available, however at distances far from the cuboidal cell, the numerical evaluation of the analytical expression can be very inaccurate. Due to this large-distance inaccuracy numerical packages such as OOMMF compute the demagnetizing tensor using the explicit formula at distances close to the originating cell, but at distances far from the originating cell a formula based on an asymptotic expansion has to be used. In this work, we describe a method to calculate the demagnetizing field by numerical evaluation of the multidimensional integral in the demagnetizing tensor terms using a sparse grid integration scheme. This method improves the accuracy of computation at intermediate distances from the origin. We compute and report the accuracy of (i) the numerical evaluation of the exact tensor expression which is best for short distances, (ii) the asymptotic expansion best suited for large distances, and (iii) the new method based on numerical integration, which is superior to methods (i) and (ii) for intermediate distances. For all three methods, we show the measurements of accuracy and execution time as a function of distance, for calculations using single precision (4-byte) and double precision (8-byte) floating point arithmetic. We make recommendations for the choice of scheme order and integrating coefficients for the numerical integration method (iii). - Highlights: • We study the accuracy of demagnetization in finite difference micromagnetics. • We introduce a new sparse integration method to compute the tensor more accurately. • Newell, sparse integration and asymptotic method are compared for all ranges
Energy Technology Data Exchange (ETDEWEB)
Zeng, Dong; Zhang, Xinyu; Bian, Zhaoying, E-mail: zybian@smu.edu.cn, E-mail: jhma@smu.edu.cn; Huang, Jing; Zhang, Hua; Lu, Lijun; Lyu, Wenbing; Feng, Qianjin; Chen, Wufan; Ma, Jianhua, E-mail: zybian@smu.edu.cn, E-mail: jhma@smu.edu.cn [Department of Biomedical Engineering, Southern Medical University, Guangzhou, Guangdong 510515, China and Guangdong Provincial Key Laboratory of Medical Image Processing, Southern Medical University, Guangzhou, Guangdong 510515 (China); Zhang, Jing [Department of Radiology, Tianjin Medical University General Hospital, Tianjin 300052 (China)
2016-05-15
Purpose: Cerebral perfusion computed tomography (PCT) imaging as an accurate and fast acute ischemic stroke examination has been widely used in clinic. Meanwhile, a major drawback of PCT imaging is the high radiation dose due to its dynamic scan protocol. The purpose of this work is to develop a robust perfusion deconvolution approach via structure tensor total variation (STV) regularization (PD-STV) for estimating an accurate residue function in PCT imaging with the low-milliampere-seconds (low-mAs) data acquisition. Methods: Besides modeling the spatio-temporal structure information of PCT data, the STV regularization of the present PD-STV approach can utilize the higher order derivatives of the residue function to enhance denoising performance. To minimize the objective function, the authors propose an effective iterative algorithm with a shrinkage/thresholding scheme. A simulation study on a digital brain perfusion phantom and a clinical study on an old infarction patient were conducted to validate and evaluate the performance of the present PD-STV approach. Results: In the digital phantom study, visual inspection and quantitative metrics (i.e., the normalized mean square error, the peak signal-to-noise ratio, and the universal quality index) assessments demonstrated that the PD-STV approach outperformed other existing approaches in terms of the performance of noise-induced artifacts reduction and accurate perfusion hemodynamic maps (PHM) estimation. In the patient data study, the present PD-STV approach could yield accurate PHM estimation with several noticeable gains over other existing approaches in terms of visual inspection and correlation analysis. Conclusions: This study demonstrated the feasibility and efficacy of the present PD-STV approach in utilizing STV regularization to improve the accuracy of residue function estimation of cerebral PCT imaging in the case of low-mAs.
Energy Technology Data Exchange (ETDEWEB)
Kuo, Duen Pang [Dept. of Electrical Engineering, National Taiwan University, Taipei (China); Lu, Chia Feng [Research Center of Translational Imaging, College of Medicine, Taipei Medical University, Taipei (China); Chen, Yung Chieh [Dept. of Biomedical Imaging and Radiological Sciences, National Yang-Ming University, Taipei (China); Liou, Michelle [Institute of Statistical Science, Academia Sinica, Taipei (China); Chung, Hsiao Wen [Graduate Institute of Biomedical Electrics and Bioinformatics, National Taiwan University, Taipei (China)
2017-04-15
To investigate whether the diffusion tensor imaging-derived metrics are capable of differentiating the ischemic penumbra (IP) from the infarct core (IC), and determining stroke onset within the first 4.5 hours. All procedures were approved by the local animal care committee. Eight of the eleven rats having permanent middle cerebral artery occlusion were included for analyses. Using a 7 tesla magnetic resonance system, the relative cerebral blood flow and apparent diffusion coefficient maps were generated to define IP and IC, half hour after surgery and then every hour, up to 6.5 hours. Relative fractional anisotropy, pure anisotropy (rq) and diffusion magnitude (rL) maps were obtained. One-way analysis of variance, receiver operating characteristic curve and nonlinear regression analyses were performed. The evolutions of tensor metrics were different in ischemic regions (IC and IP) and topographic subtypes (cortical, subcortical gray matter, and white matter). The rL had a significant drop of 40% at 0.5 hour, and remained stagnant up to 6.5 hours. Significant differences (p < 0.05) in rL values were found between IP, IC, and normal tissue for all topographic subtypes. Optimal rL threshold in discriminating IP from IC was about -29%. The evolution of rq showed an exponential decrease in cortical IC, from -26.9% to -47.6%; an rq reduction smaller than 44.6% can be used to predict an acute stroke onset in less than 4.5 hours. Diffusion tensor metrics may potentially help discriminate IP from IC and determine the acute stroke age within the therapeutic time window.
Computing the Gromov hyperbolicity constant of a discrete metric space
Ismail, Anas
2012-01-01
, and many other areas of research. The Gromov hyperbolicity constant of several families of graphs and geometric spaces has been determined. However, so far, the only known algorithm for calculating the Gromov hyperbolicity constant δ of a discrete metric
Novel computed tomographic chest metrics to detect pulmonary hypertension
International Nuclear Information System (INIS)
Chan, Andrew L; Juarez, Maya M; Shelton, David K; MacDonald, Taylor; Li, Chin-Shang; Lin, Tzu-Chun; Albertson, Timothy E
2011-01-01
Early diagnosis of pulmonary hypertension (PH) can potentially improve survival and quality of life. Detecting PH using echocardiography is often insensitive in subjects with lung fibrosis or hyperinflation. Right heart catheterization (RHC) for the diagnosis of PH adds risk and expense due to its invasive nature. Pre-defined measurements utilizing computed tomography (CT) of the chest may be an alternative non-invasive method of detecting PH. This study retrospectively reviewed 101 acutely hospitalized inpatients with heterogeneous diagnoses, who consecutively underwent CT chest and RHC during the same admission. Two separate teams, each consisting of a radiologist and pulmonologist, blinded to clinical and RHC data, individually reviewed the chest CT's. Multiple regression analyses controlling for age, sex, ascending aortic diameter, body surface area, thoracic diameter and pulmonary wedge pressure showed that a main pulmonary artery (PA) diameter ≥29 mm (odds ratio (OR) = 4.8), right descending PA diameter ≥19 mm (OR = 7.0), true right descending PA diameter ≥ 16 mm (OR = 4.1), true left descending PA diameter ≥ 21 mm (OR = 15.5), right ventricular (RV) free wall ≥ 6 mm (OR = 30.5), RV wall/left ventricular (LV) wall ratio ≥0.32 (OR = 8.8), RV/LV lumen ratio ≥1.28 (OR = 28.8), main PA/ascending aorta ratio ≥0.84 (OR = 6.0) and main PA/descending aorta ratio ≥ 1.29 (OR = 5.7) were significant predictors of PH in this population of hospitalized patients. This combination of easily measured CT-based metrics may, upon confirmatory studies, aid in the non-invasive detection of PH and hence in the determination of RHC candidacy in acutely hospitalized patients
International Nuclear Information System (INIS)
Beleggia, M.; Graef, M. de
2003-01-01
A method is presented to compute the demagnetization tensor field for uniformly magnetized particles of arbitrary shape. By means of a Fourier space approach it is possible to compute analytically the Fourier representation of the demagnetization tensor field for a given shape. Then, specifying the direction of the uniform magnetization, the demagnetizing field and the magnetostatic energy associated with the particle can be evaluated. In some particular cases, the real space representation is computable analytically. In general, a numerical inverse fast Fourier transform is required to perform the inversion. As an example, the demagnetization tensor field for the tetrahedron will be given
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.
First results from a combined analysis of CERN computing infrastructure metrics
Duellmann, Dirk; Nieke, Christian
2017-10-01
The IT Analysis Working Group (AWG) has been formed at CERN across individual computing units and the experiments to attempt a cross cutting analysis of computing infrastructure and application metrics. In this presentation we will describe the first results obtained using medium/long term data (1 months — 1 year) correlating box level metrics, job level metrics from LSF and HTCondor, IO metrics from the physics analysis disk pools (EOS) and networking and application level metrics from the experiment dashboards. We will cover in particular the measurement of hardware performance and prediction of job duration, the latency sensitivity of different job types and a search for bottlenecks with the production job mix in the current infrastructure. The presentation will conclude with the proposal of a small set of metrics to simplify drawing conclusions also in the more constrained environment of public cloud deployments.
Energy Technology Data Exchange (ETDEWEB)
Ibrahim, Khaled Z. [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Computational Research Division; Epifanovsky, Evgeny [Q-Chem, Inc., Pleasanton, CA (United States); Williams, Samuel W. [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Computational Research Division; Krylov, Anna I. [Univ. of Southern California, Los Angeles, CA (United States). Dept. of Chemistry
2016-07-26
Coupled-cluster methods provide highly accurate models of molecular structure by explicit numerical calculation of tensors representing the correlation between electrons. These calculations are dominated by a sequence of tensor contractions, motivating the development of numerical libraries for such operations. While based on matrix-matrix multiplication, these libraries are specialized to exploit symmetries in the molecular structure and in electronic interactions, and thus reduce the size of the tensor representation and the complexity of contractions. The resulting algorithms are irregular and their parallelization has been previously achieved via the use of dynamic scheduling or specialized data decompositions. We introduce our efforts to extend the Libtensor framework to work in the distributed memory environment in a scalable and energy efficient manner. We achieve up to 240 speedup compared with the best optimized shared memory implementation. We attain scalability to hundreds of thousands of compute cores on three distributed-memory architectures, (Cray XC30&XC40, BlueGene/Q), and on a heterogeneous GPU-CPU system (Cray XK7). As the bottlenecks shift from being compute-bound DGEMM's to communication-bound collectives as the size of the molecular system scales, we adopt two radically different parallelization approaches for handling load-imbalance. Nevertheless, we preserve a uni ed interface to both programming models to maintain the productivity of computational quantum chemists.
Directory of Open Access Journals (Sweden)
Natarajan Meghanathan
2017-01-01
Full Text Available We identify three different levels of correlation (pair-wise relative ordering, network-wide ranking and linear regression that could be assessed between a computationally-light centrality metric and a computationally-heavy centrality metric for real-world networks. The Kendall's concordance-based correlation measure could be used to quantitatively assess how well we could consider the relative ordering of two vertices vi and vj with respect to a computationally-light centrality metric as the relative ordering of the same two vertices with respect to a computationally-heavy centrality metric. We hypothesize that the pair-wise relative ordering (concordance-based assessment of the correlation between centrality metrics is the most strictest of all the three levels of correlation and claim that the Kendall's concordance-based correlation coefficient will be lower than the correlation coefficient observed with the more relaxed levels of correlation measures (linear regression-based Pearson's product-moment correlation coefficient and the network wide ranking-based Spearman's correlation coefficient. We validate our hypothesis by evaluating the three correlation coefficients between two sets of centrality metrics: the computationally-light degree and local clustering coefficient complement-based degree centrality metrics and the computationally-heavy eigenvector centrality, betweenness centrality and closeness centrality metrics for a diverse collection of 50 real-world networks.
Energy Technology Data Exchange (ETDEWEB)
Abdel Razek, Ahmed Abdel Khalek; El-Serougy, Lamiaa; Gaballa, Gada; Talaat, Mona [Mansoura Faculty of Medicine, Department of Diagnostic Radiology, Mansoura (Egypt); Abdelsalam, Mohamed [Mansoura Faculty of Medicine, Department of Neurology, Mansoura (Egypt)
2018-02-15
The aim of this study is to differentiate recurrent/residual gliomas from postradiation changes using arterial spin labeling (ASL) perfusion and diffusion tensor imaging (DTI)-derived metrics. Prospective study was conducted upon 42 patients with high-grade gliomas after radiotherapy only or prior to other therapies that underwent routine MR imaging, ASL, and DTI. The tumor blood flow (TBF), fractional anisotropy (FA), and mean diffusivity (MD) of the enhanced lesion and related edema were calculated. The lesion was categorized as recurrence/residual or postradiation changes. There was significant differences between residual/recurrent gliomas and postradiation changes of TBF (P = 0.001), FA (P = 0.001 and 0.04), and MD (P = 0.001) of enhanced lesion and related edema respectively. The area under the curve (AUC) of TBF of enhanced lesion and related edema used to differentiate residual/recurrent gliomas from postradiation changes were 0.95 and 0.93 and of MD were 0.95 and 0.81 and of FA were 0.81 and 0.695, respectively. Combined ASL and DTI metrics of the enhanced lesion revealed AUC of 0.98, accuracy of 95%, sensitivity of 93.8%, specificity of 95.8%, positive predictive value (PPV) of 93.8%, and negative predictive value (NPV) of 95.8%. Combined metrics of ASL and DTI of related edema revealed AUC of 0.97, accuracy of 92.5%, sensitivity of 93.8%, specificity of 91.7%, PPV of 88.2%, and NPV of 95.7. Combined ASL and DTI metrics of enhanced lesion and related edema are valuable noninvasive tools in differentiating residual/recurrent gliomas from postradiation changes. (orig.)
A C++11 implementation of arbitrary-rank tensors for high-performance computing
Aragón, Alejandro M.
2014-11-01
This article discusses an efficient implementation of tensors of arbitrary rank by using some of the idioms introduced by the recently published C++ ISO Standard (C++11). With the aims at providing a basic building block for high-performance computing, a single Array class template is carefully crafted, from which vectors, matrices, and even higher-order tensors can be created. An expression template facility is also built around the array class template to provide convenient mathematical syntax. As a result, by using templates, an extra high-level layer is added to the C++ language when dealing with algebraic objects and their operations, without compromising performance. The implementation is tested running on both CPU and GPU.
Tensor Voting A Perceptual Organization Approach to Computer Vision and Machine Learning
Mordohai, Philippos
2006-01-01
This lecture presents research on a general framework for perceptual organization that was conducted mainly at the Institute for Robotics and Intelligent Systems of the University of Southern California. It is not written as a historical recount of the work, since the sequence of the presentation is not in chronological order. It aims at presenting an approach to a wide range of problems in computer vision and machine learning that is data-driven, local and requires a minimal number of assumptions. The tensor voting framework combines these properties and provides a unified perceptual organiza
Safety Metrics for Human-Computer Controlled Systems
Leveson, Nancy G; Hatanaka, Iwao
2000-01-01
The rapid growth of computer technology and innovation has played a significant role in the rise of computer automation of human tasks in modem production systems across all industries. Although the rationale for automation has been to eliminate "human error" or to relieve humans from manual repetitive tasks, various computer-related hazards and accidents have emerged as a direct result of increased system complexity attributed to computer automation. The risk assessment techniques utilized for electromechanical systems are not suitable for today's software-intensive systems or complex human-computer controlled systems.This thesis will propose a new systemic model-based framework for analyzing risk in safety-critical systems where both computers and humans are controlling safety-critical functions. A new systems accident model will be developed based upon modem systems theory and human cognitive processes to better characterize system accidents, the role of human operators, and the influence of software in its direct control of significant system functions Better risk assessments will then be achievable through the application of this new framework to complex human-computer controlled systems.
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.
Bogdanov, Alexander; Degtyarev, Alexander; Khramushin, Vasily; Shichkina, Yulia
2018-02-01
Stages of direct computational experiments in hydromechanics based on tensor mathematics tools are represented by conditionally independent mathematical models for calculations separation in accordance with physical processes. Continual stage of numerical modeling is constructed on a small time interval in a stationary grid space. Here coordination of continuity conditions and energy conservation is carried out. Then, at the subsequent corpuscular stage of the computational experiment, kinematic parameters of mass centers and surface stresses at the boundaries of the grid cells are used in modeling of free unsteady motions of volume cells that are considered as independent particles. These particles can be subject to vortex and discontinuous interactions, when restructuring of free boundaries and internal rheological states has place. Transition from one stage to another is provided by interpolation operations of tensor mathematics. Such interpolation environment formalizes the use of physical laws for mechanics of continuous media modeling, provides control of rheological state and conditions for existence of discontinuous solutions: rigid and free boundaries, vortex layers, their turbulent or empirical generalizations.
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 ventricula...
MathGR: a tensor and GR computation package to keep it simple
Wang, Yi
2013-01-01
We introduce the MathGR package, written in Mathematica. The package can manipulate tensor and GR calculations with either abstract or explicit indices, simplify tensors with permutational symmetries, decompose tensors from abstract indices to partially or completely explicit indices and convert partial derivatives into total derivatives. Frequently used GR tensors and a model of FRW universe with ADM type perturbations are predefined. The package is built around the philosophy to "keep it si...
The Computation of Nash Equilibrium in Fashion Games via Semi-Tensor Product Method
Institute of Scientific and Technical Information of China (English)
GUO Peilian; WANG Yuzhen
2016-01-01
Using the semi-tensor product of matrices,this paper investigates the computation of pure-strategy Nash equilibrium (PNE) for fashion games,and presents several new results.First,a formal fashion game model on a social network is given.Second,the utility function of each player is converted into an algebraic form via the semi-tensor product of matrices,based on which the case of two-strategy fashion game is studied and two methods are obtained for the case to verify the existence of PNE.Third,the multi-strategy fashion game model is investigated and an algorithm is established to find all the PNEs for the general case.Finally,two kinds of optimization problems,that is,the so-called social welfare and normalized satisfaction degree optimization problems are investigated and two useful results are given.The study of several illustrative examples shows that the new results obtained in this paper are effective.
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)
Tandon, S.; Beleggia, M.; Zhu, Y.; De Graef, M.
2004-01-01
A Fourier space formalism based on the shape amplitude of a particle is used to compute the demagnetization tensor field for uniformly magnetized particles of arbitrary shape. We provide a list of explicit shape amplitudes for important particle shapes, among others: the sphere, the cylindrical tube, an arbitrary polyhedral shape, a truncated paraboloid, and a cone truncated by a spherical cap. In Part I of this two-part paper, an analytical representation of the demagnetization tensor field for particles with cylindrical symmetry is provided, as well as expressions for the magnetostatic energy and the volumetric demagnetization factors
Quantum anomalies for generalized Euclidean Taub-NUT metrics
International Nuclear Information System (INIS)
Cotaescu, Ion I; Moroianu, Sergiu; Visinescu, Mihai
2005-01-01
The generalized Taub-NUT metrics exhibit in general gravitational anomalies. This is in contrast with the fact that the original Taub-NUT metric does not exhibit gravitational anomalies, which is a consequence of the fact that it admits Killing-Yano tensors forming Staeckel-Killing tensors as products. We have found that for axial anomalies, interpreted as the index of the Dirac operator, the presence of Killing-Yano tensors is irrelevant. In order to evaluate the axial anomalies, we compute the index of the Dirac operator with the APS boundary condition on balls and on annular domains. The result is an explicit number-theoretic quantity depending on the radii of the domain. This quantity is 0 for metrics close to the original Taub-NUT metric but it does not vanish in general
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
Gauge theories, duality relations and the tensor hierarchy
International Nuclear Information System (INIS)
Bergshoeff, Eric A.; Hohm, Olaf; Hartong, Jelle; Huebscher, Mechthild; OrtIn, Tomas
2009-01-01
We compute the complete 3- and 4-dimensional tensor hierarchies, i.e. sets of p-form fields, with 1 ≤ p ≤ D, which realize an off-shell algebra of bosonic gauge transformations. We show how these tensor hierarchies can be put on-shell by introducing a set of duality relations, thereby introducing additional scalars and a metric tensor. These so-called duality hierarchies encode the equations of motion of the bosonic part of the most general gauged supergravity theories in those dimensions, including the (projected) scalar equations of motion. We construct gauge-invariant actions that include all the fields in the tensor hierarchies. We elucidate the relation between the gauge transformations of the p-form fields in the action and those of the same fields in the tensor hierarchy.
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.
Symmetries of Taub-NUT dual metrics
International Nuclear Information System (INIS)
Baleanu, D.; Codoban, S.
1998-01-01
Recently geometric duality was analyzed for a metric which admits Killing tensors. An interesting example arises when the manifold has Killing-Yano tensors. The symmetries of the dual metrics in the case of Taub-NUT metric are investigated. Generic and non-generic symmetries of dual Taub-NUT metric are analyzed
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.
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...
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
Computation of the Response Surface in the Tensor Train data format
Dolgov, Sergey; Khoromskij, Boris N.; Litvinenko, Alexander; Matthies, Hermann G.
2014-01-01
We apply the Tensor Train (TT) approximation to construct the Polynomial Chaos Expansion (PCE) of a random field, and solve the stochastic elliptic diffusion PDE with the stochastic Galerkin discretization. We compare two strategies of the polynomial chaos expansion: sparse and full polynomial (multi-index) sets. In the full set, the polynomial orders are chosen independently in each variable, which provides higher flexibility and accuracy. However, the total amount of degrees of freedom grows exponentially with the number of stochastic coordinates. To cope with this curse of dimensionality, the data is kept compressed in the TT decomposition, a recurrent low-rank factorization. PCE computations on sparse grids sets are extensively studied, but the TT representation for PCE is a novel approach that is investigated in this paper. We outline how to deduce the PCE from the covariance matrix, assemble the Galerkin operator, and evaluate some post-processing (mean, variance, Sobol indices), staying within the low-rank framework. The most demanding are two stages. First, we interpolate PCE coefficients in the TT format using a few number of samples, which is performed via the block cross approximation method. Second, we solve the discretized equation (large linear system) via the alternating minimal energy algorithm. In the numerical experiments we demonstrate that the full expansion set encapsulated in the TT format is indeed preferable in cases when high accuracy and high polynomial orders are required.
Computation of the Response Surface in the Tensor Train data format
Dolgov, Sergey
2014-06-11
We apply the Tensor Train (TT) approximation to construct the Polynomial Chaos Expansion (PCE) of a random field, and solve the stochastic elliptic diffusion PDE with the stochastic Galerkin discretization. We compare two strategies of the polynomial chaos expansion: sparse and full polynomial (multi-index) sets. In the full set, the polynomial orders are chosen independently in each variable, which provides higher flexibility and accuracy. However, the total amount of degrees of freedom grows exponentially with the number of stochastic coordinates. To cope with this curse of dimensionality, the data is kept compressed in the TT decomposition, a recurrent low-rank factorization. PCE computations on sparse grids sets are extensively studied, but the TT representation for PCE is a novel approach that is investigated in this paper. We outline how to deduce the PCE from the covariance matrix, assemble the Galerkin operator, and evaluate some post-processing (mean, variance, Sobol indices), staying within the low-rank framework. The most demanding are two stages. First, we interpolate PCE coefficients in the TT format using a few number of samples, which is performed via the block cross approximation method. Second, we solve the discretized equation (large linear system) via the alternating minimal energy algorithm. In the numerical experiments we demonstrate that the full expansion set encapsulated in the TT format is indeed preferable in cases when high accuracy and high polynomial orders are required.
Hu, Bo; Kalfoglou, Yannis; Dupplaw, David; Alani, Harith; Lewis, Paul; Shadbolt, Nigel
2006-01-01
In the context of the Semantic Web, many ontology-related operations, e.g. ontology ranking, segmentation, alignment, articulation, reuse, evaluation, can be boiled down to one fundamental operation: computing the similarity and/or dissimilarity among ontological entities, and in some cases among ontologies themselves. In this paper, we review standard metrics for computing distance measures and we propose a series of semantic metrics. We give a formal account of semantic metrics drawn from a...
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
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.
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.
Enhancing reproducibility in scientific computing: Metrics and registry for Singularity containers.
Directory of Open Access Journals (Sweden)
Vanessa V Sochat
Full Text Available Here we present Singularity Hub, a framework to build and deploy Singularity containers for mobility of compute, and the singularity-python software with novel metrics for assessing reproducibility of such containers. Singularity containers make it possible for scientists and developers to package reproducible software, and Singularity Hub adds automation to this workflow by building, capturing metadata for, visualizing, and serving containers programmatically. Our novel metrics, based on custom filters of content hashes of container contents, allow for comparison of an entire container, including operating system, custom software, and metadata. First we will review Singularity Hub's primary use cases and how the infrastructure has been designed to support modern, common workflows. Next, we conduct three analyses to demonstrate build consistency, reproducibility metric and performance and interpretability, and potential for discovery. This is the first effort to demonstrate a rigorous assessment of measurable similarity between containers and operating systems. We provide these capabilities within Singularity Hub, as well as the source software singularity-python that provides the underlying functionality. Singularity Hub is available at https://singularity-hub.org, and we are excited to provide it as an openly available platform for building, and deploying scientific containers.
Enhancing reproducibility in scientific computing: Metrics and registry for Singularity containers
Prybol, Cameron J.; Kurtzer, Gregory M.
2017-01-01
Here we present Singularity Hub, a framework to build and deploy Singularity containers for mobility of compute, and the singularity-python software with novel metrics for assessing reproducibility of such containers. Singularity containers make it possible for scientists and developers to package reproducible software, and Singularity Hub adds automation to this workflow by building, capturing metadata for, visualizing, and serving containers programmatically. Our novel metrics, based on custom filters of content hashes of container contents, allow for comparison of an entire container, including operating system, custom software, and metadata. First we will review Singularity Hub’s primary use cases and how the infrastructure has been designed to support modern, common workflows. Next, we conduct three analyses to demonstrate build consistency, reproducibility metric and performance and interpretability, and potential for discovery. This is the first effort to demonstrate a rigorous assessment of measurable similarity between containers and operating systems. We provide these capabilities within Singularity Hub, as well as the source software singularity-python that provides the underlying functionality. Singularity Hub is available at https://singularity-hub.org, and we are excited to provide it as an openly available platform for building, and deploying scientific containers. PMID:29186161
Computing the Dilation of Edge-Augmented Graphs Embedded in Metric Spaces
DEFF Research Database (Denmark)
Wulff-Nilsen, Christian
2008-01-01
Let G = (V,E) be an undirected graph with n vertices embedded in a metric space. We consider the problem of adding a shortcut edge in G that minimizes the dilation of the resulting graph. The fastest algorithm to date for this problem has O(n^4) running time and uses O(n^2) space. We show how...... to improve running time to O(n^3*log n) while maintaining quadratic space requirement. In fact, our algorithm not only determines the best shortcut but computes the dilation of G U {(u,v)} for every pair of distinct vertices u and v....
Computing the dilation of edge-augmented graphs in metric spaces
DEFF Research Database (Denmark)
Wulff-Nilsen, Christian
2010-01-01
Let G=(V,E) be an undirected graph with n vertices embedded in a metric space. We consider the problem of adding a shortcut edge in G that minimizes the dilation of the resulting graph. The fastest algorithm to date for this problem has O(n4) running time and uses O(n2) space. We show how...... to improve the running time to O(n3logn) while maintaining quadratic space requirement. In fact, our algorithm not only determines the best shortcut but computes the dilation of G{(u,v)} for every pair of distinct vertices u and v....
Computing the Stretch Factor of Paths, Trees, and Cycles in Weighted Fixed Orientation Metrics
DEFF Research Database (Denmark)
Wulff-Nilsen, Christian
2008-01-01
Let G be a graph embedded in the L_1-plane. The stretch factor of G is the maximum over all pairs of distinct vertices p and q of G of the ratio L_1^G(p,q)/L_1(p,q), where L_1^G(p,q) is the L_1-distance in G between p and q. We show how to compute the stretch factor of an n-vertex path in O(n*(log...... n)^2) worst-case time and O(n) space and we mention generalizations to trees and cycles, to general weighted fixed orientation metrics, and to higher dimensions....
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.
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)
Properties of the stress tensor in more than two dimensions
International Nuclear Information System (INIS)
Cappelli, A.
1988-03-01
Some aspects of conformal invariance in more than two dimensions are analysed. In this case conformal (Weyl) transformations of the metric are not realized in general by coordinate transformations. The operator product expansion of the stress tensor is investigated by means of examples in the free bosonic and fermionic theories. The effective action for the general form of the trace anomaly is built in four dimensions and the Wess-Zumino consistency conditions are discussed. This gives the anomalous transformation law of the stress tensor and the relation to the Casimir effect in the geometry R x S 3 . The explicit computation of the bosonic partition function provides a check
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
Myszkowski, Karol; Tawara, Takehiro; Seidel, Hans-Peter
2002-06-01
In this paper, we consider applications of perception-based video quality metrics to improve the performance of global lighting computations for dynamic environments. For this purpose we extend the Visible Difference Predictor (VDP) developed by Daly to handle computer animations. We incorporate into the VDP the spatio-velocity CSF model developed by Kelly. The CSF model requires data on the velocity of moving patterns across the image plane. We use the 3D image warping technique to compensate for the camera motion, and we conservatively assume that the motion of animated objects (usually strong attractors of the visual attention) is fully compensated by the smooth pursuit eye motion. Our global illumination solution is based on stochastic photon tracing and takes advantage of temporal coherence of lighting distribution, by processing photons both in the spatial and temporal domains. The VDP is used to keep noise inherent in stochastic methods below the sensitivity level of the human observer. As a result a perceptually-consistent quality across all animation frames is obtained.
Symmetries of the dual metrics
International Nuclear Information System (INIS)
Baleanu, D.
1998-01-01
The geometric duality between the metric g μν and a Killing tensor K μν is studied. The conditions were found when the symmetries of the metric g μν and the dual metric K μν are the same. Dual spinning space was constructed without introduction of torsion. The general results are applied to the case of Kerr-Newmann metric
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
Syntactic Complexity Metrics and the Readability of Programs in a Functional Computer Language
van den Berg, Klaas; Engel, F.L.; Bouwhuis, D.G.; Bosser, T.; d'Ydewalle, G.
This article reports on the defintion and the measutement of the software complexity metrics of Halstead and McCabe for programs written in the functional programming language Miranda. An automated measurement of these metrics is described. In a case study, the correlation is established between the
Computing Best and Worst Shortcuts of Graphs Embedded in Metric Spaces
DEFF Research Database (Denmark)
Wulff-Nilsen, Christian; Luo, Jun
2008-01-01
Given a graph embedded in a metric space, its dilation is the maximum over all distinct pairs of vertices of the ratio between their distance in the graph and the metric distance between them. Given such a graph G with n vertices and m edges and consisting of at most two connected components, we ...
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)
Lu Wei; Low, Daniel A.; Parikh, Parag J.; Nystrom, Michelle M.; El Naqa, Issam M.; Wahab, Sasha H.; Handoko, Maureen; Fooshee, David; Bradley, Jeffrey D.
2005-01-01
An important consideration in four-dimensional CT scanning is the selection of a breathing metric for sorting the CT data and modeling internal motion. This study compared two noninvasive breathing metrics, spirometry and abdominal height, against internal air content, used as a surrogate for internal motion. Both metrics were shown to be accurate, but the spirometry showed a stronger and more reproducible relationship than the abdominal height in the lung. The abdominal height was known to be affected by sensor placement and patient positioning while the spirometer exhibited signal drift. By combining these two, a normalization of the drift-free metric to tidal volume may be generated and the overall metric precision may be improved
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...
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...
Bulliner, E. A., IV; Lindner, G. A.; Bouska, K.; Paukert, C.; Jacobson, R. B.
2017-12-01
Within large-river ecosystems, floodplains serve a variety of important ecological functions. A recent survey of 80 managers of floodplain conservation lands along the Upper and Middle Mississippi and Lower Missouri Rivers in the central United States found that the most critical information needed to improve floodplain management centered on metrics for characterizing depth, extent, frequency, duration, and timing of inundation. These metrics can be delivered to managers efficiently through cloud-based interactive maps. To calculate these metrics, we interpolated an existing one-dimensional hydraulic model for the Lower Missouri River, which simulated water surface elevations at cross sections spaced (step. To translate these water surface elevations to inundation depths, we subtracted a merged terrain model consisting of floodplain LIDAR and bathymetric surveys of the river channel. This approach resulted in a 29000+ day time series of inundation depths across the floodplain using grid cells with 30 m spatial resolution. Initially, we used these data on a local workstation to calculate a suite of nine spatially distributed inundation metrics for the entire model domain. These metrics are calculated on a per pixel basis and encompass a variety of temporal criteria generally relevant to flora and fauna of interest to floodplain managers, including, for example, the average number of days inundated per year within a growing season. Using a local workstation, calculating these metrics for the entire model domain requires several hours. However, for the needs of individual floodplain managers working at site scales, these metrics may be too general and inflexible. Instead of creating a priori a suite of inundation metrics able to satisfy all user needs, we present the usage of Google's cloud-based Earth Engine API to allow users to define and query their own inundation metrics from our dataset and produce maps nearly instantaneously. This approach allows users to
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.)
Directory of Open Access Journals (Sweden)
Bogdanov Alexander
2016-01-01
Full Text Available The architecture of a digital computing system determines the technical foundation of a unified mathematical language for exact arithmetic-logical description of phenomena and laws of continuum mechanics for applications in fluid mechanics and theoretical physics. The deep parallelization of the computing processes results in functional programming at a new technological level, providing traceability of the computing processes with automatic application of multiscale hybrid circuits and adaptive mathematical models for the true reproduction of the fundamental laws of physics and continuum mechanics.
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.
Directory of Open Access Journals (Sweden)
Basavaraj N Kallalli
2016-01-01
Full Text Available Introduction: Sex determination of unidentified human remains is very important in forensic medicine, medicolegal cases, and forensic anthropology. The mandible is the largest and hardest facial bone that commonly resists postmortem damage and forms an important source of personal identification. Additional studies have demonstrated the applicability of facial reconstruction using three-dimensional computed tomography scan (3D-CT for the purpose of individual identification. Aim: To determine the sex of human mandible using metrical parameters by CT. Materials and Methods: The study included thirty subjects (15 males and 15 females, with age group ranging between 10 and 60 years obtained from the outpatient department of Oral Medicine and Radiology, Narsinhbhai Patel Dental College and Hospital. CT scan was performed on all the subjects, and the data obtained were reconstructed for 3D viewing. After obtaining 3D-CT scan, a total of seven mandibular measurements, i.e., gonial angle (G-angle, ramus length (Ramus-L, minimum ramus breadth and gonion-gnathion length (G-G-L, bigonial breadth, bicondylar breadth (BIC-Br, and coronoid length (CO-L were measured; collected data were analyzed using SPSS statistical analysis program by Student's t-test. Results: The result of the study showed that out of seven parameters, G-angle, Ramus-L, G-G-L, BIC-Br, and CO-L showed a significant statistical difference (P < 0.05, with overall accuracy of 86% for males and 82% for females. Conclusion: Personal identification using mandible by conventional methods has already been proved but with variable efficacies. Advanced imaging modalities can aid in personal identification with much higher accuracy than conventional methods.
Graña, M; Termenon, M; Savio, A; Gonzalez-Pinto, A; Echeveste, J; Pérez, J M; Besga, A
2011-09-20
The aim of this paper is to obtain discriminant features from two scalar measures of Diffusion Tensor Imaging (DTI) data, Fractional Anisotropy (FA) and Mean Diffusivity (MD), and to train and test classifiers able to discriminate Alzheimer's Disease (AD) patients from controls on the basis of features extracted from the FA or MD volumes. In this study, support vector machine (SVM) classifier was trained and tested on FA and MD data. Feature selection is done computing the Pearson's correlation between FA or MD values at voxel site across subjects and the indicative variable specifying the subject class. Voxel sites with high absolute correlation are selected for feature extraction. Results are obtained over an on-going study in Hospital de Santiago Apostol collecting anatomical T1-weighted MRI volumes and DTI data from healthy control subjects and AD patients. FA features and a linear SVM classifier achieve perfect accuracy, sensitivity and specificity in several cross-validation studies, supporting the usefulness of DTI-derived features as an image-marker for AD and to the feasibility of building Computer Aided Diagnosis systems for AD based on them. Copyright © 2011 Elsevier Ireland Ltd. All rights reserved.
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.
Metrics with vanishing quantum corrections
International Nuclear Information System (INIS)
Coley, A A; Hervik, S; Gibbons, G W; Pope, C N
2008-01-01
We investigate solutions of the classical Einstein or supergravity equations that solve any set of quantum corrected Einstein equations in which the Einstein tensor plus a multiple of the metric is equated to a symmetric conserved tensor T μν (g αβ , ∂ τ g αβ , ∂ τ ∂ σ g αβ , ...,) constructed from sums of terms, the involving contractions of the metric and powers of arbitrary covariant derivatives of the curvature tensor. A classical solution, such as an Einstein metric, is called universal if, when evaluated on that Einstein metric, T μν is a multiple of the metric. A Ricci flat classical solution is called strongly universal if, when evaluated on that Ricci flat metric, T μν vanishes. It is well known that pp-waves in four spacetime dimensions are strongly universal. We focus attention on a natural generalization; Einstein metrics with holonomy Sim(n - 2) in which all scalar invariants are zero or constant. In four dimensions we demonstrate that the generalized Ghanam-Thompson metric is weakly universal and that the Goldberg-Kerr metric is strongly universal; indeed, we show that universality extends to all four-dimensional Sim(2) Einstein metrics. We also discuss generalizations to higher dimensions
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.
Directory of Open Access Journals (Sweden)
Chandana Kodiweera
2016-06-01
Full Text Available This article provides NODDI diffusion metrics in the brains of 52 healthy participants and computer simulation data to support compatibility of hybrid diffusion imaging (HYDI, “Hybrid diffusion imaging” [1] acquisition scheme in fitting neurite orientation dispersion and density imaging (NODDI model, “NODDI: practical in vivo neurite orientation dispersion and density imaging of the human brain” [2]. HYDI is an extremely versatile diffusion magnetic resonance imaging (dMRI technique that enables various analyzes methods using a single diffusion dataset. One of the diffusion data analysis methods is the NODDI computation, which models the brain tissue with three compartments: fast isotropic diffusion (e.g., cerebrospinal fluid, anisotropic hindered diffusion (e.g., extracellular space, and anisotropic restricted diffusion (e.g., intracellular space. The NODDI model produces microstructural metrics in the developing brain, aging brain or human brain with neurologic disorders. The first dataset provided here are the means and standard deviations of NODDI metrics in 48 white matter region-of-interest (ROI averaging across 52 healthy participants. The second dataset provided here is the computer simulation with initial conditions guided by the first dataset as inputs and gold standard for model fitting. The computer simulation data provide a direct comparison of NODDI indices computed from the HYDI acquisition [1] to the NODDI indices computed from the originally proposed acquisition [2]. These data are related to the accompanying research article “Age Effects and Sex Differences in Human Brain White Matter of Young to Middle-Aged Adults: A DTI, NODDI, and q-Space Study” [3].
Objectively Quantifying Radiation Esophagitis With Novel Computed Tomography–Based Metrics
Energy Technology Data Exchange (ETDEWEB)
Niedzielski, Joshua S., E-mail: jsniedzielski@mdanderson.org [Department of Radiation Physics, The University of Texas M. D. Anderson Cancer Center, Houston, Texas (United States); University of Texas Houston Graduate School of Biomedical Science, Houston, Texas (United States); Yang, Jinzhong [Department of Radiation Physics, The University of Texas M. D. Anderson Cancer Center, Houston, Texas (United States); University of Texas Houston Graduate School of Biomedical Science, Houston, Texas (United States); Stingo, Francesco [Department of Biostatistics, The University of Texas M. D. Anderson Cancer Center, Houston, Texas (United States); Martel, Mary K.; Mohan, Radhe [Department of Radiation Physics, The University of Texas M. D. Anderson Cancer Center, Houston, Texas (United States); University of Texas Houston Graduate School of Biomedical Science, Houston, Texas (United States); Gomez, Daniel R. [Department of Radiation Oncology, The University of Texas M. D. Anderson Cancer Center, Houston, Texas (United States); Briere, Tina M. [Department of Radiation Physics, The University of Texas M. D. Anderson Cancer Center, Houston, Texas (United States); University of Texas Houston Graduate School of Biomedical Science, Houston, Texas (United States); Liao, Zhongxing [Department of Radiation Oncology, The University of Texas M. D. Anderson Cancer Center, Houston, Texas (United States); Court, Laurence E. [Department of Radiation Physics, The University of Texas M. D. Anderson Cancer Center, Houston, Texas (United States); University of Texas Houston Graduate School of Biomedical Science, Houston, Texas (United States)
2016-02-01
Purpose: To study radiation-induced esophageal expansion as an objective measure of radiation esophagitis in patients with non-small cell lung cancer (NSCLC) treated with intensity modulated radiation therapy. Methods and Materials: Eighty-five patients had weekly intra-treatment CT imaging and esophagitis scoring according to Common Terminlogy Criteria for Adverse Events 4.0, (24 Grade 0, 45 Grade 2, and 16 Grade 3). Nineteen esophageal expansion metrics based on mean, maximum, spatial length, and volume of expansion were calculated as voxel-based relative volume change, using the Jacobian determinant from deformable image registration between the planning and weekly CTs. An anatomic variability correction method was validated and applied to these metrics to reduce uncertainty. An analysis of expansion metrics and radiation esophagitis grade was conducted using normal tissue complication probability from univariate logistic regression and Spearman rank for grade 2 and grade 3 esophagitis endpoints, as well as the timing of expansion and esophagitis grade. Metrics' performance in classifying esophagitis was tested with receiver operating characteristic analysis. Results: Expansion increased with esophagitis grade. Thirteen of 19 expansion metrics had receiver operating characteristic area under the curve values >0.80 for both grade 2 and grade 3 esophagitis endpoints, with the highest performance from maximum axial expansion (MaxExp1) and esophageal length with axial expansion ≥30% (LenExp30%) with area under the curve values of 0.93 and 0.91 for grade 2, 0.90 and 0.90 for grade 3 esophagitis, respectively. Conclusions: Esophageal expansion may be a suitable objective measure of esophagitis, particularly maximum axial esophageal expansion and esophageal length with axial expansion ≥30%, with 2.1 Jacobian value and 98.6 mm as the metric value for 50% probability of grade 3 esophagitis. The uncertainty in esophageal Jacobian calculations can be reduced
Objectively Quantifying Radiation Esophagitis With Novel Computed Tomography–Based Metrics
International Nuclear Information System (INIS)
Niedzielski, Joshua S.; Yang, Jinzhong; Stingo, Francesco; Martel, Mary K.; Mohan, Radhe; Gomez, Daniel R.; Briere, Tina M.; Liao, Zhongxing; Court, Laurence E.
2016-01-01
Purpose: To study radiation-induced esophageal expansion as an objective measure of radiation esophagitis in patients with non-small cell lung cancer (NSCLC) treated with intensity modulated radiation therapy. Methods and Materials: Eighty-five patients had weekly intra-treatment CT imaging and esophagitis scoring according to Common Terminlogy Criteria for Adverse Events 4.0, (24 Grade 0, 45 Grade 2, and 16 Grade 3). Nineteen esophageal expansion metrics based on mean, maximum, spatial length, and volume of expansion were calculated as voxel-based relative volume change, using the Jacobian determinant from deformable image registration between the planning and weekly CTs. An anatomic variability correction method was validated and applied to these metrics to reduce uncertainty. An analysis of expansion metrics and radiation esophagitis grade was conducted using normal tissue complication probability from univariate logistic regression and Spearman rank for grade 2 and grade 3 esophagitis endpoints, as well as the timing of expansion and esophagitis grade. Metrics' performance in classifying esophagitis was tested with receiver operating characteristic analysis. Results: Expansion increased with esophagitis grade. Thirteen of 19 expansion metrics had receiver operating characteristic area under the curve values >0.80 for both grade 2 and grade 3 esophagitis endpoints, with the highest performance from maximum axial expansion (MaxExp1) and esophageal length with axial expansion ≥30% (LenExp30%) with area under the curve values of 0.93 and 0.91 for grade 2, 0.90 and 0.90 for grade 3 esophagitis, respectively. Conclusions: Esophageal expansion may be a suitable objective measure of esophagitis, particularly maximum axial esophageal expansion and esophageal length with axial expansion ≥30%, with 2.1 Jacobian value and 98.6 mm as the metric value for 50% probability of grade 3 esophagitis. The uncertainty in esophageal Jacobian calculations can be reduced
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.
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.
Wang, Lusheng; Yang, Yong; Lin, Guohui
Finding the closest object for a query in a database is a classical problem in computer science. For some modern biological applications, computing the similarity between two objects might be very time consuming. For example, it takes a long time to compute the edit distance between two whole chromosomes and the alignment cost of two 3D protein structures. In this paper, we study the nearest neighbor search problem in metric space, where the pair-wise distance between two objects in the database is known and we want to minimize the number of distances computed on-line between the query and objects in the database in order to find the closest object. We have designed two randomized approaches for indexing metric space databases, where objects are purely described by their distances with each other. Analysis and experiments show that our approaches only need to compute O(logn) objects in order to find the closest object, where n is the total number of objects in the database.
Rotation, Reflection, and Frame Changes; Orthogonal tensors in computational engineering mechanics
Brannon, R. M.
2018-04-01
Whilst vast literature is available for the most common rotation-related tasks such as coordinate changes, most reference books tend to cover one or two methods, and resources for less-common tasks are scarce. Specialized research applications can be found in disparate journal articles, but a self-contained comprehensive review that covers both elementary and advanced concepts in a manner comprehensible to engineers is rare. Rotation, Reflection, and Frame Changes surveys a refreshingly broad range of rotation-related research that is routinely needed in engineering practice. By illustrating key concepts in computer source code, this book stands out as an unusually accessible guide for engineers and scientists in engineering mechanics.
Directory of Open Access Journals (Sweden)
Farshad Firuzi
2017-06-01
Full Text Available We consider unit tangent sphere bundle of a Riemannian manifold $ (M,g $ as a $ (2n+1 $-dimensional manifold and we equip it with pseudo-Riemannian $ g $-natural almost contact B-metric structure. Then, by computing coefficients of the structure tensor $ F$, we completely characterize the unit tangent sphere bundle equipped to this structure, with respect to the relevant classification of almost contact B-metric structures, and determine a class such that the unit tangent sphere bundle with mentioned structure belongs to it. Also, we find some curvature conditions such that the mentioned structure satisfies each of eleven basic classes.
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.
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, ...
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...
Cloud-based Computing and Applications of New Snow Metrics for Societal Benefit
Nolin, A. W.; Sproles, E. A.; Crumley, R. L.; Wilson, A.; Mar, E.; van de Kerk, M.; Prugh, L.
2017-12-01
Seasonal and interannual variability in snow cover affects socio-environmental systems including water resources, forest ecology, freshwater and terrestrial habitat, and winter recreation. We have developed two new seasonal snow metrics: snow cover frequency (SCF) and snow disappearance date (SDD). These metrics are calculated at 500-m resolution using NASA's Moderate Resolution Imaging Spectroradiometer (MODIS) snow cover data (MOD10A1). SCF is the number of times snow is observed in a pixel over the user-defined observation period. SDD is the last date of observed snow in a water year. These pixel-level metrics are calculated rapidly and globally in the Google Earth Engine cloud-based environment. SCF and SDD can be interactively visualized in a map-based interface, allowing users to explore spatial and temporal snowcover patterns from 2000-present. These metrics are especially valuable in regions where snow data are sparse or non-existent. We have used these metrics in several ongoing projects. When SCF was linked with a simple hydrologic model in the La Laguna watershed in northern Chile, it successfully predicted summer low flows with a Nash-Sutcliffe value of 0.86. SCF has also been used to help explain changes in Dall sheep populations in Alaska where sheep populations are negatively impacted by late snow cover and low snowline elevation during the spring lambing season. In forest management, SCF and SDD appear to be valuable predictors of post-wildfire vegetation growth. We see a positive relationship between winter SCF and subsequent summer greening for several years post-fire. For western US winter recreation, we are exploring trends in SDD and SCF for regions where snow sports are economically important. In a world with declining snowpacks and increasing uncertainty, these metrics extend across elevations and fill data gaps to provide valuable information for decision-making. SCF and SDD are being produced so that anyone with Internet access and a Google
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 ...
Sharp metric obstructions for quasi-Einstein metrics
Case, Jeffrey S.
2013-02-01
Using the tractor calculus to study smooth metric measure spaces, we adapt results of Gover and Nurowski to give sharp metric obstructions to the existence of quasi-Einstein metrics on suitably generic manifolds. We do this by introducing an analogue of the Weyl tractor W to the setting of smooth metric measure spaces. The obstructions we obtain can be realized as tensorial invariants which are polynomial in the Riemann curvature tensor and its divergence. By taking suitable limits of their tensorial forms, we then find obstructions to the existence of static potentials, generalizing to higher dimensions a result of Bartnik and Tod, and to the existence of potentials for gradient Ricci solitons.
International Nuclear Information System (INIS)
Panasyuk, George Y; Schotland, John C; Markel, Vadim A
2009-01-01
We obtain a short-distance expansion for the half-space, frequency domain electromagnetic Green's tensor. The small parameter of the theory is ωε 1 L/c, where ω is the frequency, ε 1 is the permittivity of the upper half-space, in which both the source and the point of observation are located, and which is assumed to be transparent, c is the speed of light in vacuum and L is a characteristic length, defined as the distance from the point of observation to the reflected (with respect to the planar interface) position of the source. In the case when the lower half-space (the substrate) is characterized by a complex permittivity ε 2 , we compute the expansion to third order. For the case when the substrate is a transparent dielectric, we compute the imaginary part of the Green's tensor to seventh order. The analytical calculations are verified numerically. The practical utility of the obtained expansion is demonstrated by computing the radiative lifetime of two electromagnetically interacting molecules in the vicinity of a transparent dielectric substrate. The computation is performed in the strong interaction regime when the quasi-particle pole approximation is inapplicable. In this regime, the integral representation for the half-space Green's tensor is difficult to use while its electrostatic limiting expression is grossly inadequate. However, the analytical expansion derived in this paper can be used directly and efficiently. The results of this study are also relevant to nano-optics and near-field imaging, especially when tomographic image reconstruction is involved
Alves, Antoine; Attik, Nina; Bayon, Yves; Royet, Elodie; Wirth, Carine; Bourges, Xavier; Piat, Alexis; Dolmazon, Gaëlle; Clermont, Gaëlle; Boutrand, Jean-Pierre; Grosgogeat, Brigitte; Gritsch, Kerstin
2018-03-14
The paradigm shift brought about by the expansion of tissue engineering and regenerative medicine away from the use of biomaterials, currently questions the value of histopathologic methods in the evaluation of biological changes. To date, the available tools of evaluation are not fully consistent and satisfactory for these advanced therapies. We have developed a new, simple and inexpensive quantitative digital approach that provides key metrics for structural and compositional characterization of the regenerated tissues. For example, metrics provide the tissue ingrowth rate (TIR) which integrates two separate indicators; the cell ingrowth rate (CIR) and the total collagen content (TCC) as featured in the equation, TIR% = CIR% + TCC%. Moreover a subset of quantitative indicators describing the directional organization of the collagen (relating structure and mechanical function of tissues), the ratio of collagen I to collagen III (remodeling quality) and the optical anisotropy property of the collagen (maturity indicator) was automatically assessed as well. Using an image analyzer, all metrics were extracted from only two serial sections stained with either Feulgen & Rossenbeck (cell specific) or Picrosirius Red F3BA (collagen specific). To validate this new procedure, three-dimensional (3D) scaffolds were intraperitoneally implanted in healthy and in diabetic rats. It was hypothesized that quantitatively, the healing tissue would be significantly delayed and of poor quality in diabetic rats in comparison to healthy rats. In addition, a chemically modified 3D scaffold was similarly implanted in a third group of healthy rats with the assumption that modulation of the ingrown tissue would be quantitatively present in comparison to the 3D scaffold-healthy group. After 21 days of implantation, both hypotheses were verified by use of this novel computerized approach. When the two methods were run in parallel, the quantitative results revealed fine details and
McLaughlin, Laura; Bond, Raymond; Hughes, Ciara; McConnell, Jonathan; McFadden, Sonyia
2017-09-01
To investigate image interpretation performance by diagnostic radiography students, diagnostic radiographers and reporting radiographers by computing eye gaze metrics using eye tracking technology. Three groups of participants were studied during their interpretation of 8 digital radiographic images including the axial and appendicular skeleton, and chest (prevalence of normal images was 12.5%). A total of 464 image interpretations were collected. Participants consisted of 21 radiography students, 19 qualified radiographers and 18 qualified reporting radiographers who were further qualified to report on the musculoskeletal (MSK) system. Eye tracking data was collected using the Tobii X60 eye tracker and subsequently eye gaze metrics were computed. Voice recordings, confidence levels and diagnoses provided a clear demonstration of the image interpretation and the cognitive processes undertaken by each participant. A questionnaire afforded the participants an opportunity to offer information on their experience in image interpretation and their opinion on the eye tracking technology. Reporting radiographers demonstrated a 15% greater accuracy rate (p≤0.001), were more confident (p≤0.001) and took a mean of 2.4s longer to clinically decide on all features compared to students. Reporting radiographers also had a 15% greater accuracy rate (p≤0.001), were more confident (p≤0.001) and took longer to clinically decide on an image diagnosis (p=0.02) than radiographers. Reporting radiographers had a greater mean fixation duration (p=0.01), mean fixation count (p=0.04) and mean visit count (p=0.04) within the areas of pathology compared to students. Eye tracking patterns, presented within heat maps, were a good reflection of group expertise and search strategies. Eye gaze metrics such as time to first fixate, fixation count, fixation duration and visit count within the areas of pathology were indicative of the radiographer's competency. The accuracy and confidence of
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.
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.
Tensor fields on orbits of quantum states and applications
Energy Technology Data Exchange (ETDEWEB)
Volkert, Georg Friedrich
2010-07-19
On classical Lie groups, which act by means of a unitary representation on finite dimensional Hilbert spaces H, we identify two classes of tensor field constructions. First, as pull-back tensor fields of order two from modified Hermitian tensor fields, constructed on Hilbert spaces by means of the property of having the vertical distributions of the C{sub 0}-principal bundle H{sub 0} {yields} P(H) over the projective Hilbert space P(H) in the kernel. And second, directly constructed on the Lie group, as left-invariant representation-dependent operator-valued tensor fields (LIROVTs) of arbitrary order being evaluated on a quantum state. Within the NP-hard problem of deciding whether a given state in a n-level bi-partite quantum system is entangled or separable (Gurvits, 2003), we show that both tensor field constructions admit a geometric approach to this problem, which evades the traditional ambiguity on defining metrical structures on the convex set of mixed states. In particular by considering manifolds associated to orbits passing through a selected state when acted upon by the local unitary group U(n) x U(n) of Schmidt coefficient decomposition inducing transformations, we find the following results: In the case of pure states we show that Schmidt-equivalence classes which are Lagrangian submanifolds define maximal entangled states. This implies a stronger statement as the one proposed by Bengtsson (2007). Moreover, Riemannian pull-back tensor fields split on orbits of separable states and provide a quantitative characterization of entanglement which recover the entanglement measure proposed by Schlienz and Mahler (1995). In the case of mixed states we highlight a relation between LIROVTs of order two and a class of computable separability criteria based on the Bloch-representation (de Vicente, 2007). (orig.)
Tensor fields on orbits of quantum states and applications
International Nuclear Information System (INIS)
Volkert, Georg Friedrich
2010-01-01
On classical Lie groups, which act by means of a unitary representation on finite dimensional Hilbert spaces H, we identify two classes of tensor field constructions. First, as pull-back tensor fields of order two from modified Hermitian tensor fields, constructed on Hilbert spaces by means of the property of having the vertical distributions of the C 0 -principal bundle H 0 → P(H) over the projective Hilbert space P(H) in the kernel. And second, directly constructed on the Lie group, as left-invariant representation-dependent operator-valued tensor fields (LIROVTs) of arbitrary order being evaluated on a quantum state. Within the NP-hard problem of deciding whether a given state in a n-level bi-partite quantum system is entangled or separable (Gurvits, 2003), we show that both tensor field constructions admit a geometric approach to this problem, which evades the traditional ambiguity on defining metrical structures on the convex set of mixed states. In particular by considering manifolds associated to orbits passing through a selected state when acted upon by the local unitary group U(n) x U(n) of Schmidt coefficient decomposition inducing transformations, we find the following results: In the case of pure states we show that Schmidt-equivalence classes which are Lagrangian submanifolds define maximal entangled states. This implies a stronger statement as the one proposed by Bengtsson (2007). Moreover, Riemannian pull-back tensor fields split on orbits of separable states and provide a quantitative characterization of entanglement which recover the entanglement measure proposed by Schlienz and Mahler (1995). In the case of mixed states we highlight a relation between LIROVTs of order two and a class of computable separability criteria based on the Bloch-representation (de Vicente, 2007). (orig.)
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 ...
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.
Directory of Open Access Journals (Sweden)
Miroslav Kališnik
2011-05-01
Full Text Available In the introduction the evolution of methods for numerical density estimation of particles is presented shortly. Three pairs of methods have been analysed and compared: (1 classical methods for particles counting in thin and thick sections, (2 original and modified differential counting methods and (3 physical and optical disector methods. Metric characteristics such as accuracy, efficiency, robustness, and feasibility of methods have been estimated and compared. Logical, geometrical and mathematical analysis as well as computer simulations have been applied. In computer simulations a model of randomly distributed equal spheres with maximal contrast against surroundings has been used. According to our computer simulation all methods give accurate results provided that the sample is representative and sufficiently large. However, there are differences in their efficiency, robustness and feasibility. Efficiency and robustness increase with increasing slice thickness in all three pairs of methods. Robustness is superior in both differential and both disector methods compared to both classical methods. Feasibility can be judged according to the additional equipment as well as to the histotechnical and counting procedures necessary for performing individual counting methods. However, it is evident that not all practical problems can efficiently be solved with models.
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.
METRIC context unit architecture
Energy Technology Data Exchange (ETDEWEB)
Simpson, R.O.
1988-01-01
METRIC is an architecture for a simple but powerful Reduced Instruction Set Computer (RISC). Its speed comes from the simultaneous processing of several instruction streams, with instructions from the various streams being dispatched into METRIC's execution pipeline as they become available for execution. The pipeline is thus kept full, with a mix of instructions for several contexts in execution at the same time. True parallel programming is supported within a single execution unit, the METRIC Context Unit. METRIC's architecture provides for expansion through the addition of multiple Context Units and of specialized Functional Units. The architecture thus spans a range of size and performance from a single-chip microcomputer up through large and powerful multiprocessors. This research concentrates on the specification of the METRIC Context Unit at the architectural level. Performance tradeoffs made during METRIC's design are discussed, and projections of METRIC's performance are made based on simulation studies.
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...
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)
Enhancing Information Security in Cloud Computing Services using SLA based metrics
, Nia; Mganga, Ramadianti Putri;; Charles, Medard
2011-01-01
Context: Cloud computing is a prospering technology that most organizations are considering for adoption as a cost effective strategy for managing IT. However, organizations also still consider the technology to be associated with many business risks that are not yet resolved. Such issues include security, privacy as well as legal and regulatory risks. As an initiative to address such risks, organizations can develop and implement SLA to establish common expectations and goals between the clo...
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.
Tensor-based cortical surface morphometry via weighted spherical harmonic representation.
Chung, Moo K; Dalton, Kim M; Davidson, Richard J
2008-08-01
We present a new tensor-based morphometric framework that quantifies cortical shape variations using a local area element. The local area element is computed from the Riemannian metric tensors, which are obtained from the smooth functional parametrization of a cortical mesh. For the smooth parametrization, we have developed a novel weighted spherical harmonic (SPHARM) representation, which generalizes the traditional SPHARM as a special case. For a specific choice of weights, the weighted-SPHARM is shown to be the least squares approximation to the solution of an isotropic heat diffusion on a unit sphere. The main aims of this paper are to present the weighted-SPHARM and to show how it can be used in the tensor-based morphometry. As an illustration, the methodology has been applied in the problem of detecting abnormal cortical regions in the group of high functioning autistic subjects.
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.)
Some curvature properties of quarter symmetric metric connections
International Nuclear Information System (INIS)
Rastogi, S.C.
1986-08-01
A linear connection Γ ji h with torsion tensor T j h P i -T i h P j , where T j h is an arbitrary (1,1) tensor field and P i is a 1-form, has been called a quarter-symmetric connection by Golab. Some properties of such connections have been studied by Rastogi, Mishra and Pandey, and Yano and Imai. In this paper based on the curvature tensor of quarter-symmetric metric connection we define a tensor analogous to conformal curvature tensor and study some properties of such a tensor. (author)
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.
Directory of Open Access Journals (Sweden)
Jochen eSchubert
2015-11-01
Full Text Available Metric resolution digital terrain models (DTMs of rivers now make it possible for multi-dimensional fluid mechanics models to be applied to characterize flow at fine scales that are relevant to studies of river morphology and ecological habitat, or microscales. These developments are important for managing rivers because of the potential to better understand system dynamics, anthropogenic impacts, and the consequences of proposed interventions. However, the data volumes and computational demands of microscale river modeling have largely constrained applications to small multiples of the channel width, or the mesoscale. This report presents computational methods to extend a microscale river model beyond the mesoscale to the macroscale, defined as large multiples of the channel width. A method of automated unstructured grid generation is presented that automatically clusters fine resolution cells in areas of curvature (e.g., channel banks, and places relatively coarse cells in areas lacking topographic variability. This overcomes the need to manually generate breaklines to constrain the grid, which is painstaking at the mesoscale and virtually impossible at the macroscale. The method is applied to a braided river with an extremely complex channel network configuration and shown to yield an efficient fine resolution model. The sensitivity of model output to grid design and resistance parameters is also examined as it relates to analysis of hydrology, hydraulic geometry and river habitats and the findings reiterate the importance of model calibration and validation.
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.
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.
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...
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.
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...
Paniagua, Beatriz; Ehlers, Cindy; Crews, Fulton; Budin, Francois; Larson, Garrett; Styner, Martin; Oguz, Ipek
2011-03-01
Understanding the effects of adolescent binge drinking that persist into adulthood is a crucial public health issue. Adolescent intermittent ethanol exposure (AIE) is an animal model that can be used to investigate these effects in rodents. In this work, we investigate the application of a particular image analysis technique, tensor-based morphometry, for detecting anatomical differences between AIE and control rats using Diffusion Tensor Imaging (DTI). Deformation field analysis is a popular method for detecting volumetric changes analyzing Jacobian determinants calculated on deformation fields. Recent studies showed that computing deformation field metrics on the full deformation tensor, often referred to as tensor-based morphometry (TBM), increases the sensitivity to anatomical differences. In this paper we conduct a comprehensive TBM study for precisely locating differences between control and AIE rats. Using a DTI RARE sequence designed for minimal geometric distortion, 12-directional images were acquired postmortem for control and AIE rats (n=9). After preprocessing, average images for the two groups were constructed using an unbiased atlas building approach. We non-rigidly register the two atlases using Large Deformation Diffeomorphic Metric Mapping, and analyze the resulting deformation field using TBM. In particular, we evaluate the tensor determinant, geodesic anisotropy, and deformation direction vector (DDV) on the deformation field to detect structural differences. This yields data on the local amount of growth, shrinkage and the directionality of deformation between the groups. We show that TBM can thus be used to measure group morphological differences between rat populations, demonstrating the potential of the proposed framework.
Atomic orbital-based SOS-MP2 with tensor hypercontraction. II. Local tensor hypercontraction
Song, Chenchen; Martínez, Todd J.
2017-01-01
In the first paper of the series [Paper I, C. Song and T. J. Martinez, J. Chem. Phys. 144, 174111 (2016)], we showed how tensor-hypercontracted (THC) SOS-MP2 could be accelerated by exploiting sparsity in the atomic orbitals and using graphical processing units (GPUs). This reduced the formal scaling of the SOS-MP2 energy calculation to cubic with respect to system size. The computational bottleneck then becomes the THC metric matrix inversion, which scales cubically with a large prefactor. In this work, the local THC approximation is proposed to reduce the computational cost of inverting the THC metric matrix to linear scaling with respect to molecular size. By doing so, we have removed the primary bottleneck to THC-SOS-MP2 calculations on large molecules with O(1000) atoms. The errors introduced by the local THC approximation are less than 0.6 kcal/mol for molecules with up to 200 atoms and 3300 basis functions. Together with the graphical processing unit techniques and locality-exploiting approaches introduced in previous work, the scaled opposite spin MP2 (SOS-MP2) calculations exhibit O(N2.5) scaling in practice up to 10 000 basis functions. The new algorithms make it feasible to carry out SOS-MP2 calculations on small proteins like ubiquitin (1231 atoms/10 294 atomic basis functions) on a single node in less than a day.
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
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.
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)
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.
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-...
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....
Quantum inflaton, primordial metric perturbations and CMB fluctuations
International Nuclear Information System (INIS)
Cao, F J
2007-01-01
We compute the primordial scalar, vector and tensor metric perturbations arising from quantum field inflation. Quantum field inflation takes into account the nonperturbative quantum dynamics of the inflaton consistently coupled to the dynamics of the (classical) cosmological metric. For chaotic inflation, the quantum treatment avoids the unnatural requirements of an initial state with all the energy in the zero mode. For new inflation it allows a consistent treatment of the explosive particle production due to spinodal instabilities. Quantum field inflation (under conditions that are the quantum analog of slow roll) leads, upon evolution, to the formation of a condensate starting a regime of effective classical inflation. We compute the primordial perturbations taking the dominant quantum effects into account. The results for the scalar, vector and tensor primordial perturbations are expressed in terms of the classical inflation results. For a N-component field in a O(N) symmetric model, adiabatic fluctuations dominate while isocurvature or entropy fluctuations are negligible. The results agree with the current WMAP observations and predict corrections to the power spectrum in classical inflation. Such corrections are estimated to be of the order of m 2 /[NH 2 ] where m is the inflaton mass and H the Hubble constant at horizon crossing. This turns to be about 4% for the cosmologically relevant scales. This quantum field treatment of inflation provides the foundations to the classical inflation and permits to compute quantum corrections to it
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
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
Thermodynamic metrics and optimal paths.
Sivak, David A; Crooks, Gavin E
2012-05-11
A fundamental problem in modern thermodynamics is how a molecular-scale machine performs useful work, while operating away from thermal equilibrium without excessive dissipation. To this end, we derive a friction tensor that induces a Riemannian manifold on the space of thermodynamic states. Within the linear-response regime, this metric structure controls the dissipation of finite-time transformations, and bestows optimal protocols with many useful properties. We discuss the connection to the existing thermodynamic length formalism, and demonstrate the utility of this metric by solving for optimal control parameter protocols in a simple nonequilibrium model.
Algebraic computing program for studying the gauge theory
International Nuclear Information System (INIS)
Zet, G.
2005-01-01
An algebraic computing program running on Maple V platform is presented. The program is devoted to the study of the gauge theory with an internal Lie group as local symmetry. The physical quantities (gauge potentials, strength tensors, dual tensors etc.) are introduced either as equations in terms of previous defined quantities (tensors), or by manual entry of the component values. The components of the strength tensor and of its dual are obtained with respect to a given metric of the space-time used for describing the gauge theory. We choose a Minkowski space-time endowed with spherical symmetry and give some example of algebraic computing that are adequate for studying electroweak or gravitational interactions. The field equations are also obtained and their solutions are determined using the DEtools facilities of the Maple V computing program. (author)
Directory of Open Access Journals (Sweden)
2007-01-01
Full Text Available Many software and IT projects fail in completing theirs objectives because different causes of which the management of the projects has a high weight. In order to have successfully projects, lessons learned have to be used, historical data to be collected and metrics and indicators have to be computed and used to compare them with past projects and avoid failure to happen. This paper presents some metrics that can be used for the IT project management.
About the possibility of a generalized metric
International Nuclear Information System (INIS)
Lukacs, B.; Ladik, J.
1991-10-01
The metric (the structure of the space-time) may be dependent on the properties of the object measuring it. The case of size dependence of the metric was examined. For this dependence the simplest possible form of the metric tensor has been constructed which fulfils the following requirements: there be two extremal characteristic scales; the metric be unique and the usual between them; the change be sudden in the neighbourhood of these scales; the size of the human body appear as a parameter (postulated on the basis of some philosophical arguments). Estimates have been made for the two extremal length scales according to existing observations. (author) 19 refs
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.
Software metrics: Software quality metrics for distributed systems. [reliability engineering
Post, J. V.
1981-01-01
Software quality metrics was extended to cover distributed computer systems. Emphasis is placed on studying embedded computer systems and on viewing them within a system life cycle. The hierarchy of quality factors, criteria, and metrics was maintained. New software quality factors were added, including survivability, expandability, and evolvability.
Energy Technology Data Exchange (ETDEWEB)
Kothe, Douglas B [ORNL; Roche, Kenneth J [ORNL; Kendall, Ricky A [ORNL
2010-01-01
The Joule Software Metric for Computational Effectiveness is established by Public Authorizations PL 95-91, Department of Energy Organization Act, and PL 103-62, Government Performance and Results Act. The U.S. Office of Management and Budget (OMB) oversees the preparation and administration of the President s budget; evaluates the effectiveness of agency programs, policies, and procedures; assesses competing funding demands across agencies; and sets the funding priorities for the federal government. The OMB has the power of audit and exercises this right annually for each federal agency. According to the Government Performance and Results Act of 1993 (GPRA), federal agencies are required to develop three planning and performance documents: 1.Strategic Plan: a broad, 3 year outlook; 2.Annual Performance Plan: a focused, 1 year outlook of annual goals and objectives that is reflected in the annual budget request (What results can the agency deliver as part of its public funding?); and 3.Performance and Accountability Report: an annual report that details the previous fiscal year performance (What results did the agency produce in return for its public funding?). OMB uses its Performance Assessment Rating Tool (PART) to perform evaluations. PART has seven worksheets for seven types of agency functions. The function of Research and Development (R&D) programs is included. R&D programs are assessed on the following criteria: Does the R&D program perform a clear role? Has the program set valid long term and annual goals? Is the program well managed? Is the program achieving the results set forth in its GPRA documents? In Fiscal Year (FY) 2003, the Department of Energy Office of Science (DOE SC-1) worked directly with OMB to come to a consensus on an appropriate set of performance measures consistent with PART requirements. The scientific performance expectations of these requirements reach the scope of work conducted at the DOE national laboratories. The Joule system
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)
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 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.
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.
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.
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.
The normal conformal Cartan connection and the Bach tensor
International Nuclear Information System (INIS)
Korzynski, Mikolaj; Lewandowski, Jerzy
2003-01-01
The goal of this paper is to express the Bach tensor of a four-dimensional conformal geometry of an arbitrary signature by the Cartan normal conformal (CNC) connection. We show that the Bach tensor can be identified with the Yang-Mills current of the connection. It follows from that result that a conformal geometry whose CNC connection is reducible in an appropriate way has a degenerate Bach tensor. As an example we study the case of a CNC connection which admits a twisting covariantly constant twistor field. This class of conformal geometries of this property is known as given by the Fefferman metric tensors. We use our result to calculate the Bach tensor of an arbitrary Fefferman metric and show that it is proportional to the tensorial square of the four-fold eigenvector of the Weyl tensor. Finally, we solve the Yang-Mills equations imposed on the CNC connection for all the homogeneous Fefferman metrics. The only solution is the Nurowski-Plebanski metric
The U.S. Environmental Protection Agency (EPA) Computational Toxicology Program integrates advances in biology, chemistry, and computer science to help prioritize chemicals for further research based on potential human health risks. This work involves computational and data drive...
Efficient Tensor Strategy for Recommendation
Directory of Open Access Journals (Sweden)
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.
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.
Attack-Resistant Trust Metrics
Levien, Raph
The Internet is an amazingly powerful tool for connecting people together, unmatched in human history. Yet, with that power comes great potential for spam and abuse. Trust metrics are an attempt to compute the set of which people are trustworthy and which are likely attackers. This chapter presents two specific trust metrics developed and deployed on the Advogato Website, which is a community blog for free software developers. This real-world experience demonstrates that the trust metrics fulfilled their goals, but that for good results, it is important to match the assumptions of the abstract trust metric computation to the real-world implementation.
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
Applying tensor-based morphometry to parametric surfaces can improve MRI-based disease diagnosis.
Wang, Yalin; Yuan, Lei; Shi, Jie; Greve, Alexander; Ye, Jieping; Toga, Arthur W; Reiss, Allan L; Thompson, Paul M
2013-07-01
Many methods have been proposed for computer-assisted diagnostic classification. Full tensor information and machine learning with 3D maps derived from brain images may help detect subtle differences or classify subjects into different groups. Here we develop a new approach to apply tensor-based morphometry to parametric surface models for diagnostic classification. We use this approach to identify cortical surface features for use in diagnostic classifiers. First, with holomorphic 1-forms, we compute an efficient and accurate conformal mapping from a multiply connected mesh to the so-called slit domain. Next, the surface parameterization approach provides a natural way to register anatomical surfaces across subjects using a constrained harmonic map. To analyze anatomical differences, we then analyze the full Riemannian surface metric tensors, which retain multivariate information on local surface geometry. As the number of voxels in a 3D image is large, sparse learning is a promising method to select a subset of imaging features and to improve classification accuracy. Focusing on vertices with greatest effect sizes, we train a diagnostic classifier using the surface features selected by an L1-norm based sparse learning method. Stability selection is applied to validate the selected feature sets. We tested the algorithm on MRI-derived cortical surfaces from 42 subjects with genetically confirmed Williams syndrome and 40 age-matched controls, multivariate statistics on the local tensors gave greater effect sizes for detecting group differences relative to other TBM-based statistics including analysis of the Jacobian determinant and the largest eigenvalue of the surface metric. Our method also gave reasonable classification results relative to the Jacobian determinant, the pair of eigenvalues of the Jacobian matrix and volume features. This analysis pipeline may boost the power of morphometry studies, and may assist with image-based classification. Copyright © 2013
Bellet, Aurelien; Sebban, Marc
2015-01-01
Similarity between objects plays an important role in both human cognitive processes and artificial systems for recognition and categorization. How to appropriately measure such similarities for a given task is crucial to the performance of many machine learning, pattern recognition and data mining methods. This book is devoted to metric learning, a set of techniques to automatically learn similarity and distance functions from data that has attracted a lot of interest in machine learning and related fields in the past ten years. In this book, we provide a thorough review of the metric learnin
Self-dual metrics with self-dual Killing vectors
International Nuclear Information System (INIS)
Tod, K.P.; Ward, R.S.
1979-01-01
Twistor methods are used to derive a class of solutions to Einstein's vacuum equations, with anti-self dual Weyl tensor. In particular, all metrics with a Killing vector whose derivative is anti-self-dual and which admit a real positive-definite section are exhibited and shown to coincide with the metrics of Hawking. (author)
Radiating c metric: an example of a proper Ricci Collineation
International Nuclear Information System (INIS)
Aulestia, L.; Nunez, L.; Patino, A.; Rago, H.; Herrera, L.
1984-01-01
A generalization of the charged c metric to the nonstationary case is given. The possibility of associating the energy-momentum tensor with the electromagnetic or neutrino field is discussed. It is shown that, for a specific choice of the time-dependent parameters, the metric admits at least a two-parameter group of proper Ricci collineations
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 ...
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.
Gauvin, Laetitia; Panisson, André; Cattuto, Ciro
2014-01-01
The increasing availability of temporal network data is calling for more research on extracting and characterizing mesoscopic structures in temporal networks and on relating such structure to specific functions or properties of the system. An outstanding challenge is the extension of the results achieved for static networks to time-varying networks, where the topological structure of the system and the temporal activity patterns of its components are intertwined. Here we investigate the use of a latent factor decomposition technique, non-negative tensor factorization, to extract the community-activity structure of temporal networks. The method is intrinsically temporal and allows to simultaneously identify communities and to track their activity over time. We represent the time-varying adjacency matrix of a temporal network as a three-way tensor and approximate this tensor as a sum of terms that can be interpreted as communities of nodes with an associated activity time series. We summarize known computational techniques for tensor decomposition and discuss some quality metrics that can be used to tune the complexity of the factorized representation. We subsequently apply tensor factorization to a temporal network for which a ground truth is available for both the community structure and the temporal activity patterns. The data we use describe the social interactions of students in a school, the associations between students and school classes, and the spatio-temporal trajectories of students over time. We show that non-negative tensor factorization is capable of recovering the class structure with high accuracy. In particular, the extracted tensor components can be validated either as known school classes, or in terms of correlated activity patterns, i.e., of spatial and temporal coincidences that are determined by the known school activity schedule. PMID:24497935
Categorical Tensor Network States
Directory of Open Access Journals (Sweden)
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.
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
Some spacetimes with higher rank Killing-Staeckel tensors
International Nuclear Information System (INIS)
Gibbons, G.W.; Houri, T.; Kubiznak, D.; Warnick, C.M.
2011-01-01
By applying the lightlike Eisenhart lift to several known examples of low-dimensional integrable systems admitting integrals of motion of higher-order in momenta, we obtain four- and higher-dimensional Lorentzian spacetimes with irreducible higher-rank Killing tensors. Such metrics, we believe, are first examples of spacetimes admitting higher-rank Killing tensors. Included in our examples is a four-dimensional supersymmetric pp-wave spacetime, whose geodesic flow is superintegrable. The Killing tensors satisfy a non-trivial Poisson-Schouten-Nijenhuis algebra. We discuss the extension to the quantum regime.
Scalar-Tensor Black Holes Embedded in an Expanding Universe
Tretyakova, Daria; Latosh, Boris
2018-02-01
In this review we focus our attention on scalar-tensor gravity models and their empirical verification in terms of black hole and wormhole physics. We focus on a black hole, embedded in an expanding universe, describing both cosmological and astrophysical scales. We show that in scalar-tensor gravity it is quite common that the local geometry is isolated from the cosmological expansion, so that it does not backreact on the black hole metric. We try to extract common features of scalar-tensor black holes in an expanding universe and point out the gaps that must be filled.
Scalar-Tensor Black Holes Embedded in an Expanding Universe
Directory of Open Access Journals (Sweden)
Daria Tretyakova
2018-02-01
Full Text Available In this review, we focus our attention on scalar-tensor gravity models and their empirical verification in terms of black hole and wormhole physics. We focus on black holes, embedded in an expanding universe, describing both cosmological and astrophysical scales. We show that in scalar-tensor gravity it is quite common that the local geometry is isolated from the cosmological expansion, so that it does not backreact on the black hole metric. We try to extract common features of scalar-tensor black holes in an expanding universe and point out the issues that are not fully investigated.
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.
International Nuclear Information System (INIS)
Harper, A.F.A.; Digby, R.B.; Thong, S.P.; Lacey, F.
1978-04-01
In April 1978 a meeting of senior metrication officers convened by the Commonwealth Science Council of the Commonwealth Secretariat, was held in London. The participants were drawn from Australia, Bangladesh, Britain, Canada, Ghana, Guyana, India, Jamaica, Papua New Guinea, Solomon Islands and Trinidad and Tobago. Among other things, the meeting resolved to develop a set of guidelines to assist countries to change to SI and to compile such guidelines in the form of a working manual
Parks, Sean; Holsinger, Lisa M.; Voss, Morgan; Loehman, Rachel A.; Robinson, Nathaniel P.
2018-01-01
Landsat-based fire severity datasets are an invaluable resource for monitoring and research purposes. These gridded fire severity datasets are generally produced with pre-and post-fire imagery to estimate the degree of fire-induced ecological change. Here, we introduce methods to produce three Landsat-based fire severity metrics using the Google Earth Engine (GEE) platform: the delta normalized burn ratio (dNBR), the relativized delta normalized burn ratio (RdNBR), and the relativized burn ratio (RBR). Our methods do not rely on time-consuming a priori scene selection and instead use a mean compositing approach in which all valid pixels (e.g. cloud-free) over a pre-specified date range (pre- and post-fire) are stacked and the mean value for each pixel over each stack is used to produce the resulting fire severity datasets. This approach demonstrates that fire severity datasets can be produced with relative ease and speed compared the standard approach in which one pre-fire and post-fire scene are judiciously identified and used to produce fire severity datasets. We also validate the GEE-derived fire severity metrics using field-based fire severity plots for 18 fires in the western US. These validations are compared to Landsat-based fire severity datasets produced using only one pre- and post-fire scene, which has been the standard approach in producing such datasets since their inception. Results indicate that the GEE-derived fire severity datasets show improved validation statistics compared to parallel versions in which only one pre-fire and post-fire scene are used. We provide code and a sample geospatial fire history layer to produce dNBR, RdNBR, and RBR for the 18 fires we evaluated. Although our approach requires that a geospatial fire history layer (i.e. fire perimeters) be produced independently and prior to applying our methods, we suggest our GEE methodology can reasonably be implemented on hundreds to thousands of fires, thereby increasing opportunities
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.
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.)
DEFF Research Database (Denmark)
Gravesen, Jens
2015-01-01
and found the MacAdam ellipses which are often interpreted as defining the metric tensor at their centres. An important question is whether it is possible to define colour coordinates such that the Euclidean distance in these coordinates correspond to human perception. Using cubic splines to represent......The space of colours is a fascinating space. It is a real vector space, but no matter what inner product you put on the space the resulting Euclidean distance does not correspond to human perception of difference between colours. In 1942 MacAdam performed the first experiments on colour matching...
Papapetrou energy-momentum tensor for Chern-Simons modified gravity
International Nuclear Information System (INIS)
Guarrera, David; Hariton, A. J.
2007-01-01
We construct a conserved, symmetric energy-momentum (pseudo-)tensor for Chern-Simons modified gravity, thus demonstrating that the theory is Lorentz invariant. The tensor is discussed in relation to other gravitational energy-momentum tensors and analyzed for the Schwarzschild, Reissner-Nordstrom, and Friedmann-Robertson-Walker solutions. To our knowledge this is the first confirmation that the Reissner-Nordstrom and Friedmann-Robertson-Walker metrics are solutions of the modified theory
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...
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.
Harris, Jeremy P; Chang-Halpenny, Christine N; Maxim, Peter G; Quon, Andrew; Graves, Edward E; Diehn, Maximilian; Loo, Billy W
2015-11-01
Many patients with lung tumors have tumors too large for stereotactic ablative radiotherapy and comorbidities precluding concurrent chemotherapy. We report the outcomes of 29 patients treated with hypofractionated radiotherapy (RT) to 60 to 66 Gy in 3-Gy fractions. We also report an exploratory analysis of the prognostic value of the pre- and mid-RT positron emission tomography-computed tomography. Modestly hypofractionated radiation therapy (HypoRT; 60-66 Gy in 3-Gy fractions) allows patients with locally advanced thoracic tumors and poor performance status to complete treatment within a shorter period without concurrent chemotherapy. We evaluated the outcomes and imaging prognostic factors of HypoRT. We retrospectively reviewed the data from all patients with primary and metastatic intrathoracic tumors treated with HypoRT from 2006 to 2012. We analyzed the survival and toxicity outcomes, including overall survival (OS), progression-free survival (PFS), local recurrence (LR), and distant metastasis. We also evaluated the following tumor metrics in an exploratory analysis: gross tumor volume (GTV), maximum standardized uptake value (SUVMax), and metabolic tumor volume using a threshold of ≥ 50% of the SUVMax (MTV50%) or the maximum gradient of fluorine-18 fluorodeoxyglucose uptake (MTVEdge). We assessed the association of these metrics and their changes from before to mid-RT using positron emission tomography-computed tomography (PET-CT) with OS and PFS. We identified 29 patients, all with pre-RT and 20 with mid-RT PET-CT scans. The median follow-up period was 15 months. The 2-year overall and non-small-cell lung cancer-only rate for OS, PFS, and LR, was 59% and 59%, 52% and 41%, and 27% and 32%, respectively. No grade ≥ 3 toxicities developed. The median decrease in GTV, SUVMax, and MTVEdge was 11%, 24%, and 18%, respectively. Inferior OS was associated with a larger pre-RT MTVEdge (P = .005) and pre-RT MTV50% (P = .007). Inferior PFS was associated with a
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
Structure of the Einstein tensor for class-1 embedded space time
Energy Technology Data Exchange (ETDEWEB)
Krause, J [Universidad Central de Venezuela, Caracas
1976-04-11
Continuing previous work, some features of the flat embedding theory of class-1 curved space-time are further discussed. In the two-metric formalism provided by the embedding approach the Gauss tensor obtains as the flat-covariant gradient of a fundamental vector potential. The Einstein tensor is then examined in terms of the Gauss tensor. It is proved that the Einstein tensor is divergence free in flat space-time, i.e. a true Lorentz-covariant conservation law for the Einstein tensor is shown to hold. The form of the Einstein tensor in flat space-time also appears as a canonical energy-momentum tensor of the vector potential. The corresponding Lagrangian density, however, does not provide us with a set of field equations for the fundamental vector potential; indeed, the Euler-Lagrange ''equations'' collapse to a useless identity, while the Lagrangian density has the form of a flat divergence.
Collineations of the curvature tensor in general relativity
Indian Academy of Sciences (India)
Curvature collineations for the curvature tensor, constructed from a fundamental Bianchi Type-V metric, are studied. We are concerned with a symmetry property of space-time which is called curvature collineation, and we briefly discuss the physical and kinematical properties of the models.
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.)
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.
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
Fast evaluation of nonlinear functionals of tensor product wavelet expansions
Schwab, C.; Stevenson, R.
2011-01-01
Abstract For a nonlinear functional f, and a function u from the span of a set of tensor product interpolets, it is shown how to compute the interpolant of f (u) from the span of this set of tensor product interpolets in linear complexity, assuming that the index set has a certain multiple tree
Gauge theories, duality relations and the tensor hierarchy
Bergshoeff, Eric A.; Hartong, Jelle; Hohm, Olaf; Huebscher, Mechthild; Ortin, Tomas; Hübscher, Mechthild
We compute the complete 3- and 4-dimensional tensor hierarchies, i.e. sets of p-form fields, with 1 We construct gauge-invariant actions that include all the fields in the tensor hierarchies. We elucidate the relation between the gauge transformations of the p-form fields in the action and those of
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
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.)
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.
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.
Wang, Yalin; Zhang, Jie; Gutman, Boris; Chan, Tony F; Becker, James T; Aizenstein, Howard J; Lopez, Oscar L; Tamburo, Robert J; Toga, Arthur W; Thompson, Paul M
2010-02-01
Here we developed a new method, called multivariate tensor-based surface morphometry (TBM), and applied it to study lateral ventricular surface differences associated with HIV/AIDS. Using concepts from differential geometry and the theory of differential forms, we created mathematical structures known as holomorphic one-forms, to obtain an efficient and accurate conformal parameterization of the lateral ventricular surfaces in the brain. The new meshing approach also provides a natural way to register anatomical surfaces across subjects, and improves on prior methods as it handles surfaces that branch and join at complex 3D junctions. To analyze anatomical differences, we computed new statistics from the Riemannian surface metrics-these retain multivariate information on local surface geometry. We applied this framework to analyze lateral ventricular surface morphometry in 3D MRI data from 11 subjects with HIV/AIDS and 8 healthy controls. Our method detected a 3D profile of surface abnormalities even in this small sample. Multivariate statistics on the local tensors gave better effect sizes for detecting group differences, relative to other TBM-based methods including analysis of the Jacobian determinant, the largest and smallest eigenvalues of the surface metric, and the pair of eigenvalues of the Jacobian matrix. The resulting analysis pipeline may improve the power of surface-based morphometry studies of the brain. Copyright (c) 2009 Elsevier Inc. All rights reserved.
Interiors of Vaidya's radiating metric: Gravitational collapse
International Nuclear Information System (INIS)
Fayos, F.; Jaen, X.; Llanta, E.; Senovilla, J.M.M.
1992-01-01
Using the Darmois junction conditions, we give the necessary and sufficient conditions for the matching of a general spherically symmetric metric to a Vaidya radiating solution. We present also these conditions in terms of the physical quantities of the corresponding energy-momentum tensors. The physical interpretation of the results and their possible applications are studied, and we also perform a detailed analysis of previous work on the subject by other authors
Directory of Open Access Journals (Sweden)
F. Joos
2013-03-01
Full Text Available The responses of carbon dioxide (CO2 and other climate variables to an emission pulse of CO2 into the atmosphere are often used to compute the Global Warming Potential (GWP and Global Temperature change Potential (GTP, to characterize the response timescales of Earth System models, and to build reduced-form models. In this carbon cycle-climate model intercomparison project, which spans the full model hierarchy, we quantify responses to emission pulses of different magnitudes injected under different conditions. The CO2 response shows the known rapid decline in the first few decades followed by a millennium-scale tail. For a 100 Gt-C emission pulse added to a constant CO2 concentration of 389 ppm, 25 ± 9% is still found in the atmosphere after 1000 yr; the ocean has absorbed 59 ± 12% and the land the remainder (16 ± 14%. The response in global mean surface air temperature is an increase by 0.20 ± 0.12 °C within the first twenty years; thereafter and until year 1000, temperature decreases only slightly, whereas ocean heat content and sea level continue to rise. Our best estimate for the Absolute Global Warming Potential, given by the time-integrated response in CO2 at year 100 multiplied by its radiative efficiency, is 92.5 × 10−15 yr W m−2 per kg-CO2. This value very likely (5 to 95% confidence lies within the range of (68 to 117 × 10−15 yr W m−2 per kg-CO2. Estimates for time-integrated response in CO2 published in the IPCC First, Second, and Fourth Assessment and our multi-model best estimate all agree within 15% during the first 100 yr. The integrated CO2 response, normalized by the pulse size, is lower for pre-industrial conditions, compared to present day, and lower for smaller pulses than larger pulses. In contrast, the response in temperature, sea level and ocean heat content is less sensitive to these choices. Although, choices in pulse size, background concentration, and model lead to uncertainties, the most important and
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.
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...
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
A Closed-Form Solution to Tensor Voting: Theory and Applications
Wu, Tai-Pang; Yeung, Sai-Kit; Jia, Jiaya; Tang, Chi-Keung; Medioni, Gerard
2016-01-01
We prove a closed-form solution to tensor voting (CFTV): given a point set in any dimensions, our closed-form solution provides an exact, continuous and efficient algorithm for computing a structure-aware tensor that simultaneously achieves salient structure detection and outlier attenuation. Using CFTV, we prove the convergence of tensor voting on a Markov random field (MRF), thus termed as MRFTV, where the structure-aware tensor at each input site reaches a stationary state upon convergence...
Danilǎ, Bogdan; Harko, Tiberiu; Lobo, Francisco S. N.; Mak, M. K.
2017-02-01
We consider the internal structure and the physical properties of specific classes of neutron, quark and Bose-Einstein condensate stars in the recently proposed hybrid metric-Palatini gravity theory, which is a combination of the metric and Palatini f (R ) formalisms. It turns out that the theory is very successful in accounting for the observed phenomenology, since it unifies local constraints at the Solar System level and the late-time cosmic acceleration, even if the scalar field is very light. In this paper, we derive the equilibrium equations for a spherically symmetric configuration (mass continuity and Tolman-Oppenheimer-Volkoff) in the framework of the scalar-tensor representation of the hybrid metric-Palatini theory, and we investigate their solutions numerically for different equations of state of neutron and quark matter, by adopting for the scalar field potential a Higgs-type form. It turns out that the scalar-tensor definition of the potential can be represented as an Clairaut differential equation, and provides an explicit form for f (R ) given by f (R )˜R +Λeff, where Λeff is an effective cosmological constant. Furthermore, stellar models, described by the stiff fluid, radiation-like, bag model and the Bose-Einstein condensate equations of state are explicitly constructed in both general relativity and hybrid metric-Palatini gravity, thus allowing an in-depth comparison between the predictions of these two gravitational theories. As a general result it turns out that for all the considered equations of state, hybrid gravity stars are more massive than their general relativistic counterparts. Furthermore, two classes of stellar models corresponding to two particular choices of the functional form of the scalar field (constant value, and logarithmic form, respectively) are also investigated. Interestingly enough, in the case of a constant scalar field the equation of state of the matter takes the form of the bag model equation of state describing
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...
The continuous determination of spacetime geometry by the Riemann curvature tensor
International Nuclear Information System (INIS)
Rendall, A.D.
1988-01-01
It is shown that generically the Riemann tensor of a Lorentz metric on an n-dimensional manifold (n ≥ 4) determines the metric up to a constant factor and hence determines the associated torsion-free connection uniquely. The resulting map from Riemann tensors to connections is continuous in the Whitney Csup(∞) topology but, at least for some manifolds, constant factors cannot be chosen so as to make the map from Riemann tensors to metrics continuous in that topology. The latter map is, however, continuous in the compact open Csup(∞) topology so that estimates of the metric and its derivatives on a compact set can be obtained from similar estimates on the curvature and its derivatives. (author)
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.
Stress-energy tensors for vector fields outside a static black hole
International Nuclear Information System (INIS)
Barrios, F.A.; Vaz, C.
1989-01-01
We obtain new, approximate stress-energy tensors to describe gauge fields in the neighborhood of a Schwarzschild black hole. We assume that the coefficient of ∇ 2 R in the trace anomaly is correctly given by ζ-function regularization. Our approximation differs from that of Page and of Brown and Ottewill and relies upon a new, improved ansatz for the form of the stress-energy tensor in the ultrastatic optical metric of the black hole. The Israel-Hartle-Hawking thermal tensor is constructed to be regular on the horizon and possess the correct asymptotic behavior. Our approximation of Unruh's tensor is likewise constructed to be regular on the future horizon and exhibit a luminosity which agrees with Page's numerically obtained value. Geometric expressions for the approximate tensors are given, and the approximate energy density of the thermal tensor on the horizon is compared with recent numerical estimates
Dolgov, Sergey; Khoromskij, Boris N.; Litvinenko, Alexander; Matthies, Hermann G.
2015-01-01
We apply the tensor train (TT) decomposition to construct the tensor product polynomial chaos expansion (PCE) of a random field, to solve the stochastic elliptic diffusion PDE with the stochastic Galerkin discretization, and to compute some
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…
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.
A bi-metric theory of gravitation
International Nuclear Information System (INIS)
Rosen, N.
1975-01-01
The bi-metric theory of gravitation proposed previously is simplified in that the auxiliary conditions are discarded, the two metric tensors being tied together only by means of the boundary conditions. Some of the properties of the field of a particle are investigated; there is no black hole, and it appears that no gravitational collapse can take place. Although the proposed theory and general relativity are at present observationally indistinguishable, some differences are pointed out which may some day be susceptible of observation. An alternative bi-metric theory is considered which gives for the precession of the perihelion 5/6 of the value given by general relativity; it seems less satisfactory than the present theory from the aesthetic point of view. (author)
Exact tensor network ansatz for strongly interacting systems
Zaletel, Michael P.
It appears that the tensor network ansatz, while not quite complete, is an efficient coordinate system for the tiny subset of a many-body Hilbert space which can be realized as a low energy state of a local Hamiltonian. However, we don't fully understand precisely which phases are captured by the tensor network ansatz, how to compute their physical observables (even numerically), or how to compute a tensor network representation for a ground state given a microscopic Hamiltonian. These questions are algorithmic in nature, but their resolution is intimately related to understanding the nature of quantum entanglement in many-body systems. For this reason it is useful to compute the tensor network representation of various `model' wavefunctions representative of different phases of matter; this allows us to understand how the entanglement properties of each phase are expressed in the tensor network ansatz, and can serve as test cases for algorithm development. Condensed matter physics has many illuminating model wavefunctions, such as Laughlin's celebrated wave function for the fractional quantum Hall effect, the Bardeen-Cooper-Schrieffer wave function for superconductivity, and Anderson's resonating valence bond ansatz for spin liquids. This thesis presents some results on exact tensor network representations of these model wavefunctions. In addition, a tensor network representation is given for the time evolution operator of a long-range one-dimensional Hamiltonian, which allows one to numerically simulate the time evolution of power-law interacting spin chains as well as two-dimensional strips and cylinders.
Atomic-batched tensor decomposed two-electron repulsion integrals
Schmitz, Gunnar; Madsen, Niels Kristian; Christiansen, Ove
2017-04-01
We present a new integral format for 4-index electron repulsion integrals, in which several strategies like the Resolution-of-the-Identity (RI) approximation and other more general tensor-decomposition techniques are combined with an atomic batching scheme. The 3-index RI integral tensor is divided into sub-tensors defined by atom pairs on which we perform an accelerated decomposition to the canonical product (CP) format. In a first step, the RI integrals are decomposed to a high-rank CP-like format by repeated singular value decompositions followed by a rank reduction, which uses a Tucker decomposition as an intermediate step to lower the prefactor of the algorithm. After decomposing the RI sub-tensors (within the Coulomb metric), they can be reassembled to the full decomposed tensor (RC approach) or the atomic batched format can be maintained (ABC approach). In the first case, the integrals are very similar to the well-known tensor hypercontraction integral format, which gained some attraction in recent years since it allows for quartic scaling implementations of MP2 and some coupled cluster methods. On the MP2 level, the RC and ABC approaches are compared concerning efficiency and storage requirements. Furthermore, the overall accuracy of this approach is assessed. Initial test calculations show a good accuracy and that it is not limited to small systems.
International Nuclear Information System (INIS)
Ma Zhihao; Chen Jingling
2011-01-01
In this work we study metrics of quantum states, which are natural generalizations of the usual trace metric and Bures metric. Some useful properties of the metrics are proved, such as the joint convexity and contractivity under quantum operations. Our result has a potential application in studying the geometry of quantum states as well as the entanglement detection.
Metrics of a 'mole hole' against the Lobachevsky space background
International Nuclear Information System (INIS)
Tentyukov, M.N.
1994-01-01
'Classical' mole hole are the Euclidean metrics consisting of two large space regions connected by a throat. They are the instanton solutions of the Einstein equations. It is shown that for existence of mole holes in the general relativity theory it is required the energy-momentum tensor breaking energetic conditions. 9 refs., 7 figs
Metric approach for sound propagation in nematic liquid crystals
Pereira, E.; Fumeron, S.; Moraes, F.
2013-02-01
In the eikonal approach, we describe sound propagation near topological defects of nematic liquid crystals as geodesics of a non-Euclidian manifold endowed with an effective metric tensor. The relation between the acoustics of the medium and this geometrical description is given by Fermat's principle. We calculate the ray trajectories and propose a diffraction experiment to retrieve information about the elastic constants.
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.
The Twist Tensor Nuclear Norm for Video Completion.
Hu, Wenrui; Tao, Dacheng; Zhang, Wensheng; Xie, Yuan; Yang, Yehui
2017-12-01
In this paper, we propose a new low-rank tensor model based on the circulant algebra, namely, twist tensor nuclear norm (t-TNN). The twist tensor denotes a three-way tensor representation to laterally store 2-D data slices in order. On one hand, t-TNN convexly relaxes the tensor multirank of the twist tensor in the Fourier domain, which allows an efficient computation using fast Fourier transform. On the other, t-TNN is equal to the nuclear norm of block circulant matricization of the twist tensor in the original domain, which extends the traditional matrix nuclear norm in a block circulant way. We test the t-TNN model on a video completion application that aims to fill missing values and the experiment results validate its effectiveness, especially when dealing with video recorded by a nonstationary panning camera. The block circulant matricization of the twist tensor can be transformed into a circulant block representation with nuclear norm invariance. This representation, after transformation, exploits the horizontal translation relationship between the frames in a video, and endows the t-TNN model with a more powerful ability to reconstruct panning videos than the existing state-of-the-art low-rank models.
Gaba, Yaé Ulrich
2017-01-01
In this paper, we discuss recent results about generalized metric spaces and fixed point theory. We introduce the notion of $\\eta$-cone metric spaces, give some topological properties and prove some fixed point theorems for contractive type maps on these spaces. In particular we show that theses $\\eta$-cone metric spaces are natural generalizations of both cone metric spaces and metric type spaces.
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...
On the geometry of mixed states and the Fisher information tensor
Energy Technology Data Exchange (ETDEWEB)
Contreras, I., E-mail: icontrer@illinois.edu [Department of Mathematics, University of Illinois at Urbana-Champaign, 1409 W. Green Street, Urbana, Illinois 61801 (United States); Ercolessi, E., E-mail: ercolessi@bo.infn.it [Dipartimento di Fisica e Astronomia, Università di Bologna and INFN, V. Irnerio 46, 40127 Bologna (Italy); Schiavina, M., E-mail: michele.schiavina@math.uzh.ch [Institut für Mathematik, Winterthurerstrasse 190, 8057 Zürich (Switzerland)
2016-06-15
In this paper, we will review the co-adjoint orbit formulation of finite dimensional quantum mechanics, and in this framework, we will interpret the notion of quantum Fisher information index (and metric). Following previous work of part of the authors, who introduced the definition of Fisher information tensor, we will show how its antisymmetric part is the pullback of the natural Kostant–Kirillov–Souriau symplectic form along some natural diffeomorphism. In order to do this, we will need to understand the symmetric logarithmic derivative as a proper 1-form, settling the issues about its very definition and explicit computation. Moreover, the fibration of co-adjoint orbits, seen as spaces of mixed states, is also discussed.
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
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.
Path integral in area tensor Regge calculus and complex connections
International Nuclear Information System (INIS)
Khatsymovsky, V.M.
2006-01-01
Euclidean quantum measure in Regge calculus with independent area tensors is considered using example of the Regge manifold of a simple structure. We go over to integrations along certain contours in the hyperplane of complex connection variables. Discrete connection and curvature on classical solutions of the equations of motion are not, strictly speaking, genuine connection and curvature, but more general quantities and, therefore, these do not appear as arguments of a function to be averaged, but are the integration (dummy) variables. We argue that upon integrating out the latter the resulting measure can be well-defined on physical hypersurface (for the area tensors corresponding to certain edge vectors, i.e. to certain metric) as positive and having exponential cutoff at large areas on condition that we confine ourselves to configurations which do not pass through degenerate metrics
Cosmological implications of modified gravity induced by quantum metric fluctuations
Energy Technology Data Exchange (ETDEWEB)
Liu, Xing [Sun Yat-Sen University, School of Physics, Guangzhou (China); Sun Yat-Sen University, Yat Sen School, Guangzhou (China); Harko, Tiberiu [Babes-Bolyai University, Department of Physics, Cluj-Napoca (Romania); University College London, Department of Mathematics, London (United Kingdom); Liang, Shi-Dong [Sun Yat-Sen University, School of Physics, Guangzhou (China); Sun Yat-Sen University, State Key Laboratory of Optoelectronic Material and Technology, Guangdong Province Key Laboratory of Display Material and Technology, School of Physics, Guangzhou (China)
2016-08-15
We investigate the cosmological implications of modified gravities induced by the quantum fluctuations of the gravitational metric. If the metric can be decomposed as the sum of the classical and of a fluctuating part, of quantum origin, then the corresponding Einstein quantum gravity generates at the classical level modified gravity models with a non-minimal coupling between geometry and matter. As a first step in our study, after assuming that the expectation value of the quantum correction can be generally expressed in terms of an arbitrary second order tensor constructed from the metric and from the thermodynamic quantities characterizing the matter content of the Universe, we derive the (classical) gravitational field equations in their general form. We analyze in detail the cosmological models obtained by assuming that the quantum correction tensor is given by the coupling of a scalar field and of a scalar function to the metric tensor, and by a term proportional to the matter energy-momentum tensor. For each considered model we obtain the gravitational field equations, and the generalized Friedmann equations for the case of a flat homogeneous and isotropic geometry. In some of these models the divergence of the matter energy-momentum tensor is non-zero, indicating a process of matter creation, which corresponds to an irreversible energy flow from the gravitational field to the matter fluid, and which is direct consequence of the non-minimal curvature-matter coupling. The cosmological evolution equations of these modified gravity models induced by the quantum fluctuations of the metric are investigated in detail by using both analytical and numerical methods, and it is shown that a large variety of cosmological models can be constructed, which, depending on the numerical values of the model parameters, can exhibit both accelerating and decelerating behaviors. (orig.)
TensorFlow: A system for large-scale machine learning
Abadi, Martín; Barham, Paul; Chen, Jianmin; Chen, Zhifeng; Davis, Andy; Dean, Jeffrey; Devin, Matthieu; Ghemawat, Sanjay; Irving, Geoffrey; Isard, Michael; Kudlur, Manjunath; Levenberg, Josh; Monga, Rajat; Moore, Sherry; Murray, Derek G.
2016-01-01
TensorFlow is a machine learning system that operates at large scale and in heterogeneous environments. TensorFlow uses dataflow graphs to represent computation, shared state, and the operations that mutate that state. It maps the nodes of a dataflow graph across many machines in a cluster, and within a machine across multiple computational devices, including multicore CPUs, general-purpose GPUs, and custom designed ASICs known as Tensor Processing Units (TPUs). This architecture gives flexib...
Extracting the diffusion tensor from molecular dynamics simulation with Milestoning
International Nuclear Information System (INIS)
Mugnai, Mauro L.; Elber, Ron
2015-01-01
We propose an algorithm to extract the diffusion tensor from Molecular Dynamics simulations with Milestoning. A Kramers-Moyal expansion of a discrete master equation, which is the Markovian limit of the Milestoning theory, determines the diffusion tensor. To test the algorithm, we analyze overdamped Langevin trajectories and recover a multidimensional Fokker-Planck equation. The recovery process determines the flux through a mesh and estimates local kinetic parameters. Rate coefficients are converted to the derivatives of the potential of mean force and to coordinate dependent diffusion tensor. We illustrate the computation on simple models and on an atomically detailed system—the diffusion along the backbone torsions of a solvated alanine dipeptide
A Nonlinear GMRES Optimization Algorithm for Canonical Tensor Decomposition
De Sterck, Hans
2011-01-01
A new algorithm is presented for computing a canonical rank-R tensor approximation that has minimal distance to a given tensor in the Frobenius norm, where the canonical rank-R tensor consists of the sum of R rank-one components. Each iteration of the method consists of three steps. In the first step, a tentative new iterate is generated by a stand-alone one-step process, for which we use alternating least squares (ALS). In the second step, an accelerated iterate is generated by a nonlinear g...
Enhancing Authentication Models Characteristic Metrics via ...
African Journals Online (AJOL)
In this work, we derive the universal characteristic metrics set for authentication models based on security, usability and design issues. We then compute the probability of the occurrence of each characteristic metrics in some single factor and multifactor authentication models in order to determine the effectiveness of these ...
Software Power Metric Model: An Implementation | Akwukwuma ...
African Journals Online (AJOL)
... and the execution time (TIME) in each case was recorded. We then obtain the application functions point count. Our result shows that the proposed metric is computable, consistent in its use of unit, and is programming language independent. Keywords: Software attributes, Software power, measurement, Software metric, ...
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.
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...
Compact stars in vector-tensor-Horndeski theory of gravity
Energy Technology Data Exchange (ETDEWEB)
Momeni, Davood; Myrzakulov, Kairat; Myrzakulov, Ratbay [Eurasian National University, Department of General and Theoretical Physics, Eurasian International Center for Theoretical Physics, Astana (Kazakhstan); Faizal, Mir [University of British Columbia-Okanagan, Irving K. Barber School of Arts and Sciences, Kelowna, BC (Canada); University of Lethbridge, Department of Physics and Astronomy, Lethbridge, AB (Canada)
2017-01-15
In this paper, we will analyze a theory of modified gravity, in which the field content of general relativity will be increased to include a vector field. We will use the Horndeski formalism to non-minimally couple this vector field to the metric. As we will be using the Horndeski formalism, this theory will not contain Ostrogradsky ghost degree of freedom. We will analyze compact stars using this vector-tensor-Horndeski theory. (orig.)
Scalar-tensor theory of fourth-order gravity
International Nuclear Information System (INIS)
Accioly, A.J.; Goncalves, A.T.
1986-04-01
A scalar-tensor theory of fourth-order gravity is considered. Some cosmological consequences, due to the presence of the scalar field, as well as of metric derivatives higher than second order, are analysed. In particular, upperbpunds are obtained for the coupling constant α and for the scale factor of the universe, respectively. The discussion is restricted to Robertson-Walker universes. (Author) [pt
Li, Xutao; Ng, Michael K; Cong, Gao; Ye, Yunming; Wu, Qingyao
2017-08-01
With the advancement of data acquisition techniques, tensor (multidimensional data) objects are increasingly accumulated and generated, for example, multichannel electroencephalographies, multiview images, and videos. In these applications, the tensor objects are usually nonnegative, since the physical signals are recorded. As the dimensionality of tensor objects is often very high, a dimension reduction technique becomes an important research topic of tensor data. From the perspective of geometry, high-dimensional objects often reside in a low-dimensional submanifold of the ambient space. In this paper, we propose a new approach to perform the dimension reduction for nonnegative tensor objects. Our idea is to use nonnegative Tucker decomposition (NTD) to obtain a set of core tensors of smaller sizes by finding a common set of projection matrices for tensor objects. To preserve geometric information in tensor data, we employ a manifold regularization term for the core tensors constructed in the Tucker decomposition. An algorithm called manifold regularization NTD (MR-NTD) is developed to solve the common projection matrices and core tensors in an alternating least squares manner. The convergence of the proposed algorithm is shown, and the computational complexity of the proposed method scales linearly with respect to the number of tensor objects and the size of the tensor objects, respectively. These theoretical results show that the proposed algorithm can be efficient. Extensive experimental results have been provided to further demonstrate the effectiveness and efficiency of the proposed MR-NTD algorithm.
Nonlinear metric perturbation enhancement of primordial gravitational waves.
Bastero-Gil, M; Macias-Pérez, J; Santos, D
2010-08-20
We present the evolution of the full set of Einstein equations during preheating after inflation. We study a generic supersymmetric model of hybrid inflation, integrating fields and metric fluctuations in a 3-dimensional lattice. We take initial conditions consistent with Einstein's constraint equations. The induced preheating of the metric fluctuations is not large enough to backreact onto the fields, but preheating of the scalar modes does affect the evolution of vector and tensor modes. In particular, they do enhance the induced stochastic background of gravitational waves during preheating, giving an energy density in general an order of magnitude larger than that obtained by evolving the tensor fluctuations in an homogeneous background metric. This enhancement can improve the expectations for detection by planned gravitational wave observatories.
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...
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...
A single action for the scalar-tensor theory of gravity
International Nuclear Information System (INIS)
Roxburgh, I.W.
1977-01-01
The standard form of the scalar-tensor theory gives eleven equations for eleven unknowns, the metric tensor Gsub(ij) and the scalar field phi. Here the scalar field is eliminated to produce a theory that has just ten equations for ten unknown gsub(ij). The resulting expression for the action of fields and matter is contained completely in a single expression. (author)
Structural connectivity via the tensor-based morphometry
Kim, S.; Chung, M.; Hanson, J.; Avants, B.; Gee, J.; Davidson, R.; Pollak, S.
2011-01-01
The tensor-based morphometry (TBM) has been widely used in characterizing tissue volume difference between populations at voxel level. We present a novel computational framework for investigating the white matter connectivity using TBM. Unlike other diffusion tensor imaging (DTI) based white matter connectivity studies, we do not use DTI but only T1-weighted magnetic resonance imaging (MRI). To construct brain network graphs, we have developed a new data-driven approach called the ε-neighbor ...
Optimization via separated representations and the canonical tensor decomposition
Reynolds, Matthew J.; Beylkin, Gregory; Doostan, Alireza
2017-11-01
We introduce a new, quadratically convergent algorithm for finding maximum absolute value entries of tensors represented in the canonical format. The computational complexity of the algorithm is linear in the dimension of the tensor. We show how to use this algorithm to find global maxima of non-convex multivariate functions in separated form. We demonstrate the performance of the new algorithms on several examples.
Optimization via Separated Representations and the Canonical Tensor Decomposition
Reynolds, Matthew J; Beylkin, Gregory; Doostan, Alireza
2016-01-01
We introduce a new, quadratically convergent algorithm for finding maximum absolute value entries of tensors represented in the canonical format. The computational complexity of the algorithm is linear in the dimension of the tensor. We show how to use this algorithm to find global maxima of non-convex multivariate functions in separated form. We demonstrate the performance of the new algorithms on several examples.
Computational tools for Breakthrough Propulsion Physics: State of the art and future prospects
International Nuclear Information System (INIS)
Maccone, Claudio
2000-01-01
To address problems in Breakthrough Propulsion Physics (BPP) one needs sheer computing capabilities. This is because General Relativity and Quantum Field Theory are so mathematically sophisticated that the amount of analytical calculations is prohibitive and one can hardly do all of them by hand. In this paper we make a comparative review of the main tensor calculus capabilities of the three most advanced and commercially available 'symbolic manipulator' codes: Macsyma, Maple V and Mathematica. We also point out that currently one faces such a variety of different conventions in tensor calculus that it is difficult or impossible to compare results obtained by different scholars in General Relativity and Quantum Field Theory. Mathematical physicists, experimental physicists and engineers have each their own way of customizing tensors, especially by using the different metric signatures, different metric determinant signs, different definitions of the basic Riemann and Ricci tensors, and by adopting different systems of physical units. This chaos greatly hampers progress toward the chief NASA BPP goal: the design of the NASA Warp Drive. It is thus concluded that NASA should put order by establishing international standards in symbolic tensor calculus and enforcing anyone working in BPP to adopt these NASA BPP Standards
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.
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
A solution for tensor reduction of one-loop N-point functions with N{>=}6
Energy Technology Data Exchange (ETDEWEB)
Fleischer, J. [Bielefeld Univ. (Germany). Fakultaet fuer Physik; Riemann, T. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany)
2011-11-15
Collisions at the LHC produce many-particle final states, and for precise predictions the one-loop N-point corrections are needed. We study here the tensor reduction for Feynman integrals with N{>=}6. A general, recursive solution by Binoth et al. expresses N-point Feynman integrals of rank R in terms of (N-1)-point Feynman integrals of rank (R-1) (for N{>=}6). We show that the coefficients can be obtained analytically from suitable representations of the metric tensor. Contractions of the tensor integrals with external momenta can be efficiently expressed as well. We consider our approach particularly well suited for automatization. (orig.)
Cylindrically symmetric solutions of a scalar--tensor theory of gravitation
International Nuclear Information System (INIS)
Singh, T.
1975-01-01
The cylindrically symmetric solutions for the Einstein--Rosen metric of a scalar--tensor theory proposed by Dunn have been obtained. A method has been given by which one can obtain, under certain conditions, solutions of this scalar--tensor theory from known solutions of the empty space field equations of Einstein's theory of gravitation. It is also found that one of the solutions of the scalar--tensor theory is nonsingular in the sense of Bonnor. Further some special solutions are obtained which reduce to the well-known solution of Levi-Civita and a time dependent solution obtained by Misra and Radhakrishna
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.
Tensor-Based Dictionary Learning for Spectral CT Reconstruction.
Zhang, Yanbo; Mou, Xuanqin; Wang, Ge; Yu, Hengyong
2017-01-01
Spectral computed tomography (CT) produces an energy-discriminative attenuation map of an object, extending a conventional image volume with a spectral dimension. In spectral CT, an image can be sparsely represented in each of multiple energy channels, and are highly correlated among energy channels. According to this characteristics, we propose a tensor-based dictionary learning method for spectral CT reconstruction. In our method, tensor patches are extracted from an image tensor, which is reconstructed using the filtered backprojection (FBP), to form a training dataset. With the Candecomp/Parafac decomposition, a tensor-based dictionary is trained, in which each atom is a rank-one tensor. Then, the trained dictionary is used to sparsely represent image tensor patches during an iterative reconstruction process, and the alternating minimization scheme is adapted for optimization. The effectiveness of our proposed method is validated with both numerically simulated and real preclinical mouse datasets. The results demonstrate that the proposed tensor-based method generally produces superior image quality, and leads to more accurate material decomposition than the currently popular popular methods.
Tensor-based Dictionary Learning for Spectral CT Reconstruction
Zhang, Yanbo; Wang, Ge
2016-01-01
Spectral computed tomography (CT) produces an energy-discriminative attenuation map of an object, extending a conventional image volume with a spectral dimension. In spectral CT, an image can be sparsely represented in each of multiple energy channels, and are highly correlated among energy channels. According to this characteristics, we propose a tensor-based dictionary learning method for spectral CT reconstruction. In our method, tensor patches are extracted from an image tensor, which is reconstructed using the filtered backprojection (FBP), to form a training dataset. With the Candecomp/Parafac decomposition, a tensor-based dictionary is trained, in which each atom is a rank-one tensor. Then, the trained dictionary is used to sparsely represent image tensor patches during an iterative reconstruction process, and the alternating minimization scheme is adapted for optimization. The effectiveness of our proposed method is validated with both numerically simulated and real preclinical mouse datasets. The results demonstrate that the proposed tensor-based method generally produces superior image quality, and leads to more accurate material decomposition than the currently popular popular methods. PMID:27541628
Analytical effective tensor for flow-through composites
Sviercoski, Rosangela De Fatima [Los Alamos, NM
2012-06-19
A machine, method and computer-usable medium for modeling an average flow of a substance through a composite material. Such a modeling includes an analytical calculation of an effective tensor K.sup.a suitable for use with a variety of media. The analytical calculation corresponds to an approximation to the tensor K, and follows by first computing the diagonal values, and then identifying symmetries of the heterogeneity distribution. Additional calculations include determining the center of mass of the heterogeneous cell and its angle according to a defined Cartesian system, and utilizing this angle into a rotation formula to compute the off-diagonal values and determining its sign.
Gopikrishna Deshpande; Gopikrishna Deshpande; Gopikrishna Deshpande; D. Rangaprakash; D. Rangaprakash; Luke Oeding; Andrzej Cichocki; Andrzej Cichocki; Andrzej Cichocki; Xiaoping P. Hu
2017-01-01
A Brain-Computer Interface (BCI) is a setup permitting the control of external devices by decoding brain activity. Electroencephalography (EEG) has been extensively used for decoding brain activity since it is non-invasive, cheap, portable, and has high temporal resolution to allow real-time operation. Due to its poor spatial specificity, BCIs based on EEG can require extensive training and multiple trials to decode brain activity (consequently slowing down the operation of the BCI). On the o...
Beyond Lovelock gravity: Higher derivative metric theories
Crisostomi, M.; Noui, K.; Charmousis, C.; Langlois, D.
2018-02-01
We consider theories describing the dynamics of a four-dimensional metric, whose Lagrangian is diffeomorphism invariant and depends at most on second derivatives of the metric. Imposing degeneracy conditions we find a set of Lagrangians that, apart form the Einstein-Hilbert one, are either trivial or contain more than 2 degrees of freedom. Among the partially degenerate theories, we recover Chern-Simons gravity, endowed with constraints whose structure suggests the presence of instabilities. Then, we enlarge the class of parity violating theories of gravity by introducing new "chiral scalar-tensor theories." Although they all raise the same concern as Chern-Simons gravity, they can nevertheless make sense as low energy effective field theories or, by restricting them to the unitary gauge (where the scalar field is uniform), as Lorentz breaking theories with a parity violating sector.
Euclidean supersymmetric solutions with the self-dual Weyl tensor
Directory of Open Access Journals (Sweden)
Masato Nozawa
2017-07-01
Full Text Available We explore the Euclidean supersymmetric solutions admitting the self-dual gauge field in the framework of N=2 minimal gauged supergravity in four dimensions. According to the classification scheme utilizing the spinorial geometry or the bilinears of Killing spinors, the general solution preserves one quarter of supersymmetry and is described by the Przanowski–Tod class with the self-dual Weyl tensor. We demonstrate that there exists an additional Killing spinor, provided the Przanowski–Tod metric admits a Killing vector that commutes with the principal one. The proof proceeds by recasting the metric into another Przanowski–Tod form. This formalism enables us to show that the self-dual Reissner–Nordström–Taub–NUT–AdS metric possesses a second Killing spinor, which has been missed over many years. We also address the supersymmetry when the Przanowski–Tod space is conformal to each of the self-dual ambi-toric Kähler metrics. It turns out that three classes of solutions are all reduced to the self-dual Carter family, by virtue of the nondegenerate Killing–Yano tensor.
Distance Adaptive Tensor Discriminative Geometry Preserving Projection for Face Recognition
Directory of Open Access Journals (Sweden)
Ziqiang Wang
2012-09-01
Full Text Available There is a growing interest in dimensionality reduction techniques for face recognition, however, the traditional dimensionality reduction algorithms often transform the input face image data into vectors before embedding. Such vectorization often ignores the underlying data structure and leads to higher computational complexity. To effectively cope with these problems, a novel dimensionality reduction algorithm termed distance adaptive tensor discriminative geometry preserving projection (DATDGPP is proposed in this paper. The key idea of DATDGPP is as follows: first, the face image data are directly encoded in high-order tensor structure so that the relationships among the face image data can be preserved; second, the data-adaptive tensor distance is adopted to model the correlation among different coordinates of tensor data; third, the transformation matrix which can preserve discrimination and local geometry information is obtained by an iteration algorithm. Experimental results on three face databases show that the proposed algorithm outperforms other representative dimensionality reduction algorithms.
Ryu-Takayanagi formula for symmetric random tensor networks
Chirco, Goffredo; Oriti, Daniele; Zhang, Mingyi
2018-06-01
We consider the special case of random tensor networks (RTNs) endowed with gauge symmetry constraints on each tensor. We compute the Rényi entropy for such states and recover the Ryu-Takayanagi (RT) formula in the large-bond regime. The result provides first of all an interesting new extension of the existing derivations of the RT formula for RTNs. Moreover, this extension of the RTN formalism brings it in direct relation with (tensorial) group field theories (and spin networks), and thus provides new tools for realizing the tensor network/geometry duality in the context of background-independent quantum gravity, and for importing quantum gravity tools into tensor network research.
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...
Two new eigenvalue localization sets for tensors and theirs applications
Directory of Open Access Journals (Sweden)
Zhao Jianxing
2017-10-01
Full Text Available A new eigenvalue localization set for tensors is given and proved to be tighter than those presented by Qi (J. Symbolic Comput., 2005, 40, 1302-1324 and Li et al. (Numer. Linear Algebra Appl., 2014, 21, 39-50. As an application, a weaker checkable sufficient condition for the positive (semi-definiteness of an even-order real symmetric tensor is obtained. Meanwhile, an S-type E-eigenvalue localization set for tensors is given and proved to be tighter than that presented by Wang et al. (Discrete Cont. Dyn.-B, 2017, 22(1, 187-198. As an application, an S-type upper bound for the Z-spectral radius of weakly symmetric nonnegative tensors is obtained. Finally, numerical examples are given to verify the theoretical results.
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.
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.
International Nuclear Information System (INIS)
Antoci, S.; Mihich, L.
1997-01-01
Given the present status of the problem of the electromagnetic energy tensor in matter, there is perhaps use in recalling a forgotten argument given in 1923 by W. Gordon. Let us consider a material medium which is homogeneous and isotropic when observed in its rest frame. For such a medium, Gordon's argument allows to reduce the above-mentioned problem to an analogous one, defined in a general relativistic vacuum. For the latter problem the form of the Lagrangian is known already, hence the determination of the energy tensor is a straightforward matter. One just performs the Hamiltonian derivative of the Lagrangian chosen in this way with respect to the true metric g ik . Abraham's tensor is thus selected as the electromagnetic energy tensor for a medium which is homogeneous and isotropic in its rest frame
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||.
Regional Sustainability: The San Luis Basin Metrics Project
There are a number of established, scientifically supported metrics of sustainability. Many of the metrics are data intensive and require extensive effort to collect data and compute. Moreover, individual metrics may not capture all aspects of a system that are relevant to sust...
Vlasova, Roza; Yalin Wang; Dirks, Holly; Dean, Douglas; O'Muircheartaigh, Jonathan; Gonzalez, Sara; Binh Kien Nguyen; Nelson, Marvin D; Deoni, Sean; Lepore, Natasha
2017-07-01
In our previous study1, we suggested that the difference between tensor-based metrics in the anterior part of the right putamen between 21 and 18 months age groups associated with speech development during this ages. Here we used a correlational analysis between verbal scores and determinant of the Jacobian matrix to confirm our hypothesis. Significant correlations in anterior part of the right putamen between verbal scores and surface metric were revealed in the 18 and 21 age groups.
Metric diffusion along foliations
Walczak, Szymon M
2017-01-01
Up-to-date research in metric diffusion along compact foliations is presented in this book. Beginning with fundamentals from the optimal transportation theory and the theory of foliations; this book moves on to cover Wasserstein distance, Kantorovich Duality Theorem, and the metrization of the weak topology by the Wasserstein distance. Metric diffusion is defined, the topology of the metric space is studied and the limits of diffused metrics along compact foliations are discussed. Essentials on foliations, holonomy, heat diffusion, and compact foliations are detailed and vital technical lemmas are proved to aide understanding. Graduate students and researchers in geometry, topology and dynamics of foliations and laminations will find this supplement useful as it presents facts about the metric diffusion along non-compact foliation and provides a full description of the limit for metrics diffused along foliation with at least one compact leaf on the two dimensions.
Chistyakov, Vyacheslav
2015-01-01
Aimed toward researchers and graduate students familiar with elements of functional analysis, linear algebra, and general topology; this book contains a general study of modulars, modular spaces, and metric modular spaces. Modulars may be thought of as generalized velocity fields and serve two important purposes: generate metric spaces in a unified manner and provide a weaker convergence, the modular convergence, whose topology is non-metrizable in general. Metric modular spaces are extensions of metric spaces, metric linear spaces, and classical modular linear spaces. The topics covered include the classification of modulars, metrizability of modular spaces, modular transforms and duality between modular spaces, metric and modular topologies. Applications illustrated in this book include: the description of superposition operators acting in modular spaces, the existence of regular selections of set-valued mappings, new interpretations of spaces of Lipschitzian and absolutely continuous mappings, the existe...
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...
Prognostic Performance Metrics
National Aeronautics and Space Administration — This chapter presents several performance metrics for offline evaluation of prognostics algorithms. A brief overview of different methods employed for performance...
Directory of Open Access Journals (Sweden)
Kihong Kim
2018-02-01
Full Text Available Various kinds of metrics used for the quantitative evaluation of scholarly journals are reviewed. The impact factor and related metrics including the immediacy index and the aggregate impact factor, which are provided by the Journal Citation Reports, are explained in detail. The Eigenfactor score and the article influence score are also reviewed. In addition, journal metrics such as CiteScore, Source Normalized Impact per Paper, SCImago Journal Rank, h-index, and g-index are discussed. Limitations and problems that these metrics have are pointed out. We should be cautious to rely on those quantitative measures too much when we evaluate journals or researchers.
Directory of Open Access Journals (Sweden)
Gopikrishna Deshpande
2017-06-01
Full Text Available A Brain-Computer Interface (BCI is a setup permitting the control of external devices by decoding brain activity. Electroencephalography (EEG has been extensively used for decoding brain activity since it is non-invasive, cheap, portable, and has high temporal resolution to allow real-time operation. Due to its poor spatial specificity, BCIs based on EEG can require extensive training and multiple trials to decode brain activity (consequently slowing down the operation of the BCI. On the other hand, BCIs based on functional magnetic resonance imaging (fMRI are more accurate owing to its superior spatial resolution and sensitivity to underlying neuronal processes which are functionally localized. However, due to its relatively low temporal resolution, high cost, and lack of portability, fMRI is unlikely to be used for routine BCI. We propose a new approach for transferring the capabilities of fMRI to EEG, which includes simultaneous EEG/fMRI sessions for finding a mapping from EEG to fMRI, followed by a BCI run from only EEG data, but driven by fMRI-like features obtained from the mapping identified previously. Our novel data-driven method is likely to discover latent linkages between electrical and hemodynamic signatures of neural activity hitherto unexplored using model-driven methods, and is likely to serve as a template for a novel multi-modal strategy wherein cross-modal EEG-fMRI interactions are exploited for the operation of a unimodal EEG system, leading to a new generation of EEG-based BCIs.
Deshpande, Gopikrishna; Rangaprakash, D; Oeding, Luke; Cichocki, Andrzej; Hu, Xiaoping P
2017-01-01
A Brain-Computer Interface (BCI) is a setup permitting the control of external devices by decoding brain activity. Electroencephalography (EEG) has been extensively used for decoding brain activity since it is non-invasive, cheap, portable, and has high temporal resolution to allow real-time operation. Due to its poor spatial specificity, BCIs based on EEG can require extensive training and multiple trials to decode brain activity (consequently slowing down the operation of the BCI). On the other hand, BCIs based on functional magnetic resonance imaging (fMRI) are more accurate owing to its superior spatial resolution and sensitivity to underlying neuronal processes which are functionally localized. However, due to its relatively low temporal resolution, high cost, and lack of portability, fMRI is unlikely to be used for routine BCI. We propose a new approach for transferring the capabilities of fMRI to EEG, which includes simultaneous EEG/fMRI sessions for finding a mapping from EEG to fMRI, followed by a BCI run from only EEG data, but driven by fMRI-like features obtained from the mapping identified previously. Our novel data-driven method is likely to discover latent linkages between electrical and hemodynamic signatures of neural activity hitherto unexplored using model-driven methods, and is likely to serve as a template for a novel multi-modal strategy wherein cross-modal EEG-fMRI interactions are exploited for the operation of a unimodal EEG system, leading to a new generation of EEG-based BCIs.
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.
Cyganek, Boguslaw; Smolka, Bogdan
2015-02-01
In this paper a system for real-time recognition of objects in multidimensional video signals is proposed. Object recognition is done by pattern projection into the tensor subspaces obtained from the factorization of the signal tensors representing the input signal. However, instead of taking only the intensity signal the novelty of this paper is first to build the Extended Structural Tensor representation from the intensity signal that conveys information on signal intensities, as well as on higher-order statistics of the input signals. This way the higher-order input pattern tensors are built from the training samples. Then, the tensor subspaces are built based on the Higher-Order Singular Value Decomposition of the prototype pattern tensors. Finally, recognition relies on measurements of the distance of a test pattern projected into the tensor subspaces obtained from the training tensors. Due to high-dimensionality of the input data, tensor based methods require high memory and computational resources. However, recent achievements in the technology of the multi-core microprocessors and graphic cards allows real-time operation of the multidimensional methods as is shown and analyzed in this paper based on real examples of object detection in digital images.
Using Activity Metrics for DEVS Simulation Profiling
Directory of Open Access Journals (Sweden)
Muzy A.
2014-01-01
Full Text Available Activity metrics can be used to profile DEVS models before and during the simulation. It is critical to get good activity metrics of models before and during their simulation. Having a means to compute a-priori activity of components (analytic activity may be worth when simulating a model (or parts of it for the first time. After, during the simulation, analytic activity can be corrected using dynamic one. In this paper, we introduce McCabe cyclomatic complexity metric (MCA to compute analytic activity. Both static and simulation activity metrics have been implemented through a plug-in of the DEVSimPy (DEVS Simulator in Python language environment and applied to DEVS models.
Evaluating and Estimating the WCET Criticality Metric
DEFF Research Database (Denmark)
Jordan, Alexander
2014-01-01
a programmer (or compiler) from targeting optimizations the right way. A possible resort is to use a metric that targets WCET and which can be efficiently computed for all code parts of a program. Similar to dynamic profiling techniques, which execute code with input that is typically expected...... for the application, based on WCET analysis we can indicate how critical a code fragment is, in relation to the worst-case bound. Computing such a metric on top of static analysis, incurs a certain overhead though, which increases with the complexity of the underlying WCET analysis. We present our approach...... to estimate the Criticality metric, by relaxing the precision of WCET analysis. Through this, we can reduce analysis time by orders of magnitude, while only introducing minor error. To evaluate our estimation approach and share our garnered experience using the metric, we evaluate real-time programs, which...
A Comment on the geometry of some scalar-tensor theories
Energy Technology Data Exchange (ETDEWEB)
Lindstrom, U
1986-08-01
We show that the scalar field in scalar-tensor theories such as the Jordan-Brans-Dicke theory has an interpretation as a potential for the torsion in a Riemannian manifold. The relation is similar to that of the metric to the connection.
Piecewise linear manifolds: Einstein metrics and Ricci flows
International Nuclear Information System (INIS)
Schrader, Robert
2016-01-01
This article provides an attempt to extend concepts from the theory of Riemannian manifolds to piecewise linear (p.l.) spaces. In particular we propose an analogue of the Ricci tensor, which we give the name of an Einstein vector field . On a given set of p.l. spaces we define and discuss (normalized) Einstein flows. p.l. Einstein metrics are defined and examples are provided. Criteria for flows to approach Einstein metrics are formulated. Second variations of the total scalar curvature at a specific Einstein space are calculated. (paper)
Tensor-GMRES method for large sparse systems of nonlinear equations
Feng, Dan; Pulliam, Thomas H.
1994-01-01
This paper introduces a tensor-Krylov method, the tensor-GMRES method, for large sparse systems of nonlinear equations. This method is a coupling of tensor model formation and solution techniques for nonlinear equations with Krylov subspace projection techniques for unsymmetric systems of linear equations. Traditional tensor methods for nonlinear equations are based on a quadratic model of the nonlinear function, a standard linear model augmented by a simple second order term. These methods are shown to be significantly more efficient than standard methods both on nonsingular problems and on problems where the Jacobian matrix at the solution is singular. A major disadvantage of the traditional tensor methods is that the solution of the tensor model requires the factorization of the Jacobian matrix, which may not be suitable for problems where the Jacobian matrix is large and has a 'bad' sparsity structure for an efficient factorization. We overcome this difficulty by forming and solving the tensor model using an extension of a Newton-GMRES scheme. Like traditional tensor methods, we show that the new tensor method has significant computational advantages over the analogous Newton counterpart. Consistent with Krylov subspace based methods, the new tensor method does not depend on the factorization of the Jacobian matrix. As a matter of fact, the Jacobian matrix is never needed explicitly.
Metrics for image segmentation
Rees, Gareth; Greenway, Phil; Morray, Denise
1998-07-01
An important challenge in mapping image-processing techniques onto applications is the lack of quantitative performance measures. From a systems engineering perspective these are essential if system level requirements are to be decomposed into sub-system requirements which can be understood in terms of algorithm selection and performance optimization. Nowhere in computer vision is this more evident than in the area of image segmentation. This is a vigorous and innovative research activity, but even after nearly two decades of progress, it remains almost impossible to answer the question 'what would the performance of this segmentation algorithm be under these new conditions?' To begin to address this shortcoming, we have devised a well-principled metric for assessing the relative performance of two segmentation algorithms. This allows meaningful objective comparisons to be made between their outputs. It also estimates the absolute performance of an algorithm given ground truth. Our approach is an information theoretic one. In this paper, we describe the theory and motivation of our method, and present practical results obtained from a range of state of the art segmentation methods. We demonstrate that it is possible to measure the objective performance of these algorithms, and to use the information so gained to provide clues about how their performance might be improved.
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
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
Muntinga, D.; Bernritter, S.
2017-01-01
Het merk staat steeds meer centraal in de organisatie. Het is daarom essentieel om de gezondheid, prestaties en ontwikkelingen van het merk te meten. Het is echter een uitdaging om de juiste brand metrics te selecteren. Een enorme hoeveelheid metrics vraagt de aandacht van merkbeheerders. Maar welke
Privacy Metrics and Boundaries
L-F. Pau (Louis-François)
2005-01-01
textabstractThis paper aims at defining a set of privacy metrics (quantitative and qualitative) in the case of the relation between a privacy protector ,and an information gatherer .The aims with such metrics are: -to allow to assess and compare different user scenarios and their differences; for
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.
Group field theory and tensor networks: towards a Ryu–Takayanagi formula in full quantum gravity
Chirco, Goffredo; Oriti, Daniele; Zhang, Mingyi
2018-06-01
We establish a dictionary between group field theory (thus, spin networks and random tensors) states and generalized random tensor networks. Then, we use this dictionary to compute the Rényi entropy of such states and recover the Ryu–Takayanagi formula, in two different cases corresponding to two different truncations/approximations, suggested by the established correspondence.
Kaliman, Ilya A; Krylov, Anna I
2017-04-30
A new hardware-agnostic contraction algorithm for tensors of arbitrary symmetry and sparsity is presented. The algorithm is implemented as a stand-alone open-source code libxm. This code is also integrated with general tensor library libtensor and with the Q-Chem quantum-chemistry package. An overview of the algorithm, its implementation, and benchmarks are presented. Similarly to other tensor software, the algorithm exploits efficient matrix multiplication libraries and assumes that tensors are stored in a block-tensor form. The distinguishing features of the algorithm are: (i) efficient repackaging of the individual blocks into large matrices and back, which affords efficient graphics processing unit (GPU)-enabled calculations without modifications of higher-level codes; (ii) fully asynchronous data transfer between disk storage and fast memory. The algorithm enables canonical all-electron coupled-cluster and equation-of-motion coupled-cluster calculations with single and double substitutions (CCSD and EOM-CCSD) with over 1000 basis functions on a single quad-GPU machine. We show that the algorithm exhibits predicted theoretical scaling for canonical CCSD calculations, O(N 6 ), irrespective of the data size on disk. © 2017 Wiley Periodicals, Inc. © 2017 Wiley Periodicals, Inc.
Fauzi, Wan Nor Farhana Wan Mohd; Idrus, Nor'ashiqin Mohd; Masri, Rohaidah; Ting, Tan Yee; Sarmin, Nor Haniza; Hassim, Hazzirah Izzati Mat
2014-12-01
One of the homological functors of a group, is the nonabelian tensor square. It is important in the determination of the other homological functors of a group. In order to compute the nonabelian tensor square, we need to get its independent generators and its presentation. In this paper, we present the calculation of getting the presentation of the nonabelian tensor square of the group. The presentation is computed based on its independent generators by using the polycyclic method.
Unified cosmology with scalar-tensor theory of gravity
Energy Technology Data Exchange (ETDEWEB)
Tajahmad, Behzad [Faculty of Physics, University of Tabriz, Tabriz (Iran, Islamic Republic of); Sanyal, Abhik Kumar [Jangipur College, Department of Physics, Murshidabad (India)
2017-04-15
Unlike the Noether symmetry, a metric independent general conserved current exists for non-minimally coupled scalar-tensor theory of gravity if the trace of the energy-momentum tensor vanishes. Thus, in the context of cosmology, a symmetry exists both in the early vacuum and radiation dominated era. For slow roll, symmetry is sacrificed, but at the end of early inflation, such a symmetry leads to a Friedmann-like radiation era. Late-time cosmic acceleration in the matter dominated era is realized in the absence of symmetry, in view of the same decayed and redshifted scalar field. Thus, unification of early inflation with late-time cosmic acceleration with a single scalar field may be realized. (orig.)
Unified cosmology with scalar-tensor theory of gravity
International Nuclear Information System (INIS)
Tajahmad, Behzad; Sanyal, Abhik Kumar
2017-01-01
Unlike the Noether symmetry, a metric independent general conserved current exists for non-minimally coupled scalar-tensor theory of gravity if the trace of the energy-momentum tensor vanishes. Thus, in the context of cosmology, a symmetry exists both in the early vacuum and radiation dominated era. For slow roll, symmetry is sacrificed, but at the end of early inflation, such a symmetry leads to a Friedmann-like radiation era. Late-time cosmic acceleration in the matter dominated era is realized in the absence of symmetry, in view of the same decayed and redshifted scalar field. Thus, unification of early inflation with late-time cosmic acceleration with a single scalar field may be realized. (orig.)
Covariant conserved currents for scalar-tensor Horndeski theory
Schmidt, J.; Bičák, J.
2018-04-01
The scalar-tensor theories have become popular recently in particular in connection with attempts to explain present accelerated expansion of the universe, but they have been considered as a natural extension of general relativity long time ago. The Horndeski scalar-tensor theory involving four invariantly defined Lagrangians is a natural choice since it implies field equations involving at most second derivatives. Following the formalisms of defining covariant global quantities and conservation laws for perturbations of spacetimes in standard general relativity, we extend these methods to the general Horndeski theory and find the covariant conserved currents for all four Lagrangians. The current is also constructed in the case of linear perturbations involving both metric and scalar fields. As a specific illustration, we derive a superpotential that leads to the covariantly conserved current in the Branse-Dicke theory.
Energy-momentum tensor of intermediate vector bosons in an external electromagnetic field
International Nuclear Information System (INIS)
Mostepanenko, V.M.; Sokolov, I.Yu.
1988-01-01
Expressions are obtained for the canonical and metric energy-momentum tensors of the vector field of intermediate bosons in an external electromagnetic field. It is shown that in the case of a gyromagnetic ratio not equal to unity the energy-momentum tensor cannot be symmetrized on its indices, and an additional term proportional to the anomalous magnetic moment appears in the conservation laws. A modification of the canonical formalism for scalar and vector fields in an external field is proposed in accordance with which the Hamiltonian density is equal to the 00 component of the energy-momentum tensor. An expression for the energy-momentum tensor of a closed system containing a gauge field of intermediate bosons and an electromagnetic field is obtained
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.
Holographic Spherically Symmetric Metrics
Petri, Michael
The holographic principle (HP) conjectures, that the maximum number of degrees of freedom of any realistic physical system is proportional to the system's boundary area. The HP has its roots in the study of black holes. It has recently been applied to cosmological solutions. In this article we apply the HP to spherically symmetric static space-times. We find that any regular spherically symmetric object saturating the HP is subject to tight constraints on the (interior) metric, energy-density, temperature and entropy-density. Whenever gravity can be described by a metric theory, gravity is macroscopically scale invariant and the laws of thermodynamics hold locally and globally, the (interior) metric of a regular holographic object is uniquely determined up to a constant factor and the interior matter-state must follow well defined scaling relations. When the metric theory of gravity is general relativity, the interior matter has an overall string equation of state (EOS) and a unique total energy-density. Thus the holographic metric derived in this article can serve as simple interior 4D realization of Mathur's string fuzzball proposal. Some properties of the holographic metric and its possible experimental verification are discussed. The geodesics of the holographic metric describe an isotropically expanding (or contracting) universe with a nearly homogeneous matter-distribution within the local Hubble volume. Due to the overall string EOS the active gravitational mass-density is zero, resulting in a coasting expansion with Ht = 1, which is compatible with the recent GRB-data.
On the L2-metric of vortex moduli spaces
Baptista, J.M.
2011-01-01
We derive general expressions for the Kähler form of the L2-metric in terms of standard 2-forms on vortex moduli spaces. In the case of abelian vortices in gauged linear sigma-models, this allows us to compute explicitly the Kähler class of the L2-metric. As an application we compute the total
Diffusion tensor imaging of the human skeletal muscle: contributions and applications
International Nuclear Information System (INIS)
Neji, Radhouene
2010-01-01
In this thesis, we present several techniques for the processing of diffusion tensor images. They span a wide range of tasks such as estimation and regularization, clustering and segmentation, as well as registration. The variational framework proposed for recovering a tensor field from noisy diffusion weighted images exploits the fact that diffusion data represent populations of fibers and therefore each tensor can be reconstructed using a weighted combination of tensors lying in its neighborhood. The segmentation approach operates both at the voxel and the fiber tract levels. It is based on the use of Mercer kernels over Gaussian diffusion probabilities to model tensor similarity and spatial interactions, allowing the definition of fiber metrics that combine information from spatial localization and diffusion tensors. Several clustering techniques can be subsequently used to segment tensor fields and fiber tractographies. Moreover, we show how to develop supervised extensions of these algorithms. The registration algorithm uses probability kernels in order to match moving and target images. The deformation consistency is assessed using the distortion induced in the distances between neighboring probabilities. Discrete optimization is used to seek an optimum of the defined objective function. The experimental validation is done over a dataset of manually segmented diffusion images of the lower leg muscle for healthy and diseased subjects. The results of the techniques developed throughout this thesis are promising. (author)
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.
Voepel, H.; Hodge, R. A.; Leyland, J.; Sear, D. A.; Ahmed, S. I.
2014-12-01
Uncertainty for bedload estimates in gravel bed rivers is largely driven by our inability to characterize the arrangement and orientation of the sediment grains within the bed. The characteristics of the surface structure are produced by the water working of grains, which leads to structural differences in bedforms through differential patterns of grain sorting, packing, imbrication, mortaring and degree of bed armoring. Until recently the technical and logistical difficulties of characterizing the arrangement of sediment in 3D have prohibited a full understanding of how grains interact with stream flow and the feedback mechanisms that exist. Micro-focus X-ray CT has been used for non-destructive 3D imaging of grains within a series of intact sections of river bed taken from key morphological units (see Figure 1). Volume, center of mass, points of contact, protrusion and spatial orientation of individual surface grains are derived from these 3D images, which in turn, facilitates estimates of 3D static force properties at the grain-scale such as pivoting angles, buoyancy and gravity forces, and grain exposure. By aggregating representative samples of grain-scale properties of localized interacting sediment into overall metrics, we can compare and contrast bed stability at a macro-scale with respect to stream bed morphology. Understanding differences in bed stability through representative metrics derived at the grain-scale will ultimately lead to improved bedload estimates with reduced uncertainty and increased understanding of interactions between grain-scale properties on channel morphology. Figure 1. CT-Scans of a water worked gravel-filled pot. a. 3D rendered scan showing the outer mesh, and b. the same pot with the mesh removed. c. vertical change in porosity of the gravels sampled in 5mm volumes. Values are typical of those measured in the field and lab. d. 2-D slices through the gravels at 20% depth from surface (porosity = 0.35), and e. 75% depth from
International Nuclear Information System (INIS)
Stachel, J.
1977-01-01
A first-order Lagrangian is given, from which follow the definitions of the fully covariant form of the Riemann tensor Rsub(μνkappalambda) in terms of the affine connection and metric; the definition of the affine connection in terms of the metric; the Einstein field equations; and the definition of a set of gravitational 'superpotentials' closely connected with the Komar conservation laws (Phys. Rev.; 113:934 (1959)). Substitution of the definition of the affine connection into this Lagrangian results in a second-order Lagrangian, from which follow the definition of the fully covariant Riemann tensor in terms of the metric, the Einstein equations, and the definition of the gravitational 'superpotentials'. (author)
Stress tensor for GYM in 4p dimensions and viability of GYM-Higgs in four dimensions
International Nuclear Information System (INIS)
O'Brien, G.M.; Tchrakian, D.H.
1985-01-01
We present the stress tensor for GYM systems in 4p dimensions and give a method to compute this tensor density for a GYM-Higgs system in four dimensions. This computation is made explicitly for the first such system and its viability in four Euclidean dimensions is checked. The possibility of extracting phenomenological models from this system is analysed briefly. (Author)
Schweizer, B
2005-01-01
Topics include special classes of probabilistic metric spaces, topologies, and several related structures, such as probabilistic normed and inner-product spaces. 1983 edition, updated with 3 new appendixes. Includes 17 illustrations.
National Research Council Canada - National Science Library
Olson, Teresa; Lee, Harry; Sanders, Johnnie
2002-01-01
.... We have developed the Tracker Performance Metric (TPM) specifically for this purpose. It was designed to measure the output performance, on a frame-by-frame basis, using its output position and quality...
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.
Mass Customization Measurements Metrics
DEFF Research Database (Denmark)
Nielsen, Kjeld; Brunø, Thomas Ditlev; Jørgensen, Kaj Asbjørn
2014-01-01
A recent survey has indicated that 17 % of companies have ceased mass customizing less than 1 year after initiating the effort. This paper presents measurement for a company’s mass customization performance, utilizing metrics within the three fundamental capabilities: robust process design, choice...... navigation, and solution space development. A mass customizer when assessing performance with these metrics can identify within which areas improvement would increase competitiveness the most and enable more efficient transition to mass customization....
Product Operations Status Summary Metrics
Takagi, Atsuya; Toole, Nicholas
2010-01-01
The Product Operations Status Summary Metrics (POSSUM) computer program provides a readable view into the state of the Phoenix Operations Product Generation Subsystem (OPGS) data pipeline. POSSUM provides a user interface that can search the data store, collect product metadata, and display the results in an easily-readable layout. It was designed with flexibility in mind for support in future missions. Flexibility over various data store hierarchies is provided through the disk-searching facilities of Marsviewer. This is a proven program that has been in operational use since the first day of the Phoenix mission.
STRUCTURAL CONNECTIVITY VIA THE TENSOR-BASED MORPHOMETRY.
Kim, Seung-Goo; Chung, Moo K; Hanson, Jamie L; Avants, Brian B; Gee, James C; Davidson, Richard J; Pollak, Seth D
2011-01-01
The tensor-based morphometry (TBM) has been widely used in characterizing tissue volume difference between populations at voxel level. We present a novel computational framework for investigating the white matter connectivity using TBM. Unlike other diffusion tensor imaging (DTI) based white matter connectivity studies, we do not use DTI but only T1-weighted magnetic resonance imaging (MRI). To construct brain network graphs, we have developed a new data-driven approach called the ε -neighbor method that does not need any predetermined parcellation. The proposed pipeline is applied in detecting the topological alteration of the white matter connectivity in maltreated children.
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.
Sensory Metrics of Neuromechanical Trust.
Softky, William; Benford, Criscillia
2017-09-01
Today digital sources supply a historically unprecedented component of human sensorimotor data, the consumption of which is correlated with poorly understood maladies such as Internet addiction disorder and Internet gaming disorder. Because both natural and digital sensorimotor data share common mathematical descriptions, one can quantify our informational sensorimotor needs using the signal processing metrics of entropy, noise, dimensionality, continuity, latency, and bandwidth. Such metrics describe in neutral terms the informational diet human brains require to self-calibrate, allowing individuals to maintain trusting relationships. With these metrics, we define the trust humans experience using the mathematical language of computational models, that is, as a primitive statistical algorithm processing finely grained sensorimotor data from neuromechanical interaction. This definition of neuromechanical trust implies that artificial sensorimotor inputs and interactions that attract low-level attention through frequent discontinuities and enhanced coherence will decalibrate a brain's representation of its world over the long term by violating the implicit statistical contract for which self-calibration evolved. Our hypersimplified mathematical understanding of human sensorimotor processing as multiscale, continuous-time vibratory interaction allows equally broad-brush descriptions of failure modes and solutions. For example, we model addiction in general as the result of homeostatic regulation gone awry in novel environments (sign reversal) and digital dependency as a sub-case in which the decalibration caused by digital sensorimotor data spurs yet more consumption of them. We predict that institutions can use these sensorimotor metrics to quantify media richness to improve employee well-being; that dyads and family-size groups will bond and heal best through low-latency, high-resolution multisensory interaction such as shared meals and reciprocated touch; and
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....
On the axial anomalies in external tensor fields
International Nuclear Information System (INIS)
Khudaverdyan, O.M.; Mkrtchyan, R.L.; Zurabyan, L.A.
1985-01-01
Computation of the axial anomaly for Dirac fermions in external tensor fields is studied. The sequence of the supersymmetric one-dimensional models is presented. Their supercharges are equal, after quantization, to Dirac operators in external tensor fields, and the density of Witten's partition function gives the anomaly. It is shown that action in the corresponding path integral differs from the classical one. Gaussian approximation gives the anomaly only in the case of third-rank tensor with zero exterior derivative and in that case anomaly is calculated in all dimensions. The interpretation of that field as the torsion of gravitational field and also connection with the results of Witten and Alvarez-Gaume and Atiyah-Singer index theorem are discussed
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.
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.
Gradients estimation from random points with volumetric tensor in turbulence
Watanabe, Tomoaki; Nagata, Koji
2017-12-01
We present an estimation method of fully-resolved/coarse-grained gradients from randomly distributed points in turbulence. The method is based on a linear approximation of spatial gradients expressed with the volumetric tensor, which is a 3 × 3 matrix determined by a geometric distribution of the points. The coarse grained gradient can be considered as a low pass filtered gradient, whose cutoff is estimated with the eigenvalues of the volumetric tensor. The present method, the volumetric tensor approximation, is tested for velocity and passive scalar gradients in incompressible planar jet and mixing layer. Comparison with a finite difference approximation on a Cartesian grid shows that the volumetric tensor approximation computes the coarse grained gradients fairly well at a moderate computational cost under various conditions of spatial distributions of points. We also show that imposing the solenoidal condition improves the accuracy of the present method for solenoidal vectors, such as a velocity vector in incompressible flows, especially when the number of the points is not large. The volumetric tensor approximation with 4 points poorly estimates the gradient because of anisotropic distribution of the points. Increasing the number of points from 4 significantly improves the accuracy. Although the coarse grained gradient changes with the cutoff length, the volumetric tensor approximation yields the coarse grained gradient whose magnitude is close to the one obtained by the finite difference. We also show that the velocity gradient estimated with the present method well captures the turbulence characteristics such as local flow topology, amplification of enstrophy and strain, and energy transfer across scales.
Generalized metric formulation of double field theory on group manifolds
International Nuclear Information System (INIS)
Blumenhagen, Ralph; Bosque, Pascal du; Hassler, Falk; Lüst, Dieter
2015-01-01
We rewrite the recently derived cubic action of Double Field Theory on group manifolds http://dx.doi.org/10.1007/JHEP02(2015)001 in terms of a generalized metric and extrapolate it to all orders in the fields. For the resulting action, we derive the field equations and state them in terms of a generalized curvature scalar and a generalized Ricci tensor. Compared to the generalized metric formulation of DFT derived from tori, all these quantities receive additional contributions related to the non-trivial background. It is shown that the action is invariant under its generalized diffeomorphisms and 2D-diffeomorphisms. Imposing additional constraints relating the background and fluctuations around it, the precise relation between the proposed generalized metric formulation of DFT WZW and of original DFT from tori is clarified. Furthermore, we show how to relate DFT WZW of the WZW background with the flux formulation of original DFT.
Generalized metric formulation of double field theory on group manifolds
Energy Technology Data Exchange (ETDEWEB)
Blumenhagen, Ralph [Max-Planck-Institut für Physik,Föhringer Ring 6, 80805 München (Germany); Bosque, Pascal du [Arnold-Sommerfeld-Center für Theoretische Physik,Department für Physik, Ludwig-Maximilians-Universität München,Theresienstraße 37, 80333 München (Germany); Hassler, Falk [Max-Planck-Institut für Physik,Föhringer Ring 6, 80805 München (Germany); Lüst, Dieter [Max-Planck-Institut für Physik,Föhringer Ring 6, 80805 München (Germany); Arnold-Sommerfeld-Center für Theoretische Physik,Department für Physik, Ludwig-Maximilians-Universität München,Theresienstraße 37, 80333 München (Germany); CERN, PH-TH,1211 Geneva 23 (Switzerland)
2015-08-13
We rewrite the recently derived cubic action of Double Field Theory on group manifolds http://dx.doi.org/10.1007/JHEP02(2015)001 in terms of a generalized metric and extrapolate it to all orders in the fields. For the resulting action, we derive the field equations and state them in terms of a generalized curvature scalar and a generalized Ricci tensor. Compared to the generalized metric formulation of DFT derived from tori, all these quantities receive additional contributions related to the non-trivial background. It is shown that the action is invariant under its generalized diffeomorphisms and 2D-diffeomorphisms. Imposing additional constraints relating the background and fluctuations around it, the precise relation between the proposed generalized metric formulation of DFT{sub WZW} and of original DFT from tori is clarified. Furthermore, we show how to relate DFT{sub WZW} of the WZW background with the flux formulation of original DFT.
Balanced metrics for vector bundles and polarised manifolds
DEFF Research Database (Denmark)
Garcia Fernandez, Mario; Ross, Julius
2012-01-01
leads to a Hermitian-Einstein metric on E and a constant scalar curvature Kähler metric in c_1(L). For special values of α, limits of balanced metrics are solutions of a system of coupled equations relating a Hermitian-Einstein metric on E and a Kähler metric in c1(L). For this, we compute the top two......We consider a notion of balanced metrics for triples (X, L, E) which depend on a parameter α, where X is smooth complex manifold with an ample line bundle L and E is a holomorphic vector bundle over X. For generic choice of α, we prove that the limit of a convergent sequence of balanced metrics...
Johnson, Stephen B.; Ghoshal, Sudipto; Haste, Deepak; Moore, Craig
2017-01-01
This paper describes the theory and considerations in the application of metrics to measure the effectiveness of fault management. Fault management refers here to the operational aspect of system health management, and as such is considered as a meta-control loop that operates to preserve or maximize the system's ability to achieve its goals in the face of current or prospective failure. As a suite of control loops, the metrics to estimate and measure the effectiveness of fault management are similar to those of classical control loops in being divided into two major classes: state estimation, and state control. State estimation metrics can be classified into lower-level subdivisions for detection coverage, detection effectiveness, fault isolation and fault identification (diagnostics), and failure prognosis. State control metrics can be classified into response determination effectiveness and response effectiveness. These metrics are applied to each and every fault management control loop in the system, for each failure to which they apply, and probabilistically summed to determine the effectiveness of these fault management control loops to preserve the relevant system goals that they are intended to protect.
Deep Transfer Metric Learning.
Junlin Hu; Jiwen Lu; Yap-Peng Tan; Jie Zhou
2016-12-01
Conventional metric learning methods usually assume that the training and test samples are captured in similar scenarios so that their distributions are assumed to be the same. This assumption does not hold in many real visual recognition applications, especially when samples are captured across different data sets. In this paper, we propose a new deep transfer metric learning (DTML) method to learn a set of hierarchical nonlinear transformations for cross-domain visual recognition by transferring discriminative knowledge from the labeled source domain to the unlabeled target domain. Specifically, our DTML learns a deep metric network by maximizing the inter-class variations and minimizing the intra-class variations, and minimizing the distribution divergence between the source domain and the target domain at the top layer of the network. To better exploit the discriminative information from the source domain, we further develop a deeply supervised transfer metric learning (DSTML) method by including an additional objective on DTML, where the output of both the hidden layers and the top layer are optimized jointly. To preserve the local manifold of input data points in the metric space, we present two new methods, DTML with autoencoder regularization and DSTML with autoencoder regularization. Experimental results on face verification, person re-identification, and handwritten digit recognition validate the effectiveness of the proposed methods.
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
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...
Cockrell, Chase; An, Gary
2017-10-07
Sepsis affects nearly 1 million people in the United States per year, has a mortality rate of 28-50% and requires more than $20 billion a year in hospital costs. Over a quarter century of research has not yielded a single reliable diagnostic test or a directed therapeutic agent for sepsis. Central to this insufficiency is the fact that sepsis remains a clinical/physiological diagnosis representing a multitude of molecularly heterogeneous pathological trajectories. Advances in computational capabilities offered by High Performance Computing (HPC) platforms call for an evolution in the investigation of sepsis to attempt to define the boundaries of traditional research (bench, clinical and computational) through the use of computational proxy models. We present a novel investigatory and analytical approach, derived from how HPC resources and simulation are used in the physical sciences, to identify the epistemic boundary conditions of the study of clinical sepsis via the use of a proxy agent-based model of systemic inflammation. Current predictive models for sepsis use correlative methods that are limited by patient heterogeneity and data sparseness. We address this issue by using an HPC version of a system-level validated agent-based model of sepsis, the Innate Immune Response ABM (IIRBM), as a proxy system in order to identify boundary conditions for the possible behavioral space for sepsis. We then apply advanced analysis derived from the study of Random Dynamical Systems (RDS) to identify novel means for characterizing system behavior and providing insight into the tractability of traditional investigatory methods. The behavior space of the IIRABM was examined by simulating over 70 million sepsis patients for up to 90 days in a sweep across the following parameters: cardio-respiratory-metabolic resilience; microbial invasiveness; microbial toxigenesis; and degree of nosocomial exposure. In addition to using established methods for describing parameter space, we
An accurate metric for the spacetime around rotating neutron stars
Pappas, George
2017-04-01
The problem of having an accurate description of the spacetime around rotating neutron stars is of great astrophysical interest. For astrophysical applications, one needs to have a metric that captures all the properties of the spacetime around a rotating neutron star. Furthermore, an accurate appropriately parametrized metric, I.e. a metric that is given in terms of parameters that are directly related to the physical structure of the neutron star, could be used to solve the inverse problem, which is to infer the properties of the structure of a neutron star from astrophysical observations. In this work, we present such an approximate stationary and axisymmetric metric for the exterior of rotating neutron stars, which is constructed using the Ernst formalism and is parametrized by the relativistic multipole moments of the central object. This metric is given in terms of an expansion on the Weyl-Papapetrou coordinates with the multipole moments as free parameters and is shown to be extremely accurate in capturing the physical properties of a neutron star spacetime as they are calculated numerically in general relativity. Because the metric is given in terms of an expansion, the expressions are much simpler and easier to implement, in contrast to previous approaches. For the parametrization of the metric in general relativity, the recently discovered universal 3-hair relations are used to produce a three-parameter metric. Finally, a straightforward extension of this metric is given for scalar-tensor theories with a massless scalar field, which also admit a formulation in terms of an Ernst potential.
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.)
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
Energy Technology Data Exchange (ETDEWEB)
Frye, Jason Neal; Veitch, Cynthia K.; Mateski, Mark Elliot; Michalski, John T.; Harris, James Mark; Trevino, Cassandra M.; Maruoka, Scott
2012-03-01
Threats are generally much easier to list than to describe, and much easier to describe than to measure. As a result, many organizations list threats. Fewer describe them in useful terms, and still fewer measure them in meaningful ways. This is particularly true in the dynamic and nebulous domain of cyber threats - a domain that tends to resist easy measurement and, in some cases, appears to defy any measurement. We believe the problem is tractable. In this report we describe threat metrics and models for characterizing threats consistently and unambiguously. The purpose of this report is to support the Operational Threat Assessment (OTA) phase of risk and vulnerability assessment. To this end, we focus on the task of characterizing cyber threats using consistent threat metrics and models. In particular, we address threat metrics and models for describing malicious cyber threats to US FCEB agencies and systems.
Millie, David F.; Weckman, Gary R.; Young, William A.; Ivey, James E.; Fries, David P.; Ardjmand, Ehsan; Fahnenstiel, Gary L.
2013-07-01
Coastal monitoring has become reliant upon automated sensors for data acquisition. Such a technical commitment comes with a cost; particularly, the generation of large, high-dimensional data streams ('Big Data') that personnel must search through to identify data structures. Nature-inspired computation, inclusive of artificial neural networks (ANNs), affords the unearthing of complex, recurring patterns within sizable data volumes. In 2009, select meteorological and hydrological data were acquired via autonomous instruments in Sarasota Bay, Florida (USA). ANNs estimated continuous chlorophyll (CHL) a concentrations from abiotic predictors, with correlations between measured:modeled concentrations >0.90 and model efficiencies ranging from 0.80 to 0.90. Salinity and water temperature were the principal influences for modeled CHL within the Bay; concentrations steadily increased at temperatures >28° C and were greatest at salinities 6.1 μg CHL L-1 maximized at a salinity of ca. 36.3 and a temperature of ca. 29.5 °C. A 10th-order Chebyshev bivariate polynomial equation was fit (adj. r2 = 0.99, p turbidity, temperature, and salinity (and to lesser degrees, wind speed, wind/current direction, irradiance, and urea-nitrogen) were key variables for quantitative rules in tree formalisms. Taken together, computations enabled knowledge provision for and quantifiable representations of the non-linear relationships between environmental variables and CHL a.
Relaxed metrics and indistinguishability operators: the relationship
Energy Technology Data Exchange (ETDEWEB)
Martin, J.
2017-07-01
In 1982, the notion of indistinguishability operator was introduced by E. Trillas in order to fuzzify the crisp notion of equivalence relation (/cite{Trillas}). In the study of such a class of operators, an outstanding property must be pointed out. Concretely, there exists a duality relationship between indistinguishability operators and metrics. The aforesaid relationship was deeply studied by several authors that introduced a few techniques to generate metrics from indistinguishability operators and vice-versa (see, for instance, /cite{BaetsMesiar,BaetsMesiar2}). In the last years a new generalization of the metric notion has been introduced in the literature with the purpose of developing mathematical tools for quantitative models in Computer Science and Artificial Intelligence (/cite{BKMatthews,Ma}). The aforementioned generalized metrics are known as relaxed metrics. The main target of this talk is to present a study of the duality relationship between indistinguishability operators and relaxed metrics in such a way that the aforementioned classical techniques to generate both concepts, one from the other, can be extended to the new framework. (Author)
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
Kim, Seung-Goo; Lee, Hyekyoung; Chung, Moo K.; Hanson, Jamie L.; Avants, Brian B.; Gee, James C.; Davidson, Richard J.; Pollak, Seth D.
2012-01-01
We are interested in investigating white matter connectivity using a novel computational framework that does not use diffusion tensor imaging (DTI) but only uses T1-weighted magnetic resonance imaging. The proposed method relies on correlating Jacobian determinants across different voxels based on the tensor-based morphometry (TBM) framework. In this paper, we show agreement between the TBM-based white matter connectivity and the DTI-based white matter atlas. As an application, altered white ...
Adaptive metric kernel regression
DEFF Research Database (Denmark)
Goutte, Cyril; Larsen, Jan
2000-01-01
Kernel smoothing is a widely used non-parametric pattern recognition technique. By nature, it suffers from the curse of dimensionality and is usually difficult to apply to high input dimensions. In this contribution, we propose an algorithm that adapts the input metric used in multivariate...... regression by minimising a cross-validation estimate of the generalisation error. This allows to automatically adjust the importance of different dimensions. The improvement in terms of modelling performance is illustrated on a variable selection task where the adaptive metric kernel clearly outperforms...
Adaptive Metric Kernel Regression
DEFF Research Database (Denmark)
Goutte, Cyril; Larsen, Jan
1998-01-01
Kernel smoothing is a widely used nonparametric pattern recognition technique. By nature, it suffers from the curse of dimensionality and is usually difficult to apply to high input dimensions. In this paper, we propose an algorithm that adapts the input metric used in multivariate regression...... by minimising a cross-validation estimate of the generalisation error. This allows one to automatically adjust the importance of different dimensions. The improvement in terms of modelling performance is illustrated on a variable selection task where the adaptive metric kernel clearly outperforms the standard...
Noether symmetries, energy-momentum tensors, and conformal invariance in classical field theory
International Nuclear Information System (INIS)
Pons, Josep M.
2011-01-01
In the framework of classical field theory, we first review the Noether theory of symmetries, with simple rederivations of its essential results, with special emphasis given to the Noether identities for gauge theories. With this baggage on board, we next discuss in detail, for Poincare invariant theories in flat spacetime, the differences between the Belinfante energy-momentum tensor and a family of Hilbert energy-momentum tensors. All these tensors coincide on shell but they split their duties in the following sense: Belinfante's tensor is the one to use in order to obtain the generators of Poincare symmetries and it is a basic ingredient of the generators of other eventual spacetime symmetries which may happen to exist. Instead, Hilbert tensors are the means to test whether a theory contains other spacetime symmetries beyond Poincare. We discuss at length the case of scale and conformal symmetry, of which we give some examples. We show, for Poincare invariant Lagrangians, that the realization of scale invariance selects a unique Hilbert tensor which allows for an easy test as to whether conformal invariance is also realized. Finally we make some basic remarks on metric generally covariant theories and classical field theory in a fixed curved background.
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.
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.
Bakaraju, Ravi C; Ehrmann, Klaus; Ho, Arthur
To compare the computed optical performance of prototype lenses designed using deliberate manipulation of higher-order spherical aberrations to extend depth-of-focus (EDOF) with two commercial multifocals. Emmetropic, presbyopic, schematic eyes were coupled with prototype EDOF and commercial multifocal lenses (Acuvue Oasys for presbyopia, AOP, Johnson & Johnson & Air Optix Aqua multifocal, AOMF, Alcon). For each test configuration, the through-focus retinal image quality (TFRIQ) values were computed over 21 vergences, ranging from -0.50 to 2.00D, in 0.125D steps. Analysis was performed considering eyes with three different inherent aberration profiles: five different pupils and five different lens decentration levels. Except the LOW design, the AOP lenses offered 'bifocal' like TFRIQ performance. Lens performance was relatively independent to pupil and aberrations but not centration. Contrastingly, AOMF demonstrated distance centric performance, most dominant in LOW followed by MED and HIGH designs. AOMF lenses were the most sensitive to pupil, aberrations and centration. The prototypes demonstrated a 'lift-off' in the TFRIQ performance, particularly at intermediate and near, without trading performance at distance. When compared with AOP and AOMF, EDOF lenses demonstrated reduced sensitivity to pupil, aberrations and centration. With the through focus retinal image quality as the gauge of optical performance, we demonstrated that the prototype EDOF designs were less susceptible to variations in pupil, inherent ocular aberrations and decentration, compared to the commercial designs. To ascertain whether these incremental improvements translate to a clinically palpable outcome requires investigation through human trials. Copyright © 2017 Spanish General Council of Optometry. Published by Elsevier España, S.L.U. All rights reserved.
Tice, Bradley S.
Metrical phonology, a linguistic process of phonological stress assessment and diagrammatic simplification of sentence and word stress, is discussed as it is found in the English language with the intention that it may be used in second language instruction. Stress is defined by its physical and acoustical correlates, and the principles of…
Engineering performance metrics
Delozier, R.; Snyder, N.
1993-03-01
Implementation of a Total Quality Management (TQM) approach to engineering work required the development of a system of metrics which would serve as a meaningful management tool for evaluating effectiveness in accomplishing project objectives and in achieving improved customer satisfaction. A team effort was chartered with the goal of developing a system of engineering performance metrics which would measure customer satisfaction, quality, cost effectiveness, and timeliness. The approach to developing this system involved normal systems design phases including, conceptual design, detailed design, implementation, and integration. The lessons teamed from this effort will be explored in this paper. These lessons learned may provide a starting point for other large engineering organizations seeking to institute a performance measurement system accomplishing project objectives and in achieving improved customer satisfaction. To facilitate this effort, a team was chartered to assist in the development of the metrics system. This team, consisting of customers and Engineering staff members, was utilized to ensure that the needs and views of the customers were considered in the development of performance measurements. The development of a system of metrics is no different than the development of any type of system. It includes the steps of defining performance measurement requirements, measurement process conceptual design, performance measurement and reporting system detailed design, and system implementation and integration.
Metrics for Probabilistic Geometries
DEFF Research Database (Denmark)
Tosi, Alessandra; Hauberg, Søren; Vellido, Alfredo
2014-01-01
the distribution over mappings is given by a Gaussian process. We treat the corresponding latent variable model as a Riemannian manifold and we use the expectation of the metric under the Gaussian process prior to define interpolating paths and measure distance between latent points. We show how distances...
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...
International Nuclear Information System (INIS)
Roege, Paul E.; Collier, Zachary A.; Mancillas, James; McDonagh, John A.; Linkov, Igor
2014-01-01
Energy lies at the backbone of any advanced society and constitutes an essential prerequisite for economic growth, social order and national defense. However there is an Achilles heel to today's energy and technology relationship; namely a precarious intimacy between energy and the fiscal, social, and technical systems it supports. Recently, widespread and persistent disruptions in energy systems have highlighted the extent of this dependence and the vulnerability of increasingly optimized systems to changing conditions. Resilience is an emerging concept that offers to reconcile considerations of performance under dynamic environments and across multiple time frames by supplementing traditionally static system performance measures to consider behaviors under changing conditions and complex interactions among physical, information and human domains. This paper identifies metrics useful to implement guidance for energy-related planning, design, investment, and operation. Recommendations are presented using a matrix format to provide a structured and comprehensive framework of metrics relevant to a system's energy resilience. The study synthesizes previously proposed metrics and emergent resilience literature to provide a multi-dimensional model intended for use by leaders and practitioners as they transform our energy posture from one of stasis and reaction to one that is proactive and which fosters sustainable growth. - Highlights: • Resilience is the ability of a system to recover from adversity. • There is a need for methods to quantify and measure system resilience. • We developed a matrix-based approach to generate energy resilience metrics. • These metrics can be used in energy planning, system design, and operations
Software Quality Assurance Metrics
McRae, Kalindra A.
2004-01-01
Software Quality Assurance (SQA) is a planned and systematic set of activities that ensures conformance of software life cycle processes and products conform to requirements, standards and procedures. In software development, software quality means meeting requirements and a degree of excellence and refinement of a project or product. Software Quality is a set of attributes of a software product by which its quality is described and evaluated. The set of attributes includes functionality, reliability, usability, efficiency, maintainability, and portability. Software Metrics help us understand the technical process that is used to develop a product. The process is measured to improve it and the product is measured to increase quality throughout the life cycle of software. Software Metrics are measurements of the quality of software. Software is measured to indicate the quality of the product, to assess the productivity of the people who produce the product, to assess the benefits derived from new software engineering methods and tools, to form a baseline for estimation, and to help justify requests for new tools or additional training. Any part of the software development can be measured. If Software Metrics are implemented in software development, it can save time, money, and allow the organization to identify the caused of defects which have the greatest effect on software development. The summer of 2004, I worked with Cynthia Calhoun and Frank Robinson in the Software Assurance/Risk Management department. My task was to research and collect, compile, and analyze SQA Metrics that have been used in other projects that are not currently being used by the SA team and report them to the Software Assurance team to see if any metrics can be implemented in their software assurance life cycle process.
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.
Suresh, Niraj; Stephens, Sean A; Adams, Lexor; Beck, Anthon N; McKinney, Adriana L; Varga, Tamas
2016-04-26
Plant roots play a critical role in plant-soil-microbe interactions that occur in the rhizosphere, as well as processes with important implications to climate change and crop management. Quantitative size information on roots in their native environment is invaluable for studying root growth and environmental processes involving plants. X-ray computed tomography (XCT) has been demonstrated to be an effective tool for in situ root scanning and analysis. We aimed to develop a costless and efficient tool that approximates the surface and volume of the root regardless of its shape from three-dimensional (3D) tomography data. The root structure of a Prairie dropseed (Sporobolus heterolepis) specimen was imaged using XCT. The root was reconstructed, and the primary root structure was extracted from the data using a combination of licensed and open-source software. An isosurface polygonal mesh was then created for ease of analysis. We have developed the standalone application imeshJ, generated in MATLAB(1), to calculate root volume and surface area from the mesh. The outputs of imeshJ are surface area (in mm(2)) and the volume (in mm(3)). The process, utilizing a unique combination of tools from imaging to quantitative root analysis, is described. A combination of XCT and open-source software proved to be a powerful combination to noninvasively image plant root samples, segment root data, and extract quantitative information from the 3D data. This methodology of processing 3D data should be applicable to other material/sample systems where there is connectivity between components of similar X-ray attenuation and difficulties arise with segmentation.
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.
Fauzi, Wan Nor Farhana Wan Mohd; Idrus, Nor'ashiqin Mohd; Masri, Rohaidah; Sarmin, Nor Haniza
2014-07-01
The nonabelian tensor product was originated in homotopy theory as well as in algebraic K-theory. The nonabelian tensor square is a special case of the nonabelian tensor product where the product is defined if the two groups act on each other in a compatible way and their action are taken to be conjugation. In this paper, the computation of nonabelian tensor square of a Bieberbach group, which is a torsion free crystallographic group, of dimension five with dihedral point group of order eight is determined. Groups, Algorithms and Programming (GAP) software has been used to assist and verify the results.
Tarabichi, Osama; Kozin, Elliott D; Kanumuri, Vivek V; Barber, Samuel; Ghosh, Satra; Sitek, Kevin R; Reinshagen, Katherine; Herrmann, Barbara; Remenschneider, Aaron K; Lee, Daniel J
2018-03-01
Objective The radiologic evaluation of patients with hearing loss includes computed tomography and magnetic resonance imaging (MRI) to highlight temporal bone and cochlear nerve anatomy. The central auditory pathways are often not studied for routine clinical evaluation. Diffusion tensor imaging (DTI) is an emerging MRI-based modality that can reveal microstructural changes in white matter. In this systematic review, we summarize the value of DTI in the detection of structural changes of the central auditory pathways in patients with sensorineural hearing loss. Data Sources PubMed, Embase, and Cochrane. Review Methods We used the Preferred Reporting Items for Systematic Reviews and Meta-Analysis statement checklist for study design. All studies that included at least 1 sensorineural hearing loss patient with DTI outcome data were included. Results After inclusion and exclusion criteria were met, 20 articles were analyzed. Patients with bilateral hearing loss comprised 60.8% of all subjects. Patients with unilateral or progressive hearing loss and tinnitus made up the remaining studies. The auditory cortex and inferior colliculus (IC) were the most commonly studied regions using DTI, and most cases were found to have changes in diffusion metrics, such as fractional anisotropy, compared to normal hearing controls. Detectable changes in other auditory regions were reported, but there was a higher degree of variability. Conclusion White matter changes based on DTI metrics can be seen in patients with sensorineural hearing loss, but studies are few in number with modest sample sizes. Further standardization of DTI using a prospective study design with larger sample sizes is needed.
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.
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.
On renormalisation of the quantum stress tensor in curved space-time by dimensional regularisation
International Nuclear Information System (INIS)
Bunch, T.S.
1979-01-01
Using dimensional regularisation, a prescription is given for obtaining a finite renormalised stress tensor in curved space-time. Renormalisation is carried out by renormalising coupling constants in the n-dimensional Einstein equation generalised to include tensors which are fourth order in derivatives of the metric. Except for the special case of a massless conformal field in a conformally flat space-time, this procedure is not unique. There exists an infinite one-parameter family of renormalisation ansatze differing from each other in the finite renormalisation that takes place. Nevertheless, the renormalised stress tensor for a conformally invariant field theory acquires a nonzero trace which is independent of the renormalisation ansatz used and which has a value in agreement with that obtained by other methods. A comparison is made with some earlier work using dimensional regularisation which is shown to be in error. (author)
On the Averaging of Cardiac Diffusion Tensor MRI Data: The Effect of Distance Function Selection
Giannakidis, Archontis; Melkus, Gerd; Yang, Guang; Gullberg, Grant T.
2016-01-01
Diffusion tensor magnetic resonance imaging (DT-MRI) allows a unique insight into the microstructure of highly-directional tissues. The selection of the most proper distance function for the space of diffusion tensors is crucial in enhancing the clinical application of this imaging modality. Both linear and nonlinear metrics have been proposed in the literature over the years. The debate on the most appropriate DT-MRI distance function is still ongoing. In this paper, we presented a framework to compare the Euclidean, affine-invariant Riemannian and log-Euclidean metrics using actual high-resolution DT-MRI rat heart data. We employed temporal averaging at the diffusion tensor level of three consecutive and identically-acquired DT-MRI datasets from each of five rat hearts as a means to rectify the background noise-induced loss of myocyte directional regularity. This procedure is applied here for the first time in the context of tensor distance function selection. When compared with previous studies that used a different concrete application to juxtapose the various DT-MRI distance functions, this work is unique in that it combined the following: (i) Metrics were judged by quantitative –rather than qualitative– criteria, (ii) the comparison tools were non-biased, (iii) a longitudinal comparison operation was used on a same-voxel basis. The statistical analyses of the comparison showed that the three DT-MRI distance functions tend to provide equivalent results. Hence, we came to the conclusion that the tensor manifold for cardiac DT-MRI studies is a curved space of almost zero curvature. The signal to noise ratio dependence of the operations was investigated through simulations. Finally, the “swelling effect” occurrence following Euclidean averaging was found to be too unimportant to be worth consideration. PMID:27754986
On the averaging of cardiac diffusion tensor MRI data: the effect of distance function selection
Giannakidis, Archontis; Melkus, Gerd; Yang, Guang; Gullberg, Grant T.
2016-11-01
Diffusion tensor magnetic resonance imaging (DT-MRI) allows a unique insight into the microstructure of highly-directional tissues. The selection of the most proper distance function for the space of diffusion tensors is crucial in enhancing the clinical application of this imaging modality. Both linear and nonlinear metrics have been proposed in the literature over the years. The debate on the most appropriate DT-MRI distance function is still ongoing. In this paper, we presented a framework to compare the Euclidean, affine-invariant Riemannian and log-Euclidean metrics using actual high-resolution DT-MRI rat heart data. We employed temporal averaging at the diffusion tensor level of three consecutive and identically-acquired DT-MRI datasets from each of five rat hearts as a means to rectify the background noise-induced loss of myocyte directional regularity. This procedure is applied here for the first time in the context of tensor distance function selection. When compared with previous studies that used a different concrete application to juxtapose the various DT-MRI distance functions, this work is unique in that it combined the following: (i) metrics were judged by quantitative—rather than qualitative—criteria, (ii) the comparison tools were non-biased, (iii) a longitudinal comparison operation was used on a same-voxel basis. The statistical analyses of the comparison showed that the three DT-MRI distance functions tend to provide equivalent results. Hence, we came to the conclusion that the tensor manifold for cardiac DT-MRI studies is a curved space of almost zero curvature. The signal to noise ratio dependence of the operations was investigated through simulations. Finally, the ‘swelling effect’ occurrence following Euclidean averaging was found to be too unimportant to be worth consideration.
Conserved current for the Cotton tensor, black hole entropy and equivariant Pontryagin forms
Energy Technology Data Exchange (ETDEWEB)
Ferreiro Perez, Roberto, E-mail: roferreiro@ccee.ucm.e [Departamento de Economia Financiera y Contabilidad I Facultad de Ciencias Economicas y Empresariales, UCM Campus de Somosaguas, 28223-Pozuelo de Alarcon (Spain)
2010-07-07
The Chern-Simons Lagrangian density in the space of metrics of a three-dimensional manifold M is not invariant under the action of diffeomorphisms on M. However, its Euler-Lagrange operator can be identified with the Cotton tensor, which is invariant under diffeomorphims. As the Lagrangian is not invariant, the Noether theorem cannot be applied to obtain conserved currents. We show that it is possible to obtain an equivariant conserved current for the Cotton tensor by using the first equivariant Pontryagin form on the bundle of metrics. Finally we define a Hamiltonian current which gives the contribution of the Chern-Simons term to the black hole entropy, energy and angular momentum.
Conserved current for the Cotton tensor, black hole entropy and equivariant Pontryagin forms
International Nuclear Information System (INIS)
Ferreiro Perez, Roberto
2010-01-01
The Chern-Simons Lagrangian density in the space of metrics of a three-dimensional manifold M is not invariant under the action of diffeomorphisms on M. However, its Euler-Lagrange operator can be identified with the Cotton tensor, which is invariant under diffeomorphims. As the Lagrangian is not invariant, the Noether theorem cannot be applied to obtain conserved currents. We show that it is possible to obtain an equivariant conserved current for the Cotton tensor by using the first equivariant Pontryagin form on the bundle of metrics. Finally we define a Hamiltonian current which gives the contribution of the Chern-Simons term to the black hole entropy, energy and angular momentum.
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.
Steiner trees for fixed orientation metrics
DEFF Research Database (Denmark)
Brazil, Marcus; Zachariasen, Martin
2009-01-01
We consider the problem of constructing Steiner minimum trees for a metric defined by a polygonal unit circle (corresponding to s = 2 weighted legal orientations in the plane). A linear-time algorithm to enumerate all angle configurations for degree three Steiner points is given. We provide...... a simple proof that the angle configuration for a Steiner point extends to all Steiner points in a full Steiner minimum tree, such that at most six orientations suffice for edges in a full Steiner minimum tree. We show that the concept of canonical forms originally introduced for the uniform orientation...... metric generalises to the fixed orientation metric. Finally, we give an O(s n) time algorithm to compute a Steiner minimum tree for a given full Steiner topology with n terminal leaves....
Enterprise Sustainment Metrics
2015-06-19
are negatively impacting KPIs” (Parmenter, 2010: 31). In the current state, the Air Force’s AA and PBL metrics are once again split . AA does...must have the authority to “take immediate action to rectify situations that are negatively impacting KPIs” (Parmenter, 2010: 31). 3. Measuring...highest profitability and shareholder value for each company” (2014: 273). By systematically diagraming a process, either through a swim lane flowchart
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.
Energy Technology Data Exchange (ETDEWEB)
Schatz, Martin D. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Kolda, Tamara G. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); van de Geijn, Robert [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
2015-09-01
Large-scale datasets in computational chemistry typically require distributed-memory parallel methods to perform a special operation known as tensor contraction. Tensors are multidimensional arrays, and a tensor contraction is akin to matrix multiplication with special types of permutations. Creating an efficient algorithm and optimized im- plementation in this domain is complex, tedious, and error-prone. To address this, we develop a notation to express data distributions so that we can apply use automated methods to find optimized implementations for tensor contractions. We consider the spin-adapted coupled cluster singles and doubles method from computational chemistry and use our methodology to produce an efficient implementation. Experiments per- formed on the IBM Blue Gene/Q and Cray XC30 demonstrate impact both improved performance and reduced memory consumption.
Tensor models, Kronecker coefficients and permutation centralizer algebras
Geloun, Joseph Ben; Ramgoolam, Sanjaye
2017-11-01
We show that the counting of observables and correlators for a 3-index tensor model are organized by the structure of a family of permutation centralizer algebras. These algebras are shown to be semi-simple and their Wedderburn-Artin decompositions into matrix blocks are given in terms of Clebsch-Gordan coefficients of symmetric groups. The matrix basis for the algebras also gives an orthogonal basis for the tensor observables which diagonalizes the Gaussian two-point functions. The centres of the algebras are associated with correlators which are expressible in terms of Kronecker coefficients (Clebsch-Gordan multiplicities of symmetric groups). The color-exchange symmetry present in the Gaussian model, as well as a large class of interacting models, is used to refine the description of the permutation centralizer algebras. This discussion is extended to a general number of colors d: it is used to prove the integrality of an infinite family of number sequences related to color-symmetrizations of colored graphs, and expressible in terms of symmetric group representation theory data. Generalizing a connection between matrix models and Belyi maps, correlators in Gaussian tensor models are interpreted in terms of covers of singular 2-complexes. There is an intriguing difference, between matrix and higher rank tensor models, in the computational complexity of superficially comparable correlators of observables parametrized by Young diagrams.
Numerical evaluation of tensor Feynman integrals in Euclidean kinematics
Energy Technology Data Exchange (ETDEWEB)
Gluza, J.; Kajda [Silesia Univ., Katowice (Poland). Inst. of Physics; Riemann, T.; Yundin, V. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany)
2010-10-15
For the investigation of higher order Feynman integrals, potentially with tensor structure, it is highly desirable to have numerical methods and automated tools for dedicated, but sufficiently 'simple' numerical approaches. We elaborate two algorithms for this purpose which may be applied in the Euclidean kinematical region and in d=4-2{epsilon} dimensions. One method uses Mellin-Barnes representations for the Feynman parameter representation of multi-loop Feynman integrals with arbitrary tensor rank. Our Mathematica package AMBRE has been extended for that purpose, and together with the packages MB (M. Czakon) or MBresolve (A. V. Smirnov and V. A. Smirnov) one may perform automatically a numerical evaluation of planar tensor Feynman integrals. Alternatively, one may apply sector decomposition to planar and non-planar multi-loop {epsilon}-expanded Feynman integrals with arbitrary tensor rank. We automatized the preparations of Feynman integrals for an immediate application of the package sectordecomposition (C. Bogner and S. Weinzierl) so that one has to give only a proper definition of propagators and numerators. The efficiency of the two implementations, based on Mellin-Barnes representations and sector decompositions, is compared. The computational packages are publicly available. (orig.)
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...
A Metric on Phylogenetic Tree Shapes.
Colijn, C; Plazzotta, G
2018-01-01
The shapes of evolutionary trees are influenced by the nature of the evolutionary process but comparisons of trees from different processes are hindered by the challenge of completely describing tree shape. We present a full characterization of the shapes of rooted branching trees in a form that lends itself to natural tree comparisons. We use this characterization to define a metric, in the sense of a true distance function, on tree shapes. The metric distinguishes trees from random models known to produce different tree shapes. It separates trees derived from tropical versus USA influenza A sequences, which reflect the differing epidemiology of tropical and seasonal flu. We describe several metrics based on the same core characterization, and illustrate how to extend the metric to incorporate trees' branch lengths or other features such as overall imbalance. Our approach allows us to construct addition and multiplication on trees, and to create a convex metric on tree shapes which formally allows computation of average tree shapes. © The Author(s) 2017. Published by Oxford University Press, on behalf of the Society of Systematic Biologists.
Comparative Study of Trace Metrics between Bibliometrics and Patentometrics
Directory of Open Access Journals (Sweden)
Fred Y. Ye
2016-06-01
Full Text Available Purpose: To comprehensively evaluate the overall performance of a group or an individual in both bibliometrics and patentometrics. Design/methodology/approach: Trace metrics were applied to the top 30 universities in the 2014 Academic Ranking of World Universities (ARWU — computer sciences, the top 30 ESI highly cited papers in the computer sciences field in 2014, as well as the top 30 assignees and the top 30 most cited patents in the National Bureau of Economic Research (NBER computer hardware and software category. Findings: We found that, by applying trace metrics, the research or marketing impact efficiency, at both group and individual levels, was clearly observed. Furthermore, trace metrics were more sensitive to the different publication-citation distributions than the average citation and h-index were. Research limitations: Trace metrics considered publications with zero citations as negative contributions. One should clarify how he/she evaluates a zero-citation paper or patent before applying trace metrics. Practical implications: Decision makers could regularly examinine the performance of their university/company by applying trace metrics and adjust their policies accordingly. Originality/value: Trace metrics could be applied both in bibliometrics and patentometrics and provide a comprehensive view. Moreover, the high sensitivity and unique impact efficiency view provided by trace metrics can facilitate decision makers in examining and adjusting their policies.
Effecting IT infrastructure culture change: management by processes and metrics
Miller, R. L.
2001-01-01
This talk describes the processes and metrics used by Jet Propulsion Laboratory to bring about the required IT infrastructure culture change to update and certify, as Y2K compliant, thousands of computers and millions of lines of code.
Software bug prediction using object-oriented metrics
Indian Academy of Sciences (India)
Dharmendra Lal Gupta
2 Department of Computer Science and Engineering, Mewar University, Chittorgarh 312901, India e-mail: ... the object-oriented technology has been widely accepted ... whereas project metrics cover the number of staff members involved in ...
An inheritance complexity metric for object-oriented code: A ...
Indian Academy of Sciences (India)
Department of Computer Engineering, Atilim University, 06836, Ankara, Turkey ... applied our metric on a real project for empirical validation and compared it with ... being insufficiently generalized or too implementation technology dependent.
Stress tensor correlators of CCFT{sub 2} using flat-space holography
Energy Technology Data Exchange (ETDEWEB)
Asadi, Mohammad; Baghchesaraei, Omid; Fareghbal, Reza [Shahid Beheshti University, Department of Physics, Tehran (Iran, Islamic Republic of)
2017-11-15
We use the correspondence between three-dimensional asymptotically flat spacetimes and two-dimensional contracted conformal field theories (CCFTs) to derive the stress tensor correlators of CCFT{sub 2}. On the gravity side we use the metric formulation instead of the Chern-Simons formulation of three-dimensional gravity. This method can also be used for the four-dimensional case, where there is no Chern-Simons formulation for the bulk theory. (orig.)
Analytical Cost Metrics : Days of Future Past
Energy Technology Data Exchange (ETDEWEB)
Prajapati, Nirmal [Colorado State Univ., Fort Collins, CO (United States); Rajopadhye, Sanjay [Colorado State Univ., Fort Collins, CO (United States); Djidjev, Hristo Nikolov [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2018-02-20
As we move towards the exascale era, the new architectures must be capable of running the massive computational problems efficiently. Scientists and researchers are continuously investing in tuning the performance of extreme-scale computational problems. These problems arise in almost all areas of computing, ranging from big data analytics, artificial intelligence, search, machine learning, virtual/augmented reality, computer vision, image/signal processing to computational science and bioinformatics. With Moore’s law driving the evolution of hardware platforms towards exascale, the dominant performance metric (time efficiency) has now expanded to also incorporate power/energy efficiency. Therefore the major challenge that we face in computing systems research is: “how to solve massive-scale computational problems in the most time/power/energy efficient manner?”
Normal estimation for pointcloud using GPU based sparse tensor voting
Liu , Ming; Pomerleau , François; Colas , Francis; Siegwart , Roland
2012-01-01
International audience; Normal estimation is the basis for most applications using pointcloud, such as segmentation. However, it is still a challenging problem regarding computational complexity and observation noise. In this paper, we propose a normal estimation method for pointcloud using results from tensor voting. Comparing with other approaches, we show it has smaller estimation error. Moreover, by varying the voting kernel size, we find it is a flexible approach for structure extraction...
Cosmological simulations using a static scalar-tensor theory
Energy Technology Data Exchange (ETDEWEB)
RodrIguez-Meza, M A [Depto. de Fisica, Instituto Nacional de Investigaciones Nucleares, Col. Escandon, Apdo. Postal 18-1027, 11801 Mexico D.F (Mexico); Gonzalez-Morales, A X [Departamento Ingenierias, Universidad Iberoamericana, Prol. Paseo de la Reforma 880 Lomas de Santa Fe, Mexico D.F. Mexico (Mexico); Gabbasov, R F [Depto. de Fisica, Instituto Nacional de Investigaciones Nucleares, Col. Escandon, Apdo. Postal 18-1027, 11801 Mexico D.F (Mexico); Cervantes-Cota, Jorge L [Depto. de Fisica, Instituto Nacional de Investigaciones Nucleares, Col. Escandon, Apdo. Postal 18-1027, 11801 Mexico D.F (Mexico)
2007-11-15
We present {lambda}CDM N-body cosmological simulations in the framework of of a static general scalar-tensor theory of gravity. Due to the influence of the non-minimally coupled scalar field, the gravitational potential is modified by a Yukawa type term, yielding a new structure formation dynamics. We present some preliminary results and, in particular, we compute the density and velocity profiles of the most massive group.
A Random Riemannian Metric for Probabilistic Shortest-Path Tractography
DEFF Research Database (Denmark)
Hauberg, Søren; Schober, Michael; Liptrot, Matthew George
2015-01-01
of the diffusion tensor as a “random Riemannian metric”, where a geodesic is a distribution over tracts. We approximate this distribution with a Gaussian process and present a probabilistic numerics algorithm for computing the geodesic distribution. We demonstrate SPT improvements on data from the Human Connectome...
Kerr metric in cosmological background
Energy Technology Data Exchange (ETDEWEB)
Vaidya, P C [Gujarat Univ., Ahmedabad (India). Dept. of Mathematics
1977-06-01
A metric satisfying Einstein's equation is given which in the vicinity of the source reduces to the well-known Kerr metric and which at large distances reduces to the Robertson-Walker metric of a nomogeneous cosmological model. The radius of the event horizon of the Kerr black hole in the cosmological background is found out.
Probabilistic inference with noisy-threshold models based on a CP tensor decomposition
Czech Academy of Sciences Publication Activity Database
Vomlel, Jiří; Tichavský, Petr
2014-01-01
Roč. 55, č. 4 (2014), s. 1072-1092 ISSN 0888-613X R&D Projects: GA ČR GA13-20012S; GA ČR GA102/09/1278 Institutional support: RVO:67985556 Keywords : Bayesian networks * Probabilistic inference * Candecomp-Parafac tensor decomposition * Symmetric tensor rank Subject RIV: JD - Computer Applications, Robotics Impact factor: 2.451, year: 2014 http://library.utia.cas.cz/separaty/2014/MTR/vomlel-0427059.pdf
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.
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...
Learning Low-Dimensional Metrics
Jain, Lalit; Mason, Blake; Nowak, Robert
2017-01-01
This paper investigates the theoretical foundations of metric learning, focused on three key questions that are not fully addressed in prior work: 1) we consider learning general low-dimensional (low-rank) metrics as well as sparse metrics; 2) we develop upper and lower (minimax)bounds on the generalization error; 3) we quantify the sample complexity of metric learning in terms of the dimension of the feature space and the dimension/rank of the underlying metric;4) we also bound the accuracy ...
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.
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.
CT-derived Biomechanical Metrics Improve Agreement Between Spirometry and Emphysema.
Bhatt, Surya P; Bodduluri, Sandeep; Newell, John D; Hoffman, Eric A; Sieren, Jessica C; Han, Meilan K; Dransfield, Mark T; Reinhardt, Joseph M
2016-10-01
Many patients with chronic obstructive pulmonary disease (COPD) have marked discordance between forced expiratory volume in 1 second (FEV1) and degree of emphysema on computed tomography (CT). Biomechanical differences between these patients have not been studied. We aimed to identify reasons for the discordance between CT and spirometry in some patients with COPD. Subjects with Global initiative for chronic Obstructive Lung Disease stages I-IV from a large multicenter study (The Genetic Epidemiology of COPD) were arranged by percentiles of %predicted FEV1 and emphysema on CT. Three categories were created using differences in percentiles: Catspir with predominant airflow obstruction/minimal emphysema, CatCT with predominant emphysema/minimal airflow obstruction, and Catmatched with matched FEV1 and emphysema. Image registration was used to derive Jacobian determinants, a measure of lung elasticity, anisotropy, and strain tensors, to assess biomechanical differences between groups. Regression models were created with the previously mentioned categories as outcome variable, adjusting for demographics, scanner type, quantitative CT-derived emphysema, gas trapping, and airway thickness (model 1), and after adding biomechanical CT metrics (model 2). Jacobian determinants, anisotropy, and strain tensors were strongly associated with FEV1. With Catmatched as control, model 2 predicted Catspir and CatCT better than model 1 (Akaike information criterion 255.8 vs. 320.8). In addition to demographics, the strongest independent predictors of FEV1 were Jacobian mean (β = 1.60,95%confidence intervals [CI] = 1.16 to 1.98; P spirometry, offering the potential for new insights into the linkage between regional parenchymal destruction and global decrement in lung function in patients with COPD. Copyright © 2016 The Association of University Radiologists. Published by Elsevier Inc. All rights reserved.
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...
arXiv Hybrid Fluid Models from Mutual Effective Metric Couplings
Kurkela, Aleksi; Preis, Florian; Rebhan, Anton; Soloviev, Alexander
Motivated by a semi-holographic approach to the dynamics of quark-gluon plasma which combines holographic and perturbative descriptions of a strongly coupled infrared and a more weakly coupled ultraviolet sector, we construct a hybrid two-fluid model where interactions between its two sectors are encoded by their effective metric backgrounds, which are determined mutually by their energy-momentum tensors. We derive the most general consistent ultralocal interactions such that the full system has a total conserved energy-momentum tensor in flat Minkowski space and study its consequences in and near thermal equilibrium by working out its phase structure and its hydrodynamic modes.
A higher-order tensor vessel tractography for segmentation of vascular structures.
Cetin, Suheyla; Unal, Gozde
2015-10-01
A new vascular structure segmentation method, which is based on a cylindrical flux-based higher order tensor (HOT), is presented. On a vessel structure, the HOT naturally models branching points, which create challenges for vessel segmentation algorithms. In a general linear HOT model embedded in 3D, one has to work with an even order tensor due to an enforced antipodal-symmetry on the unit sphere. However, in scenarios such as in a bifurcation, the antipodally-symmetric tensor embedded in 3D will not be useful. In order to overcome that limitation, we embed the tensor in 4D and obtain a structure that can model asymmetric junction scenarios. During construction of a higher order tensor (e.g. third or fourth order) in 4D, the orientation vectors lie on the unit 3-sphere, in contrast to the unit 2-sphere in 3D tensor modeling. This 4D tensor is exploited in a seed-based vessel segmentation algorithm, where the principal directions of the 4D HOT is obtained by decomposition, and used in a HOT tractography approach. We demonstrate quantitative validation of the proposed algorithm on both synthetic complex tubular structures as well as real cerebral vasculature in Magnetic Resonance Angiography (MRA) datasets and coronary arteries from Computed Tomography Angiography (CTA) volumes.
International Nuclear Information System (INIS)
Hartono, Albert; Lu, Qingda; Henretty, Thomas; Krishnamoorthy, Sriram; Zhang, Huaijian; Baumgartner, Gerald; Bernholdt, David E.; Nooijen, Marcel; Pitzer, Russell M.; Ramanujam, J.; Sadayappan, Ponnuswamy
2009-01-01
Complex tensor contraction expressions arise in accurate electronic structure models in quantum chemistry, such as the coupled cluster method. This paper addresses two complementary aspects of performance optimization of such tensor contraction expressions. Transformations using algebraic properties of commutativity and associativity can be used to significantly decrease the number of arithmetic operations required for evaluation of these expressions. The identification of common subexpressions among a set of tensor contraction expressions can result in a reduction of the total number of operations required to evaluate the tensor contractions. The first part of the paper describes an effective algorithm for operation minimization with common subexpression identification and demonstrates its effectiveness on tensor contraction expressions for coupled cluster equations. The second part of the paper highlights the importance of data layout transformation in the optimization of tensor contraction computations on modern processors. A number of considerations such as minimization of cache misses and utilization of multimedia vector instructions are discussed. A library for efficient index permutation of multi-dimensional tensors is described and experimental performance data is provided that demonstrates its effectiveness.
International Nuclear Information System (INIS)
Krishnamoorthy, Sriram; Bernholdt, David E.; Pitzer, R.M.; Sadayappan, Ponnuswamy
2009-01-01
Complex tensor contraction expressions arise in accurate electronic structure models in quantum chemistry, such as the coupled cluster method. This paper addresses two complementary aspects of performance optimization of such tensor contraction expressions. Transformations using algebraic properties of commutativity and associativity can be used to significantly decrease the number of arithmetic operations required for evaluation of these expressions. The identification of common subexpressions among a set of tensor contraction expressions can result in a reduction of the total number of operations required to evaluate the tensor contractions. The first part of the paper describes an effective algorithm for operation minimization with common subexpression identification and demonstrates its effectiveness on tensor contraction expressions for coupled cluster equations. The second part of the paper highlights the importance of data layout transformation in the optimization of tensor contraction computations on modern processors. A number of considerations, such as minimization of cache misses and utilization of multimedia vector instructions, are discussed. A library for efficient index permutation of multidimensional tensors is described, and experimental performance data is provided that demonstrates its effectiveness.
Tri-Clustered Tensor Completion for Social-Aware Image Tag Refinement.
Tang, Jinhui; Shu, Xiangbo; Qi, Guo-Jun; Li, Zechao; Wang, Meng; Yan, Shuicheng; Jain, Ramesh
2017-08-01
Social image tag refinement, which aims to improve tag quality by automatically completing the missing tags and rectifying the noise-corrupted ones, is an essential component for social image search. Conventional approaches mainly focus on exploring the visual and tag information, without considering the user information, which often reveals important hints on the (in)correct tags of social images. Towards this end, we propose a novel tri-clustered tensor completion framework to collaboratively explore these three kinds of information to improve the performance of social image tag refinement. Specifically, the inter-relations among users, images and tags are modeled by a tensor, and the intra-relations between users, images and tags are explored by three regularizations respectively. To address the challenges of the super-sparse and large-scale tensor factorization that demands expensive computing and memory cost, we propose a novel tri-clustering method to divide the tensor into a certain number of sub-tensors by simultaneously clustering users, images and tags into a bunch of tri-clusters. And then we investigate two strategies to complete these sub-tensors by considering (in)dependence between the sub-tensors. Experimental results on a real-world social image database demonstrate the superiority of the proposed method compared with the state-of-the-art methods.
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.)
A Tensor Statistical Model for Quantifying Dynamic Functional Connectivity.
Zhu, Yingying; Zhu, Xiaofeng; Kim, Minjeong; Yan, Jin; Wu, Guorong
2017-06-01
-of-the-art methods which in contrast perform above two steps separately. We have applied our tensor statistical model to identify ASD (Autism Spectrum Disorder) by using the learned dFC patterns. Promising classification results have been achieved demonstrating high discrimination power and great potentials in computer assisted diagnosis of neuro-disorders.
Alvizuri, Celso R.
We present a catalog of full seismic moment tensors for 63 events from Uturuncu volcano in Bolivia. The events were recorded during 2011-2012 in the PLUTONS seismic array of 24 broadband stations. Most events had magnitudes between 0.5 and 2.0 and did not generate discernible surface waves; the largest event was Mw 2.8. For each event we computed the misfit between observed and synthetic waveforms, and we used first-motion polarity measurements to reduce the number of possible solutions. Each moment tensor solution was obtained using a grid search over the six-dimensional space of moment tensors. For each event we show the misfit function in eigenvalue space, represented by a lune. We identify three subsets of the catalog: (1) 6 isotropic events, (2) 5 tensional crack events, and (3) a swarm of 14 events southeast of the volcanic center that appear to be double couples. The occurrence of positively isotropic events is consistent with other published results from volcanic and geothermal regions. Several of these previous results, as well as our results, cannot be interpreted within the context of either an oblique opening crack or a crack-plus-double-couple model. Proper characterization of uncertainties for full moment tensors is critical for distinguishing among physical models of source processes. A seismic moment tensor is a 3x3 symmetric matrix that provides a compact representation of a seismic source. We develop an algorithm to estimate moment tensors and their uncertainties from observed seismic data. For a given event, the algorithm performs a grid search over the six-dimensional space of moment tensors by generating synthetic waveforms for each moment tensor and then evaluating a misfit function between the observed and synthetic waveforms. 'The' moment tensor M0 for the event is then the moment tensor with minimum misfit. To describe the uncertainty associated with M0, we first convert the misfit function to a probability function. The uncertainty, or
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).
International Nuclear Information System (INIS)
Minkowski, P.
1986-01-01
The metric and contorsion tensors are constructed which yield a combined Riemann curvature tensor of the form Rsup(+-)sub(μνsigmatau)=(1/2a 2 )(gsub(μsigma)gsub(νtau) - gsub(μtau)gsub(νsigma)+-√g epsilonsub(μνsigmatau)). The metric with euclidean signature (++++) describes a sphere S 4 with radius a, i.e. admits the isometry group O5. For selfdual (antiselfdual) curvature tensor the contorsion tensor is given by the antiselfdual (selfdual) instanton configuration with respect to the spin gauge group SU2sub(R) (SU2sub(L)). The selfdual (antiselfdual) Riemann tensor admits two covariantly constant right-handed (left-handed) spin 1/2 fermion zero modes, one J=1/2 and one J=3/2 right-handed (left-handed) multiplet corresponding to L=1, transforming as a pseudoreal representation of O4 (SU2sub(R(L))). The hermitean Dirac equation retains only the two constant chiral modes. (orig.)
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.
Emergent gravity from vanishing energy-momentum tensor
Energy Technology Data Exchange (ETDEWEB)
Carone, Christopher D.; Erlich, Joshua [High Energy Theory Group, Department of Physics, College of William and Mary,Williamsburg, VA 23187-8795 (United States); Vaman, Diana [Department of Physics, University of Virginia,Box 400714, Charlottesville, VA 22904 (United States)
2017-03-27
A constraint of vanishing energy-momentum tensor is motivated by a variety of perspectives on quantum gravity. We demonstrate in a concrete example how this constraint leads to a metric-independent theory in which quantum gravity emerges as a nonperturbative artifact of regularization-scale physics. We analyze a scalar theory similar to the Dirac-Born-Infeld (DBI) theory with vanishing gauge fields, with the DBI Lagrangian modulated by a scalar potential. In the limit of a large number of scalars, we explicitly demonstrate the existence of a composite massless spin-2 graviton in the spectrum that couples to matter as in Einstein gravity. We comment on the cosmological constant problem and the generalization to theories with fermions and gauge fields.
Emergent gravity from vanishing energy-momentum tensor
International Nuclear Information System (INIS)
Carone, Christopher D.; Erlich, Joshua; Vaman, Diana
2017-01-01
A constraint of vanishing energy-momentum tensor is motivated by a variety of perspectives on quantum gravity. We demonstrate in a concrete example how this constraint leads to a metric-independent theory in which quantum gravity emerges as a nonperturbative artifact of regularization-scale physics. We analyze a scalar theory similar to the Dirac-Born-Infeld (DBI) theory with vanishing gauge fields, with the DBI Lagrangian modulated by a scalar potential. In the limit of a large number of scalars, we explicitly demonstrate the existence of a composite massless spin-2 graviton in the spectrum that couples to matter as in Einstein gravity. We comment on the cosmological constant problem and the generalization to theories with fermions and gauge fields.
Kaluza-Klein gravity and scalar-tensor theories
International Nuclear Information System (INIS)
Chauvineau, Bertrand
2007-01-01
In this paper, we propose a Kaluza-Klein approach to gravity in Δ=4+n 1 +n 2 +... dimensions, where n 1 ,n 2 ,... are the dimensions of independent internal spaces. One is interested in the case where each internal metric depends on the four-dimensional coordinates by a conformal factor. If all these conformal factors depend on the four-dimensional coordinates through a common scalar function Ψ, the induced effective four-dimensional gravity theory turns out to be of general scalar-tensor type. One shows that, if there are at least two internal spaces, the theory is not ruled out by experimental tests on gravitation, even if there is no massive scalar-potential term in the effective four-dimensional Lagrangian (contrary to what happens if there is only one internal space, in which case ω is of order unity, whatever the dimension of this internal space)
Image processing tensor transform and discrete tomography with Matlab
Grigoryan, Artyom M
2012-01-01
Focusing on mathematical methods in computer tomography, Image Processing: Tensor Transform and Discrete Tomography with MATLAB(R) introduces novel approaches to help in solving the problem of image reconstruction on the Cartesian lattice. Specifically, it discusses methods of image processing along parallel rays to more quickly and accurately reconstruct images from a finite number of projections, thereby avoiding overradiation of the body during a computed tomography (CT) scan. The book presents several new ideas, concepts, and methods, many of which have not been published elsewhere. New co
Tensor numerical methods in quantum chemistry: from Hartree-Fock to excitation energies.
Khoromskaia, Venera; Khoromskij, Boris N
2015-12-21
We resume the recent successes of the grid-based tensor numerical methods and discuss their prospects in real-space electronic structure calculations. These methods, based on the low-rank representation of the multidimensional functions and integral operators, first appeared as an accurate tensor calculus for the 3D Hartree potential using 1D complexity operations, and have evolved to entirely grid-based tensor-structured 3D Hartree-Fock eigenvalue solver. It benefits from tensor calculation of the core Hamiltonian and two-electron integrals (TEI) in O(n log n) complexity using the rank-structured approximation of basis functions, electron densities and convolution integral operators all represented on 3D n × n × n Cartesian grids. The algorithm for calculating TEI tensor in a form of the Cholesky decomposition is based on multiple factorizations using algebraic 1D "density fitting" scheme, which yield an almost irreducible number of product basis functions involved in the 3D convolution integrals, depending on a threshold ε > 0. The basis functions are not restricted to separable Gaussians, since the analytical integration is substituted by high-precision tensor-structured numerical quadratures. The tensor approaches to post-Hartree-Fock calculations for the MP2 energy correction and for the Bethe-Salpeter excitation energies, based on using low-rank factorizations and the reduced basis method, were recently introduced. Another direction is towards the tensor-based Hartree-Fock numerical scheme for finite lattices, where one of the numerical challenges is the summation of electrostatic potentials of a large number of nuclei. The 3D grid-based tensor method for calculation of a potential sum on a L × L × L lattice manifests the linear in L computational work, O(L), instead of the usual O(L(3) log L) scaling by the Ewald-type approaches.
High Order Tensor Formulation for Convolutional Sparse Coding
Bibi, Adel Aamer
2017-12-25
Convolutional sparse coding (CSC) has gained attention for its successful role as a reconstruction and a classification tool in the computer vision and machine learning community. Current CSC methods can only reconstruct singlefeature 2D images independently. However, learning multidimensional dictionaries and sparse codes for the reconstruction of multi-dimensional data is very important, as it examines correlations among all the data jointly. This provides more capacity for the learned dictionaries to better reconstruct data. In this paper, we propose a generic and novel formulation for the CSC problem that can handle an arbitrary order tensor of data. Backed with experimental results, our proposed formulation can not only tackle applications that are not possible with standard CSC solvers, including colored video reconstruction (5D- tensors), but it also performs favorably in reconstruction with much fewer parameters as compared to naive extensions of standard CSC to multiple features/channels.
Boundary stress tensors for spherically-symmetric conformal Rindler observers
Energy Technology Data Exchange (ETDEWEB)
Culetu, Hristu [Ovidius University, Constanta (Romania)
2010-06-15
The boundary energy-momentum tensors for a static observer in the conformally flat Rindler geometry are considered. We find that the surface energy density is positive far from the Planck world, but that the transversal pressures are negative. The kinematical parameters associated with the nongeodesic congruence of static observers are computed. The entropy S corresponding to the degrees of freedom on the 2-surface of constant {rho} and t equals the horizon entropy of a black hole with a time-dependent mass, and the Padmanabhan expression E = 2ST is obeyed. The 2-surface shear tensor is vanishing, and the coefficient of the bulk viscosity {zeta} is 1/16 {pi}, so the negative pressure due to it acts as a surface tension.
Effective gravitational wave stress-energy tensor in alternative theories of gravity
International Nuclear Information System (INIS)
Stein, Leo C.; Yunes, Nicolas
2011-01-01
The inspiral of binary systems in vacuum is controlled by the stress-energy of gravitational radiation and any other propagating degrees of freedom. For gravitational waves, the dominant contribution is characterized by an effective stress-energy tensor at future null infinity. We employ perturbation theory and the short-wavelength approximation to compute this stress-energy tensor in a wide class of alternative theories. We find that this tensor is generally a modification of that first computed by Isaacson, where the corrections can dominate over the general relativistic term. In a wide class of theories, however, these corrections identically vanish at asymptotically flat, future, null infinity, reducing the stress-energy tensor to Isaacson's. We exemplify this phenomenon by first considering dynamical Chern-Simons modified gravity, which corrects the action via a scalar field and the contraction of the Riemann tensor and its dual. We then consider a wide class of theories with dynamical scalar fields coupled to higher-order curvature invariants and show that the gravitational wave stress-energy tensor still reduces to Isaacson's. The calculations presented in this paper are crucial to perform systematic tests of such modified gravity theories through the orbital decay of binary pulsars or through gravitational wave observations.
Tensor decomposition in electronic structure calculations on 3D Cartesian grids
International Nuclear Information System (INIS)
Khoromskij, B.N.; Khoromskaia, V.; Chinnamsetty, S.R.; Flad, H.-J.
2009-01-01
In this paper, we investigate a novel approach based on the combination of Tucker-type and canonical tensor decomposition techniques for the efficient numerical approximation of functions and operators in electronic structure calculations. In particular, we study applicability of tensor approximations for the numerical solution of Hartree-Fock and Kohn-Sham equations on 3D Cartesian grids. We show that the orthogonal Tucker-type tensor approximation of electron density and Hartree potential of simple molecules leads to low tensor rank representations. This enables an efficient tensor-product convolution scheme for the computation of the Hartree potential using a collocation-type approximation via piecewise constant basis functions on a uniform nxnxn grid. Combined with the Richardson extrapolation, our approach exhibits O(h 3 ) convergence in the grid-size h=O(n -1 ). Moreover, this requires O(3rn+r 3 ) storage, where r denotes the Tucker rank of the electron density with r=O(logn), almost uniformly in n. For example, calculations of the Coulomb matrix and the Hartree-Fock energy for the CH 4 molecule, with a pseudopotential on the C atom, achieved accuracies of the order of 10 -6 hartree with a grid-size n of several hundreds. Since the tensor-product convolution in 3D is performed via 1D convolution transforms, our scheme markedly outperforms the 3D-FFT in both the computing time and storage requirements.
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.
Completion of a Dislocated Metric Space
Directory of Open Access Journals (Sweden)
P. Sumati Kumari
2015-01-01
Full Text Available We provide a construction for the completion of a dislocated metric space (abbreviated d-metric space; we also prove that the completion of the metric associated with a d-metric coincides with the metric associated with the completion of the d-metric.
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.
Metric adjusted skew information
DEFF Research Database (Denmark)
Hansen, Frank
2008-01-01
) that vanishes for observables commuting with the state. We show that the skew information is a convex function on the manifold of states. It also satisfies other requirements, proposed by Wigner and Yanase, for an effective measure-of-information content of a state relative to a conserved observable. We...... establish a connection between the geometrical formulation of quantum statistics as proposed by Chentsov and Morozova and measures of quantum information as introduced by Wigner and Yanase and extended in this article. We show that the set of normalized Morozova-Chentsov functions describing the possible......We extend the concept of Wigner-Yanase-Dyson skew information to something we call "metric adjusted skew information" (of a state with respect to a conserved observable). This "skew information" is intended to be a non-negative quantity bounded by the variance (of an observable in a state...
INFORMATIVE ENERGY METRIC FOR SIMILARITY MEASURE IN REPRODUCING KERNEL HILBERT SPACES
Directory of Open Access Journals (Sweden)
Songhua Liu
2012-02-01
Full Text Available In this paper, information energy metric (IEM is obtained by similarity computing for high-dimensional samples in a reproducing kernel Hilbert space (RKHS. Firstly, similar/dissimilar subsets and their corresponding informative energy functions are defined. Secondly, IEM is proposed for similarity measure of those subsets, which converts the non-metric distances into metric ones. Finally, applications of this metric is introduced, such as classification problems. Experimental results validate the effectiveness of the proposed method.
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
lakemorpho: Calculating lake morphometry metrics in R.
Hollister, Jeffrey; Stachelek, Joseph
2017-01-01
Metrics describing the shape and size of lakes, known as lake morphometry metrics, are important for any limnological study. In cases where a lake has long been the subject of study these data are often already collected and are openly available. Many other lakes have these data collected, but access is challenging as it is often stored on individual computers (or worse, in filing cabinets) and is available only to the primary investigators. The vast majority of lakes fall into a third category in which the data are not available. This makes broad scale modelling of lake ecology a challenge as some of the key information about in-lake processes are unavailable. While this valuable in situ information may be difficult to obtain, several national datasets exist that may be used to model and estimate lake morphometry. In particular, digital elevation models and hydrography have been shown to be predictive of several lake morphometry metrics. The R package lakemorpho has been developed to utilize these data and estimate the following morphometry metrics: surface area, shoreline length, major axis length, minor axis length, major and minor axis length ratio, shoreline development, maximum depth, mean depth, volume, maximum lake length, mean lake width, maximum lake width, and fetch. In this software tool article we describe the motivation behind developing lakemorpho , discuss the implementation in R, and describe the use of lakemorpho with an example of a typical use case.
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
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.
The metric system: An introduction
Energy Technology Data Exchange (ETDEWEB)
Lumley, S.M.
1995-05-01
On July 13, 1992, Deputy Director Duane Sewell restated the Laboratory`s policy on conversion to the metric system which was established in 1974. Sewell`s memo announced the Laboratory`s intention to continue metric conversion on a reasonable and cost effective basis. Copies of the 1974 and 1992 Administrative Memos are contained in the Appendix. There are three primary reasons behind the Laboratory`s conversion to the metric system. First, Public Law 100-418, passed in 1988, states that by the end of fiscal year 1992 the Federal Government must begin using metric units in grants, procurements, and other business transactions. Second, on July 25, 1991, President George Bush signed Executive Order 12770 which urged Federal agencies to expedite conversion to metric units. Third, the contract between the University of California and the Department of Energy calls for the Laboratory to convert to the metric system. Thus, conversion to the metric system is a legal requirement and a contractual mandate with the University of California. Public Law 100-418 and Executive Order 12770 are discussed in more detail later in this section, but first they examine the reasons behind the nation`s conversion to the metric system. The second part of this report is on applying the metric system.
The metric system: An introduction
Lumley, Susan M.
On 13 Jul. 1992, Deputy Director Duane Sewell restated the Laboratory's policy on conversion to the metric system which was established in 1974. Sewell's memo announced the Laboratory's intention to continue metric conversion on a reasonable and cost effective basis. Copies of the 1974 and 1992 Administrative Memos are contained in the Appendix. There are three primary reasons behind the Laboratory's conversion to the metric system. First, Public Law 100-418, passed in 1988, states that by the end of fiscal year 1992 the Federal Government must begin using metric units in grants, procurements, and other business transactions. Second, on 25 Jul. 1991, President George Bush signed Executive Order 12770 which urged Federal agencies to expedite conversion to metric units. Third, the contract between the University of California and the Department of Energy calls for the Laboratory to convert to the metric system. Thus, conversion to the metric system is a legal requirement and a contractual mandate with the University of California. Public Law 100-418 and Executive Order 12770 are discussed in more detail later in this section, but first they examine the reasons behind the nation's conversion to the metric system. The second part of this report is on applying the metric system.
Metric-adjusted skew information
DEFF Research Database (Denmark)
Liang, Cai; Hansen, Frank
2010-01-01
on a bipartite system and proved superadditivity of the Wigner-Yanase-Dyson skew informations for such states. We extend this result to the general metric-adjusted skew information. We finally show that a recently introduced extension to parameter values 1 ...We give a truly elementary proof of the convexity of metric-adjusted skew information following an idea of Effros. We extend earlier results of weak forms of superadditivity to general metric-adjusted skew information. Recently, Luo and Zhang introduced the notion of semi-quantum states...... of (unbounded) metric-adjusted skew information....
Directory of Open Access Journals (Sweden)
Isabel Garrido
2016-04-01
Full Text Available The class of metric spaces (X,d known as small-determined spaces, introduced by Garrido and Jaramillo, are properly defined by means of some type of real-valued Lipschitz functions on X. On the other hand, B-simple metric spaces introduced by Hejcman are defined in terms of some kind of bornologies of bounded subsets of X. In this note we present a common framework where both classes of metric spaces can be studied which allows us to see not only the relationships between them but also to obtain new internal characterizations of these metric properties.
Cosmology of hybrid metric-Palatini f(X)-gravity
International Nuclear Information System (INIS)
Capozziello, Salvatore; Harko, Tiberiu; Koivisto, Tomi S.; Lobo, Francisco S.N.; Olmo, Gonzalo J.
2013-01-01
A new class of modified theories of gravity, consisting of the superposition of the metric Einstein-Hilbert Lagrangian with an f(R) term constructed à la Palatini was proposed recently. The dynamically equivalent scalar-tensor representation of the model was also formulated, and it was shown that even if the scalar field is very light, the theory passes the Solar System observational constraints. Therefore the model predicts the existence of a long-range scalar field, modifying the cosmological and galactic dynamics. An explicit model that passes the local tests and leads to cosmic acceleration was also obtained. In the present work, it is shown that the theory can be also formulated in terms of the quantity X≡κ 2 T+R, where T and R are the traces of the stress-energy and Ricci tensors, respectively. The variable X represents the deviation with respect to the field equation trace of general relativity. The cosmological applications of this hybrid metric-Palatini gravitational theory are also explored, and cosmological solutions coming from the scalar-tensor representation of f(X)-gravity are presented. Criteria to obtain cosmic acceleration are discussed and the field equations are analyzed as a dynamical system. Several classes of dynamical cosmological solutions, depending on the functional form of the effective scalar field potential, describing both accelerating and decelerating Universes are explicitly obtained. Furthermore, the cosmological perturbation equations are derived and applied to uncover the nature of the propagating scalar degree of freedom and the signatures these models predict in the large-scale structure
Metric elasticity in a collapsing star: Gravitational radiation coupled to torsional motion
International Nuclear Information System (INIS)
Gerlach, U.H.; Scott, J.F.
1986-01-01
Torsional oscillatory matter motion as well as differential rotation couple via the linearized Einstein field equations to the gravitational degrees of freedom. For an arbitrary spherically symmetric background, such as that of a wildly pulsating or a catastrophically collapsing star, we exhibit (a) the strain tensor and (b) the corresponding stress-energy tensor. It is found that in the star there are two elasticity tensors. One expresses the familiar elasticity of matter, the other expresses the elasticity of the geometry. This metric elasticity is responsible for coupling the gravitational and matter degrees of freedom. The two coupled scalar wave equations for these degrees of freedom are exhibited. Also exhibited are their characteristics as well as the junction conditions for their solutions across any spherical surface of discontinuity
On degenerate metrics, dark matter and unification
Searight, Trevor P.
2017-12-01
A five-dimensional theory of relativity is presented which suggests that gravitation and electromagnetism may be unified using a degenerate metric. There are four fields (in the four-dimensional sense): a tensor field, two vector fields, and a scalar field, and they are unified with a combination of a gauge-like invariance and a reflection symmetry which means that both vector fields are photons. The gauge-like invariance implies that the fifth dimension is not directly observable; it also implies that charge is a constant of motion. The scalar field is analogous to the Brans-Dicke scalar field, and the theory tends towards the Einstein-Maxwell theory in the limit as the coupling constant tends to infinity. As there is some scope for fields to vary in the fifth dimension, it is possible for the photons to have wave behaviour in the fifth dimension. The wave behaviour has two effects: it gives mass to the photons, and it prevents them from interacting directly with normal matter. These massive photons still act as a source of gravity, however, and therefore they are candidates for dark matter.
Characterizing granular networks using topological metrics
Dijksman, Joshua A.; Kovalcinova, Lenka; Ren, Jie; Behringer, Robert P.; Kramar, Miroslav; Mischaikow, Konstantin; Kondic, Lou
2018-04-01
We carry out a direct comparison of experimental and numerical realizations of the exact same granular system as it undergoes shear jamming. We adjust the numerical methods used to optimally represent the experimental settings and outcomes up to microscopic contact force dynamics. Measures presented here range from microscopic through mesoscopic to systemwide characteristics of the system. Topological properties of the mesoscopic force networks provide a key link between microscales and macroscales. We report two main findings: (1) The number of particles in the packing that have at least two contacts is a good predictor for the mechanical state of the system, regardless of strain history and packing density. All measures explored in both experiments and numerics, including stress-tensor-derived measures and contact numbers depend in a universal manner on the fraction of nonrattler particles, fNR. (2) The force network topology also tends to show this universality, yet the shape of the master curve depends much more on the details of the numerical simulations. In particular we show that adding force noise to the numerical data set can significantly alter the topological features in the data. We conclude that both fNR and topological metrics are useful measures to consider when quantifying the state of a granular system.
Self-benchmarking Guide for Cleanrooms: Metrics, Benchmarks, Actions
Energy Technology Data Exchange (ETDEWEB)
Mathew, Paul; Sartor, Dale; Tschudi, William
2009-07-13
This guide describes energy efficiency metrics and benchmarks that can be used to track the performance of and identify potential opportunities to reduce energy use in laboratory buildings. This guide is primarily intended for personnel who have responsibility for managing energy use in existing laboratory facilities - including facilities managers, energy managers, and their engineering consultants. Additionally, laboratory planners and designers may also use the metrics and benchmarks described in this guide for goal-setting in new construction or major renovation. This guide provides the following information: (1) A step-by-step outline of the benchmarking process. (2) A set of performance metrics for the whole building as well as individual systems. For each metric, the guide provides a definition, performance benchmarks, and potential actions that can be inferred from evaluating this metric. (3) A list and descriptions of the data required for computing the metrics. This guide is complemented by spreadsheet templates for data collection and for computing the benchmarking metrics. This guide builds on prior research supported by the national Laboratories for the 21st Century (Labs21) program, supported by the U.S. Department of Energy and the U.S. Environmental Protection Agency. Much of the benchmarking data are drawn from the Labs21 benchmarking database and technical guides. Additional benchmark data were obtained from engineering experts including laboratory designers and energy managers.
Self-benchmarking Guide for Laboratory Buildings: Metrics, Benchmarks, Actions
Energy Technology Data Exchange (ETDEWEB)
Mathew, Paul; Greenberg, Steve; Sartor, Dale
2009-07-13
This guide describes energy efficiency metrics and benchmarks that can be used to track the performance of and identify potential opportunities to reduce energy use in laboratory buildings. This guide is primarily intended for personnel who have responsibility for managing energy use in existing laboratory facilities - including facilities managers, energy managers, and their engineering consultants. Additionally, laboratory planners and designers may also use the metrics and benchmarks described in this guide for goal-setting in new construction or major renovation. This guide provides the following information: (1) A step-by-step outline of the benchmarking process. (2) A set of performance metrics for the whole building as well as individual systems. For each metric, the guide provides a definition, performance benchmarks, and potential actions that can be inferred from evaluating this metric. (3) A list and descriptions of the data required for computing the metrics. This guide is complemented by spreadsheet templates for data collection and for computing the benchmarking metrics. This guide builds on prior research supported by the national Laboratories for the 21st Century (Labs21) program, supported by the U.S. Department of Energy and the U.S. Environmental Protection Agency. Much of the benchmarking data are drawn from the Labs21 benchmarking database and technical guides. Additional benchmark data were obtained from engineering experts including laboratory designers and energy managers.
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.
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.
Multimetric indices: How many metrics?
Multimetric indices (MMI’s) often include 5 to 15 metrics, each representing a different attribute of assemblage condition, such as species diversity, tolerant taxa, and nonnative taxa. Is there an optimal number of metrics for MMIs? To explore this question, I created 1000 9-met...
Metrical Phonology: German Sound System.
Tice, Bradley S.
Metrical phonology, a linguistic process of phonological stress assessment and diagrammatic simplification of sentence and word stress, is discussed as it is found in the English and German languages. The objective is to promote use of metrical phonology as a tool for enhancing instruction in stress patterns in words and sentences, particularly in…
Extending cosmology: the metric approach
Mendoza, S.
2012-01-01
Comment: 2012, Extending Cosmology: The Metric Approach, Open Questions in Cosmology; Review article for an Intech "Open questions in cosmology" book chapter (19 pages, 3 figures). Available from: http://www.intechopen.com/books/open-questions-in-cosmology/extending-cosmology-the-metric-approach
International Nuclear Information System (INIS)
Douglas, Michael R.; Karp, Robert L.; Lukic, Sergio; Reinbacher, Rene
2008-01-01
We develop numerical methods for approximating Ricci flat metrics on Calabi-Yau hypersurfaces in projective spaces. Our approach is based on finding balanced metrics and builds on recent theoretical work by Donaldson. We illustrate our methods in detail for a one parameter family of quintics. We also suggest several ways to extend our results
High resolution metric imaging payload
Delclaud, Y.
2017-11-01
Alcatel Space Industries has become Europe's leader in the field of high and very high resolution optical payloads, in the frame work of earth observation system able to provide military government with metric images from space. This leadership allowed ALCATEL to propose for the export market, within a French collaboration frame, a complete space based system for metric observation.
Wireless Sensor Network Metrics for Real-Time Systems
2009-05-20
Wireless Sensor Network Metrics for Real-Time Systems Phoebus Wei-Chih Chen Electrical Engineering and Computer Sciences University of California at...3. DATES COVERED 00-00-2009 to 00-00-2009 4. TITLE AND SUBTITLE Wireless Sensor Network Metrics for Real-Time Systems 5a. CONTRACT NUMBER 5b... wireless sensor networks (WSNs) is moving from studies of WSNs in isolation toward studies where the WSN is treated as a component of a larger system
User Metrics in NASA Earth Science Data Systems
Lynnes, Chris
2018-01-01
This presentation the collection and use of user metrics in NASA's Earth Science data systems. A variety of collection methods is discussed, with particular emphasis given to the American Customer Satisfaction Index (ASCI). User sentiment on potential use of cloud computing is presented, with generally positive responses. The presentation also discusses various forms of automatically collected metrics, including an example of the relative usage of different functions within the Giovanni analysis system.
TensorFlow: Large-Scale Machine Learning on Heterogeneous Distributed Systems
Abadi, Martín; Agarwal, Ashish; Barham, Paul; Brevdo, Eugene; Chen, Zhifeng; Citro, Craig; Corrado, Greg S.; Davis, Andy; Dean, Jeffrey; Devin, Matthieu; Ghemawat, Sanjay; Goodfellow, Ian; Harp, Andrew; Irving, Geoffrey; Isard, Michael
2016-01-01
TensorFlow is an interface for expressing machine learning algorithms, and an implementation for executing such algorithms. A computation expressed using TensorFlow can be executed with little or no change on a wide variety of heterogeneous systems, ranging from mobile devices such as phones and tablets up to large-scale distributed systems of hundreds of machines and thousands of computational devices such as GPU cards. The system is flexible and can be used to express a wide variety of algo...
Energy Technology Data Exchange (ETDEWEB)
Gibbons, Gary W. [DAMTP, University of Cambridge, Wilberforce Road, Cambridge, CB3 0WA U.K. (United Kingdom); Volkov, Mikhail S., E-mail: gwg1@cam.ac.uk, E-mail: volkov@lmpt.univ-tours.fr [Laboratoire de Mathématiques et Physique Théorique, LMPT CNRS—UMR 7350, Université de Tours, Parc de Grandmont, Tours, 37200 France (France)
2017-05-01
We study solutions obtained via applying dualities and complexifications to the vacuum Weyl metrics generated by massive rods and by point masses. Rescaling them and extending to complex parameter values yields axially symmetric vacuum solutions containing singularities along circles that can be viewed as singular matter sources. These solutions have wormhole topology with several asymptotic regions interconnected by throats and their sources can be viewed as thin rings of negative tension encircling the throats. For a particular value of the ring tension the geometry becomes exactly flat although the topology remains non-trivial, so that the rings literally produce holes in flat space. To create a single ring wormhole of one metre radius one needs a negative energy equivalent to the mass of Jupiter. Further duality transformations dress the rings with the scalar field, either conventional or phantom. This gives rise to large classes of static, axially symmetric solutions, presumably including all previously known solutions for a gravity-coupled massless scalar field, as for example the spherically symmetric Bronnikov-Ellis wormholes with phantom scalar. The multi-wormholes contain infinite struts everywhere at the symmetry axes, apart from solutions with locally flat geometry.
Flavour fields in steady state: stress tensor and free energy
International Nuclear Information System (INIS)
Banerjee, Avik; Kundu, Arnab; Kundu, Sandipan
2016-01-01
The dynamics of a probe brane in a given gravitational background is governed by the Dirac-Born-Infeld action. The corresponding open string metric arises naturally in studying the fluctuations on the probe. In Gauge-String duality, it is known that in the presence of a constant electric field on the worldvolume of the probe, the open string metric acquires an event horizon and therefore the fluctuation modes on the probe experience an effective temperature. In this article, we bring together various properties of such a system to a formal definition and a subsequent narration of the effective thermodynamics and the stress tensor of the corresponding flavour fields, also including a non-vanishing chemical potential. In doing so, we point out a potentially infinitely-degenerate scheme-dependence of regularizing the free energy, which nevertheless yields a universal contribution in certain cases. This universal piece appears as the coefficient of a log-divergence in free energy when a space-filling probe brane is embedded in AdS d+1 -background, for d=2,4, and is related to conformal anomaly. For the special case of d=2, the universal factor has a striking resemblance to the well-known heat current formula in (1+1)-dimensional conformal field theory in steady-state, which endows a plausible physical interpretation to it. Interestingly, we observe a vanishing conformal anomaly in d=6.
Sparse tensor spherical harmonics approximation in radiative transfer
International Nuclear Information System (INIS)
Grella, K.; Schwab, Ch.
2011-01-01
The stationary monochromatic radiative transfer equation is a partial differential transport equation stated on a five-dimensional phase space. To obtain a well-posed problem, boundary conditions have to be prescribed on the inflow part of the domain boundary. We solve the equation with a multi-level Galerkin FEM in physical space and a spectral discretization with harmonics in solid angle and show that the benefits of the concept of sparse tensor products, known from the context of sparse grids, can also be leveraged in combination with a spectral discretization. Our method allows us to include high spectral orders without incurring the 'curse of dimension' of a five-dimensional computational domain. Neglecting boundary conditions, we find analytically that for smooth solutions, the convergence rate of the full tensor product method is retained in our method up to a logarithmic factor, while the number of degrees of freedom grows essentially only as fast as for the purely spatial problem. For the case with boundary conditions, we propose a splitting of the physical function space and a conforming tensorization. Numerical experiments in two physical and one angular dimension show evidence for the theoretical convergence rates to hold in the latter case as well.
Metric regularity and subdifferential calculus
International Nuclear Information System (INIS)
Ioffe, A D
2000-01-01
The theory of metric regularity is an extension of two classical results: the Lyusternik tangent space theorem and the Graves surjection theorem. Developments in non-smooth analysis in the 1980s and 1990s paved the way for a number of far-reaching extensions of these results. It was also well understood that the phenomena behind the results are of metric origin, not connected with any linear structure. At the same time it became clear that some basic hypotheses of the subdifferential calculus are closely connected with the metric regularity of certain set-valued maps. The survey is devoted to the metric theory of metric regularity and its connection with subdifferential calculus in Banach spaces
Greene, Samuel M; Batista, Victor S
2017-09-12
We introduce the "tensor-train split-operator Fourier transform" (TT-SOFT) method for simulations of multidimensional nonadiabatic quantum dynamics. TT-SOFT is essentially the grid-based SOFT method implemented in dynamically adaptive tensor-train representations. In the same spirit of all matrix product states, the tensor-train format enables the representation, propagation, and computation of observables of multidimensional wave functions in terms of the grid-based wavepacket tensor components, bypassing the need of actually computing the wave function in its full-rank tensor product grid space. We demonstrate the accuracy and efficiency of the TT-SOFT method as applied to propagation of 24-dimensional wave packets, describing the S 1 /S 2 interconversion dynamics of pyrazine after UV photoexcitation to the S 2 state. Our results show that the TT-SOFT method is a powerful computational approach for simulations of quantum dynamics of polyatomic systems since it avoids the exponential scaling problem of full-rank grid-based representations.
Metrics for measuring distances in configuration spaces
International Nuclear Information System (INIS)
Sadeghi, Ali; Ghasemi, S. Alireza; Schaefer, Bastian; Mohr, Stephan; Goedecker, Stefan; Lill, Markus A.
2013-01-01
In order to characterize molecular structures we introduce configurational fingerprint vectors which are counterparts of quantities used experimentally to identify structures. The Euclidean distance between the configurational fingerprint vectors satisfies the properties of a metric and can therefore safely be used to measure dissimilarities between configurations in the high dimensional configuration space. In particular we show that these metrics are a perfect and computationally cheap replacement for the root-mean-square distance (RMSD) when one has to decide whether two noise contaminated configurations are identical or not. We introduce a Monte Carlo approach to obtain the global minimum of the RMSD between configurations, which is obtained from a global minimization over all translations, rotations, and permutations of atomic indices
Self-organizing weights for Internet AS-graphs and surprisingly simple routing metrics
DEFF Research Database (Denmark)
Scholz, Jan Carsten; Greiner, Martin
The transport capacity of Internet-like communication networks and hence their efficiency may be improved by a factor of 5-10 through the use of highly optimized routing metrics, as demonstrated previously. Numerical determination of such routing metrics can be computationally demanding...... metrics. The new metrics have negligible computational cost and result in an approximately 5-fold performance increase, providing distinguished competitiveness with the computationally costly counterparts. They are applicable to very large networks and easy to implement in today's Internet routing...
Kim, Seung-Goo; Lee, Hyekyoung; Chung, Moo K; Hanson, Jamie L; Avants, Brian B; Gee, James C; Davidson, Richard J; Pollak, Seth D
2012-01-01
We are interested in investigating white matter connectivity using a novel computational framework that does not use diffusion tensor imaging (DTI) but only uses T1-weighted magnetic resonance imaging. The proposed method relies on correlating Jacobian determinants across different voxels based on the tensor-based morphometry (TBM) framework. In this paper, we show agreement between the TBM-based white matter connectivity and the DTI-based white matter atlas. As an application, altered white matter connectivity in a clinical population is determined.
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)
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...
Deep Into the Fibers! Postmortem Diffusion Tensor Imaging in Forensic Radiology.
Flach, Patricia Mildred; Schroth, Sarah; Schweitzer, Wolf; Ampanozi, Garyfalia; Slotboom, Johannes; Kiefer, Claus; Germerott, Tanja; Thali, Michael J; El-Koussy, Marwan
2015-09-01
In traumatic brain injury, diffusion-weighted and diffusion tensor imaging of the brain are essential techniques for determining the pathology sustained and the outcome. Postmortem cross-sectional imaging is an established adjunct to forensic autopsy in death investigation. The purpose of this prospective study was to evaluate postmortem diffusion tensor imaging in forensics for its feasibility, influencing factors and correlation to the cause of death compared with autopsy. Postmortem computed tomography, magnetic resonance imaging, and diffusion tensor imaging with fiber tracking were performed in 10 deceased subjects. The Likert scale grading of colored fractional anisotropy maps was correlated to the body temperature and intracranial pathology to assess the diagnostic feasibility of postmortem diffusion tensor imaging and fiber tracking. Optimal fiber tracking (>15,000 fiber tracts) was achieved with a body temperature at 10°C. Likert scale grading showed no linear correlation (P > 0.7) to fiber tract counts. No statistically significant correlation between total fiber count and postmortem interval could be observed (P = 0.122). Postmortem diffusion tensor imaging and fiber tracking allowed for radiological diagnosis in cases with shearing injuries but was impaired in cases with pneumencephalon and intracerebral mass hemorrhage. Postmortem diffusion tensor imaging with fiber tracking provides an exceptional in situ insight "deep into the fibers" of the brain with diagnostic benefit in traumatic brain injury and axonal injuries in the assessment of the underlying cause of death, considering influencing factors for optimal imaging technique.
A closed-form solution to tensor voting: theory and applications.
Wu, Tai-Pang; Yeung, Sai-Kit; Jia, Jiaya; Tang, Chi-Keung; Medioni, Gérard
2012-08-01
We prove a closed-form solution to tensor voting (CFTV): Given a point set in any dimensions, our closed-form solution provides an exact, continuous, and efficient algorithm for computing a structure-aware tensor that simultaneously achieves salient structure detection and outlier attenuation. Using CFTV, we prove the convergence of tensor voting on a Markov random field (MRF), thus termed as MRFTV, where the structure-aware tensor at each input site reaches a stationary state upon convergence in structure propagation. We then embed structure-aware tensor into expectation maximization (EM) for optimizing a single linear structure to achieve efficient and robust parameter estimation. Specifically, our EMTV algorithm optimizes both the tensor and fitting parameters and does not require random sampling consensus typically used in existing robust statistical techniques. We performed quantitative evaluation on its accuracy and robustness, showing that EMTV performs better than the original TV and other state-of-the-art techniques in fundamental matrix estimation for multiview stereo matching. The extensions of CFTV and EMTV for extracting multiple and nonlinear structures are underway.
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.
Auriat, A M; Borich, M R; Snow, N J; Wadden, K P; Boyd, L A
2015-01-01
not DTI. CSD identified ipsilesional CST pathways in 9 stroke participants who did not have tracts identified with DTI. Additionally, CSD differentiated between stroke ipsilesional and healthy control non-dominant CST for several measures (number of tracts, tract volume, FA, ADC, and RD) whereas DTI only detected group differences for number of tracts. In the stroke group, motor behavior correlated with fewer diffusion metrics derived from the DTI as compared to CSD-reconstructed ipsilesional CST and CC. CSD is superior to DTI-based tractography in detecting differences in diffusion characteristics between the nondominant healthy control and ipsilesional CST. CSD measures of microstructure tissue properties related to more motor outcomes than DTI measures did. Our results suggest the potential utility and functional relevance of characterizing complex fiber organization using tensor-free diffusion modeling approaches to investigate white matter pathways in the brain after stroke.
Directory of Open Access Journals (Sweden)
A.M. Auriat
2015-01-01
using CSD but not DTI. CSD identified ipsilesional CST pathways in 9 stroke participants who did not have tracts identified with DTI. Additionally, CSD differentiated between stroke ipsilesional and healthy control non-dominant CST for several measures (number of tracts, tract volume, FA, ADC, and RD whereas DTI only detected group differences for number of tracts. In the stroke group, motor behavior correlated with fewer diffusion metrics derived from the DTI as compared to CSD-reconstructed ipsilesional CST and CC. CSD is superior to DTI-based tractography in detecting differences in diffusion characteristics between the nondominant healthy control and ipsilesional CST. CSD measures of microstructure tissue properties related to more motor outcomes than DTI measures did. Our results suggest the potential utility and functional relevance of characterizing complex fiber organization using tensor-free diffusion modeling approaches to investigate white matter pathways in the brain after stroke.
METRICS DEVELOPMENT FOR PATENTS.
Veiga, Daniela Francescato; Ferreira, Lydia Masako
2015-01-01
To develop a proposal for metrics for patents to be applied in assessing the postgraduate programs of Medicine III - Capes. From the reading and analysis of the 2013 area documents of all the 48 areas of Capes, a proposal for metrics for patents was developed to be applied in Medicine III programs. Except for the areas Biotechnology, Food Science, Biological Sciences III, Physical Education, Engineering I, III and IV and Interdisciplinary, most areas do not adopt a scoring system for patents. The proposal developed was based on the criteria of Biotechnology, with adaptations. In general, it will be valued, in ascending order, the deposit, the granting and licensing/production. It will also be assigned higher scores to patents registered abroad and whenever there is a participation of students. This proposal can be applied to the item Intellectual Production of the evaluation form, in subsection Technical Production/Patents. The percentage of 10% for academic programs and 40% for Masters Professionals should be maintained. The program will be scored as Very Good when it reaches 400 points or over; Good, between 200 and 399 points; Regular, between 71 and 199 points; Weak up to 70 points; Insufficient, no punctuation. Desenvolver uma proposta de métricas para patentes a serem aplicadas na avaliação dos Programas de Pós-Graduação da Área Medicina III - Capes. A partir da leitura e análise dos documentos de área de 2013 de todas as 48 Áreas da Capes, desenvolveu-se uma proposta de métricas para patentes, a ser aplicada na avaliação dos programas da área. Constatou-se que, com exceção das áreas Biotecnologia, Ciência de Alimentos, Ciências Biológicas III, Educação Física, Engenharias I, III e IV e Interdisciplinar, a maioria não adota sistema de pontuação para patentes. A proposta desenvolvida baseou-se nos critérios da Biotecnologia, com adaptações. De uma forma geral, foi valorizado, em ordem crescente, o depósito, a concessão e o
Directory of Open Access Journals (Sweden)
Ehab Malkawi
2014-01-01
Full Text Available The classical free Lagrangian admitting a constant of motion, in one- and two-dimensional space, is generalized using the Caputo derivative of fractional calculus. The corresponding metric is obtained and the fractional Christoffel symbols, Killing vectors, and Killing-Yano tensors are derived. Some exact solutions of these quantities are reported.
International Nuclear Information System (INIS)
Jolapara, Milan; Kesavadas, Chandrasekharan; Saini, Jitender; Patro, Satya Narayan; Gupta, Arun Kumar; Kapilamoorthy, Tirur Raman; Bodhey, Narendra; Radhakrishnan, V.V.
2009-01-01
The signal characteristics of an epidermoid on T2-weighted imaging have been attributed to the presence of increased water content within the tumor. In this study, we explore the utility of diffusion tensor imaging (DTI) and diffusion tensor metrics (DTM) in knowing the microstructural anatomy of epidermoid cysts. DTI was performed in ten patients with epidermoid cysts. Directionally averaged mean diffusivity (D av ), exponential diffusion, and DTM-like fractional anisotropy (FA), diffusion tensor mode (mode), linear (CL), planar (CP), and spherical (CS) anisotropy were measured from the tumor as well as from the normal-looking white matter. Epidermoid cysts showed high FA. However, D av and exponential diffusion values did not show any restriction of diffusion. Diffusion tensor mode values were near -1, and CP values were high within the tumor. This suggested preferential diffusion of water molecules along a two-dimensional geometry (plane) in epidermoid cysts, which could be attributed to the parallel-layered arrangement of keratin filaments and flakes within these tumors. Thus, advanced imaging modalities like DTI with DTM can provide information regarding the microstructural anatomy of the epidermoid cysts. (orig.)
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
Scalar-tensor Theories of Gravity: Some personal history
Brans, Carl H.
2008-12-01
From a perspective of some 50 years or more, this paper reviews my recall of the early days of scalar-tensor alternatives to standard Einstein general relativistic theory of gravity. Of course, the story begins long before my involvement, going back to the proposals of Nordström in 1914, and that of Kaluza, Klein, et al., a few years later, sol include reviews of these seminal ideas and those that followed in the 1920's through the 1940's. This early work concerned the search for a Unified Field Theory, unifying gravity and Electromagnetism, using five dimensional manifolds. This formalism included not only the electromagnetic spacetime vector potential within the five-metric, but also a spacetime scalar as the five-five metric component. Although this was at first regarded more as a nuisance, to be set to a constant, it turned out later that Fierz, Jordan, Einstein and Bergmann noticed that this scalar could be a field, possibly related to the Newtonian gravitational constant. Relatively little theoretical and experimental attention was given to these ideas until after the second world war when Bob Dicke, motivated by the ideas of Mach, Dirac, and others, suggested that this additional scalar, coupled only to the metric and matter, could provide a reasonable and viable alternative to standard Einstein theory. This is the point of my direct involvement with these topics. However, it was Dicke's prominence and expertise in experimental work, together with the blossoming of NASA's experimental tools, that caused the explosion of interest, experimental and theoretical, in this possible alternative to standard Einstein theory. This interest has waxed and waned over the last 50 years, and we summarize some of this work.
Transfer metrics analytics project
Matonis, Zygimantas
2016-01-01
This report represents work done towards predicting transfer rates/latencies on Worldwide LHC Computing Grid (WLCG) sites using Machine Learning techniques. Topic covered are technologies used for the project, data preparation for ML suitable format and attribute selection as well as a comparison of different ML algorithms.
Candelas, Philip; de la Ossa, Xenia; McOrist, Jock
2017-12-01
Heterotic vacua of string theory are realised, at large radius, by a compact threefold with vanishing first Chern class together with a choice of stable holomorphic vector bundle. These form a wide class of potentially realistic four-dimensional vacua of string theory. Despite all their phenomenological promise, there is little understanding of the metric on the moduli space of these. What is sought is the analogue of special geometry for these vacua. The metric on the moduli space is important in phenomenology as it normalises D-terms and Yukawa couplings. It is also of interest in mathematics, since it generalises the metric, first found by Kobayashi, on the space of gauge field connections, to a more general context. Here we construct this metric, correct to first order in {α^{\\backprime}}, in two ways: first by postulating a metric that is invariant under background gauge transformations of the gauge field, and also by dimensionally reducing heterotic supergravity. These methods agree and the resulting metric is Kähler, as is required by supersymmetry. Checking the metric is Kähler is intricate and the anomaly cancellation equation for the H field plays an essential role. The Kähler potential nevertheless takes a remarkably simple form: it is the Kähler potential of special geometry with the Kähler form replaced by the {α^{\\backprime}}-corrected hermitian form.
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
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.