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.
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
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)
Diffusion tensor MRI: clinical applications
International Nuclear Information System (INIS)
Meli, Francisco; Romero, Carlos; Carpintiero, Silvina; Salvatico, Rosana; Lambre, Hector; Vila, Jose
2005-01-01
Purpose: To evaluate the usefulness of diffusion-tensor imaging (DTI) on different neurological diseases, and to know if this technique shows additional information than conventional Magnetic Resonance Imaging (MRI). Materials and method: Eight patients, with neurological diseases (five patients with brain tumors, one with multiple sclerosis (MS), one with variant Creutzfeldt-Jakob disease (vCJD) and the other with delayed CO intoxication were evaluated. A MR scanner of 1.5 T was used and conventional sequences and DTI with twenty-five directions were done. Quantitative maps were gotten, where the fractional anisotropy (FA) through regions of interest (ROIs) in specific anatomic area were quantified (i.e.: internal and external capsules, frontal and temporal bundles, corpus fibers). Results: In the patients with brain tumors, there was a decrease of FA on intra and peritumoral fibers. Some of them had a disruption in their pattern. In patients with MS and CO intoxication, partial interruption along white matter bundles was demonstrated. However, a 'mismatch' between the findings of FLAIR, Diffusion-weighted images (DWI) and DTI, in the case of CO intoxication, was seen. Conclusions: DTI gave more information compared to conventional sequences about ultrastructural brain tissue in almost all the diseases above mentioned. Therefore, there is a work in progress about DTI acquisition, to evaluate a new technique, called tractography. (author)
The evaluation of a population based diffusion tensor image atlas using a ground truth method
Van Hecke, Wim; Leemans, Alexander; D'Agostino, Emiliano; De Backer, Steve; Vandervliet, Evert; Parizel, Paul M.; Sijbers, Jan
2008-03-01
Purpose: Voxel based morphometry (VBM) is increasingly being used to detect diffusion tensor (DT) image abnormalities in patients for different pathologies. An important requisite for these VBM studies is the use of a high-dimensional, non-rigid coregistration technique, which is able to align both the spatial and the orientational information. Recent studies furthermore indicate that high-dimensional DT information should be included during coregistration for an optimal alignment. In this context, a population based DTI atlas is created that preserves the orientational DT information robustly and contains a minimal bias towards any specific individual data set. Methods: A ground truth evaluation method is developed using a single subject DT image that is deformed with 20 deformation fields. Thereafter, an atlas is constructed based on these 20 resulting images. Thereby, the non-rigid coregistration algorithm is based on a viscous fluid model and on mutual information. The fractional anisotropy (FA) maps as well as the DT elements are used as DT image information during the coregistration algorithm, in order to minimize the orientational alignment inaccuracies. Results: The population based DT atlas is compared with the ground truth image using accuracy and precision measures of spatial and orientational dependent metrics. Results indicate that the population based atlas preserves the orientational information in a robust way. Conclusion: A subject independent population based DT atlas is constructed and evaluated with a ground truth method. This atlas contains all available orientational information and can be used in future VBM studies as a reference system.
The ATLAS detector simulation application
International Nuclear Information System (INIS)
Rimoldi, A.
2007-01-01
The simulation program for the ATLAS experiment at CERN is currently in a full operational mode and integrated into the ATLAS common analysis framework, Athena. The OO approach, based on GEANT4, has been interfaced within Athena and to GEANT4 using the LCG dictionaries and Python scripting. The robustness of the application was proved during the test productions since 2004. The Python interface has added the flexibility, modularity and interactivity that the simulation tool requires in order to be able to provide a common implementation of different full ATLAS simulation setups, test beams and cosmic ray applications. Generation, simulation and digitization steps were exercised for performance and robustness tests. The comparison with real data has been possible in the context of the ATLAS Combined Test Beam (2004-2005) and cosmic ray studies (2006)
Kronecker-Basis-Representation Based Tensor Sparsity and Its Applications to Tensor Recovery.
Xie, Qi; Zhao, Qian; Meng, Deyu; Xu, Zongben
2017-08-02
It is well known that the sparsity/low-rank of a vector/matrix can be rationally measured by nonzero-entries-number ($l_0$ norm)/nonzero- singular-values-number (rank), respectively. However, data from real applications are often generated by the interaction of multiple factors, which obviously cannot be sufficiently represented by a vector/matrix, while a high order tensor is expected to provide more faithful representation to deliver the intrinsic structure underlying such data ensembles. Unlike the vector/matrix case, constructing a rational high order sparsity measure for tensor is a relatively harder task. To this aim, in this paper we propose a measure for tensor sparsity, called Kronecker-basis-representation based tensor sparsity measure (KBR briefly), which encodes both sparsity insights delivered by Tucker and CANDECOMP/PARAFAC (CP) low-rank decompositions for a general tensor. Then we study the KBR regularization minimization (KBRM) problem, and design an effective ADMM algorithm for solving it, where each involved parameter can be updated with closed-form equations. Such an efficient solver makes it possible to extend KBR to various tasks like tensor completion and tensor robust principal component analysis. A series of experiments, including multispectral image (MSI) denoising, MSI completion and background subtraction, substantiate the superiority of the proposed methods beyond state-of-the-arts.
Tensor algebra and tensor analysis for engineers with applications to continuum mechanics
Itskov, Mikhail
2015-01-01
This is the fourth and revised edition of a well-received book that aims at bridging the gap between the engineering course of tensor algebra on the one side and the mathematical course of classical linear algebra on the other side. In accordance with the contemporary way of scientific publications, a modern absolute tensor notation is preferred throughout. The book provides a comprehensible exposition of the fundamental mathematical concepts of tensor calculus and enriches the presented material with many illustrative examples. In addition, the book also includes advanced chapters dealing with recent developments in the theory of isotropic and anisotropic tensor functions and their applications to continuum mechanics. Hence, this monograph addresses graduate students as well as scientists working in this field. In each chapter numerous exercises are included, allowing for self-study and intense practice. Solutions to the exercises are also provided.
Tensor valuations and their applications in stochastic geometry and imaging
Kiderlen, Markus
2017-01-01
The purpose of this volume is to give an up-to-date introduction to tensor valuations and their applications. Starting with classical results concerning scalar-valued valuations on the families of convex bodies and convex polytopes, it proceeds to the modern theory of tensor valuations. Product and Fourier-type transforms are introduced and various integral formulae are derived. New and well-known results are presented, together with generalizations in several directions, including extensions to the non-Euclidean setting and to non-convex sets. A variety of applications of tensor valuations to models in stochastic geometry, to local stereology and to imaging are also discussed.
Aggarwal, Manisha; Zhang, Jiangyang; Pletnikova, Olga; Crain, Barbara; Troncoso, Juan; Mori, Susumu
2013-07-01
A three-dimensional stereotaxic atlas of the human brainstem based on high resolution ex vivo diffusion tensor imaging (DTI) is introduced. The atlas consists of high resolution (125-255 μm isotropic) three-dimensional DT images of the formalin-fixed brainstem acquired at 11.7 T. The DTI data revealed microscopic neuroanatomical details, allowing three-dimensional visualization and reconstruction of fiber pathways including the decussation of the pyramidal tract fibers, and interdigitating fascicles of the corticospinal and transverse pontine fibers. Additionally, strong gray-white matter contrasts in the apparent diffusion coefficient (ADC) maps enabled precise delineation of gray matter nuclei in the brainstem, including the cranial nerve and the inferior olivary nuclei. Comparison with myelin-stained histology shows that at the level of resolution achieved in this study, the structural details resolved with DTI contrasts in the brainstem were comparable to anatomical delineation obtained with histological sectioning. Major neural structures delineated from DTI contrasts in the brainstem are segmented and three-dimensionally reconstructed. Further, the ex vivo DTI data are nonlinearly mapped to a widely-used in vivo human brain atlas, to construct a high-resolution atlas of the brainstem in the Montreal Neurological Institute (MNI) stereotaxic coordinate space. The results demonstrate the feasibility of developing a 3D DTI based atlas for detailed characterization of brainstem neuroanatomy with high resolution and contrasts, which will be a useful resource for research and clinical applications. Copyright © 2013 Elsevier Inc. All rights reserved.
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.
Review of diffusion tensor imaging and its application in children
Energy Technology Data Exchange (ETDEWEB)
Vorona, Gregory A. [Children' s Hospital of Richmond at Virginia Commonwealth University, Department of Radiology, Richmond, VA (United States); Berman, Jeffrey I. [Children' s Hospital of Philadelphia, Department of Radiology, Philadelphia, PA (United States)
2015-09-15
Diffusion MRI is an imaging technique that uses the random motion of water to probe tissue microstructure. Diffusion tensor imaging (DTI) can quantitatively depict the organization and connectivity of white matter. Given the non-invasiveness of the technique, DTI has become a widely used tool for researchers and clinicians to examine the white matter of children. This review covers the basics of diffusion-weighted imaging and diffusion tensor imaging and discusses examples of their clinical application in children. (orig.)
An eigenvalue localization set for tensors and its applications
Directory of Open Access Journals (Sweden)
Jianxing Zhao
2017-03-01
Full Text Available Abstract A new eigenvalue localization set for tensors is given and proved to be tighter than those presented by Li et al. (Linear Algebra Appl. 481:36-53, 2015 and Huang et al. (J. Inequal. Appl. 2016:254, 2016. As an application of this set, new bounds for the minimum eigenvalue of M $\\mathcal{M}$ -tensors are established and proved to be sharper than some known results. Compared with the results obtained by Huang et al., the advantage of our results is that, without considering the selection of nonempty proper subsets S of N = { 1 , 2 , … , n } $N=\\{1,2,\\ldots,n\\}$ , we can obtain a tighter eigenvalue localization set for tensors and sharper bounds for the minimum eigenvalue of M $\\mathcal{M}$ -tensors. Finally, numerical examples are given to verify the theoretical results.
An eigenvalue localization set for tensors and its applications.
Zhao, Jianxing; Sang, Caili
2017-01-01
A new eigenvalue localization set for tensors is given and proved to be tighter than those presented by Li et al . (Linear Algebra Appl. 481:36-53, 2015) and Huang et al . (J. Inequal. Appl. 2016:254, 2016). As an application of this set, new bounds for the minimum eigenvalue of [Formula: see text]-tensors are established and proved to be sharper than some known results. Compared with the results obtained by Huang et al ., the advantage of our results is that, without considering the selection of nonempty proper subsets S of [Formula: see text], we can obtain a tighter eigenvalue localization set for tensors and sharper bounds for the minimum eigenvalue of [Formula: see text]-tensors. Finally, numerical examples are given to verify the theoretical results.
Classification of the Weyl tensor in higher dimensions and applications
International Nuclear Information System (INIS)
Coley, A
2008-01-01
We review the theory of alignment in Lorentzian geometry and apply it to the algebraic classification of the Weyl tensor in higher dimensions. This classification reduces to the well-known Petrov classification of the Weyl tensor in four dimensions. We discuss the algebraic classification of a number of known higher dimensional spacetimes. There are many applications of the Weyl classification scheme, especially when used in conjunction with the higher dimensional frame formalism that has been developed in order to generalize the four-dimensional Newman-Penrose formalism. For example, we discuss higher dimensional generalizations of the Goldberg-Sachs theorem and the peeling theorem. We also discuss the higher dimensional Lorentzian spacetimes with vanishing scalar curvature invariants and constant scalar curvature invariants, which are of interest since they are solutions of supergravity theory. (topical review)
Energy Technology Data Exchange (ETDEWEB)
Saur, R. [Sektion fuer Experimentelle Kernspinresonanz des ZNS, Abt. Neuroradiologie, Universitaetsklinikum Tuebingen (Germany); Augenklinik des Universitaetsklinikums Tuebingen (Germany); Klinik fuer Psychiatrie und Psychotherapie des Universitaetsklinikums Tuebingen (Germany); Gharabaghi, A. [Klinik fuer Neurochirurgie des Universitaetsklinikums Tuebingen (Germany); Erb, M. [Sektion fuer Experimentelle Kernspinresonanz des ZNS, Abt. Neuroradiologie, Universitaetsklinikum Tuebingen (Germany)
2007-07-01
Knowledge about integrity and location of fibre tracts arising from eloquent cortical areas is important to plan neurosurgical interventions and to allow maximization of resection of pathological tissue while preserving vital white matter tracts. Diffusion Tensor Imaging (DTI) is so far the only method to get preoperatively an impression of the individual complexity of nerve bundles. Thereby nerve fibres are not mapped directly. They are derived indirectly by analysis of the directional distribution of diffusion of water molecules which is influenced mainly by large fibre tracts. From acquisition to reconstruction and visualisation of the fibre tracts many representational stages and working steps have to be passed. Exact knowledge about problems of Diffusion Imaging is important for interpretation of the results. Particularly, brain tumor edema, intraoperative brain shift, MR-artefacts and limitations of the mathematical models and algorithms challenge DTI-developers and applicants. (orig.)
ATLAS: Applications experiences and further developments
International Nuclear Information System (INIS)
Beraha, D.; Pointner, W.; Voggenberger, T.
1999-01-01
An overview of the plant analyzer ATLAS is given, describing its configuration, the process models and the supplementary modules which enhance the functionality of ATLAS for a range of applications in reactor safety analysis. These modules include the Reliability Advisory System, which supports the user by information from probabilistic safety analysis, the Procedure Analysis for development and test of emergency operating procedures, and a diagnostic system for steam-generator tube rupture. The development of plant specific analysers for various power plants is described, and the user experience related. Finally, the intended further development directions are discussed, centering on a tracking simulator, the migration of the visualisation system to Windows NT, and the construction of the Analysis Center as a multimedia environment for the operation of ATLAS. (author)
Hendrix, Philipp; Griessenauer, Christoph J; Cohen-Adad, Julien; Rajasekaran, Shanmuganathan; Cauley, Keith A; Shoja, Mohammadali M; Pezeshk, Parham; Tubbs, R Shane
2015-01-01
Magnetic resonance imaging technology allows for in vivo visualization of fiber tracts of the central nervous system using diffusion-weighted imaging sequences and data processing referred to as "diffusion tensor imaging" and "diffusion tensor tractography." While protocols for high-fidelity diffusion tensor imaging of the brain are well established, the spinal cord has proven a more difficult target for diffusion tensor methods. Here, we review the current literature on spinal diffusion tensor imaging and tractography with special emphasis on neuroanatomical correlations and clinical applications. © 2014 Wiley Periodicals, Inc.
STUDY ABOUT CLINICAL APPLICATION OF BRAIN ATLAS IN PAEDIATRICS
Institute of Scientific and Technical Information of China (English)
MENG Fanhang; LIU Cuiping; RENG Xiaoping; JIANG Lian
2002-01-01
Objectives To explore clinical application on brain atlas in paediatrics. Methode: Brain atlas was applied in diagnosis and treatment of paediatric diseases and its clinical value was discussed in 1990 ～2001. The manifestation of these diseases in brain atlas were analysed and the manifestation of CT of 67 cases and manifestations of EEG of 37 cases with that of BA were compared. Results The changes of cerebral electrical activity of these diseases were reflected objectively and showed directly in BA. Conclusion Brain atlas not only can point out quality of disease but also define position of disease. Therefore, brain atlas has important clinical value in paediatrics.
Tensors and Manifolds With Applications to Physics (2nd edn)
International Nuclear Information System (INIS)
Dray, T
2005-01-01
On the one hand, this is an excellent introduction for mathematicians to the differential geometry underlying general relativity. On the other hand, this is definitely a book for mathematicians. The book's greatest strength is its clear, precise presentation of the basic ideas in differential geometry, combined with equally clear and precise applications to theoretical physics, notably general relativity. But the book's precision is also its greatest weakness; this is not an easy book to read for non-mathematicians, who may not appreciate the notational complexity, some of which is nonstandard. The present edition is very similar to the original, published in 1992. In addition to minor revisions and clarifications of the material, there is now a brief introduction to fibre bundles, and a (very) brief discussion of the gauge theory description of fundamental particles. The index to the symbols used is also a more complete than in the past, but without the descriptive material present in the previous edition. The bulk of the book consists of a careful introduction to tensors and their properties. Tensors are introduced first as linear maps on vector spaces, and only later generalized to tensor fields on manifolds. The differentiation and integration of differential forms is discussed in detail, including Stokes' theorem, Lie differentiation and Hodge duality, and connections, curvature and torsion. To this point, Wasserman's text can be viewed as an expanded version of Bishop and Goldberg's classic text, one major difference being Wasserman's inclusion of the pseudo-Riemannian case from the beginning (in particular, when discussing Hodge duality). Whether one prefers Wasserman's approach to Bishop and Goldberg's is largely a matter of taste: Wasserman's treatment is both more complete and more precise, making it easier to check calculations in detail, but occasionally more difficult to remember what one is calculating. An instructor using this text would be well
Tensors and Manifolds With Applications to Physics (2nd edn)
Energy Technology Data Exchange (ETDEWEB)
Dray, T [Oregon State University (United States)
2005-10-21
On the one hand, this is an excellent introduction for mathematicians to the differential geometry underlying general relativity. On the other hand, this is definitely a book for mathematicians. The book's greatest strength is its clear, precise presentation of the basic ideas in differential geometry, combined with equally clear and precise applications to theoretical physics, notably general relativity. But the book's precision is also its greatest weakness; this is not an easy book to read for non-mathematicians, who may not appreciate the notational complexity, some of which is nonstandard. The present edition is very similar to the original, published in 1992. In addition to minor revisions and clarifications of the material, there is now a brief introduction to fibre bundles, and a (very) brief discussion of the gauge theory description of fundamental particles. The index to the symbols used is also a more complete than in the past, but without the descriptive material present in the previous edition. The bulk of the book consists of a careful introduction to tensors and their properties. Tensors are introduced first as linear maps on vector spaces, and only later generalized to tensor fields on manifolds. The differentiation and integration of differential forms is discussed in detail, including Stokes' theorem, Lie differentiation and Hodge duality, and connections, curvature and torsion. To this point, Wasserman's text can be viewed as an expanded version of Bishop and Goldberg's classic text, one major difference being Wasserman's inclusion of the pseudo-Riemannian case from the beginning (in particular, when discussing Hodge duality). Whether one prefers Wasserman's approach to Bishop and Goldberg's is largely a matter of taste: Wasserman's treatment is both more complete and more precise, making it easier to check calculations in detail, but occasionally more difficult to remember what one is calculating. An
Applicability of transfer tensor method for open quantum system dynamics.
Gelzinis, Andrius; Rybakovas, Edvardas; Valkunas, Leonas
2017-12-21
Accurate simulations of open quantum system dynamics is a long standing issue in the field of chemical physics. Exact methods exist, but are costly, while perturbative methods are limited in their applicability. Recently a new black-box type method, called transfer tensor method (TTM), was proposed [J. Cerrillo and J. Cao, Phys. Rev. Lett. 112, 110401 (2014)]. It allows one to accurately simulate long time dynamics with a numerical cost of solving a time-convolution master equation, provided many initial system evolution trajectories are obtained from some exact method beforehand. The possible time-savings thus strongly depend on the ratio of total versus initial evolution lengths. In this work, we investigate the parameter regimes where an application of TTM would be most beneficial in terms of computational time. We identify several promising parameter regimes. Although some of them correspond to cases when perturbative theories could be expected to perform well, we find that the accuracy of such approaches depends on system parameters in a more complex way than it is commonly thought. We propose that the TTM should be applied whenever system evolution is expected to be long and accuracy of perturbative methods cannot be ensured or in cases when the system under consideration does not correspond to any single perturbative regime.
A generalization of tensor calculus and its application to physics
International Nuclear Information System (INIS)
Ashtekar, A.
1982-01-01
Penrose's abstract index notation and axiomatic introduction of covariant derivatives in tensor calculus is generalized to fields with internal degrees of freedom. The result provides, in particular, an intrinsic formulation of gauge theories without the use of bundles. (author)
Gao, Yurui; Parvathaneni, Prasanna; Schilling, Kurt G; Wang, Feng; Stepniewska, Iwona; Xu, Zhoubing; Choe, Ann S; Ding, Zhaohua; Gore, John C; Chen, Li Min; Landman, Bennett A; Anderson, Adam W
2016-02-27
Modern magnetic resonance imaging (MRI) brain atlases are high quality 3-D volumes with specific structures labeled in the volume. Atlases are essential in providing a common space for interpretation of results across studies, for anatomical education, and providing quantitative image-based navigation. Extensive work has been devoted to atlas construction for humans, macaque, and several non-primate species (e.g., rat). One notable gap in the literature is the common squirrel monkey - for which the primary published atlases date from the 1960's. The common squirrel monkey has been used extensively as surrogate for humans in biomedical studies, given its anatomical neuro-system similarities and practical considerations. This work describes the continued development of a multi-modal MRI atlas for the common squirrel monkey, for which a structural imaging space and gray matter parcels have been previously constructed. This study adds white matter tracts to the atlas. The new atlas includes 49 white matter (WM) tracts, defined using diffusion tensor imaging (DTI) in three animals and combines these data to define the anatomical locations of these tracks in a standardized coordinate system compatible with previous development. An anatomist reviewed the resulting tracts and the inter-animal reproducibility (i.e., the Dice index of each WM parcel across animals in common space) was assessed. The Dice indices range from 0.05 to 0.80 due to differences of local registration quality and the variation of WM tract position across individuals. However, the combined WM labels from the 3 animals represent the general locations of WM parcels, adding basic connectivity information to the atlas.
Gao, Yurui; Parvathaneni, Prasanna; Schilling, Kurt G.; Wang, Feng; Stepniewska, Iwona; Xu, Zhoubing; Choe, Ann S.; Ding, Zhaohua; Gore, John C.; Chen, Li min; Landman, Bennett A.; Anderson, Adam W.
2016-03-01
Modern magnetic resonance imaging (MRI) brain atlases are high quality 3-D volumes with specific structures labeled in the volume. Atlases are essential in providing a common space for interpretation of results across studies, for anatomical education, and providing quantitative image-based navigation. Extensive work has been devoted to atlas construction for humans, macaque, and several non-primate species (e.g., rat). One notable gap in the literature is the common squirrel monkey - for which the primary published atlases date from the 1960's. The common squirrel monkey has been used extensively as surrogate for humans in biomedical studies, given its anatomical neuro-system similarities and practical considerations. This work describes the continued development of a multi-modal MRI atlas for the common squirrel monkey, for which a structural imaging space and gray matter parcels have been previously constructed. This study adds white matter tracts to the atlas. The new atlas includes 49 white matter (WM) tracts, defined using diffusion tensor imaging (DTI) in three animals and combines these data to define the anatomical locations of these tracks in a standardized coordinate system compatible with previous development. An anatomist reviewed the resulting tracts and the inter-animal reproducibility (i.e., the Dice index of each WM parcel across animals in common space) was assessed. The Dice indices range from 0.05 to 0.80 due to differences of local registration quality and the variation of WM tract position across individuals. However, the combined WM labels from the 3 animals represent the general locations of WM parcels, adding basic connectivity information to the atlas.
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.)
Tensor and vector analysis with applications to differential geometry
Springer, C E
2012-01-01
Concise and user-friendly, this college-level text assumes only a knowledge of basic calculus in its elementary and gradual development of tensor theory. The introductory approach bridges the gap between mere manipulation and a genuine understanding of an important aspect of both pure and applied mathematics.Beginning with a consideration of coordinate transformations and mappings, the treatment examines loci in three-space, transformation of coordinates in space and differentiation, tensor algebra and analysis, and vector analysis and algebra. Additional topics include differentiation of vect
He, Lifang; Kong, Xiangnan; Yu, Philip S.; Ragin, Ann B.; Hao, Zhifeng; Yang, Xiaowei
2015-01-01
With advances in data collection technologies, tensor data is assuming increasing prominence in many applications and the problem of supervised tensor learning has emerged as a topic of critical significance in the data mining and machine learning community. Conventional methods for supervised tensor learning mainly focus on learning kernels by flattening the tensor into vectors or matrices, however structural information within the tensors will be lost. In this paper, we introduce a new scheme to design structure-preserving kernels for supervised tensor learning. Specifically, we demonstrate how to leverage the naturally available structure within the tensorial representation to encode prior knowledge in the kernel. We proposed a tensor kernel that can preserve tensor structures based upon dual-tensorial mapping. The dual-tensorial mapping function can map each tensor instance in the input space to another tensor in the feature space while preserving the tensorial structure. Theoretically, our approach is an extension of the conventional kernels in the vector space to tensor space. We applied our novel kernel in conjunction with SVM to real-world tensor classification problems including brain fMRI classification for three different diseases (i.e., Alzheimer's disease, ADHD and brain damage by HIV). Extensive empirical studies demonstrate that our proposed approach can effectively boost tensor classification performances, particularly with small sample sizes. PMID:25927014
He, Lifang; Kong, Xiangnan; Yu, Philip S; Ragin, Ann B; Hao, Zhifeng; Yang, Xiaowei
With advances in data collection technologies, tensor data is assuming increasing prominence in many applications and the problem of supervised tensor learning has emerged as a topic of critical significance in the data mining and machine learning community. Conventional methods for supervised tensor learning mainly focus on learning kernels by flattening the tensor into vectors or matrices, however structural information within the tensors will be lost. In this paper, we introduce a new scheme to design structure-preserving kernels for supervised tensor learning. Specifically, we demonstrate how to leverage the naturally available structure within the tensorial representation to encode prior knowledge in the kernel. We proposed a tensor kernel that can preserve tensor structures based upon dual-tensorial mapping. The dual-tensorial mapping function can map each tensor instance in the input space to another tensor in the feature space while preserving the tensorial structure. Theoretically, our approach is an extension of the conventional kernels in the vector space to tensor space. We applied our novel kernel in conjunction with SVM to real-world tensor classification problems including brain fMRI classification for three different diseases ( i.e ., Alzheimer's disease, ADHD and brain damage by HIV). Extensive empirical studies demonstrate that our proposed approach can effectively boost tensor classification performances, particularly with small sample sizes.
Diffusion Tensor Imaging: Application to the Study of the Developing Brain
Cascio, Carissa J.; Gerig, Guido; Piven, Joseph
2007-01-01
Objective: To provide an overview of diffusion tensor imaging (DTI) and its application to the study of white matter in the developing brain in both healthy and clinical samples. Method: The development of DTI and its application to brain imaging of white matter tracts is discussed. Forty-eight studies using DTI to examine diffusion properties of…
ATLAS database application enhancements using Oracle 11g
Dimitrov, G; The ATLAS collaboration; Blaszczyk, M; Sorokoletov, R
2012-01-01
The ATLAS experiment at LHC relies on databases for detector online data-taking, storage and retrieval of configurations, calibrations and alignments, post data-taking analysis, file management over the grid, job submission and management, condition data replication to remote sites. Oracle Relational Database Management System (RDBMS) has been addressing the ATLAS database requirements to a great extent for many years. Ten database clusters are currently deployed for the needs of the different applications, divided in production, integration and standby databases. The data volume, complexity and demands from the users are increasing steadily with time. Nowadays more than 20 TB of data are stored in the ATLAS production Oracle databases at CERN (not including the index overhead), but the most impressive number is the hosted 260 database schemas (for the most common case each schema is related to a dedicated client application with its own requirements). At the beginning of 2012 all ATLAS databases at CERN have...
Tensor Minkowski Functionals: first application to the CMB
Energy Technology Data Exchange (ETDEWEB)
Ganesan, Vidhya [Indian Institute of Astrophysics, Koramangala II Block, Bangalore 560 034 (India); Chingangbam, Pravabati, E-mail: vidhya@iiap.res.in, E-mail: prava@iiap.res.in [Indian Institute of Science, C.V. Raman Ave, Bangalore 560 012 (India)
2017-06-01
Tensor Minkowski Functionals (TMFs) are tensor generalizations of the usual Minkowski Functionals which are scalar quantities. We introduce them here for use in cosmological analysis, in particular to analyze the Cosmic Microwave Background (CMB) radiation. They encapsulate information about the shapes of structures and the orientation of distributions of structures. We focus on one of the TMFs, namely W {sub 2}{sup 1,1}, which is the (1,1) rank tensor generalization of the genus. The ratio of the eigenvalues of the average of W {sub 2}{sup 1,1} over all structures, α, encodes the net orientation of the structures; and the average of the ratios of the eigenvalues of W {sub 2}{sup 1,1} for each structure, β, encodes the net intrinsic anisotropy of the structures. We have developed a code that computes W {sub 2}{sup 1,1}, and from it α and β, for a set of structures on the 2-dimensional Euclidean plane. We use it to compute α and β as functions of chosen threshold levels for simulated Gaussian and isotropic CMB temperature and E mode fields. We obtain the value of α to be one for both temperature and E mode, which means that we recover the statistical isotropy of density fluctuations that we input in the simulations. We find that the standard ΛCDM model predicts a charateristic shape of β for temperature and E mode as a function of the threshold, and the average over thresholds is β∼ 0.62 for temperature and β∼ 0.63 for E mode. Accurate measurements of α and β can be used to test the standard model of cosmology and to search for deviations from it. For this purpose we compute α and β for temperature and E mode data of various data sets from PLANCK mission. We compare the values measured from observed data with those obtained from simulations to which instrument beam and noise characteristics of the 44GHz frequency channel have been added (which are provided as part of the PLANCK data release). We find very good agreement of β and α between all
TensorLy: Tensor Learning in Python
Kossaifi, Jean; Panagakis, Yannis; Pantic, Maja
2016-01-01
Tensor methods are gaining increasing traction in machine learning. However, there are scant to no resources available to perform tensor learning and decomposition in Python. To answer this need we developed TensorLy. TensorLy is a state of the art general purpose library for tensor learning.
Hess, Siegfried
2015-01-01
This book presents the science of tensors in a didactic way. The various types and ranks of tensors and the physical basis is presented. Cartesian Tensors are needed for the description of directional phenomena in many branches of physics and for the characterization the anisotropy of material properties. The first sections of the book provide an introduction to the vector and tensor algebra and analysis, with applications to physics, at undergraduate level. Second rank tensors, in particular their symmetries, are discussed in detail. Differentiation and integration of fields, including generalizations of the Stokes law and the Gauss theorem, are treated. The physics relevant for the applications in mechanics, quantum mechanics, electrodynamics and hydrodynamics is presented. The second part of the book is devoted to tensors of any rank, at graduate level. Special topics are irreducible, i.e. symmetric traceless tensors, isotropic tensors, multipole potential tensors, spin tensors, integration and spin-...
Low Multilinear Rank Approximation of Tensors and Application in Missing Traffic Data
Directory of Open Access Journals (Sweden)
Huachun Tan
2014-02-01
Full Text Available The problem of missing data in multiway arrays (i.e., tensors is common in many fields such as bibliographic data analysis, image processing, and computer vision. We consider the problems of approximating a tensor by another tensor with low multilinear rank in the presence of missing data and possibly reconstructing it (i.e., tensor completion. In this paper, we propose a weighted Tucker model which models only the known elements for capturing the latent structure of the data and reconstructing the missing elements. To treat the nonuniqueness of the proposed weighted Tucker model, a novel gradient descent algorithm based on a Grassmann manifold, which is termed Tucker weighted optimization (Tucker-Wopt, is proposed for guaranteeing the global convergence to a local minimum of the problem. Based on extensive experiments, Tucker-Wopt is shown to successfully reconstruct tensors with noise and up to 95% missing data. Furthermore, the experiments on traffic flow volume data demonstrate the usefulness of our algorithm on real-world application.
TENSOR CALCULUS with applications to Differential Theory of Surfaces and Dynamics
DEFF Research Database (Denmark)
Nielsen, Søren R. K.
The present outline on tensor calculus with special application to differential theory of surfaces and dynamics represents a modified and extended version of a lecture note written by the author as an introduction to a course on shell theory given together with Ph.D. Jesper Winther Stærdahl...
Diffusion tensor imaging. Theory, sequence optimization and application in Alzheimer's disease
International Nuclear Information System (INIS)
Stieltjes, B.; Schlueter, M.; Hahn, H.K.; Wilhelm, T.; Essig, M.
2003-01-01
Diffusion tensor imaging (DTI) offers an in vivo view into the microarchitecture of the brain. Furthermore it allows a three-dimensional reconstruction of fiber tracts. We will discuss the principles of DTI and possibilities for sequence optimization. Finally we will give an overview of DTI and its application in Alzheimer's disease. (orig.) [de
Applications of tensor (multiway array) factorizations and decompositions in data mining
DEFF Research Database (Denmark)
Mørup, Morten
2011-01-01
Tensor (multiway array) factorization and decomposition has become an important tool for data mining. Fueled by the computational power of modern computer researchers can now analyze large-scale tensorial structured data that only a few years ago would have been impossible. Tensor factorizations...... have several advantages over two-way matrix factorizations including uniqueness of the optimal solution and component identification even when most of the data is missing. Furthermore, multiway decomposition techniques explicitly exploit the multiway structure that is lost when collapsing some...... of the modes of the tensor in order to analyze the data by regular matrix factorization approaches. Multiway decomposition is being applied to new fields every year and there is no doubt that the future will bring many exciting new applications. The aim of this overview is to introduce the basic concepts...
A new S-type eigenvalue inclusion set for tensors and its applications.
Huang, Zheng-Ge; Wang, Li-Gong; Xu, Zhong; Cui, Jing-Jing
2016-01-01
In this paper, a new S -type eigenvalue localization set for a tensor is derived by dividing [Formula: see text] into disjoint subsets S and its complement. It is proved that this new set is sharper than those presented by Qi (J. Symb. Comput. 40:1302-1324, 2005), Li et al. (Numer. Linear Algebra Appl. 21:39-50, 2014) and Li et al. (Linear Algebra Appl. 481:36-53, 2015). As applications of the results, new bounds for the spectral radius of nonnegative tensors and the minimum H -eigenvalue of strong M -tensors are established, and we prove that these bounds are tighter than those obtained by Li et al. (Numer. Linear Algebra Appl. 21:39-50, 2014) and He and Huang (J. Inequal. Appl. 2014:114, 2014).
The ATLAS multi-user upgrade and potential applications
Energy Technology Data Exchange (ETDEWEB)
Mustapha, B.; Nolen, J. A.; Savard, G.; Ostroumov, P. N.
2017-12-01
With the recent integration of the CARIBU-EBIS charge breeder into the ATLAS accelerator system to provide for more pure and efficient charge breeding of radioactive beams, a multi-user upgrade of the ATLAS facility is being proposed to serve multiple users simultaneously. ATLAS was the first superconducting ion linac in the world and is the US DOE low-energy Nuclear Physics National User Facility. The proposed upgrade will take advantage of the continuous-wave nature of ATLAS and the pulsed nature of the EBIS charge breeder in order to simultaneously accelerate two beams with very close mass-to-charge ratios; one stable from the existing ECR ion source and one radioactive from the newly commissioned EBIS charge breeder. In addition to enhancing the nuclear physics program, beam extraction at different points along the linac will open up the opportunity for other potential applications; for instance, material irradiation studies at ~ 1 MeV/u and isotope production at ~ 6 MeV/u or at the full ATLAS energy of ~ 15 MeV/u. The concept and proposed implementation of the ATLAS multi-user upgrade will be presented. Future plans to enhance the flexibility of this upgrade will also be presented.
ATLAS database application enhancements using Oracle 11g
International Nuclear Information System (INIS)
Dimitrov, G; Canali, L; Blaszczyk, M; Sorokoletov, R
2012-01-01
The ATLAS experiment at LHC relies on databases for detector online data-taking, storage and retrieval of configurations, calibrations and alignments, post data-taking analysis, file management over the grid, job submission and management, condition data replication to remote sites. Oracle Relational Database Management System (RDBMS) has been addressing the ATLAS database requirements to a great extent for many years. Ten database clusters are currently deployed for the needs of the different applications, divided in production, integration and standby databases. The data volume, complexity and demands from the users are increasing steadily with time. Nowadays more than 20 TB of data are stored in the ATLAS production Oracle databases at CERN (not including the index overhead), but the most impressive number is the hosted 260 database schemes (for the most common case each schema is related to a dedicated client application with its own requirements). At the beginning of 2012 all ATLAS databases at CERN have been upgraded to the newest Oracle version at the time: Oracle 11g Release 2. Oracle 11g come with several key improvements compared to previous database engine versions. In this work we present our evaluation of the most relevant new features of Oracle 11g of interest for ATLAS applications and use cases. Notably we report on the performance and scalability enhancements obtained in production since the Oracle 11g deployment during Q1 2012 and we outline plans for future work in this area.
Refresher Course on Tensors and their Applications in Engineering ...
Indian Academy of Sciences (India)
Applications in Engineering Sciences. Department of Mechanical Engineering, Indian Institute of Science, Bangalore. December 11-23,2006 sponsored by Indian Academy of Sciences, Bangalore in collaboration with Indian Institute of Science, Bangalore. Applications are invited from University/College teachers, Research ...
Gaussian mixtures on tensor fields for segmentation: applications to medical imaging.
de Luis-García, Rodrigo; Westin, Carl-Fredrik; Alberola-López, Carlos
2011-01-01
In this paper, we introduce a new approach for tensor field segmentation based on the definition of mixtures of Gaussians on tensors as a statistical model. Working over the well-known Geodesic Active Regions segmentation framework, this scheme presents several interesting advantages. First, it yields a more flexible model than the use of a single Gaussian distribution, which enables the method to better adapt to the complexity of the data. Second, it can work directly on tensor-valued images or, through a parallel scheme that processes independently the intensity and the local structure tensor, on scalar textured images. Two different applications have been considered to show the suitability of the proposed method for medical imaging segmentation. First, we address DT-MRI segmentation on a dataset of 32 volumes, showing a successful segmentation of the corpus callosum and favourable comparisons with related approaches in the literature. Second, the segmentation of bones from hand radiographs is studied, and a complete automatic-semiautomatic approach has been developed that makes use of anatomical prior knowledge to produce accurate segmentation results. Copyright © 2010 Elsevier Ltd. All rights reserved.
Stress strain tensors with their application to x-ray stress measurement
International Nuclear Information System (INIS)
Kurita, Masanori
2015-01-01
This paper describes in detail the method of obtaining the formulas of stress-strain tensor that express the directional dependence of stress-strain, that is, how these values change in response to coordinate transformation, and clarifies the preconditions for supporting both formulas. The two conversion formulas are both the second order of tensor, and the formula of strain tensor not only does not use the relational expression of stress and strain at all, but also is obtained completely independently of the formula of stress tensor. Except for the condition that the strain is very small (elastic deformation) in the conversion formula of strain, both formulas unconditionally come into effect. In other words, both formulas hold true even in the isotropic elastic body or anisotropic elastic body. It was shown that the conversion formula of strain can be derived from the conversion formula of stress using the formula of Hooke for isotropic elastic body. From these three-dimensional expressions, the two-dimensional stress-strain coordinate conversion formula that is used for Mohr's stress-strain circle was derived. It was shown that these formulas hold true for three-dimensional stress condition with stress-strain components in the three-axial direction that are not plane stress nor plane strain condition. In addition, as an application case of this theory, two-dimensional and three-dimensional X-ray stress measurements that are effective for residual stress measurement were shown. (A.O.)
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 ...
Federal Laboratory Consortium — ATLAS is a particle physics experiment at the Large Hadron Collider at CERN, the European Organization for Nuclear Research. Scientists from Brookhaven have played...
Liang, Shengxiang; Wu, Shang; Huang, Qi; Duan, Shaofeng; Liu, Hua; Li, Yuxiao; Zhao, Shujun; Nie, Binbin; Shan, Baoci
2017-11-01
To automatically analyze diffusion tensor images of the rat brain via both voxel-based and ROI-based approaches, we constructed a new white matter atlas of the rat brain with fine tracts delineation in the Paxinos and Watson space. Unlike in previous studies, we constructed a digital atlas image from the latest edition of the Paxinos and Watson. This atlas contains 111 carefully delineated white matter fibers. A white matter network of rat brain based on anatomy was constructed by locating the intersection of all these tracts and recording the nuclei on the pathway of each white matter tract. Moreover, a compatible rat brain template from DTI images was created and standardized into the atlas space. To evaluate the automated application of the atlas in DTI data analysis, a group of rats with right-side middle cerebral artery occlusion (MCAO) and those without were enrolled in this study. The voxel-based analysis result shows that the brain region showing significant declines in signal in the MCAO rats was consistent with the occlusion position. We constructed a stereotaxic white matter atlas of the rat brain with fine tract delineation and a compatible template for the data analysis of DTI images of the rat brain. Copyright © 2017 Elsevier Inc. All rights reserved.
Grid-search Moment Tensor Estimation: Implementation and CTBT-related Application
Stachnik, J. C.; Baker, B. I.; Rozhkov, M.; Friberg, P. A.; Leifer, J. M.
2017-12-01
This abstract presents a review work related to moment tensor estimation for Expert Technical Analysis at the Comprehensive Test Ban Treaty Organization. In this context of event characterization, estimation of key source parameters provide important insights into the nature of failure in the earth. For example, if the recovered source parameters are indicative of a shallow source with large isotropic component then one conclusion is that it is a human-triggered explosive event. However, an important follow-up question in this application is - does an alternative hypothesis like a deeper source with a large double couple component explain the data approximately as well as the best solution? Here we address the issue of both finding a most likely source and assessing its uncertainty. Using the uniform moment tensor discretization of Tape and Tape (2015) we exhaustively interrogate and tabulate the source eigenvalue distribution (i.e., the source characterization), tensor orientation, magnitude, and source depth. The benefit of the grid-search is that we can quantitatively assess the extent to which model parameters are resolved. This provides a valuable opportunity during the assessment phase to focus interpretation on source parameters that are well-resolved. Another benefit of the grid-search is that it proves to be a flexible framework where different pieces of information can be easily incorporated. To this end, this work is particularly interested in fitting teleseismic body waves and regional surface waves as well as incorporating teleseismic first motions when available. Being that the moment tensor search methodology is well-established we primarily focus on the implementation and application. We present a highly scalable strategy for systematically inspecting the entire model parameter space. We then focus on application to regional and teleseismic data recorded during a handful of natural and anthropogenic events, report on the grid-search optimum, and
Wind Atlas for South Africa (WASA) – Best practice guide for application of WASA
DEFF Research Database (Denmark)
Hansen, Jens Carsten; Mortensen, Niels Gylling; Cronin, Tom
The present report is a best practice guide for application of results from the Wind Atlas for South Africa (WASA). A general description of the methodological framework – the wind atlas methodology – is given, including validation results of the numerical wind atlas at 10 measurement sites...
Tensor-based morphometry of fibrous structures with application to human brain white matter.
Zhang, Hui; Yushkevich, Paul A; Rueckert, Daniel; Gee, James C
2009-01-01
Tensor-based morphometry (TBM) is a powerful approach for examining shape changes in anatomy both across populations and in time. Our work extends the standard TBM for quantifying local volumetric changes to establish both rich and intuitive descriptors of shape changes in fibrous structures. It leverages the data from diffusion tensor imaging to determine local spatial configuration of fibrous structures and combines this information with spatial transformations derived from image registration to quantify fibrous structure-specific changes, such as local changes in fiber length and in thickness of fiber bundles. In this paper, we describe the theoretical framework of our approach in detail and illustrate its application to study brain white matter. Our results show that additional insights can be gained with the proposed analysis.
Loss, Leandro A.; Bebis, George; Parvin, Bahram
2012-01-01
In this paper, a novel approach is proposed for perceptual grouping and localization of ill-defined curvilinear structures. Our approach builds upon the tensor voting and the iterative voting frameworks. Its efficacy lies on iterative refinements of curvilinear structures by gradually shifting from an exploratory to an exploitative mode. Such a mode shifting is achieved by reducing the aperture of the tensor voting fields, which is shown to improve curve grouping and inference by enhancing the concentration of the votes over promising, salient structures. The proposed technique is applied to delineation of adherens junctions imaged through fluorescence microscopy. This class of membrane-bound macromolecules maintains tissue structural integrity and cell-cell interactions. Visually, it exhibits fibrous patterns that may be diffused, punctate and frequently perceptual. Besides the application to real data, the proposed method is compared to prior methods on synthetic and annotated real data, showing high precision rates. PMID:21421432
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...
International Nuclear Information System (INIS)
Qin, Yuan-Yuan; Li, Mu-Wei; Oishi, Kenichi; Zhang, Shun; Zhang, Yan; Zhao, Ling-Yun; Zhu, Wen-Zhen; Lei, Hao
2013-01-01
Diffusion tensor imaging (DTI) has been applied to characterize the pathological features of Alzheimer's disease (AD) in a mouse model, although little is known about whether these features are structure specific. Voxel-based analysis (VBA) and atlas-based analysis (ABA) are good complementary tools for whole-brain DTI analysis. The purpose of this study was to identify the spatial localization of disease-related pathology in an AD mouse model. VBA and ABA quantification were used for the whole-brain DTI analysis of nine APP/PS1 mice and wild-type (WT) controls. Multiple scalar measurements, including fractional anisotropy (FA), trace, axial diffusivity (DA), and radial diffusivity (DR), were investigated to capture the various types of pathology. The accuracy of the image transformation applied for VBA and ABA was evaluated by comparing manual and atlas-based structure delineation using kappa statistics. Following the MR examination, the brains of the animals were analyzed for microscopy. Extensive anatomical alterations were identified in APP/PS1 mice, in both the gray matter areas (neocortex, hippocampus, caudate putamen, thalamus, hypothalamus, claustrum, amygdala, and piriform cortex) and the white matter areas (corpus callosum/external capsule, cingulum, septum, internal capsule, fimbria, and optic tract), evidenced by an increase in FA or DA, or both, compared to WT mice (p 0.05). The histopathological changes in the gray matter areas were confirmed by microscopy studies. DTI did, however, demonstrate significant changes in white matter areas, where the difference was not apparent by qualitative observation of a single-slice histological specimen. This study demonstrated the structure-specific nature of pathological changes in APP/PS1 mouse, and also showed the feasibility of applying whole-brain analysis methods to the investigation of an AD mouse model. (orig.)
ELATE: an open-source online application for analysis and visualization of elastic tensors
International Nuclear Information System (INIS)
Gaillac, Romain; Coudert, François-Xavier; Pullumbi, Pluton
2016-01-01
We report on the implementation of a tool for the analysis of second-order elastic stiffness tensors, provided with both an open-source Python module and a standalone online application allowing the visualization of anisotropic mechanical properties. After describing the software features, how we compute the conventional elastic constants and how we represent them graphically, we explain our technical choices for the implementation. In particular, we focus on why a Python module is used to generate the HTML web page with embedded Javascript for dynamical plots. (paper)
Energy Technology Data Exchange (ETDEWEB)
Qin, Yuan-Yuan [Huazhong University of Science and Technology, Department of Radiology, Tongji Hospital, Tongji Medical College, Wuhan (China); The Johns Hopkins University School of Medicine, The Russell H. Morgan Department of Radiology and Radiological Science, Baltimore, MD (United States); Li, Mu-Wei; Oishi, Kenichi [The Johns Hopkins University School of Medicine, The Russell H. Morgan Department of Radiology and Radiological Science, Baltimore, MD (United States); Zhang, Shun; Zhang, Yan; Zhao, Ling-Yun; Zhu, Wen-Zhen [Huazhong University of Science and Technology, Department of Radiology, Tongji Hospital, Tongji Medical College, Wuhan (China); Lei, Hao [Chinese Academy of Sciences, Wuhan Center for Magnetic Resonance, State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Wuhan (China)
2013-08-15
Diffusion tensor imaging (DTI) has been applied to characterize the pathological features of Alzheimer's disease (AD) in a mouse model, although little is known about whether these features are structure specific. Voxel-based analysis (VBA) and atlas-based analysis (ABA) are good complementary tools for whole-brain DTI analysis. The purpose of this study was to identify the spatial localization of disease-related pathology in an AD mouse model. VBA and ABA quantification were used for the whole-brain DTI analysis of nine APP/PS1 mice and wild-type (WT) controls. Multiple scalar measurements, including fractional anisotropy (FA), trace, axial diffusivity (DA), and radial diffusivity (DR), were investigated to capture the various types of pathology. The accuracy of the image transformation applied for VBA and ABA was evaluated by comparing manual and atlas-based structure delineation using kappa statistics. Following the MR examination, the brains of the animals were analyzed for microscopy. Extensive anatomical alterations were identified in APP/PS1 mice, in both the gray matter areas (neocortex, hippocampus, caudate putamen, thalamus, hypothalamus, claustrum, amygdala, and piriform cortex) and the white matter areas (corpus callosum/external capsule, cingulum, septum, internal capsule, fimbria, and optic tract), evidenced by an increase in FA or DA, or both, compared to WT mice (p < 0.05, corrected). The average kappa value between manual and atlas-based structure delineation was approximately 0.8, and there was no significant difference between APP/PS1 and WT mice (p > 0.05). The histopathological changes in the gray matter areas were confirmed by microscopy studies. DTI did, however, demonstrate significant changes in white matter areas, where the difference was not apparent by qualitative observation of a single-slice histological specimen. This study demonstrated the structure-specific nature of pathological changes in APP/PS1 mouse, and also showed the
Ecker, Katharina Maria; Kortner, Sandra
The tensor structure of the Higgs boson couplings to gluons and heavy weak gauge bosons has been probed for small admixtures of non-Standard Model CP-odd and, only for heavy vector bosons, CP-even couplings to the CP-even Standard Model coupling. The Higgs boson candidates are reconstructed in the $\\HZZllll$ $(\\ell\\equiv e,\\mu)$ decay channel using proton-proton collision data recorded by the ATLAS detector at the Large Hadron Collider (LHC) in 2011 and 2012 at centre-of-mass energies of $\\sqrt{s}=7$ and $8\\,\\tev$ corresponding to an integrated luminosity of $\\intlumisetot\\,\\ifb$ and in 2015 and 2016 at $\\ecms$ corresponding to $\\intlumi\\,\\ifb$.\\\\ The non-Standard Model coupling parameters are defined within an effective field theory, the so-called Higgs characterisation framework. The relative contributions of the CP-even and CP-odd terms are described by the CP mixing angle $\\alpha$. The parameter $\\kaggnoma$ denotes the CP-odd non-Standard Model coupling at the Higgs to gluon interaction vertex and $\\khvv...
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
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...
Akhnazarov, V; Canepa, A; Bremer, J; Burckhart, H; Cattai, A; Voss, R; Hervas, L; Kaplon, J; Nessi, M; Werner, P; Ten kate, H; Tyrvainen, H; Vandelli, W; Krasznahorkay, A; Gray, H; Alvarez gonzalez, B; Eifert, T F; Rolando, G; Oide, H; Barak, L; Glatzer, J; Backhaus, M; Schaefer, D M; Maciejewski, J P; Milic, A; Jin, S; Von torne, E; Limbach, C; Medinnis, M J; Gregor, I; Levonian, S; Schmitt, S; Waananen, A; Monnier, E; Muanza, S G; Pralavorio, P; Talby, M; Tiouchichine, E; Tocut, V M; Rybkin, G; Wang, S; Lacour, D; Laforge, B; Ocariz, J H; Bertoli, W; Malaescu, B; Sbarra, C; Yamamoto, A; Sasaki, O; Koriki, T; Hara, K; Da silva gomes, A; Carvalho maneira, J; Marcalo da palma, A; Chekulaev, S; Tikhomirov, V; Snesarev, A; Buzykaev, A; Maslennikov, A; Peleganchuk, S; Sukharev, A; Kaplan, B E; Swiatlowski, M J; Nef, P D; Schnoor, U; Oakham, G F; Ueno, R; Orr, R S; Abouzeid, O; Haug, S; Peng, H; Kus, V; Vitek, M; Temming, K K; Dang, N P; Meier, K; Schultz-coulon, H; Geisler, M P; Sander, H; Schaefer, U; Ellinghaus, F; Rieke, S; Nussbaumer, A; Liu, Y; Richter, R; Kortner, S; Fernandez-bosman, M; Ullan comes, M; Espinal curull, J; Chiriotti alvarez, S; Caubet serrabou, M; Valladolid gallego, E; Kaci, M; Carrasco vela, N; Lancon, E C; Besson, N E; Gautard, V; Bracinik, J; Bartsch, V C; Potter, C J; Lester, C G; Moeller, V A; Rosten, J; Crooks, D; Mathieson, K; Houston, S C; Wright, M; Jones, T W; Harris, O B; Byatt, T J; Dobson, E; Hodgson, P; Hodgkinson, M C; Dris, M; Karakostas, K; Ntekas, K; Oren, D; Duchovni, E; Etzion, E; Oren, Y; Ferrer, L M; Testa, M; Doria, A; Merola, L; Sekhniaidze, G; Giordano, R; Ricciardi, S; Milazzo, A; Falciano, S; De pedis, D; Dionisi, C; Veneziano, S; Cardarelli, R; Verzegnassi, C; Soualah, R; Ochi, A; Ohshima, T; Kishiki, S; Linde, F L; Vreeswijk, M; Werneke, P; Muijs, A; Vankov, P H; Jansweijer, P P M; Dale, O; Lund, E; Bruckman de renstrom, P; Dabrowski, W; Adamek, J D; Wolters, H; Micu, L; Pantea, D; Tudorache, V; Mjoernmark, J; Klimek, P J; 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2002-01-01
% ATLAS \\\\ \\\\ ATLAS is a general-purpose experiment for recording proton-proton collisions at LHC. The ATLAS collaboration consists of 144 participating institutions (June 1998) with more than 1750~physicists and engineers (700 from non-Member States). The detector design has been optimized to cover the largest possible range of LHC physics: searches for Higgs bosons and alternative schemes for the spontaneous symmetry-breaking mechanism; searches for supersymmetric particles, new gauge bosons, leptoquarks, and quark and lepton compositeness indicating extensions to the Standard Model and new physics beyond it; studies of the origin of CP violation via high-precision measurements of CP-violating B-decays; high-precision measurements of the third quark family such as the top-quark mass and decay properties, rare decays of B-hadrons, spectroscopy of rare B-hadrons, and $ B ^0 _{s} $-mixing. \\\\ \\\\The ATLAS dectector, shown in the Figure includes an inner tracking detector inside a 2~T~solenoid providing an axial...
Tensor-based Multi-view Feature Selection with Applications to Brain Diseases
Cao, Bokai; He, Lifang; Kong, Xiangnan; Yu, Philip S.; Hao, Zhifeng; Ragin, Ann B.
2015-01-01
In the era of big data, we can easily access information from multiple views which may be obtained from different sources or feature subsets. Generally, different views provide complementary information for learning tasks. Thus, multi-view learning can facilitate the learning process and is prevalent in a wide range of application domains. For example, in medical science, measurements from a series of medical examinations are documented for each subject, including clinical, imaging, immunologic, serologic and cognitive measures which are obtained from multiple sources. Specifically, for brain diagnosis, we can have different quantitative analysis which can be seen as different feature subsets of a subject. It is desirable to combine all these features in an effective way for disease diagnosis. However, some measurements from less relevant medical examinations can introduce irrelevant information which can even be exaggerated after view combinations. Feature selection should therefore be incorporated in the process of multi-view learning. In this paper, we explore tensor product to bring different views together in a joint space, and present a dual method of tensor-based multi-view feature selection (dual-Tmfs) based on the idea of support vector machine recursive feature elimination. Experiments conducted on datasets derived from neurological disorder demonstrate the features selected by our proposed method yield better classification performance and are relevant to disease diagnosis. PMID:25937823
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.
Bischoff, Marcel; Longo, Roberto; Rehren, Karl-Henning
2015-01-01
C* tensor categories are a point of contact where Operator Algebras and Quantum Field Theory meet. They are the underlying unifying concept for homomorphisms of (properly infinite) von Neumann algebras and representations of quantum observables. The present introductory text reviews the basic notions and their cross-relations in different contexts. The focus is on Q-systems that serve as complete invariants, both for subfactors and for extensions of quantum field theory models. It proceeds with various operations on Q-systems (several decompositions, the mirror Q-system, braided product, centre and full centre of Q-systems) some of which are defined only in the presence of a braiding. The last chapter gives a brief exposition of the relevance of the mathematical structures presented in the main body for applications in Quantum Field Theory (in particular two-dimensional Conformal Field Theory, also with boundaries or defects).
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.
Reweighted Low-Rank Tensor Completion and its Applications in Video Recovery
M., Baburaj; George, Sudhish N.
2016-01-01
This paper focus on recovering multi-dimensional data called tensor from randomly corrupted incomplete observation. Inspired by reweighted $l_1$ norm minimization for sparsity enhancement, this paper proposes a reweighted singular value enhancement scheme to improve tensor low tubular rank in the tensor completion process. An efficient iterative decomposition scheme based on t-SVD is proposed which improves low-rank signal recovery significantly. The effectiveness of the proposed method is es...
Papastavridis, John G
1999-01-01
Tensor Calculus and Analytical Dynamics provides a concise, comprehensive, and readable introduction to classical tensor calculus - in both holonomic and nonholonomic coordinates - as well as to its principal applications to the Lagrangean dynamics of discrete systems under positional or velocity constraints. The thrust of the book focuses on formal structure and basic geometrical/physical ideas underlying most general equations of motion of mechanical systems under linear velocity constraints.
The ATLAS Wide-Range Database & Application Monitoring
Vasileva, Petya Tsvetanova; The ATLAS collaboration
2018-01-01
In HEP experiments at LHC the database applications often become complex by reflecting the ever demanding requirements of the researchers. The ATLAS experiment has several Oracle DB clusters with over 216 database schemes each with its own set of database objects. To effectively monitor them, we designed a modern and portable application with exceptionally good characteristics. Some of them include: concise view of the most important DB metrics; top SQL statements based on CPU, executions, block reads, etc.; volume growth plots per schema and DB object type; database jobs section with signaling for problematic ones; in-depth analysis in case of contention on data or processes. This contribution describes also the technical aspects of the implementation. The project can be separated into three independent layers. The first layer consists in highly-optimized database objects hiding all complicated calculations. The second layer represents a server providing REST access to the underlying database backend. The th...
Geng, Xiujuan; Gu, Hong; Shin, Wanyong; Ross, Thomas J; Yang, Yihong
2011-10-01
We propose an unbiased implicit-reference group-wise (IRG) image registration method and demonstrate its applications in the construction of a brain white matter fiber tract atlas and the analysis of resting-state functional MRI (fMRI) connectivity. Most image registration techniques pair-wise align images to a selected reference image and group analyses are performed in the reference space, which may produce bias. The proposed method jointly estimates transformations, with an elastic deformation model, registering all images to an implicit reference corresponding to the group average. The unbiased registration is applied to build a fiber tract atlas by registering a group of diffusion tensor images. Compared to reference-based registration, the IRG registration improves the fiber track overlap within the group. After applying the method in the fMRI connectivity analysis, results suggest a general improvement in functional connectivity maps at a group level in terms of larger cluster size and higher average t-scores.
Luo, Yao; Wu, Mei-Ping; Wang, Ping; Duan, Shu-Ling; Liu, Hao-Jun; Wang, Jin-Long; An, Zhan-Feng
2015-09-01
The full magnetic gradient tensor (MGT) refers to the spatial change rate of the three field components of the geomagnetic field vector along three mutually orthogonal axes. The tensor is of use to geological mapping, resources exploration, magnetic navigation, and others. However, it is very difficult to measure the full magnetic tensor gradient using existing engineering technology. We present a method to use triaxial aeromagnetic gradient measurements for deriving the full MGT. The method uses the triaxial gradient data and makes full use of the variation of the magnetic anomaly modulus in three dimensions to obtain a self-consistent magnetic tensor gradient. Numerical simulations show that the full MGT data obtained with the proposed method are of high precision and satisfy the requirements of data processing. We selected triaxial aeromagnetic gradient data from the Hebei Province for calculating the full MGT. Data processing shows that using triaxial tensor gradient data allows to take advantage of the spatial rate of change of the total field in three dimensions and suppresses part of the independent noise in the aeromagnetic gradient. The calculated tensor components have improved resolution, and the transformed full tensor gradient satisfies the requirement of geological mapping and interpretation.
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)
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
Tape, C.; Alvizuri, C. R.; Silwal, V.; Tape, W.
2017-12-01
When considered as a point source, a seismic source can be characterized in terms of its origin time, hypocenter, moment tensor, and source time function. The seismologist's task is to estimate these parameters--and their uncertainties--from three-component ground motion recorded at irregularly spaced stations. We will focus on one portion of this problem: the estimation of the moment tensor and its uncertainties. With magnitude estimated separately, we are left with five parameters describing the normalized moment tensor. A lune of normalized eigenvalue triples can be used to visualize the two parameters (lune longitude and lune latitude) describing the source type, while the conventional strike, dip, and rake angles can be used to characterize the orientation. Slight modifications of these five parameters lead to a uniform parameterization of moment tensors--uniform in the sense that equal volumes in the coordinate domain of the parameterization correspond to equal volumes of moment tensors. For a moment tensor m that we have inferred from seismic data for an earthquake, we define P(V) to be the probability that the true moment tensor for the earthquake lies in the neighborhood of m that has fractional volume V. The average value of P(V) is then a measure of our confidence in our inference of m. The calculation of P(V) requires knowing both the probability P(w) and the fractional volume V(w) of the set of moment tensors within a given angular radius w of m. We apply this approach to several different data sets, including nuclear explosions from the Nevada Test Site, volcanic events from Uturuncu (Bolivia), and earthquakes. Several challenges remain: choosing an appropriate misfit function, handling time shifts between data and synthetic waveforms, and extending the uncertainty estimation to include more source parameters (e.g., hypocenter and source time function).
Comments on "A closed-form solution to Tensor voting: theory and applications"
Maggiori, Emmanuel; Lotito, Pablo Andres; Manterola, Hugo Luis; del Fresno, Mariana
2017-01-01
We comment on a paper that describes a closed-form formulation to Tensor Voting, a technique to perceptually group clouds of points, usually applied to infer features in images. The authors proved an analytic solution to the technique, a highly relevant contribution considering that the original formulation required numerical integration, a time-consuming task. Their work constitutes the first closed-form expression for the Tensor Voting framework. In this work we first observe that the propo...
An application of the tensor virial theorem to hole + vortex + bulge systems
Caimmi, R.
2009-04-01
The tensor virial theorem for subsystems is formulated for three-component systems and further effort is devoted to a special case where the inner subsystems and the central region of the outer one are homogeneous, the last surrounded by an isothermal homeoid. The virial equations are explicitly written under the additional restrictions: (i) similar and similarly placed inner subsystems, and (ii) spherical outer subsystem. An application is made to hole + vortex + bulge systems, in the limit of flattened inner subsystems, which implies three virial equations in three unknowns. Using the Faber-Jackson relation, R∝σ02, the standard M- σ0 form (M∝σ04) is deduced from qualitative considerations. The projected bulge velocity dispersion to projected vortex velocity ratio, η=(σ)33/{[(v)qq]2+[(σ)qq]2}, as a function of the fractional radius, y=R/R, and the fractional masses, m=M/M and m=M/M, is studied in the range of interest, 0⩽m=M/M⩽5 [Escala, A., 2006. ApJ, 648, L13] and 229⩽m⩽795 [Marconi, A., Hunt, L.H., 2003. ApJ 589, L21], consistent with observations. The related curves appear to be similar to Maxwell velocity distributions, which implies a fixed value of η below the maximum corresponds to two different configurations: a compact bulge on the left of the maximum, and an extended bulge on the right. All curves lie very close one to the other on the left of the maximum, and parallel one to the other on the right. On the other hand, fixed m or m, and y, are found to imply more massive bulges passing from bottom to top along a vertical line on the (Oyη) plane, and vice versa. The model is applied to NGC 4374 and NGC 4486, taking the fractional mass, m, and the fractional radius, y, as unknowns, and the bulge mass is inferred from the knowledge of the hole mass, and compared with results from different methods. In presence of a massive vortex (m=5), the hole mass has to be reduced by a factor 2-3 with respect to the case of a massless vortex, to get
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.
Hu, Weiming; Gao, Jin; Xing, Junliang; Zhang, Chao; Maybank, Stephen
2017-01-01
An appearance model adaptable to changes in object appearance is critical in visual object tracking. In this paper, we treat an image patch as a two-order tensor which preserves the original image structure. We design two graphs for characterizing the intrinsic local geometrical structure of the tensor samples of the object and the background. Graph embedding is used to reduce the dimensions of the tensors while preserving the structure of the graphs. Then, a discriminant embedding space is constructed. We prove two propositions for finding the transformation matrices which are used to map the original tensor samples to the tensor-based graph embedding space. In order to encode more discriminant information in the embedding space, we propose a transfer-learning- based semi-supervised strategy to iteratively adjust the embedding space into which discriminative information obtained from earlier times is transferred. We apply the proposed semi-supervised tensor-based graph embedding learning algorithm to visual tracking. The new tracking algorithm captures an object's appearance characteristics during tracking and uses a particle filter to estimate the optimal object state. Experimental results on the CVPR 2013 benchmark dataset demonstrate the effectiveness of the proposed tracking algorithm.
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.
Energy Technology Data Exchange (ETDEWEB)
Peng, Bo [William R. Wiley Environmental; Kowalski, Karol [William R. Wiley Environmental
2017-08-11
The representation and storage of two-electron integral tensors are vital in large- scale applications of accurate electronic structure methods. Low-rank representation and efficient storage strategy of integral tensors can significantly reduce the numerical overhead and consequently time-to-solution of these methods. In this paper, by combining pivoted incomplete Cholesky decomposition (CD) with a follow-up truncated singular vector decomposition (SVD), we develop a decomposition strategy to approximately represent the two-electron integral tensor in terms of low-rank vectors. A systematic benchmark test on a series of 1-D, 2-D, and 3-D carbon-hydrogen systems demonstrates high efficiency and scalability of the compound two-step decomposition of the two-electron integral tensor in our implementation. For the size of atomic basis set N_b ranging from ~ 100 up to ~ 2, 000, the observed numerical scaling of our implementation shows O(N_b^{2.5~3}) versus O(N_b^{3~4}) of single CD in most of other implementations. More importantly, this decomposition strategy can significantly reduce the storage requirement of the atomic-orbital (AO) two-electron integral tensor from O(N_b^4) to O(N_b^2 log_{10}(N_b)) with moderate decomposition thresholds. The accuracy tests have been performed using ground- and excited-state formulations of coupled- cluster formalism employing single and double excitations (CCSD) on several bench- mark systems including the C_{60} molecule described by nearly 1,400 basis functions. The results show that the decomposition thresholds can be generally set to 10^{-4} to 10^{-3} to give acceptable compromise between efficiency and accuracy.
ATLAS TDAQ application gateway upgrade during LS1
KOROL, A; The ATLAS collaboration; BOGDANCHIKOV, A; BRASOLIN, F; CONTESCU, A C; DUBROV, S; HAFEEZ, M; LEE, C J; SCANNICCHIO, D A; TWOMEY, M; VORONKOV, A; ZAYTSEV, A
2014-01-01
The ATLAS Gateway service is implemented with a set of dedicated computer nodes to provide a fine-grained access control between CERN General Public Network (GPN) and ATLAS Technical Control Network (ATCN). ATCN connects the ATLAS online farm used for ATLAS Operations and data taking, including the ATLAS TDAQ (Trigger and Data Aquisition) and DCS (Detector Control System) nodes. In particular, it provides restricted access to the web services (proxy), general login sessions (via SSH and RDP protocols), NAT and mail relay from ATCN. At the Operating System level the implementation is based on virtualization technologies. Here we report on the Gateway upgrade during Long Shutdown 1 (LS1) period: it includes the transition to the last production release of the CERN Linux distribution (SLC6), the migration to the centralized configuration management system (based on Puppet) and the redesign of the internal system architecture.
Poya, Roman; Gil, Antonio J.; Ortigosa, Rogelio
2017-07-01
The paper presents aspects of implementation of a new high performance tensor contraction framework for the numerical analysis of coupled and multi-physics problems on streaming architectures. In addition to explicit SIMD instructions and smart expression templates, the framework introduces domain specific constructs for the tensor cross product and its associated algebra recently rediscovered by Bonet et al. (2015, 2016) in the context of solid mechanics. The two key ingredients of the presented expression template engine are as follows. First, the capability to mathematically transform complex chains of operations to simpler equivalent expressions, while potentially avoiding routes with higher levels of computational complexity and, second, to perform a compile time depth-first or breadth-first search to find the optimal contraction indices of a large tensor network in order to minimise the number of floating point operations. For optimisations of tensor contraction such as loop transformation, loop fusion and data locality optimisations, the framework relies heavily on compile time technologies rather than source-to-source translation or JIT techniques. Every aspect of the framework is examined through relevant performance benchmarks, including the impact of data parallelism on the performance of isomorphic and nonisomorphic tensor products, the FLOP and memory I/O optimality in the evaluation of tensor networks, the compilation cost and memory footprint of the framework and the performance of tensor cross product kernels. The framework is then applied to finite element analysis of coupled electro-mechanical problems to assess the speed-ups achieved in kernel-based numerical integration of complex electroelastic energy functionals. In this context, domain-aware expression templates combined with SIMD instructions are shown to provide a significant speed-up over the classical low-level style programming techniques.
The C-RORC PCIe Card and its Application in the ALICE and ATLAS Experiments
Engel, H; Costa, F; Crone, G J; Eschweiler, D; Francis, D; Green, B; Joos, M; Kebschull, U; Kiss, T; Kugel, A; Panduro Vasquez, J G; Soos, C; Teixeira-Dias, P; Tremblet, L; Vande Vyvre, P; Vandelli, W; Vermeulen, J C; Werner, P; Wickens, F J
2015-01-01
The ALICE and ATLAS DAQ systems read out detector data via point-to-point serial links into custom hardware modules, the ALICE RORC and ATLAS ROBIN. To meet the increase in operational requirements both experiments are replacing their respective modules with a new common module, the C-RORC. This card, developed by ALICE, implements a PCIe Gen 2 x8 interface and interfaces to twelve optical links via three QSFP transceivers. This paper presents the design of the C-RORC, its performance and its application in the ALICE and ATLAS experiments.
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.
Brain atlas for functional imaging. Clinical and research applications
International Nuclear Information System (INIS)
Nowinski, W.L.; Thirunavuukarasuu, A.; Kennedy, D.N
2001-01-01
This CD-ROM: Allows anatomical and functional images to be loaded and registered. Enables interactive placement of the Talairach landmarks in 3D Space. Provides automatic data-to-atlas warping based on the Talairaich proportional gridsystem transformation. Real-time interactive warping for fine tuning is also available. Allows the user to place marks on the activation loci in the warped functional images, display these marks with the atlas, and edit them in three planes. Mark placement is assisted by image thresholding. Provides simultaneous display of the atlas, anatomical image and functional image within one interactively blended image. Atlas-data blending and anatomical-functional image blending are controlled independently. Labels the data by means of the atlas. The atlas can be flipped left/right so that Brodmann's areas and gyri can be labeled on both hemispheres. Provides additional functions such as friendly navigation, cross-referenced display, readout of the Talairach coordinates and intensities, load coordinates, save, on-line help. (orig.)
Brain atlas for functional imaging. Clinical and research applications
Energy Technology Data Exchange (ETDEWEB)
Nowinski, W.L.; Thirunavuukarasuu, A.; Kennedy, D.N
2001-07-01
This CD-ROM: Allows anatomical and functional images to be loaded and registered. Enables interactive placement of the Talairach landmarks in 3D Space. Provides automatic data-to-atlas warping based on the Talairaich proportional gridsystem transformation. Real-time interactive warping for fine tuning is also available. Allows the user to place marks on the activation loci in the warped functional images, display these marks with the atlas, and edit them in three planes. Mark placement is assisted by image thresholding. Provides simultaneous display of the atlas, anatomical image and functional image within one interactively blended image. Atlas-data blending and anatomical-functional image blending are controlled independently. Labels the data by means of the atlas. The atlas can be flipped left/right so that Brodmann's areas and gyri can be labeled on both hemispheres. Provides additional functions such as friendly navigation, cross-referenced display, readout of the Talairach coordinates and intensities, load coordinates, save, on-line help. (orig.)
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...
Comments on "A Closed-Form Solution to Tensor Voting: Theory and Applications".
Maggiori, Emmanuel; Lotito, Pablo; Manterola, Hugo Luis; del Fresno, Mariana
2014-12-01
We comment on a paper that describes a closed-form formulation to Tensor Voting, a technique to perceptually group clouds of points, usually applied to infer features in images. The authors proved an analytic solution to the technique, a highly relevant contribution considering that the original formulation required numerical integration, a time-consuming task. Their work constitutes the first closed-form expression for the Tensor Voting framework. In this work we first observe that the proposed formulation leads to unexpected results which do not satisfy the constraints for a Tensor Voting output, hence they cannot be interpreted. Given that the closed-form expression is said to be an analytic equivalent solution, unexpected outputs should not be encountered unless there are flaws in the proof. We analyzed the underlying math to find which were the causes of these unexpected results. In this commentary we show that their proposal does not in fact provide a proper analytic solution to Tensor Voting and we indicate the flaws in the proof.
Litvinenko, Alexander
2018-03-12
Part 1: Parallel H-matrices in spatial statistics 1. Motivation: improve statistical model 2. Tools: Hierarchical matrices 3. Matern covariance function and joint Gaussian likelihood 4. Identification of unknown parameters via maximizing Gaussian log-likelihood 5. Implementation with HLIBPro. Part 2: Low-rank Tucker tensor methods in spatial statistics
An introduction to visualization of diffusion tensor imaging and its applications
Vilanova, A.; Zhang, S.; Kindlmann, G.; Laidlaw, D.H.; Weickert, J.; Hagen, H.
2005-01-01
Summary. Water diffusion is anisotropic in organized tissues such as white matter and muscle. Diffusion tensor imaging (DTI), a non-invasive MR technique, measures water self-diffusion rates and thus gives an indication of the underlying tissue microstructure. The diffusion rate is often expressed
Directory of Open Access Journals (Sweden)
Mounia Laassiri
Full Text Available For efficient exploitation of research reactors, it is important to discern neutron flux distribution inside the reactor with the best possible precision. For this reason, fission and ionization chambers are used to measure the neutron field. In these arrays, the sequences of the neutron interaction points in the fission chamber can correctly be identified in order to obtain true neutron energies emitted by nuclei of interest. However, together with the neutrons, gamma-rays are also emitted from nuclei and thereby affect neutron spectra. The originality of this study consists in the application of tensor based blind source separation methods to extract independent components from signals recorded at the fission chamber preamplifier’s output. The objective is to achieve software neutron-gamma discrimination using Nonnegative Tensor Factorization tools. For reasons of nuclear safety, we first simulate the neutron flux inside the TRIGA Mark II Reactor using Monte Carlo methods under Geant4 platform linked to Garfield++. Geant4 simulations allow the fission chamber construction whereas linking the model to Garfield++ permits to simulate drift parameters from the ionization of the filling gas, which is not possible otherwise. Keywords: Fission chamber (FC, Geant4, Garfield++, Neutron-gamma discrimination, Nonnegative Tensor Factorization (NTF
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...
Walbrecht, Verena Maria; Kortner, Sandra
In this master thesis the measurement of the Higgs boson production in the $H\\to~ZZ^*~\\to 4~\\ell$ decay channel ($\\ell=e,\\mu$) is performed together with the measurement of the tensor structure of the Higgs boson couplings to $Z$ bosons. The results are based on the Run~II dataset of LHC's proton-proton collisions at a centre-of-mass energy of 13~TeV, with the ATLAS detector and corresponding to a total integrated luminosity of $14.78$~fb$^{-1}$. Special emphasis is given to the estimation of the reducible background contribution. Based on the signal and background estimations, there are $32.0\\pm3.2$ Higgs boson candidates expected after the final event selection, while $44$ candidates are observed. The difference is compatible at the level of about $2$ standard derivations with the Standard Model predictions. All selected candidates are used in the study of the tensor structure of the $HZZ$ coupling between the Higgs boson and the two $Z$ bosons. For this study a dedicated signal model is introduced to desc...
International Nuclear Information System (INIS)
Reinges, Marcus H.T.; Schoth, Felix; Coenen, Volker A.; Krings, Timo
2004-01-01
Diffusion weighted MRI offers the possibility to study the course of the cerebral white matter tracts. In the present manuscript, the basics, the technique and the limitations of diffusion tensor imaging and anisotropic diffusion weighted MRI are presented and their applications in various neurological and neurosurgical diseases are discussed with special emphasis on the visual system. A special focus is laid on the combination of fiber tract imaging, anatomical imaging and functional MRI for presurgical planning and intraoperative neuronavigation of lesions near the visual system
International Nuclear Information System (INIS)
van Nieuwenhuizen, P.; Wu, C.C.
1977-01-01
The lowest order quantum corrections to pure gravitation are finite because there exists an integral relation between products of two Riemann tensors (the Gauss--Bonnet theorem). In this article several algebraic and integral relations are determined between products of three Riemann tensors in four- and six-dimensional spacetime. In both cases, one is left with only one invariant when R/sub μ//sub ν/=0, viz., ∫ (-g) 1 / 2 (R/sub b//sub β//sub μ//sub ν/R/sup μ//sup ν//sup rho//sup sigma/R/sub rho//sub sigma/ /sup α//sup β/).It is explicitly shown that this invariant does not vanish, even when R/sub μ//sub ν/=0. Consequently, the two-loop quantum corrections to pure gravitation will only be finite if, due to miraculous cancellation, the coefficient of this invariant vanishes
Using FPGA coprocessor for ATLAS level 2 trigger application
International Nuclear Information System (INIS)
Khomich, Andrei; Hinkelbein, Christian; Kugel, Andreas; Maenner, Reinhard; Mueller, Matthias
2006-01-01
Tracking has a central role in the event selection for the High-Level Triggers of ATLAS. It is particularly important to have fast tracking algorithms in the trigger system. This paper investigates the feasibility of using FPGA coprocessor for speeding up of the TRT LUT algorithm-one of the tracking algorithms for second level trigger for ATLAS experiment (CERN). Two realisations of the same algorithm have been compared: one in C++ and a hybrid C++/VHDL implementation. Using a FPGA coprocessor gives an increase of speed by a factor of two compared to a CPU-only implementation
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....
Miao, Xijiang; Mukhopadhyay, Rishi; Valafar, Homayoun
2008-10-01
Advances in NMR instrumentation and pulse sequence design have resulted in easier acquisition of Residual Dipolar Coupling (RDC) data. However, computational and theoretical analysis of this type of data has continued to challenge the international community of investigators because of their complexity and rich information content. Contemporary use of RDC data has required a-priori assignment, which significantly increases the overall cost of structural analysis. This article introduces a novel algorithm that utilizes unassigned RDC data acquired from multiple alignment media ( nD-RDC, n ⩾ 3) for simultaneous extraction of the relative order tensor matrices and reconstruction of the interacting vectors in space. Estimation of the relative order tensors and reconstruction of the interacting vectors can be invaluable in a number of endeavors. An example application has been presented where the reconstructed vectors have been used to quantify the fitness of a template protein structure to the unknown protein structure. This work has other important direct applications such as verification of the novelty of an unknown protein and validation of the accuracy of an available protein structure model in drug design. More importantly, the presented work has the potential to bridge the gap between experimental and computational methods of structure determination.
Rank of tensors of l-out-of-k functions: an application in probabilistic inference
Czech Academy of Sciences Publication Activity Database
Vomlel, Jiří
2011-01-01
Roč. 47, č. 3 (2011), s. 317-336 ISSN 0023-5954 R&D Projects: GA MŠk 1M0572; GA ČR GA201/09/1891; GA ČR GEICC/08/E010 Grant - others:GA MŠk(CZ) 2C06019 Institutional research plan: CEZ:AV0Z10750506 Keywords : Bayesian network * probabilistic inference * tensor rank Subject RIV: BB - Applied Statistics, Operational Research Impact factor: 0.454, year: 2011 http://library.utia.cas.cz/separaty/2011/MTR/vomlel-0361630.pdf
An application of stress energy tensor to the vanishing theorem of differential forms
Directory of Open Access Journals (Sweden)
Kairen Cai
1988-01-01
Full Text Available The author applies the stress energy of differential forms to study the vanishing theorems of the Liouville type. It is shown that for a large class of underlying manifolds such as the Euclidean n-space, the complex n-space, and the complex hyperbolic space form, if any vector bundle valued p-form with conservative stress energy tensor is of finite norm or slowly divergent norm, then the p-form vanishes. This generalizes the recent results due to Hu and Sealey.
Saitou, Sona; Iijima, Jun; Fujimoto, Mayu; Mochizuki, Yuji; Okuwaki, Koji; Doi, Hideo; Komeiji, Yuto
2018-01-01
We have applied Google's TensorFlow deep learning toolkit to recognize the visualized results of the fragment molecular orbital (FMO) calculations. Typical protein structures of alpha-helix and beta-sheet provide some characteristic patterns in the two-dimensional map of inter-fragment interaction energy termed as IFIE-map (Kurisaki et al., Biophys. Chem. 130 (2007) 1). A thousand of IFIE-map images with labels depending on the existences of alpha-helix and beta-sheet were prepared by employi...
Turbo-SMT: Parallel Coupled Sparse Matrix-Tensor Factorizations and Applications
Papalexakis, Evangelos E.; Faloutsos, Christos; Mitchell, Tom M.; Talukdar, Partha Pratim; Sidiropoulos, Nicholas D.; Murphy, Brian
2016-01-01
How can we correlate the neural activity in the human brain as it responds to typed words, with properties of these terms (like ’edible’, ’fits in hand’)? In short, we want to find latent variables, that jointly explain both the brain activity, as well as the behavioral responses. This is one of many settings of the Coupled Matrix-Tensor Factorization (CMTF) problem. Can we enhance any CMTF solver, so that it can operate on potentially very large datasets that may not fit in main memory? We introduce Turbo-SMT, a meta-method capable of doing exactly that: it boosts the performance of any CMTF algorithm, produces sparse and interpretable solutions, and parallelizes any CMTF algorithm, producing sparse and interpretable solutions (up to 65 fold). Additionally, we improve upon ALS, the work-horse algorithm for CMTF, with respect to efficiency and robustness to missing values. We apply Turbo-SMT to BrainQ, a dataset consisting of a (nouns, brain voxels, human subjects) tensor and a (nouns, properties) matrix, with coupling along the nouns dimension. Turbo-SMT is able to find meaningful latent variables, as well as to predict brain activity with competitive accuracy. Finally, we demonstrate the generality of Turbo-SMT, by applying it on a Facebook dataset (users, ’friends’, wall-postings); there, Turbo-SMT spots spammer-like anomalies. PMID:27672406
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.
Tao, Chenyang; Nichols, Thomas E; Hua, Xue; Ching, Christopher R K; Rolls, Edmund T; Thompson, Paul M; Feng, Jianfeng
2017-01-01
We propose a generalized reduced rank latent factor regression model (GRRLF) for the analysis of tensor field responses and high dimensional covariates. The model is motivated by the need from imaging-genetic studies to identify genetic variants that are associated with brain imaging phenotypes, often in the form of high dimensional tensor fields. GRRLF identifies from the structure in the data the effective dimensionality of the data, and then jointly performs dimension reduction of the covariates, dynamic identification of latent factors, and nonparametric estimation of both covariate and latent response fields. After accounting for the latent and covariate effects, GRLLF performs a nonparametric test on the remaining factor of interest. GRRLF provides a better factorization of the signals compared with common solutions, and is less susceptible to overfitting because it exploits the effective dimensionality. The generality and the flexibility of GRRLF also allow various statistical models to be handled in a unified framework and solutions can be efficiently computed. Within the field of neuroimaging, it improves the sensitivity for weak signals and is a promising alternative to existing approaches. The operation of the framework is demonstrated with both synthetic datasets and a real-world neuroimaging example in which the effects of a set of genes on the structure of the brain at the voxel level were measured, and the results compared favorably with those from existing approaches. Copyright © 2016. Published by Elsevier Inc.
A camac-based intelligent subsystem for ATLAS example application: cryogenic monitoring and control
International Nuclear Information System (INIS)
Pardo, R.; Kawarasaki, Y.; Wasniewski, K.
1985-01-01
A subunit of the CAMAC accelerator control system of ATLAS for monitoring and, eventually, controlling the cryogenic refrigeration and distribution facility is under development. This development is the first application of a philosophy of distributed intelligence which will be applied throughout the ATLAS control system. The control concept is that of an intelligent subunit of the existing ATLAS CAMAC control highway. A single board computer resides in an auxiliary crate controller which allows access to all devices within the crate. The local SBC can communicate to the host over the CAMAC highway via a protocol involving the use of memory in the SBC which can be accessed from the host in a DMA mode. This provides a mechanism for global communications, such as for alarm conditions, as well as allowing the cryogenic system to respond to the demands of the accelerator system
CAMAC-based intelligent subsystem for ATLAS example application: cryogenic monitoring and control
International Nuclear Information System (INIS)
Pardo, R.; Kawarasaki, Y.; Wasniewski, K.
1985-01-01
A subunit of the CAMAC accelerator control system of ATLAS for monitoring and, eventually, controlling the cryogenic refrigeration and distribution facility is under development. This development is the first application of a philosophy of distributed intelligence which will be applied throughout the ATLAS control system. The control concept is that of an intelligent subunit of the existing ATLAS CAMAC control highway. A single board computer resides in an auxiliary crate controller which allows access to all devices within the crate. The local SBC can communicate to the host over the CAMAC highway via a protocol involving the use of memory in the SBC which can be accessed from the host in a DMA mode. This provides a mechanism for global communications, such as for alarm conditions, as well as allowing the cryogenic system to respond to the demands of the accelerator system
The TDAQ Analytics Dashboard: a real-time web application for the ATLAS TDAQ control infrastructure
Magnoni, L; The ATLAS collaboration; Sloper, J E
2011-01-01
The ATLAS Trigger and Data Acquisition (TDAQ) infrastructure is responsible for filtering and transferring ATLAS experimental data from detectors to mass storage systems. It relies on a large, distributed computing environment composed by thousands of software applications running concurrently. In such a complex environment, information sharing is fundamental for controlling applications behavior, error reporting and operational monitoring. During data taking runs, the streams of messages sent by applications and data published via information services are constantly monitored by experts to verify correctness of running operations and to understand problematic situations. To simplify and improve system analysis and errors detection tasks, we developed the TDAQ Analytics Dashboard, a web application that aims to collect, correlate and visualize effectively this real time flow of information. The TDAQ Analytics Dashboard is composed by two main entities, that reflect the twofold scope of the application. The fi...
The TDAQ Analytics Dashboard: a real-time web application for the ATLAS TDAQ control infrastructure
Magnoni, L; Sloper, J E
2010-01-01
The ATLAS Trigger and Data Acquisition (TDAQ) infrastructure is responsible for filtering and transferring ATLAS experimental data from detectors to mass storage systems. It relies on a large, distributed computing environment composed by thousands of software applications running concurrently. In such a complex environment, information sharing is fundamental for controlling applications behavior, error reporting and operational monitoring. During data taking runs, the streams of messages sent by applications and data published via information services are constantly monitored by experts to verify correctness of running operations and to understand problematic situations. To simplify and improve system analysis and errors detection tasks, we developed the TDAQ Analytics Dashboard, a web application that aims to collect, correlate and visualize effectively this real time flow of information. The TDAQ Analytics Dashboard is composed by two main entities, that reflect the twofold scope of the application. The fi...
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...
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...
Application of the ATLAS DAQ and Monitoring System for MDT and RPC Commissioning
Pasqualucci, E
2007-01-01
The ATLAS DAQ and monitoring software are currently commonly used to test detectors during the commissioning phase. In this paper, their usage in MDT and RPC commissioning is described, both at the surface pre-commissioning and commissioning stations and in the ATLAS pit. Two main components are heavily used for detector tests. The ROD Crate DAQ software is based on the ATLAS Readout application. Based on the plug-in mechanism, it provides a complete environment to interface any kind of detector or trigger electronics to the ATLAS DAQ system. All the possible flavours of this application are used to test and run the MDT and RPC detectors at the pre-commissioning and commissioning sites. Ad-hoc plug-ins have been developed to implement data readout via VME, both with ROD prototypes and emulating final electronics to read out data with temporary solutions, and to provide trigger distribution and busy management in a multi-crate environment. Data driven event building functionality is also used to combine data f...
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...
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.
U.S. Environmental Protection Agency — This EnviroAtlas national map displays the application rate of inorganic phosphorus (P) fertilizer on agricultural land in the conterminous United States (excluding...
U.S. Environmental Protection Agency — This EnviroAtlas national map displays the application rate of phosphorus (P) as manure on croplands in the conterminous United States (excluding Hawaii and Alaska)...
U.S. Environmental Protection Agency — This EnviroAtlas dataset contains data on the mean synthetic nitrogen (N) fertilizer application to cultivated crop and hay/pasture lands per 12-digit Hydrologic...
The applicability of Greulich and Pyle atlas to assess skeletal age for four ethnic groups.
Mansourvar, Marjan; Ismail, Maizatul Akmar; Raj, Ram Gopal; Kareem, Sameem Abdul; Aik, Saw; Gunalan, Roshan; Antony, Chermaine Deepa
2014-02-01
Recently, determination of skeletal age, defined as the assessment of bone age, has rapidly become an important task between forensic experts and radiologists. The Greulich-Pyle (GP) atlas is one of the most frequently used methods for the assessment of skeletal age around the world. After presentation of the GP approach for the estimation of the bone age, much research has been conducted to examine the usability of this method in various geographic or ethnic categories. This study investigates on a small-scale and compares the reliability of the GP atlas for assessment of the bone age for four ethnic groups - Asian, African/American, Caucasian and Hispanic - for a different range of ages. Plain radiographs of 184 left hands and wrists for males from the healthy sample between 1 to 18 years of age for four ethnic groups were taken. The skeletal age (SA) was estimated by a radiologist using the GP atlas. The blind method was utilized. The mean (SA) results were compared with mean chronological ages (CA) for the separate ethnic groups. SPSS was used to conduct the analysis and the paired t-test was applied to show the difference between the mean CA and mean SA achieved from the GP atlas. The results from the GP atlas were compared to the CA of the samples. In Asian subjects the mean difference was 0.873 years. The GP atlas showed delayed bone age at 2-7 ages (from 0.2 to 2.3 year) and then advanced bone age for age 8. In the African/American subjects the difference between CA and SA was statistically significant (P-value = 0.048). The mean difference in the Caucasian and Hispanic subjects reflects no considerable distinction with a standard deviation (SD) of 0.3088 and 0.3766, respectively, (P-value >0.05 for both groups). According to the present study, it is concluded that although the GP atlas is reliable for Caucasian and Hispanic ethnic groups it is not applicable for other ethnic groups for different ranges of age, especially in the sample of the male African
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...
Jumarie, Guy
2013-04-01
By using fractional differences, one recently proposed an alternative to the formulation of fractional differential calculus, of which the main characteristics is a new fractional Taylor series and its companion Rolle's formula which apply to non-differentiable functions. The key is that now we have at hand a differential increment of fractional order which can be manipulated exactly like in the standard Leibniz differential calculus. Briefly the fractional derivative is the quotient of fractional increments. It has been proposed that this calculus can be used to construct a differential geometry on manifold of fractional order. The present paper, on the one hand, refines the framework, and on the other hand, contributes some new results related to arc length of fractional curves, area on fractional differentiable manifold, covariant fractal derivative, Riemann-Christoffel tensor of fractional order, fractional differential equations of fractional geodesic, strip modeling of fractal space time and its relation with Lorentz transformation. The relation with Nottale's fractal space-time theory then appears in quite a natural way.
Multi-template tensor-based morphometry: application to analysis of Alzheimer's disease.
Koikkalainen, Juha; Lötjönen, Jyrki; Thurfjell, Lennart; Rueckert, Daniel; Waldemar, Gunhild; Soininen, Hilkka
2011-06-01
In this paper methods for using multiple templates in tensor-based morphometry (TBM) are presented and compared to the conventional single-template approach. TBM analysis requires non-rigid registrations which are often subject to registration errors. When using multiple templates and, therefore, multiple registrations, it can be assumed that the registration errors are averaged and eventually compensated. Four different methods are proposed for multi-template TBM. The methods were evaluated using magnetic resonance (MR) images of healthy controls, patients with stable or progressive mild cognitive impairment (MCI), and patients with Alzheimer's disease (AD) from the ADNI database (N=772). The performance of TBM features in classifying images was evaluated both quantitatively and qualitatively. Classification results show that the multi-template methods are statistically significantly better than the single-template method. The overall classification accuracy was 86.0% for the classification of control and AD subjects, and 72.1% for the classification of stable and progressive MCI subjects. The statistical group-level difference maps produced using multi-template TBM were smoother, formed larger continuous regions, and had larger t-values than the maps obtained with single-template TBM. Copyright © 2011 Elsevier Inc. All rights reserved.
Bossa, Matias; Zacur, Ernesto; Olmos, Salvador
2010-07-01
Tensor-based morphometry (TBM) is an analysis technique where anatomical information is characterized by means of the spatial transformations mapping a customized template with the observed images. Therefore, accurate inter-subject non-rigid registration is an essential prerequisite for both template estimation and image warping. Subsequent statistical analysis on the spatial transformations is performed to highlight voxel-wise differences. Most of previous TBM studies did not explore the influence of the registration parameters, such as the parameters defining the deformation and the regularization models. In this work performance evaluation of TBM using stationary velocity field (SVF) diffeomorphic registration was performed in a subset of subjects from Alzheimer's Disease Neuroimaging Initiative (ADNI) study. A wide range of values of the registration parameters that define the transformation smoothness and the balance between image matching and regularization were explored in the evaluation. The proposed methodology provided brain atrophy maps with very detailed anatomical resolution and with a high significance level compared with results recently published on the same data set using a non-linear elastic registration method. Copyright (c) 2010 Elsevier Inc. All rights reserved.
Energy Technology Data Exchange (ETDEWEB)
Testaverde, Lorenzo; Caporali, Laura [University ' ' Sapienza' ' of Rome, Department of Radiological Sciences, Rome (Italy); Venditti, Eugenio; Grillea, Giovanni [U.O.C. Neuroradiologia, I.R.C.C.S. ' ' Neuromed' ' , Pozzilli (Italy); Colonnese, Claudio [University ' ' Sapienza' ' of Rome, Department of Radiological Sciences, Rome (Italy); U.O.C. Neuroradiologia, I.R.C.C.S. ' ' Neuromed' ' , Pozzilli (Italy)
2012-05-15
This study evaluated patients with multiple sclerosis using diffusion tensor imaging (DTI) to obtain fractional anisotropy (FA) and mean diffusivity (MD) values. We investigated the possible statistically significant variation of MD and FA in different MS patients, compared simultaneously, putting in comparison their normal appearing white matter (NAWM) and white matter affected by disease (plaques), both during activity and in remission, with normal white matter (NWM) of control subjects. Statistical analysis using Levene's test for comparison of variances revealed significant (P < 0.05) differences between FA values of the NWM of the controls and those of NAWM and active or inactive lesions, of the patients in the study. However, the differences between MD values of the NWM of the controls and those of NAWM and active or inactive lesions of the patients in the study were judged not significant (P > 0.05). Imaging of MS using MRI techniques is constantly searching for reproducible quantitative parameter. This study shows how these parameters can be identified in the MD and FA values, and thus suggests the implementation of MRI routine protocols for diagnosing MS with the DTI analysis, since it can provide valuable information otherwise unobtainable. (orig.)
Applications of CORBA in the ATLAS prototype DAQ
Jones, R; Mapelli, Livio P; Ryabov, Yu
2000-01-01
This paper presents the experience of using the Common Object Request Broker Architecture (CORBA) in the ATLAS prototype DAQ project. Many communication links in the DAQ system have been designed and implemented using the CORBA standard. A public domain package, called Inter-Language Unification (ILU) has been used to implement CORBA based communications between DAQ components in a local area network (LAN) of heterogeneous computers. The CORBA Naming Service provides the principal mechanism through which most clients of an ORE-based system locate objects that they intend to use. In our project, conventions are employed that meaningfully partition the name space of the Naming Service according to divisions in the DAQ system itself. The Inter Process Communication (IPC) package, implemented in C++ on the top of CORBA/ILU, incorporates this facility and hides the details of the naming schema is described. The development procedure and environment for remote database access using IPC is described. Various end-use...
Directory of Open Access Journals (Sweden)
Dobri Baldaranov
2017-12-01
Full Text Available Objective: The potential of magnetic resonance imaging (MRI as a technical biomarker for cerebral microstructural alterations in neurodegenerative diseases is under investigation. In this study, a framework for the longitudinal analysis of diffusion tensor imaging (DTI-based mapping was applied to the assessment of predefined white matter tracts in amyotrophic lateral sclerosis (ALS, as an example for a rapid progressive neurodegenerative disease.Methods: DTI was performed every 3 months in six patients with ALS (mean (M = 7.7; range 3 to 15 scans and in six controls (M = 3; range 2–5 scans with the identical scanning protocol, resulting in a total of 65 longitudinal DTI datasets. Fractional anisotropy (FA, mean diffusivity (MD, axonal diffusivity (AD, radial diffusivity (RD, and the ratio AD/RD were studied to analyze alterations within the corticospinal tract (CST which is a prominently affected tract structure in ALS and the tract correlating with Braak’s neuropathological stage 1. A correlation analysis was performed between progression rates based on DTI metrics and the revised ALS functional rating scale (ALS-FRS-R.Results: Patients with ALS showed an FA and AD/RD decline along the CST, while DTI metrics of controls did not change in longitudinal DTI scans. The FA and AD/RD decrease progression correlated significantly with ALS-FRS-R decrease progression.Conclusion: On the basis of the longitudinal assessment, DTI-based metrics can be considered as a possible noninvasive follow-up marker for disease progression in neurodegeneration. This finding was demonstrated here for ALS as a fast progressing neurodegenerative disease.
Baldaranov, Dobri; Khomenko, Andrei; Kobor, Ines; Bogdahn, Ulrich; Gorges, Martin; Kassubek, Jan; Müller, Hans-Peter
2017-01-01
Objective : The potential of magnetic resonance imaging (MRI) as a technical biomarker for cerebral microstructural alterations in neurodegenerative diseases is under investigation. In this study, a framework for the longitudinal analysis of diffusion tensor imaging (DTI)-based mapping was applied to the assessment of predefined white matter tracts in amyotrophic lateral sclerosis (ALS), as an example for a rapid progressive neurodegenerative disease. Methods : DTI was performed every 3 months in six patients with ALS (mean (M) = 7.7; range 3 to 15 scans) and in six controls ( M = 3; range 2-5 scans) with the identical scanning protocol, resulting in a total of 65 longitudinal DTI datasets. Fractional anisotropy (FA), mean diffusivity (MD), axonal diffusivity (AD), radial diffusivity (RD), and the ratio AD/RD were studied to analyze alterations within the corticospinal tract (CST) which is a prominently affected tract structure in ALS and the tract correlating with Braak's neuropathological stage 1. A correlation analysis was performed between progression rates based on DTI metrics and the revised ALS functional rating scale (ALS-FRS-R). Results : Patients with ALS showed an FA and AD/RD decline along the CST, while DTI metrics of controls did not change in longitudinal DTI scans. The FA and AD/RD decrease progression correlated significantly with ALS-FRS-R decrease progression. Conclusion : On the basis of the longitudinal assessment, DTI-based metrics can be considered as a possible noninvasive follow-up marker for disease progression in neurodegeneration. This finding was demonstrated here for ALS as a fast progressing neurodegenerative disease.
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.
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.
Applications of CORBA in the ATLAS prototype DAQ
Jones, R.; Kolos, S.; Mapelli, L.; Ryabov, Y.
2000-04-01
This paper presents the experience of using the Common Object Request Broker Architecture (CORBA) in the ATLAS prototype DAQ project. Many communication links in the DAQ system have been designed and implemented using the CORBA standard. A public domain package, called Inter-Language Unification (ILU) has been used to implement CORBA based communications between DAQ components in a local area network (LAN) of heterogeneous computers. The CORBA Naming Service provides the principal mechanism through which most clients of an ORE-based system locate objects that they intend to use. In our project, conventions are employed that meaningfully partition the name space of the Naming Service according to divisions in the DAQ system itself. The Inter Process Communication (IPC) package, implemented in C++ on the top of CORBA/ILU, incorporates this facility and hides the details of the naming schema is described. The development procedure and environment for remote database access using IPC is described. Various end-user interfaces have been implemented using the Java language that communicate with C++ servers via CORBA/ILU. To support such interfaces, a second implementation of IPC in Java has been developed. The design and implementation of such connections are described. An alternative CORBA implementation, ORBacus, has been evaluated and compared with ILU.
The TDAQ Analytics Dashboard: a real-time web application for the ATLAS TDAQ control infrastructure
International Nuclear Information System (INIS)
Miotto, Giovanna Lehmann; Magnoni, Luca; Sloper, John Erik
2011-01-01
The ATLAS Trigger and Data Acquisition (TDAQ) infrastructure is responsible for filtering and transferring ATLAS experimental data from detectors to mass storage systems. It relies on a large, distributed computing system composed of thousands of software applications running concurrently. In such a complex environment, information sharing is fundamental for controlling applications behavior, error reporting and operational monitoring. During data taking, the streams of messages sent by applications and data published via information services are constantly monitored by experts to verify the correctness of running operations and to understand problematic situations. To simplify and improve system analysis and errors detection tasks, we developed the TDAQ Analytics Dashboard, a web application that aims to collect, correlate and visualize effectively this real time flow of information. The TDAQ Analytics Dashboard is composed of two main entities that reflect the twofold scope of the application. The first is the engine, a Java service that performs aggregation, processing and filtering of real time data stream and computes statistical correlation on sliding windows of time. The results are made available to clients via a simple web interface supporting SQL-like query syntax. The second is the visualization, provided by an Ajax-based web application that runs on client's browser. The dashboard approach allows to present information in a clear and customizable structure. Several types of interactive graphs are proposed as widgets that can be dynamically added and removed from visualization panels. Each widget acts as a client for the engine, querying the web interface to retrieve data with desired criteria. In this paper we present the design, development and evolution of the TDAQ Analytics Dashboard. We also present the statistical analysis computed by the application in this first period of high energy data taking operations for the ATLAS experiment.
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.
Astola, L.J.; Florack, L.M.J.
2011-01-01
We study 3D-multidirectional images, using Finsler geometry. The application considered here is in medical image analysis, specifically in High Angular Resolution Diffusion Imaging (HARDI) (Tuch et al. in Magn. Reson. Med. 48(6):1358–1372, 2004) of the brain. The goal is to reveal the architecture
Astola, L.; Florack, L.
2011-01-01
We study 3D-multidirectional images, using Finsler geometry. The application considered here is in medical image analysis, specifically in High Angular Resolution Diffusion Imaging (HARDI) (Tuch et al. in Magn. Reson. Med. 48(6):1358–1372, 2004) of the brain. The goal is to reveal the architecture
Astola, L.J.; Florack, L.M.J.
2010-01-01
We study 3D-multidirectional images, using Finsler geometry. The application considered here is in medical image analysis, specifically in High Angular Resolution Diffusion Imaging (HARDI) [24] of the brain. The goal is to reveal the architecture of the neural fibers in brain white matter. To the
Dcs Data Viewer, an Application that Accesses ATLAS DCS Historical Data
Tsarouchas, C.; Schlenker, S.; Dimitrov, G.; Jahn, G.
2014-06-01
The ATLAS experiment at CERN is one of the four Large Hadron Collider experiments. The Detector Control System (DCS) of ATLAS is responsible for the supervision of the detector equipment, the reading of operational parameters, the propagation of the alarms and the archiving of important operational data in a relational database (DB). DCS Data Viewer (DDV) is an application that provides access to the ATLAS DCS historical data through a web interface. Its design is structured using a client-server architecture. The pythonic server connects to the DB and fetches the data by using optimized SQL requests. It communicates with the outside world, by accepting HTTP requests and it can be used stand alone. The client is an AJAX (Asynchronous JavaScript and XML) interactive web application developed under the Google Web Toolkit (GWT) framework. Its web interface is user friendly, platform and browser independent. The selection of metadata is done via a column-tree view or with a powerful search engine. The final visualization of the data is done using java applets or java script applications as plugins. The default output is a value-over-time chart, but other types of outputs like tables, ascii or ROOT files are supported too. Excessive access or malicious use of the database is prevented by a dedicated protection mechanism, allowing the exposure of the tool to hundreds of inexperienced users. The current configuration of the client and of the outputs can be saved in an XML file. Protection against web security attacks is foreseen and authentication constrains have been taken into account, allowing the exposure of the tool to hundreds of users world wide. Due to its flexible interface and its generic and modular approach, DDV could be easily used for other experiment control systems.
DCS data viewer, an application that accesses ATLAS DCS historical data
International Nuclear Information System (INIS)
Tsarouchas, C; Schlenker, S; Dimitrov, G; Jahn, G
2014-01-01
The ATLAS experiment at CERN is one of the four Large Hadron Collider experiments. The Detector Control System (DCS) of ATLAS is responsible for the supervision of the detector equipment, the reading of operational parameters, the propagation of the alarms and the archiving of important operational data in a relational database (DB). DCS Data Viewer (DDV) is an application that provides access to the ATLAS DCS historical data through a web interface. Its design is structured using a client-server architecture. The pythonic server connects to the DB and fetches the data by using optimized SQL requests. It communicates with the outside world, by accepting HTTP requests and it can be used stand alone. The client is an AJAX (Asynchronous JavaScript and XML) interactive web application developed under the Google Web Toolkit (GWT) framework. Its web interface is user friendly, platform and browser independent. The selection of metadata is done via a column-tree view or with a powerful search engine. The final visualization of the data is done using java applets or java script applications as plugins. The default output is a value-over-time chart, but other types of outputs like tables, ascii or ROOT files are supported too. Excessive access or malicious use of the database is prevented by a dedicated protection mechanism, allowing the exposure of the tool to hundreds of inexperienced users. The current configuration of the client and of the outputs can be saved in an XML file. Protection against web security attacks is foreseen and authentication constrains have been taken into account, allowing the exposure of the tool to hundreds of users world wide. Due to its flexible interface and its generic and modular approach, DDV could be easily used for other experiment control systems.
AGIS: The ATLAS Grid Information System
Anisenkov, A; The ATLAS collaboration; Klimentov, A; Senchenko, A
2012-01-01
The ATLAS Computing model embraces the Grid paradigm and a high degree of decentralization and computing resources able to meet ATLAS requirements of petabytes scale data operations. In this paper we present ATLAS Grid Information System (AGIS) designed to integrate configuration and status information about resources, services and topology of whole ATLAS Grid needed by ATLAS Distributed Computing applications and services.
Application of advanced thermal management technologies to the ATLAS SCT barrel module baseboards
Energy Technology Data Exchange (ETDEWEB)
Apsimon, R.J. [Rutherford Appleton Laboratory, Chilton, Didcot, Oxfordshire OX11 OQX (United Kingdom); Batchelor, L.E. [Rutherford Appleton Laboratory, Chilton, Didcot, Oxfordshire OX11 OQX (United Kingdom); Beck, G.A. [Department of Physics, Queen Mary University of London, Mile End Road, London E1 4NS (United Kingdom); Canard, P. [European Laboratory for Particle Physics (CERN), 1211 Geneva 23 (Switzerland); Carter, A.A. [Department of Physics, Queen Mary University of London, Mile End Road, London E1 4NS (United Kingdom)]. E-mail: a.a.carter@qmul.ac.uk; Carter, J.R. [Cavendish Laboratory, University of Cambridge, J.J. Thomson Avenue, Cambridge CB3 0HE (United Kingdom); Davis, V.R. [Rutherford Appleton Laboratory, Chilton, Didcot, Oxfordshire OX11 OQX (United Kingdom); Oliveira, R. de [European Laboratory for Particle Physics (CERN), 1211 Geneva 23 (Switzerland); Gibson, M.D. [Rutherford Appleton Laboratory, Chilton, Didcot, Oxfordshire OX11 OQX (United Kingdom); Hominal, L. [European Laboratory for Particle Physics (CERN), 1211 Geneva 23 (Switzerland); Ilie, D.M. [Department of Physics, Queen Mary University of London, Mile End Road, London E1 4NS (United Kingdom); Ilie, S.D. [European Laboratory for Particle Physics (CERN), 1211 Geneva 23 (Switzerland); Leboube, C.G. [European Laboratory for Particle Physics (CERN), 1211 Geneva 23 (Switzerland); Mistry, J. [Department of Physics, Queen Mary University of London, Mile End Road, London E1 4NS (United Kingdom); Morin, J. [Department of Physics, Queen Mary University of London, Mile End Road, London E1 4NS (United Kingdom); Morris, J.; Nagai, K. [Department of Physics, Queen Mary University of London, Mile End Road, London E1 4NS (United Kingdom); Sexton, I.; Thery, X. [European Laboratory for Particle Physics (CERN), 1211 Geneva 23 (Switzerland); Tyndel, M. [Rutherford Appleton Laboratory, Chilton, Didcot, Oxfordshire OX11 OQX (United Kingdom)
2006-09-15
The paper describes the application of advanced thermal management technologies to the design and production of the barrel module baseboard of the SemiConductor Tracker (SCT) of the ATLAS experiment at the Large Hadron Collider (LHC). The barrel modules contain silicon microstrip sensors and readout ASICs for tracking charged particles, and the baseboard forms the central element of the module, providing both its necessary thermal management and its mechanical structure. The baseboard requirements and specifications are given, and design and fabrication details are described. The properties of the 3000 baseboards successfully produced for the SCT are summarised.
Institute of Scientific and Technical Information of China (English)
TAO Xiao-feng; WANG Zhong-qiu; GONG Wan-qing; JIANG Qing-jun; SHI Zeng-ru
2009-01-01
Background With conventional imaging methods only the morphous of the visual nerve fiber bundles can be demonstrated, while the earlier period functional changes can not be demonstrated. We hypothesized that diffusion tensor imaging (DTI) would demonstrated the whole optic never fiber bundle and visual pathway and the earlier period functional changes. The purpose of the present study was to evaluate the application of DTI technique in the demonstration of the whole optic never fiber bundle and visual pathway, and the influence of orbital tumors on them. Methods GE 1.5T signa HD MR System, and the software package DTV2 were adopted. The total 45 subjects were enrolled, including 15 volunteers and 30 patients. All patients had ocular proptosis from minor to major. Seven patients had visual acuity decrescence. Results The nerve fiber bundles, e.g. optic chiasma, optic tract and optic radiation in posterior visual pathway were well demonstrated in all cases. Wherein, the intact whole visual pathway fiber bundles were clearly revealed in 10 volunteers and 17 patients, and optic nerve was not wholly revealed in the rest of the subjects. Shift of optic nerve caused by compression and partial deformation were seen in 7 patients with orbital tumor. In 6 of 7 patients, DTI displayed significant abscise and deformation of visual nerve. Chi-square test indicated significant correlation between visual acuity decrescence and DTI visual nerve non-display. Conclusions Visual nerve fiber bundles and the whole visual pathway were visualized in most of patients with DTI. It might be an effective method of providing imaging evidence for visual nerve fiber earlier period functional changes, and laid a foundation for the study in other cranial nerves.
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
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
Tang, Xiaoying; Qin, Yuanyuan; Zhu, Wenzhen; Miller, Michael I
2017-04-01
In this article, we present a unified statistical pipeline for analyzing the white matter (WM) tracts morphometry and microstructural integrity, both globally and locally within the same WM tract, from diffusion tensor imaging. Morphometry is quantified globally by the volumetric measurement and locally by the vertexwise surface areas. Meanwhile, microstructural integrity is quantified globally by the mean fractional anisotropy (FA) and trace values within the specific WM tract and locally by the FA and trace values defined at each vertex of its bounding surface. The proposed pipeline consists of four steps: (1) fully automated segmentation of WM tracts in a multi-contrast multi-atlas framework; (2) generation of the smooth surface representations for the WM tracts of interest; (3) common template surface generation on which the localized morphometric and microstructural statistics are defined and a variety of statistical analyses can be conducted; (4) multiple comparison correction to determine the significance of the statistical analysis results. Detailed herein, this pipeline has been applied to the corpus callosum in Alzheimer's disease (AD) with significantly decreased FA values and increased trace values, both globally and locally, being detected in patients with AD when compared to normal aging populations. A subdivision of the corpus callosum in both hemispheres revealed that the AD pathology primarily affects the body and splenium of the corpus callosum. Validation analyses and two multiple comparison correction strategies are provided. Hum Brain Mapp 38:1875-1893, 2017. © 2017 Wiley Periodicals, Inc. © 2017 Wiley Periodicals, Inc.
Saha, Punam K.; Liu, Yinxiao; Chen, Cheng; Jin, Dakai; Letuchy, Elena M.; Xu, Ziyue; Amelon, Ryan E.; Burns, Trudy L.; Torner, James C.; Levy, Steven M.; Calarge, Chadi A.
2015-01-01
Purpose: Osteoporosis is a common bone disease associated with increased risk of low-trauma fractures leading to substantial morbidity, mortality, and financial costs. Clinically, osteoporosis is defined by low bone mineral density (BMD); however, increasing evidence suggests that trabecular bone (TB) microarchitectural quality is an important determinant of bone strength and fracture risk. A tensor scale based algorithm for in vivo characterization of TB plate-rod microarchitecture at the distal tibia using multirow detector CT (MD-CT) imaging is presented and its performance and applications are examined. Methods: The tensor scale characterizes individual TB on the continuum between a perfect plate and a perfect rod and computes their orientation using optimal ellipsoidal representation of local structures. The accuracy of the method was evaluated using computer-generated phantom images at a resolution and signal-to-noise ratio achievable in vivo. The robustness of the method was examined in terms of stability across a wide range of voxel sizes, repeat scan reproducibility, and correlation between TB measures derived by imaging human ankle specimens under ex vivo and in vivo conditions. Finally, the application of the method was evaluated in pilot human studies involving healthy young-adult volunteers (age: 19 to 21 yr; 51 females and 46 males) and patients treated with selective serotonin reuptake inhibitors (SSRIs) (age: 19 to 21 yr; six males and six females). Results: An error of (3.2% ± 2.0%) (mean ± SD), computed as deviation from known measures of TB plate-width, was observed for computer-generated phantoms. An intraclass correlation coefficient of 0.95 was observed for tensor scale TB measures in repeat MD-CT scans where the measures were averaged over a small volume of interest of 1.05 mm diameter with limited smoothing effects. The method was found to be highly stable at different voxel sizes with an error of (2.29% ± 1.56%) at an in vivo voxel size
Nowinski, Wieslaw L.; Thirunavuukarasuu, Arumugam; Ananthasubramaniam, Anand; Chua, Beng Choon; Qian, Guoyu; Nowinska, Natalia G.; Marchenko, Yevgen; Volkau, Ihar
2009-01-01
Preparation of tests and student's assessment by the instructor are time consuming. We address these two tasks in neuroanatomy education by employing a digital media application with a three-dimensional (3D), interactive, fully segmented, and labeled brain atlas. The anatomical and vascular models in the atlas are linked to "Terminologia…
Tensor rank is not multiplicative under the tensor product
Christandl, Matthias; Jensen, Asger Kjærulff; Zuiddam, Jeroen
2017-01-01
The tensor rank of a tensor t is the smallest number r such that t can be decomposed as a sum of r simple tensors. Let s be a k-tensor and let t be an l-tensor. The tensor product of s and t is a (k + l)-tensor. Tensor rank is sub-multiplicative under the tensor product. We revisit the connection between restrictions and degenerations. A result of our study is that tensor rank is not in general multiplicative under the tensor product. This answers a question of Draisma and Saptharishi. Specif...
Tensor gauge condition and tensor field decomposition
Zhu, Ben-Chao; Chen, Xiang-Song
2015-10-01
We discuss various proposals of separating a tensor field into pure-gauge and gauge-invariant components. Such tensor field decomposition is intimately related to the effort of identifying the real gravitational degrees of freedom out of the metric tensor in Einstein’s general relativity. We show that as for a vector field, the tensor field decomposition has exact correspondence to and can be derived from the gauge-fixing approach. The complication for the tensor field, however, is that there are infinitely many complete gauge conditions in contrast to the uniqueness of Coulomb gauge for a vector field. The cause of such complication, as we reveal, is the emergence of a peculiar gauge-invariant pure-gauge construction for any gauge field of spin ≥ 2. We make an extensive exploration of the complete tensor gauge conditions and their corresponding tensor field decompositions, regarding mathematical structures, equations of motion for the fields and nonlinear properties. Apparently, no single choice is superior in all aspects, due to an awkward fact that no gauge-fixing can reduce a tensor field to be purely dynamical (i.e. transverse and traceless), as can the Coulomb gauge in a vector case.
Extending the ATLAS PanDA Workload Management System for New Big Data Applications
De, K; The ATLAS collaboration; Maeno, T; Nilsson, P; Panitkin, S; Vaniachine, A; Wenaus, T; Yu, D
2013-01-01
The LHC experiments are today at the leading edge of large scale distributed data-intensive computational science. The LHC's ATLAS experiment processes data volumes which are particularly extreme, over 130 PB to date, distributed worldwide at over of 120 sites. An important element in the success of the exciting physics results from ATLAS is the highly scalable integrated workflow and dataflow management afforded by the PanDA workload management system, used for all the distributed computing needs of the experiment. The PanDA design is not experiment specific and PanDA is now being extended to support other data intensive scientific applications. Alpha-Magnetic Spectrometer, an astro-particle experiment on the International Space Station, and the Compact Muon Solenoid, an LHC experiment, have successfully evaluated PanDA and are pursuing its adoption. PanDA was cited as an example of "a high performance, fault tolerant software for fast, scalable access to data repositories of many kinds" during the "Big Data...
Tensor structure for Nori motives
Barbieri-Viale, Luca; Huber, Annette; Prest, Mike
2018-01-01
We construct a tensor product on Freyd's universal abelian category attached to an additive tensor category or a tensor quiver and establish a universal property. This is used to give an alternative construction for the tensor product on Nori motives.
The Topology of Symmetric Tensor Fields
Levin, Yingmei; Batra, Rajesh; Hesselink, Lambertus; Levy, Yuval
1997-01-01
Combinatorial topology, also known as "rubber sheet geometry", has extensive applications in geometry and analysis, many of which result from connections with the theory of differential equations. A link between topology and differential equations is vector fields. Recent developments in scientific visualization have shown that vector fields also play an important role in the analysis of second-order tensor fields. A second-order tensor field can be transformed into its eigensystem, namely, eigenvalues and their associated eigenvectors without loss of information content. Eigenvectors behave in a similar fashion to ordinary vectors with even simpler topological structures due to their sign indeterminacy. Incorporating information about eigenvectors and eigenvalues in a display technique known as hyperstreamlines reveals the structure of a tensor field. The simplify and often complex tensor field and to capture its important features, the tensor is decomposed into an isotopic tensor and a deviator. A tensor field and its deviator share the same set of eigenvectors, and therefore they have a similar topological structure. A a deviator determines the properties of a tensor field, while the isotopic part provides a uniform bias. Degenerate points are basic constituents of tensor fields. In 2-D tensor fields, there are only two types of degenerate points; while in 3-D, the degenerate points can be characterized in a Q'-R' plane. Compressible and incompressible flows share similar topological feature due to the similarity of their deviators. In the case of the deformation tensor, the singularities of its deviator represent the area of vortex core in the field. In turbulent flows, the similarities and differences of the topology of the deformation and the Reynolds stress tensors reveal that the basic addie-viscosity assuptions have their validity in turbulence modeling under certain conditions.
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.
International Nuclear Information System (INIS)
Chen, Xin
2016-01-01
The updated Higgs measurements in various search channels with ATLAS Run 1 data are reviewed. Both the Standard Model (SM) Higgs results, such as H → γγ, ZZ, WW, ττ, μμ, bb-bar, and Beyond Standard Model (BSM) results, such as the charged Higgs, Higgs invisible decay and tensor couplings, are summarized. Prospects for future Higgs searches are briefly discussed
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.
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
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.
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.)
U.S. Environmental Protection Agency — This EnviroAtlas dataset contains data on the mean livestock manure application to cultivated crop and hay/pasture lands by 12-digit Hydrologic Unit (HUC) in 2006....
Rai, Prashant; Sargsyan, Khachik; Najm, Habib; Hermes, Matthew R.; Hirata, So
2017-09-01
A new method is proposed for a fast evaluation of high-dimensional integrals of potential energy surfaces (PES) that arise in many areas of quantum dynamics. It decomposes a PES into a canonical low-rank tensor format, reducing its integral into a relatively short sum of products of low-dimensional integrals. The decomposition is achieved by the alternating least squares (ALS) algorithm, requiring only a small number of single-point energy evaluations. Therefore, it eradicates a force-constant evaluation as the hotspot of many quantum dynamics simulations and also possibly lifts the curse of dimensionality. This general method is applied to the anharmonic vibrational zero-point and transition energy calculations of molecules using the second-order diagrammatic vibrational many-body Green's function (XVH2) theory with a harmonic-approximation reference. In this application, high dimensional PES and Green's functions are both subjected to a low-rank decomposition. Evaluating the molecular integrals over a low-rank PES and Green's functions as sums of low-dimensional integrals using the Gauss-Hermite quadrature, this canonical-tensor-decomposition-based XVH2 (CT-XVH2) achieves an accuracy of 0.1 cm-1 or higher and nearly an order of magnitude speedup as compared with the original algorithm using force constants for water and formaldehyde.
International Nuclear Information System (INIS)
Rai, Prashant; Sargsyan, Khachik; Najm, Habib; Hermes, Matthew R.; Hirata, So
2017-01-01
Here, a new method is proposed for a fast evaluation of high-dimensional integrals of potential energy surfaces (PES) that arise in many areas of quantum dynamics. It decomposes a PES into a canonical low-rank tensor format, reducing its integral into a relatively short sum of products of low-dimensional integrals. The decomposition is achieved by the alternating least squares (ALS) algorithm, requiring only a small number of single-point energy evaluations. Therefore, it eradicates a force-constant evaluation as the hotspot of many quantum dynamics simulations and also possibly lifts the curse of dimensionality. This general method is applied to the anharmonic vibrational zero-point and transition energy calculations of molecules using the second-order diagrammatic vibrational many-body Green's function (XVH2) theory with a harmonic-approximation reference. In this application, high dimensional PES and Green's functions are both subjected to a low-rank decomposition. Evaluating the molecular integrals over a low-rank PES and Green's functions as sums of low-dimensional integrals using the Gauss–Hermite quadrature, this canonical-tensor-decomposition-based XVH2 (CT-XVH2) achieves an accuracy of 0.1 cm -1 or higher and nearly an order of magnitude speedup as compared with the original algorithm using force constants for water and formaldehyde.
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.
Delineating Neural Structures of Developmental Human Brains with Diffusion Tensor Imaging
Directory of Open Access Journals (Sweden)
Hao Huang
2010-01-01
Full Text Available The human brain anatomy is characterized by dramatic structural changes during fetal development. It is extraordinarily complex and yet its origin is a simple tubular structure. Revealing detailed anatomy at different stages of brain development not only aids in understanding this highly ordered process, but also provides clues to detect abnormalities caused by genetic or environmental factors. However, anatomical studies of human brain development during the fetal period are surprisingly scarce and histology-based atlases have become available only recently. Diffusion tensor imaging (DTI measures water diffusion to delineate the underlying neural structures. The high contrasts derived from DTI can be used to establish the brain atlas. With DTI tractography, coherent neural structures, such as white matter tracts, can be three-dimensionally reconstructed. The primary eigenvector of the diffusion tensor can be further explored to characterize microstructures in the cerebral wall of the developmental brains. In this mini-review, the application of DTI in order to reveal the structures of developmental fetal brains has been reviewed in the above-mentioned aspects. The fetal brain DTI provides a unique insight for delineating the neural structures in both macroscopic and microscopic levels. The resultant DTI database will provide structural guidance for the developmental study of human fetal brains in basic neuroscience, and reference standards for diagnostic radiology of premature newborns.
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
Zhu, Lupei; Zhou, Xiaofeng
2016-10-01
Source inversion of small-magnitude events such as aftershocks or mine collapses requires use of relatively high frequency seismic waveforms which are strongly affected by small-scale heterogeneities in the crust. In this study, we developed a new inversion method called gCAP3D for determining general moment tensor of a seismic source using Green's functions of 3D models. It inherits the advantageous features of the ;Cut-and-Paste; (CAP) method to break a full seismogram into the Pnl and surface-wave segments and to allow time shift between observed and predicted waveforms. It uses grid search for 5 source parameters (relative strengths of the isotropic and compensated-linear-vector-dipole components and the strike, dip, and rake of the double-couple component) that minimize the waveform misfit. The scalar moment is estimated using the ratio of L2 norms of the data and synthetics. Focal depth can also be determined by repeating the inversion at different depths. We applied gCAP3D to the 2013 Ms 7.0 Lushan earthquake and its aftershocks using a 3D crustal-upper mantle velocity model derived from ambient noise tomography in the region. We first relocated the events using the double-difference method. We then used the finite-differences method and reciprocity principle to calculate Green's functions of the 3D model for 20 permanent broadband seismic stations within 200 km from the source region. We obtained moment tensors of the mainshock and 74 aftershocks ranging from Mw 5.2 to 3.4. The results show that the Lushan earthquake is a reverse faulting at a depth of 13-15 km on a plane dipping 40-47° to N46° W. Most of the aftershocks occurred off the main rupture plane and have similar focal mechanisms to the mainshock's, except in the proximity of the mainshock where the aftershocks' focal mechanisms display some variations.
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
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...
Computational and mathematical methods in brain atlasing.
Nowinski, Wieslaw L
2017-12-01
Brain atlases have a wide range of use from education to research to clinical applications. Mathematical methods as well as computational methods and tools play a major role in the process of brain atlas building and developing atlas-based applications. Computational methods and tools cover three areas: dedicated editors for brain model creation, brain navigators supporting multiple platforms, and atlas-assisted specific applications. Mathematical methods in atlas building and developing atlas-aided applications deal with problems in image segmentation, geometric body modelling, physical modelling, atlas-to-scan registration, visualisation, interaction and virtual reality. Here I overview computational and mathematical methods in atlas building and developing atlas-assisted applications, and share my contribution to and experience in this field.
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.
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.
Glyph-Based Comparative Visualization for Diffusion Tensor Fields.
Zhang, Changgong; Schultz, Thomas; Lawonn, Kai; Eisemann, Elmar; Vilanova, Anna
2016-01-01
Diffusion Tensor Imaging (DTI) is a magnetic resonance imaging modality that enables the in-vivo reconstruction and visualization of fibrous structures. To inspect the local and individual diffusion tensors, glyph-based visualizations are commonly used since they are able to effectively convey full aspects of the diffusion tensor. For several applications it is necessary to compare tensor fields, e.g., to study the effects of acquisition parameters, or to investigate the influence of pathologies on white matter structures. This comparison is commonly done by extracting scalar information out of the tensor fields and then comparing these scalar fields, which leads to a loss of information. If the glyph representation is kept, simple juxtaposition or superposition can be used. However, neither facilitates the identification and interpretation of the differences between the tensor fields. Inspired by the checkerboard style visualization and the superquadric tensor glyph, we design a new glyph to locally visualize differences between two diffusion tensors by combining juxtaposition and explicit encoding. Because tensor scale, anisotropy type, and orientation are related to anatomical information relevant for DTI applications, we focus on visualizing tensor differences in these three aspects. As demonstrated in a user study, our new glyph design allows users to efficiently and effectively identify the tensor differences. We also apply our new glyphs to investigate the differences between DTI datasets of the human brain in two different contexts using different b-values, and to compare datasets from a healthy and HIV-infected subject.
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.)
Chen, Y.; Huang, L.
2017-12-01
Moment tensors are key parameters for characterizing CO2-injection-induced microseismic events. Elastic-waveform inversion has the potential to providing accurate results of moment tensors. Microseismic waveforms contains information of source moment tensors and the wave propagation velocity along the wavepaths. We develop an elastic-waveform inversion method to jointly invert the seismic velocity model and moment tensor. We first use our adaptive moment-tensor joint inversion method to estimate moment tensors of microseismic events. Our adaptive moment-tensor inversion method jointly inverts multiple microseismic events with similar waveforms within a cluster to reduce inversion uncertainty for microseismic data recorded using a single borehole geophone array. We use this inversion result as the initial model for our elastic-waveform inversion to minimize the cross-correlated-based data misfit between observed data and synthetic data. We verify our method using synthetic microseismic data and obtain improved results of both moment tensors and seismic velocity model. We apply our new inversion method to microseismic data acquired at a CO2-enhanced oil recovery field in Aneth, Utah, using a single borehole geophone array. The results demonstrate that our new inversion method significantly reduces the data misfit compared to the conventional ray-theory-based moment-tensor inversion.
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.
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...
Calafiura, Paolo; The ATLAS collaboration; Seuster, Rolf; Tsulaia, Vakhtang; van Gemmeren, Peter
2015-01-01
AthenaMP is a multi-process version of the ATLAS reconstruction and data analysis framework Athena. By leveraging Linux fork and copy-on-write, it allows the sharing of memory pages between event processors running on the same compute node with little to no change in the application code. Originally targeted to optimize the memory footprint of reconstruction jobs, AthenaMP has demonstrated that it can reduce the memory usage of certain confugurations of ATLAS production jobs by a factor of 2. AthenaMP has also evolved to become the parallel event-processing core of the recently developed ATLAS infrastructure for fine-grained event processing (Event Service) which allows to run AthenaMP inside massively parallel distributed applications on hundreds of compute nodes simultaneously. We present the architecture of AthenaMP, various strategies implemented by AthenaMP for scheduling workload to worker processes (for example: Shared Event Queue and Shared Distributor of Event Tokens) and the usage of AthenaMP in the...
Calafiura, Paolo; Seuster, Rolf; Tsulaia, Vakhtang; van Gemmeren, Peter
2015-01-01
AthenaMP is a multi-process version of the ATLAS reconstruction, simulation and data analysis framework Athena. By leveraging Linux fork and copy-on-write, it allows for sharing of memory pages between event processors running on the same compute node with little to no change in the application code. Originally targeted to optimize the memory footprint of reconstruction jobs, AthenaMP has demonstrated that it can reduce the memory usage of certain configurations of ATLAS production jobs by a factor of 2. AthenaMP has also evolved to become the parallel event-processing core of the recently developed ATLAS infrastructure for fine-grained event processing (Event Service) which allows to run AthenaMP inside massively parallel distributed applications on hundreds of compute nodes simultaneously. We present the architecture of AthenaMP, various strategies implemented by AthenaMP for scheduling workload to worker processes (for example: Shared Event Queue and Shared Distributor of Event Tokens) and the usage of Ath...
Cameron, David; The ATLAS collaboration
2017-01-01
Data processing applications of the ATLAS experiment, such as event simulation and reconstruction, spend considerable amount of time in the initialization phase. This phase includes loading a large number of shared libraries, reading detector geometry and condition data from external databases, building a transient representation of the detector geometry and initializing various algorithms and services. In some cases the initialization step can take as long as 10-15 minutes. Such slow initialization, being inherently serial, has a significant negative impact on overall CPU efficiency of the production job, especially when the job is executed on opportunistic, often short-lived, resources such as commercial clouds or volunteer computing. In order to improve this situation, we can take advantage of the fact that ATLAS runs large numbers of production jobs with similar configuration parameters (e.g. jobs within the same production task). This allows us to checkpoint one job at the end of its configuration step a...
Quantum mechanics of Yano tensors: Dirac equation in curved spacetime
International Nuclear Information System (INIS)
Cariglia, Marco
2004-01-01
In spacetimes admitting Yano tensors, the classical theory of the spinning particle possesses enhanced worldline supersymmetry. Quantum mechanically generators of extra supersymmetries correspond to operators that in the classical limit commute with the Dirac operator and generate conserved quantities. We show that the result is preserved in the full quantum theory, that is, Yano symmetries are not anomalous. This was known for Yano tensors of rank 2, but our main result is to show that it extends to Yano tensors of arbitrary rank. We also describe the conformal Yano equation and show that is invariant under Hodge duality. There is a natural relationship between Yano tensors and supergravity theories. As the simplest possible example, we show that when the spacetime admits a Killing spinor then this generates Yano and conformal Yano tensors. As an application, we construct Yano tensors on maximally symmetric spaces: they are spanned by tensor products of Killing vectors
Algebraic and computational aspects of real tensor ranks
Sakata, Toshio; Miyazaki, Mitsuhiro
2016-01-01
This book provides comprehensive summaries of theoretical (algebraic) and computational aspects of tensor ranks, maximal ranks, and typical ranks, over the real number field. Although tensor ranks have been often argued in the complex number field, it should be emphasized that this book treats real tensor ranks, which have direct applications in statistics. The book provides several interesting ideas, including determinant polynomials, determinantal ideals, absolutely nonsingular tensors, absolutely full column rank tensors, and their connection to bilinear maps and Hurwitz-Radon numbers. In addition to reviews of methods to determine real tensor ranks in details, global theories such as the Jacobian method are also reviewed in details. The book includes as well an accessible and comprehensive introduction of mathematical backgrounds, with basics of positive polynomials and calculations by using the Groebner basis. Furthermore, this book provides insights into numerical methods of finding tensor ranks through...
Application of rule-based data mining techniques to real time ATLAS Grid job monitoring data
Ahrens, R; The ATLAS collaboration; Kalinin, S; Maettig, P; Sandhoff, M; dos Santos, T; Volkmer, F
2012-01-01
The Job Execution Monitor (JEM) is a job-centric grid job monitoring software developed at the University of Wuppertal and integrated into the pilot-based “PanDA” job brokerage system leveraging physics analysis and Monte Carlo event production for the ATLAS experiment on the Worldwide LHC Computing Grid (WLCG). With JEM, job progress and grid worker node health can be supervised in real time by users, site admins and shift personnel. Imminent error conditions can be detected early and countermeasures can be initiated by the Job’s owner immideatly. Grid site admins can access aggregated data of all monitored jobs to infer the site status and to detect job and Grid worker node misbehaviour. Shifters can use the same aggregated data to quickly react to site error conditions and broken production tasks. In this work, the application of novel data-centric rule based methods and data-mining techniques to the real time monitoring data is discussed. The usage of such automatic inference techniques on monitorin...
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.
Correlators in tensor models from character calculus
Directory of Open Access Journals (Sweden)
A. Mironov
2017-11-01
Full Text Available We explain how the calculations of [20], which provided the first evidence for non-trivial structures of Gaussian correlators in tensor models, are efficiently performed with the help of the (Hurwitz character calculus. This emphasizes a close similarity between technical methods in matrix and tensor models and supports a hope to understand the emerging structures in very similar terms. We claim that the 2m-fold Gaussian correlators of rank r tensors are given by r-linear combinations of dimensions with the Young diagrams of size m. The coefficients are made from the characters of the symmetric group Sm and their exact form depends on the choice of the correlator and on the symmetries of the model. As the simplest application of this new knowledge, we provide simple expressions for correlators in the Aristotelian tensor model as tri-linear combinations of dimensions.
Energy Technology Data Exchange (ETDEWEB)
Roemelt, Michael, E-mail: michael.roemelt@theochem.rub.de [Lehrstuhl für Theoretische Chemie, Ruhr-Universität Bochum, D-44780 Bochum, Germany and Max-Planck Institut für Kohlenforschung, Kaiser-Wilhelm-Platz 1, 45470 Mülheim an der Ruhr (Germany)
2015-07-28
Spin Orbit Coupling (SOC) is introduced to molecular ab initio density matrix renormalization group (DMRG) calculations. In the presented scheme, one first approximates the electronic ground state and a number of excited states of the Born-Oppenheimer (BO) Hamiltonian with the aid of the DMRG algorithm. Owing to the spin-adaptation of the algorithm, the total spin S is a good quantum number for these states. After the non-relativistic DMRG calculation is finished, all magnetic sublevels of the calculated states are constructed explicitly, and the SOC operator is expanded in the resulting basis. To this end, spin orbit coupled energies and wavefunctions are obtained as eigenvalues and eigenfunctions of the full Hamiltonian matrix which is composed of the SOC operator matrix and the BO Hamiltonian matrix. This treatment corresponds to a quasi-degenerate perturbation theory approach and can be regarded as the molecular equivalent to atomic Russell-Saunders coupling. For the evaluation of SOC matrix elements, the full Breit-Pauli SOC Hamiltonian is approximated by the widely used spin-orbit mean field operator. This operator allows for an efficient use of the second quantized triplet replacement operators that are readily generated during the non-relativistic DMRG algorithm, together with the Wigner-Eckart theorem. With a set of spin-orbit coupled wavefunctions at hand, the molecular g-tensors are calculated following the scheme proposed by Gerloch and McMeeking. It interprets the effective molecular g-values as the slope of the energy difference between the lowest Kramers pair with respect to the strength of the applied magnetic field. Test calculations on a chemically relevant Mo complex demonstrate the capabilities of the presented method.
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.
Symmetric Tensor Decomposition
DEFF Research Database (Denmark)
Brachat, Jerome; Comon, Pierre; Mourrain, Bernard
2010-01-01
We present an algorithm for decomposing a symmetric tensor, of dimension n and order d, as a sum of rank-1 symmetric tensors, extending the algorithm of Sylvester devised in 1886 for binary forms. We recall the correspondence between the decomposition of a homogeneous polynomial in n variables...... of polynomial equations of small degree in non-generic cases. We propose a new algorithm for symmetric tensor decomposition, based on this characterization and on linear algebra computations with Hankel matrices. The impact of this contribution is two-fold. First it permits an efficient computation...... of the decomposition of any tensor of sub-generic rank, as opposed to widely used iterative algorithms with unproved global convergence (e.g. Alternate Least Squares or gradient descents). Second, it gives tools for understanding uniqueness conditions and for detecting the rank....
International Nuclear Information System (INIS)
Scheunert, M.
1982-10-01
We develop a graded tensor calculus corresponding to arbitrary Abelian groups of degrees and arbitrary commutation factors. The standard basic constructions and definitions like tensor products, spaces of multilinear mappings, contractions, symmetrization, symmetric algebra, as well as the transpose, adjoint, and trace of a linear mapping, are generalized to the graded case and a multitude of canonical isomorphisms is presented. Moreover, the graded versions of the classical Lie algebras are introduced and some of their basic properties are described. (orig.)
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.
AGIS: The ATLAS Grid Information System
Anisenkov, A; The ATLAS collaboration; Klimentov, A; Oleynik, D; Petrosyan, A
2014-01-01
In this paper we describe ATLAS Grid Information System (AGIS), the system designed to integrate configuration and status information about resources, services and topology of the computing infrastructure used by ATLAS Distributed Computing applications and services.
AGIS: The ATLAS Grid Information System
Anisenkov, A; Di Girolamo, A; Klimentov, A; Oleynik, D; Petrosyan, A
2013-01-01
In this paper we describe ATLAS Grid Information System (AGIS), the system designed to integrate configuration and status information about resources, services and topology of the computing infrastructure used by ATLAS Distributed Computing applications and services.
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.
International Nuclear Information System (INIS)
Sugimoto, Satoru; Ikeda, Kiyomi; Toki, Hiroshi
2004-01-01
We propose a new mean-field-type framework which can treat the strong correlation induced by the tensor force. To treat the tensor correlation we break the charge and parity symmetries of a single-particle state and restore these symmetries of the total system by the projection method. We perform the charge and parity projections before variation and obtain a Hartree-Fock-like equation, which is solved self-consistently. We apply the Hartree-Fock-like equation to the alpha particle and find that by breaking the parity and charge symmetries, the correlation induced by the tensor force is obtained in the projected mean-field framework. We emphasize that the projection before the variation is important to pick up the tensor correlation in the present framework
Integrating Networking into ATLAS
Mc Kee, Shawn Patrick; The ATLAS collaboration
2018-01-01
Networking is foundational to the ATLAS distributed infrastructure and there are many ongoing activities related to networking both within and outside of ATLAS. We will report on the progress in a number of areas exploring ATLAS's use of networking and our ability to monitor the network, analyze metrics from the network, and tune and optimize application and end-host parameters to make the most effective use of the network. Specific topics will include work on Open vSwitch for production systems, network analytics, FTS testing and tuning, and network problem alerting and alarming.
An introduction to tensors and group theory for physicists
Jeevanjee, Nadir
2011-01-01
An Introduction to Tensors and Group Theory for Physicists provides both an intuitive and rigorous approach to tensors and groups and their role in theoretical physics and applied mathematics. A particular aim is to demystify tensors and provide a unified framework for understanding them in the context of classical and quantum physics. Connecting the component formalism prevalent in physics calculations with the abstract but more conceptual formulation found in many mathematical texts, the work will be a welcome addition to the literature on tensors and group theory. Part I of the text begins with linear algebraic foundations, follows with the modern component-free definition of tensors, and concludes with applications to classical and quantum physics through the use of tensor products. Part II introduces abstract groups along with matrix Lie groups and Lie algebras, then intertwines this material with that of Part I by introducing representation theory. Exercises and examples are provided throughout for go...
p-Norm SDD tensors and eigenvalue localization
Directory of Open Access Journals (Sweden)
Qilong Liu
2016-07-01
Full Text Available Abstract We present a new class of nonsingular tensors (p-norm strictly diagonally dominant tensors, which is a subclass of strong H $\\mathcal{H}$ -tensors. As applications of the results, we give a new eigenvalue inclusion set, which is tighter than those provided by Li et al. (Linear Multilinear Algebra 64:727-736, 2016 in some case. Based on this set, we give a checkable sufficient condition for the positive (semidefiniteness of an even-order symmetric tensor.
International Nuclear Information System (INIS)
Zhou Jianying; Tian Yong; He Qing; Li Youqiong; Han Qing; Cheng Kailiang
2013-01-01
Objective: To establish the method of using the atlas morphological indexes for sex determination in Jilin province and to evaluate its effect. Methods: The clinic neck CT images were used to reconstruct the 3D image of atlas. A total of 27 linear measurement on 8 aspects of the atlas were measured and the ratios were calculated. The 14 items were selected. Results: Of the total 27 linear measurements, 14 were sexually dimorphic (P<0.05), and the accuracies of sex determination of 27 indexes were 52.0% -89.3% . The highest accuracy was width of vertebral body (86.7% ). A function with variables predicting sex with 96.8% accuracy was derived by using stepwise method of discriminant function analysis: Y=1.308W - 0.409CDF - 0.469LTPSD - 0.849LUACD + 0.478RUACD + 0.332RDACD + 0.363ATH - 0.334PTH - 0.236PAL. Conclusion: The method of using atlas traits for sex determination in Jilin province is practicable. (authors)
A study of the application of Brain Atlas with and without +Gz acceleration conditions.
Li, Yifeng; Zhang, Lihui; Zhang, Tao; Li, Baohui
2017-07-20
The purposes of this study were to utilize Brain Atlas to investigate the fluctuations in the characteristics of human EEG, with and without +Gz acceleration produced by human centrifuge, and also to examine the G load endurance of human body. The Brain Atlas of the EEG signal with and without +Gz acceleration in a static state were compared in order to reveal the correlation and differences. When compared with those in a static state, it was found that for the EEG readings of the subjects undergoing +Gz acceleration conditions, the energy and gray scale values of the low-frequency component-delta rhythm showed significant increases, while the energy and gray scale values of the high-frequency component-beta rhythm showed significant decreases. Among these, the beta2 rhythm was determined to be significantly inhibited. These fluctuations suggested that the ischemia conditions of brain had been improved. Also, the recoveries in the energy and gray-scale values were determined to be faster, which suggested that the G load endurance of human body had been enhanced. The Brain Atlas was found to show observable changes in color. The experimental results indicated that the Brain Atlas was able to provide assistance during the exploration of the fluctuations in the characteristics of EEG, and provided a criterion to assist in the observations of the function state fluctuations of human brain with +Gz acceleration. It also assisted in the evaluations of the G load endurance of human body.
Energy Technology Data Exchange (ETDEWEB)
Kawamura, Gen; Quadt, Arnulf [II. Physikalisches Institut, Georg-August-Universitaet Goettingen (Germany)
2016-07-01
Efficient administration of computing centres requires advanced tools for the monitoring and front-end interface of the infrastructure. Providing the large-scale distributed systems as a global grid infrastructure, like the Worldwide LHC Computing Grid (WLCG) and ATLAS computing, is offering many existing web pages and information sources indicating the status of the services, systems and user jobs at grid sites. A meta-monitoring mobile application which automatically collects the information could give every administrator a sophisticated and flexible interface of the infrastructure. We describe such a solution; the MadFace mobile application developed at Goettingen. It is a HappyFace compatible mobile application which has a user-friendly interface. It also becomes very feasible to automatically investigate the status and problem from different sources and provides access of the administration roles for non-experts.
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
AGIS: The ATLAS Grid Information System
Anisenkov, Alexey; Di Girolamo, Alessandro; Gayazov, Stavro; Klimentov, Alexei; Oleynik, Danila; Senchenko, Alexander
2012-01-01
ATLAS is a particle physics experiment at the Large Hadron Collider at CERN. The experiment produces petabytes of data annually through simulation production and tens petabytes of data per year from the detector itself. The ATLAS Computing model embraces the Grid paradigm and a high degree of decentralization and computing resources able to meet ATLAS requirements of petabytes scale data operations. In this paper we present ATLAS Grid Information System (AGIS) designed to integrate configuration and status information about resources, services and topology of whole ATLAS Grid needed by ATLAS Distributed Computing applications and services.
Tensor Excitations in Nambu - Jona-Lasinio Model
Chizhov, M V
1996-01-01
It is shown that in the one-flavour NJL model the vector and axial-vector quasiparticles described by the antisymmetric tensor field are generated. These excitations have tensor interactions with quarks in contrast to usual vector ones. Phenomenological applications are discussed.
Tensor Basis Neural Network v. 1.0 (beta)
Energy Technology Data Exchange (ETDEWEB)
2017-03-28
This software package can be used to build, train, and test a neural network machine learning model. The neural network architecture is specifically designed to embed tensor invariance properties by enforcing that the model predictions sit on an invariant tensor basis. This neural network architecture can be used in developing constitutive models for applications such as turbulence modeling, materials science, and electromagnetism.
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...
ATLAS Maintenance and Operation management system
Copy, B
2007-01-01
The maintenance and operation of the ATLAS detector will involve thousands of contributors from 170 physics institutes. Planning and coordinating the action of ATLAS members, ensuring their expertise is properly leveraged and that no parts of the detector are understaffed or overstaffed will be a challenging task. The ATLAS Maintenance and Operation application (referred to as Operation Task Planner inside the ATLAS experiment) offers a fluent web based interface that combines the flexibility and comfort of a desktop application, intuitive data visualization and navigation techniques, with a lightweight service oriented architecture. We will review the application, its usage within the ATLAS experiment, its underlying design and implementation.
Application of a new interconnection technology for the ATLAS pixel upgrade at SLHC
Macchiolo, A; Beimforde, M; Moser, H G; Nisius, R; Richter, R H
2009-01-01
We present an R&D activity aiming towards a new detector concept in the framework of the ATLAS pixel detector upgrade exploiting a vertical integration technology developed at the Fraunhofer Institute IZMMunich. The Solid-Liquid InterDiffusion (SLID) technique is investigated as an alternative to the bump-bonding process. We also investigate the extraction of the signals from the back of the read-out chip through Inter-Chip-Vias to achieve a higher fraction of active area with respect to the present ATLAS pixel module. We will present the layout and the first results obtained with a production of test-structures designed to investigate the SLID interconnection efficiency as a function of different parameters, i.e. the pixel size and pitch, as well as the planarity of the underlying layers.
Multiple brain atlas database and atlas-based neuroimaging system.
Nowinski, W L; Fang, A; Nguyen, B T; Raphel, J K; Jagannathan, L; Raghavan, R; Bryan, R N; Miller, G A
1997-01-01
For the purpose of developing multiple, complementary, fully labeled electronic brain atlases and an atlas-based neuroimaging system for analysis, quantification, and real-time manipulation of cerebral structures in two and three dimensions, we have digitized, enhanced, segmented, and labeled the following print brain atlases: Co-Planar Stereotaxic Atlas of the Human Brain by Talairach and Tournoux, Atlas for Stereotaxy of the Human Brain by Schaltenbrand and Wahren, Referentially Oriented Cerebral MRI Anatomy by Talairach and Tournoux, and Atlas of the Cerebral Sulci by Ono, Kubik, and Abernathey. Three-dimensional extensions of these atlases have been developed as well. All two- and three-dimensional atlases are mutually preregistered and may be interactively registered with an actual patient's data. An atlas-based neuroimaging system has been developed that provides support for reformatting, registration, visualization, navigation, image processing, and quantification of clinical data. The anatomical index contains about 1,000 structures and over 400 sulcal patterns. Several new applications of the brain atlas database also have been developed, supported by various technologies such as virtual reality, the Internet, and electronic publishing. Fusion of information from multiple atlases assists the user in comprehensively understanding brain structures and identifying and quantifying anatomical regions in clinical data. The multiple brain atlas database and atlas-based neuroimaging system have substantial potential impact in stereotactic neurosurgery and radiotherapy by assisting in visualization and real-time manipulation in three dimensions of anatomical structures, in quantitative neuroradiology by allowing interactive analysis of clinical data, in three-dimensional neuroeducation, and in brain function studies.
Garfrerick, Adam R.
2012-01-01
Recent developments in carbon nanotube technology have allowed for semi-transparent electrodes to be created which can possibly improve the efficiency of solar cells. A method for simulating the use of semi-transparent carbon nanotube networks as a charge collector for solar cells in Silvaco ATLAS software is presented in this thesis. Semi-transparent carbon nanotube networks allow for a greater area of charge collection on the surface of solar cells as well as a lower resistance path for cha...
Alhroob, M.; Bates, R.; Battistin, M.; Berry, S.; Bitadze, A.; Bonneau, P.; Bousson, N.; Boyd, G.; Bozza, G.; Crespo-Lopez, O.; Degeorge, C.; Deterre, C.; DiGirolamo, B.; Doubek, M.; Favre, G.; Godlewski, J.; Hallewell, G.; Hasib, A.; Katunin, S.; Langevin, N.; Lombard, D.; Mathieu, M.; McMahon, S.; Nagai, K.; O'Rourke, A.; Pearson, B.; Robinson, D.; Rossi, C.; Rozanov, A.; Strauss, M.; Vacek, V.; Zwalinski, L.
2015-03-01
Precision sound velocity measurements can simultaneously determine binary gas composition and flow. We have developed an analyzer with custom microcontroller-based electronics, currently used in the ATLAS Detector Control System, with numerous potential applications. Three instruments monitor C3F8 and CO2 coolant leak rates into the nitrogen envelopes of the ATLAS silicon microstrip and Pixel detectors. Two further instruments will aid operation of the new thermosiphon coolant recirculator: one of these will monitor air leaks into the low pressure condenser while the other will measure return vapour flow along with C3F8/C2F6 blend composition, should blend operation be necessary to protect the ATLAS silicon tracker under increasing LHC luminosity. We describe these instruments and their electronics.
International Nuclear Information System (INIS)
Molfetas, Angelos; Megino, Fernando Barreiro; Tykhonov, Andrii; Lassnig, Mario; Garonne, Vincent; Barisits, Martin; Campana, Simone; Dimitrov, Gancho; Jezequel, Stephane; Ueda, Ikuo; Viegas, Florbela Tique Aires
2011-01-01
The ATLAS experiment's data management system is constantly tracing file movement operations that occur on the Worldwide LHC Computing Grid (WLCG). Due to the large scale of the WLCG, statistical analysis of the traces is infeasible in real-time. Factors that contribute to the scalability problems include the capability for users to initiate on-demand queries, high dimensionality of tracer entries combined with very low cardinality parameters, and the large size of the namespace. These scalability issues are alleviated through the adoption of an incremental model that aggregates data for all combinations occurring in selected tracer fields on a daily basis. Using this model it is possible to query on-demand relevant statistics about system usage. We present an implementation of this popularity model in the experiment's distributed data management system, DQ2, and describe a direct application example of the popularity framework, an automated cleaning system, which uses the statistics to dynamically detect and reduce unpopular replicas from grid sites. This paper describes the architecture employed by the cleaning system and reports on the results collected from a prototype during the first months of the ATLAS collision data taking.
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...
Susceptibility tensor imaging (STI) of the brain.
Li, Wei; Liu, Chunlei; Duong, Timothy Q; van Zijl, Peter C M; Li, Xu
2017-04-01
Susceptibility tensor imaging (STI) is a recently developed MRI technique that allows quantitative determination of orientation-independent magnetic susceptibility parameters from the dependence of gradient echo signal phase on the orientation of biological tissues with respect to the main magnetic field. By modeling the magnetic susceptibility of each voxel as a symmetric rank-2 tensor, individual magnetic susceptibility tensor elements as well as the mean magnetic susceptibility and magnetic susceptibility anisotropy can be determined for brain tissues that would still show orientation dependence after conventional scalar-based quantitative susceptibility mapping to remove such dependence. Similar to diffusion tensor imaging, STI allows mapping of brain white matter fiber orientations and reconstruction of 3D white matter pathways using the principal eigenvectors of the susceptibility tensor. In contrast to diffusion anisotropy, the main determinant factor of the susceptibility anisotropy in brain white matter is myelin. Another unique feature of the susceptibility anisotropy of white matter is its sensitivity to gadolinium-based contrast agents. Mechanistically, MRI-observed susceptibility anisotropy is mainly attributed to the highly ordered lipid molecules in the myelin sheath. STI provides a consistent interpretation of the dependence of phase and susceptibility on orientation at multiple scales. This article reviews the key experimental findings and physical theories that led to the development of STI, its practical implementations, and its applications for brain research. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd.
Susceptibility Tensor Imaging (STI) of the Brain
Li, Wei; Liu, Chunlei; Duong, Timothy Q.; van Zijl, Peter C.M.; Li, Xu
2016-01-01
Susceptibility tensor imaging (STI) is a recently developed MRI technique that allows quantitative determination of orientation-independent magnetic susceptibility parameters from the dependence of gradient echo signal phase on the orientation of biological tissues with respect to the main magnetic field. By modeling the magnetic susceptibility of each voxel as a symmetric rank-2 tensor, individual magnetic susceptibility tensor elements as well as the mean magnetic susceptibility (MMS) and magnetic susceptibility anisotropy (MSA) can be determined for brain tissues that would still show orientation dependence after conventional scalar-based quantitative susceptibility mapping (QSM) to remove such dependence. Similar to diffusion tensor imaging (DTI), STI allows mapping of brain white matter fiber orientations and reconstruction of 3D white matter pathways using the principal eigenvectors of the susceptibility tensor. In contrast to diffusion anisotropy, the main determinant factor of susceptibility anisotropy in brain white matter is myelin. Another unique feature of susceptibility anisotropy of white matter is its sensitivity to gadolinium-based contrast agents. Mechanistically, MRI-observed susceptibility anisotropy is mainly attributed to the highly ordered lipid molecules in myelin sheath. STI provides a consistent interpretation of the dependence of phase and susceptibility on orientation at multiple scales. This article reviews the key experimental findings and physical theories that led to the development of STI, its practical implementations, and its applications for brain research. PMID:27120169
Off-shell N = 2 tensor supermultiplets
International Nuclear Information System (INIS)
Wit, Bernard de; Saueressig, Frank
2006-01-01
A multiplet calculus is presented for an arbitrary number n of N = 2 tensor supermultiplets. For rigid supersymmetry the known couplings are reproduced. In the superconformal case the target spaces parametrized by the scalar fields are cones over (3n-1)-dimensional spaces encoded in homogeneous SU(2) invariant potentials, subject to certain constraints. The coupling to conformal supergravity enables the derivation of a large class of supergravity Lagrangians with vector and tensor multiplets and hypermultiplets. Dualizing the tensor fields into scalars leads to hypermultiplets with hyperkaehler or quaternion-Kaehler target spaces with at least n abelian isometries. It is demonstrated how to use the calculus for the construction of Lagrangians containing higher-derivative couplings of tensor multiplets. For the application of the c-map between vector and tensor supermultiplets to Lagrangians with higher-order derivatives, an off-shell version of this map is proposed. Various other implications of the results are discussed. As an example an elegant derivation of the classification of 4-dimensional quaternion-Kaehler manifolds with two commuting isometries is given
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.
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…
The average number of critical rank-one approximations to a tensor
Draisma, J.; Horobet, E.
2014-01-01
Motivated by the many potential applications of low-rank multi-way tensor approximations, we set out to count the rank-one tensors that are critical points of the distance function to a general tensor v. As this count depends on v, we average over v drawn from a Gaussian distribution, and find
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.
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...
Wang, Guoyou; Fu, Shijie; Shen, Huarui; Guan, Taiyuan; Xu, Ping
2013-10-01
To explore the effectiveness of fixation of atlas translaminar screws in the treatment of atlatoaxial instability. A retrospective analysis was made on the clinical data of 32 patients with atlatoaxial instability treated with atlantoaxial trans-pedicle screws between March 2007 and August 2009. Of them, 7 patients underwent atlas translaminar screws combined with axis transpedicle screws fixation because of fracture types, anatomic variation, and intraoperative reason, including 5 males and 2 females with an average age of 48.2 years (range, 35-69 years). A total of 9 translaminar screws were inserted. Injury was caused by traffic accident in 4 cases, falling from height in 2 cases, and crushing in 1 case. Two cases had simple odontoid fracture (Anderson type II), and 5 cases had odontoid fracture combined with other injuries (massa lateralis atlantis fracture in 2, atlantoaxial dislocation in 1, and Hangman fracture in 2). The interval between injury and operation was 4-9 days (mean, 6 days). The preoperative Japanese Orthopaedic Association (JOA) score was 8.29 +/- 1.60. The X-ray films showed good position of the screws. Healing of incision by first intention was obtained, and no patient had injuries of the spinal cord injury, nerve root, and vertebral artery. Seven cases were followed up 9-26 months (mean, 14 months). Good bone fusion was observed at 8 months on average (range, 6-11 months). No loosening, displacement, and breakage of internal fixation, re-dislocation and instability of atlantoaxial joint, or penetrating of pedicle screw into the spinal canal and the spinal cord occurred. The JOA score was significantly improved to 15.29 +/- 1.38 at 6 months after operation (t = 32.078, P = 0.000). Atlas translaminar screws fixation has the advantages of firm fixation, simple operating techniques, and relative safety, so it may be a remedial measure of atlatoaxial instability.
Newlander, Shawn M; Chu, Alan; Sinha, Usha S; Lu, Po H; Bartzokis, George
2014-02-01
To identify regional differences in apparent diffusion coefficient (ADC) and fractional anisotropy (FA) using customized preprocessing before voxel-based analysis (VBA) in 14 normal subjects with the specific genes that decrease (apolipoprotein [APO] E ε2) and that increase (APOE ε4) the risk of Alzheimer's disease. Diffusion tensor images (DTI) acquired at 1.5 Tesla were denoised with a total variation tensor regularization algorithm before affine and nonlinear registration to generate a common reference frame for the image volumes of all subjects. Anisotropic and isotropic smoothing with varying kernel sizes was applied to the aligned data before VBA to determine regional differences between cohorts segregated by allele status. VBA on the denoised tensor data identified regions of reduced FA in APOE ε4 compared with the APOE ε2 healthy older carriers. The most consistent results were obtained using the denoised tensor and anisotropic smoothing before statistical testing. In contrast, isotropic smoothing identified regional differences for small filter sizes alone, emphasizing that this method introduces bias in FA values for higher kernel sizes. Voxel-based DTI analysis can be performed on low signal to noise ratio images to detect subtle regional differences in cohorts using the proposed preprocessing techniques. Copyright © 2013 Wiley Periodicals, Inc.
International Nuclear Information System (INIS)
Higuchi, A.
1987-01-01
The symmetric tensor spherical harmonics (STSH's) on the N-sphere (S/sup N/), which are defined as the totally symmetric, traceless, and divergence-free tensor eigenfunctions of the Laplace--Beltrami (LB) operator on S/sup N/, are studied. Specifically, their construction is shown recursively starting from the lower-dimensional ones. The symmetric traceless tensors induced by STSH's are introduced. These play a crucial role in the recursive construction of STSH's. The normalization factors for STSH's are determined by using their transformation properties under SO(N+1). Then the symmetric, traceless, and divergence-free tensor eigenfunctions of the LB operator in the N-dimensional de Sitter space-time which are obtained by the analytic continuation of the STSH's on S/sup N/ are studied. Specifically, the allowed eigenvalues of the LB operator under the restriction of unitarity are determined. Our analysis gives a group-theoretical explanation of the forbidden mass range observed earlier for the spin-2 field theory in de Sitter space-time
Molfetas, A; Tykhonov, A; Garonne, V; Campana, S; Lassnig, M; Barisits, M; Dimitrov, G; Viegas, F
2011-01-01
The ATLAS experiment's data management system is constantly tracing file movement operations that occur on the Worldwide LHC Computing Grid (WLCG). Due to the large scale of the WLCG, direct statistical analysis of the traces is impossible in real-time. Factors that contribute to the scalability problems include the capability for users to initiatiate on-demand queries, high dimensionality of tracer entries combined with very low cardinality parameters, the large size of the namespace as well as rapid rate of file transactions occuring on the Grid. These scalability issues are alleviated through the adoption of an incremental model that aggregates data for all combinations occurring in selected tracer fields on a daily basis. Using this model it is possible to query on-demand relevant statistics about system usage. We present an implementation of this popularity model in the experiment's distributed data management system, DQ2, and describe a direct application example of the popularity framework, an automate...
Unno, Y; Ikegami, Y; Iwata, Y; Kohriki, T; Kondo, T; Nakano, I; Ohsugi, T; Takashima, R; Tanaka, R; Terada, S; Ujiie, N
2005-01-01
We applied the surface build-up Cu-polyimide flex-circuit technology with laser vias to the ATLAS SCT barrel hybrid to be made in one piece from the connector to the electronics sections including cables. The hybrids, reinforced with carbon-carbon substrates, provide mechanical strength, thermal conductivity, low-radiation length, and stability in application-specific integrated circuit (ASIC) operation. By following the design rules, we experienced little trouble in breaking the traces. The pitch adapter between the sensor and the ASICs was made of aluminum traces on glass substrate. We identified that the generation of whiskers around the wire-bonding feet was correlated with the hardness of metallized aluminum. The appropriate hardness has been achieved by keeping the temperature of the glasses as low as room temperature during the metallization. The argon plasma cleaning procedure cleaned the contamination on the gold pads of the hybrids for successful wire bonding, although it was unsuccessful in the alu...
Inductive Framework for Multi-Aspect Streaming Tensor Completion with Side Information
Nimishakavi, Madhav; Mishra, Bamdev; Gupta, Manish; Talukdar, Partha
2018-01-01
Low-rank tensor completion is a well-studied problem and has applications in various fields. However, in many real-world applications the data is dynamic, i.e., the tensor grows as new data arrives. Besides the tensor, in many real-world scenarios, side information is also available in the form of matrices which also grow. Existing work on dynamic tensor completion do not incorporate side information and most of the previous work is based on the assumption that the tensor grows only in one mo...
Mohammadi, Siawoosh; Hutton, Chloe; Nagy, Zoltan; Josephs, Oliver; Weiskopf, Nikolaus
2013-01-01
Diffusion tensor imaging is widely used in research and clinical applications, but this modality is highly sensitive to artefacts. We developed an easy-to-implement extension of the original diffusion tensor model to account for physiological noise in diffusion tensor imaging using measures of peripheral physiology (pulse and respiration), the so-called extended tensor model. Within the framework of the extended tensor model two types of regressors, which respectively modeled small (linear) and strong (nonlinear) variations in the diffusion signal, were derived from peripheral measures. We tested the performance of four extended tensor models with different physiological noise regressors on nongated and gated diffusion tensor imaging data, and compared it to an established data-driven robust fitting method. In the brainstem and cerebellum the extended tensor models reduced the noise in the tensor-fit by up to 23% in accordance with previous studies on physiological noise. The extended tensor model addresses both large-amplitude outliers and small-amplitude signal-changes. The framework of the extended tensor model also facilitates further investigation into physiological noise in diffusion tensor imaging. The proposed extended tensor model can be readily combined with other artefact correction methods such as robust fitting and eddy current correction. PMID:22936599
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
Decomposition of a symmetric second-order tensor
Heras, José A.
2018-05-01
In the three-dimensional space there are different definitions for the dot and cross products of a vector with a second-order tensor. In this paper we show how these products can uniquely be defined for the case of symmetric tensors. We then decompose a symmetric second-order tensor into its ‘dot’ part, which involves the dot product, and the ‘cross’ part, which involves the cross product. For some physical applications, this decomposition can be interpreted as one in which the dot part identifies with the ‘parallel’ part of the tensor and the cross part identifies with the ‘perpendicular’ part. This decomposition of a symmetric second-order tensor may be suitable for undergraduate courses of vector calculus, mechanics and electrodynamics.
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.
Dillon, Joshua V.; Langmore, Ian; Tran, Dustin; Brevdo, Eugene; Vasudevan, Srinivas; Moore, Dave; Patton, Brian; Alemi, Alex; Hoffman, Matt; Saurous, Rif A.
2017-01-01
The TensorFlow Distributions library implements a vision of probability theory adapted to the modern deep-learning paradigm of end-to-end differentiable computation. Building on two basic abstractions, it offers flexible building blocks for probabilistic computation. Distributions provide fast, numerically stable methods for generating samples and computing statistics, e.g., log density. Bijectors provide composable volume-tracking transformations with automatic caching. Together these enable...
The tensor distribution function.
Leow, A D; Zhu, S; Zhan, L; McMahon, K; de Zubicaray, G I; Meredith, M; Wright, M J; Toga, A W; Thompson, P M
2009-01-01
Diffusion weighted magnetic resonance imaging is a powerful tool that can be employed to study white matter microstructure by examining the 3D displacement profile of water molecules in brain tissue. By applying diffusion-sensitized gradients along a minimum of six directions, second-order tensors (represented by three-by-three positive definite matrices) can be computed to model dominant diffusion processes. However, conventional DTI is not sufficient to resolve more complicated white matter configurations, e.g., crossing fiber tracts. Recently, a number of high-angular resolution schemes with more than six gradient directions have been employed to address this issue. In this article, we introduce the tensor distribution function (TDF), a probability function defined on the space of symmetric positive definite matrices. Using the calculus of variations, we solve the TDF that optimally describes the observed data. Here, fiber crossing is modeled as an ensemble of Gaussian diffusion processes with weights specified by the TDF. Once this optimal TDF is determined, the orientation distribution function (ODF) can easily be computed by analytic integration of the resulting displacement probability function. Moreover, a tensor orientation distribution function (TOD) may also be derived from the TDF, allowing for the estimation of principal fiber directions and their corresponding eigenvalues.
Application of Gas Chromatographic analysis to RPC detectors in the ATLAS experiment at CERN-LHC
De Asmundis, R
2007-01-01
Starting from 2007 a large number (1200) Resistive Plate Chambers (RPC) detectors will be used as muon trigger detectors in the ATLAS Experiment at CERN-LHC accelerator. RPC are gaseous detector in which the quality and the stability of the gas mixture as well as the design of the gas supplying system, play a fundamental role in their functioning. RPC are foreseen to work more than ten years in the high radiation environment of ATLAS and the gas mixture acts really as a "lifeguard" for the detectors. For this reason a great attention has been devoted to the gas studies in order to optimize RPC performance, robustness and reliability in a high radiation environment. In this paper we describe the work done to decide how to supply and control in an optimal way the gas to the detectors, in order to ensure their best performance for a long time. The activity, based on Gas Chromatographic (GC) analysis, has been carried on a sample of final RPC working in radiation conditions much more intense than those foreseen f...
Reconstruction of tau lepton decays and applications in the ATLAS experiment
Energy Technology Data Exchange (ETDEWEB)
Wagner, Peter [Rheinische Friedrich-Wilhelms-Universitaet Bonn (Germany)
2016-07-01
Final states with hadronically decaying tau leptons play an important part in the physics programme of the ATLAS experiment. Examples are measurements of Standard Model processes, evidence of the Higgs-boson Yukawa couplings to tau leptons, and searches for new physics phenomena, such as Supersymmetry. These analyses depended on robust tau reconstruction and excellent particle identification algorithms that provided suppression of backgrounds from jets, electrons and muons. I present a new ''particle flow'' method of reconstructing the individual charged and neutral hadrons in tau decays with the ATLAS detector which leads to a significant improvement in the tau energy and directional resolution. It further gives access to the individual charged and neutral hadron four-momenta and offers a high purity decay mode selection. These features will play a particularly important role in analyses that exploit tau spin information, such as a measurement of the CP mixture of the Higgs boson in H → ττ decays.
OPERATOR NORM INEQUALITIES BETWEEN TENSOR UNFOLDINGS ON THE PARTITION LATTICE.
Wang, Miaoyan; Duc, Khanh Dao; Fischer, Jonathan; Song, Yun S
2017-05-01
Interest in higher-order tensors has recently surged in data-intensive fields, with a wide range of applications including image processing, blind source separation, community detection, and feature extraction. A common paradigm in tensor-related algorithms advocates unfolding (or flattening) the tensor into a matrix and applying classical methods developed for matrices. Despite the popularity of such techniques, how the functional properties of a tensor changes upon unfolding is currently not well understood. In contrast to the body of existing work which has focused almost exclusively on matricizations, we here consider all possible unfoldings of an order- k tensor, which are in one-to-one correspondence with the set of partitions of {1, …, k }. We derive general inequalities between the l p -norms of arbitrary unfoldings defined on the partition lattice. In particular, we demonstrate how the spectral norm ( p = 2) of a tensor is bounded by that of its unfoldings, and obtain an improved upper bound on the ratio of the Frobenius norm to the spectral norm of an arbitrary tensor. For specially-structured tensors satisfying a generalized definition of orthogonal decomposability, we prove that the spectral norm remains invariant under specific subsets of unfolding operations.
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.
Iglesias, Juan Eugenio; Augustinack, Jean C; Nguyen, Khoa; Player, Christopher M; Player, Allison; Wright, Michelle; Roy, Nicole; Frosch, Matthew P; McKee, Ann C; Wald, Lawrence L; Fischl, Bruce; Van Leemput, Koen
2015-07-15
Automated analysis of MRI data of the subregions of the hippocampus requires computational atlases built at a higher resolution than those that are typically used in current neuroimaging studies. Here we describe the construction of a statistical atlas of the hippocampal formation at the subregion level using ultra-high resolution, ex vivo MRI. Fifteen autopsy samples were scanned at 0.13 mm isotropic resolution (on average) using customized hardware. The images were manually segmented into 13 different hippocampal substructures using a protocol specifically designed for this study; precise delineations were made possible by the extraordinary resolution of the scans. In addition to the subregions, manual annotations for neighboring structures (e.g., amygdala, cortex) were obtained from a separate dataset of in vivo, T1-weighted MRI scans of the whole brain (1mm resolution). The manual labels from the in vivo and ex vivo data were combined into a single computational atlas of the hippocampal formation with a novel atlas building algorithm based on Bayesian inference. The resulting atlas can be used to automatically segment the hippocampal subregions in structural MRI images, using an algorithm that can analyze multimodal data and adapt to variations in MRI contrast due to differences in acquisition hardware or pulse sequences. The applicability of the atlas, which we are releasing as part of FreeSurfer (version 6.0), is demonstrated with experiments on three different publicly available datasets with different types of MRI contrast. The results show that the atlas and companion segmentation method: 1) can segment T1 and T2 images, as well as their combination, 2) replicate findings on mild cognitive impairment based on high-resolution T2 data, and 3) can discriminate between Alzheimer's disease subjects and elderly controls with 88% accuracy in standard resolution (1mm) T1 data, significantly outperforming the atlas in FreeSurfer version 5.3 (86% accuracy) and
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...
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.
ATLAS TDAQ System Administration:
Lee, Christopher Jon; The ATLAS collaboration; Bogdanchikov, Alexander; Ballestrero, Sergio; Contescu, Alexandru Cristian; Dubrov, Sergei; Fazio, Daniel; Korol, Aleksandr; Scannicchio, Diana; Twomey, Matthew Shaun; Voronkov, Artem
2015-01-01
The ATLAS Trigger and Data Acquisition (TDAQ) system is responsible for the online processing of live data, streaming from the ATLAS experiment at the Large Hadron Collider (LHC) at CERN. The online farm is composed of ̃3000 servers, processing the data readout from ̃100 million detector channels through multiple trigger levels. During the two years of the first Long Shutdown (LS1) there has been a tremendous amount of work done by the ATLAS TDAQ System Administrators, implementing numerous new software applications, upgrading the OS and the hardware, changing some design philosophies and exploiting the High Level Trigger farm with different purposes. During the data taking only critical security updates are applied and broken hardware is replaced to ensure a stable operational environment. The LS1 provided an excellent opportunity to look into new technologies and applications that would help to improve and streamline the daily tasks of not only the System Administrators, but also of the scientists who wil...
AGIS: The ATLAS Grid Information System
Anisenkov, A.; Di Girolamo, A.; Klimentov, A.; Oleynik, D.; Petrosyan, A.; Atlas Collaboration
2014-06-01
ATLAS, a particle physics experiment at the Large Hadron Collider at CERN, produced petabytes of data annually through simulation production and tens of petabytes of data per year from the detector itself. The ATLAS computing model embraces the Grid paradigm and a high degree of decentralization and computing resources able to meet ATLAS requirements of petabytes scale data operations. In this paper we describe the ATLAS Grid Information System (AGIS), designed to integrate configuration and status information about resources, services and topology of the computing infrastructure used by the ATLAS Distributed Computing applications and services.
LeGrand, Anne
2017-02-01
The role of medical imaging in global health systems is literally fundamental. Like labs, medical images are used at one point or another in almost every high cost, high value episode of care. CT scans, mammograms, and x-rays, for example, "atlas" the body and help chart a course forward for a patient's care team. Imaging precision has improved as a result of technological advancements and breakthroughs in related medical research. Those advancements also bring with them exponential growth in medical imaging data. As IBM trains Watson to "see" medical images, Ms. Le Grand will discuss recent advances made by Watson Health and explore the potential value of "augmented intelligence" to assist healthcare providers like radiologists and cardiologists, as well as the patients they serve.
Hejrani, Babak; Tkalčić, Hrvoje; Fichtner, Andreas
2017-07-01
Although both earthquake mechanism and 3-D Earth structure contribute to the seismic wavefield, the latter is usually assumed to be layered in source studies, which may limit the quality of the source estimate. To overcome this limitation, we implement a method that takes advantage of a 3-D heterogeneous Earth model, recently developed for the Australasian region. We calculate centroid moment tensors (CMTs) for earthquakes in Papua New Guinea (PNG) and the Solomon Islands. Our method is based on a library of Green's functions for each source-station pair for selected Geoscience Australia and Global Seismic Network stations in the region, and distributed on a 3-D grid covering the seismicity down to 50 km depth. For the calculation of Green's functions, we utilize a spectral-element method for the solution of the seismic wave equation. Seismic moment tensors were calculated using least squares inversion, and the 3-D location of the centroid is found by grid search. Through several synthetic tests, we confirm a trade-off between the location and the correct input moment tensor components when using a 1-D Earth model to invert synthetics produced in a 3-D heterogeneous Earth. Our CMT catalogue for PNG in comparison to the global CMT shows a meaningful increase in the double-couple percentage (up to 70%). Another significant difference that we observe is in the mechanism of events with depth shallower then 15 km and Mw region.
Reduction schemes for one-loop tensor integrals
International Nuclear Information System (INIS)
Denner, A.; Dittmaier, S.
2006-01-01
We present new methods for the evaluation of one-loop tensor integrals which have been used in the calculation of the complete electroweak one-loop corrections to e + e - ->4 fermions. The described methods for 3-point and 4-point integrals are, in particular, applicable in the case where the conventional Passarino-Veltman reduction breaks down owing to the appearance of Gram determinants in the denominator. One method consists of different variants for expanding tensor coefficients about limits of vanishing Gram determinants or other kinematical determinants, thereby reducing all tensor coefficients to the usual scalar integrals. In a second method a specific tensor coefficient with a logarithmic integrand is evaluated numerically, and the remaining coefficients as well as the standard scalar integral are algebraically derived from this coefficient. For 5-point tensor integrals, we give explicit formulas that reduce the corresponding tensor coefficients to coefficients of 4-point integrals with tensor rank reduced by one. Similar formulas are provided for 6-point functions, and the generalization to functions with more internal propagators is straightforward. All the presented methods are also applicable if infrared (soft or collinear) divergences are treated in dimensional regularization or if mass parameters (for unstable particles) become complex
Tensor Train Neighborhood Preserving Embedding
Wang, Wenqi; Aggarwal, Vaneet; Aeron, Shuchin
2018-05-01
In this paper, we propose a Tensor Train Neighborhood Preserving Embedding (TTNPE) to embed multi-dimensional tensor data into low dimensional tensor subspace. Novel approaches to solve the optimization problem in TTNPE are proposed. For this embedding, we evaluate novel trade-off gain among classification, computation, and dimensionality reduction (storage) for supervised learning. It is shown that compared to the state-of-the-arts tensor embedding methods, TTNPE achieves superior trade-off in classification, computation, and dimensionality reduction in MNIST handwritten digits and Weizmann face datasets.
Notes on super Killing tensors
Energy Technology Data Exchange (ETDEWEB)
Howe, P.S. [Department of Mathematics, King’s College London,The Strand, London WC2R 2LS (United Kingdom); Lindström, University [Department of Physics and Astronomy, Theoretical Physics, Uppsala University,SE-751 20 Uppsala (Sweden); Theoretical Physics, Imperial College London,Prince Consort Road, London SW7 2AZ (United Kingdom)
2016-03-14
The notion of a Killing tensor is generalised to a superspace setting. Conserved quantities associated with these are defined for superparticles and Poisson brackets are used to define a supersymmetric version of the even Schouten-Nijenhuis bracket. Superconformal Killing tensors in flat superspaces are studied for spacetime dimensions 3,4,5,6 and 10. These tensors are also presented in analytic superspaces and super-twistor spaces for 3,4 and 6 dimensions. Algebraic structures associated with superconformal Killing tensors are also briefly discussed.
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
Positivity of linear maps under tensor powers
Energy Technology Data Exchange (ETDEWEB)
Müller-Hermes, Alexander, E-mail: muellerh@ma.tum.de; Wolf, Michael M., E-mail: m.wolf@tum.de [Zentrum Mathematik, Technische Universität München, 85748 Garching (Germany); Reeb, David, E-mail: reeb.qit@gmail.com [Zentrum Mathematik, Technische Universität München, 85748 Garching (Germany); Institute for Theoretical Physics, Leibniz Universität Hannover, 30167 Hannover (Germany)
2016-01-15
We investigate linear maps between matrix algebras that remain positive under tensor powers, i.e., under tensoring with n copies of themselves. Completely positive and completely co-positive maps are trivial examples of this kind. We show that for every n ∈ ℕ, there exist non-trivial maps with this property and that for two-dimensional Hilbert spaces there is no non-trivial map for which this holds for all n. For higher dimensions, we reduce the existence question of such non-trivial “tensor-stable positive maps” to a one-parameter family of maps and show that an affirmative answer would imply the existence of non-positive partial transpose bound entanglement. As an application, we show that any tensor-stable positive map that is not completely positive yields an upper bound on the quantum channel capacity, which for the transposition map gives the well-known cb-norm bound. We, furthermore, show that the latter is an upper bound even for the local operations and classical communications-assisted quantum capacity, and that moreover it is a strong converse rate for this task.
Positivity of linear maps under tensor powers
International Nuclear Information System (INIS)
Müller-Hermes, Alexander; Wolf, Michael M.; Reeb, David
2016-01-01
We investigate linear maps between matrix algebras that remain positive under tensor powers, i.e., under tensoring with n copies of themselves. Completely positive and completely co-positive maps are trivial examples of this kind. We show that for every n ∈ ℕ, there exist non-trivial maps with this property and that for two-dimensional Hilbert spaces there is no non-trivial map for which this holds for all n. For higher dimensions, we reduce the existence question of such non-trivial “tensor-stable positive maps” to a one-parameter family of maps and show that an affirmative answer would imply the existence of non-positive partial transpose bound entanglement. As an application, we show that any tensor-stable positive map that is not completely positive yields an upper bound on the quantum channel capacity, which for the transposition map gives the well-known cb-norm bound. We, furthermore, show that the latter is an upper bound even for the local operations and classical communications-assisted quantum capacity, and that moreover it is a strong converse rate for this task
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.
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.
maximilien brice
2003-01-01
Eighteen feet made of stainless steel will support the barrel ATLAS detector in the cavern at Point 1. In total, the ATLAS feet system will carry approximately 6000 tons, and will give the same inclination to the detector as the LHC accelerator.
2003-01-01
Eighteen feet made of stainless steel will support the barrel ATLAS detector in the cavern at Point 1. In total, the ATLAS feet system will carry approximately 6000 tons, and will give the same inclination to the detector as the LHC accelerator. The installation of the feet is scheduled to finish during January 2004 with an installation precision at the 1 mm level despite their height of 5.3 metres. The manufacture was carried out in Russia (Company Izhorskiye Zavody in St. Petersburg), as part of a Russian and JINR Dubna in-kind contribution to ATLAS. Involved in the installation is a team from IHEP-Protvino (Russia), the ATLAS technical co-ordination team at CERN, and the CERN survey team. In all, about 15 people are involved. After the feet are in place, the barrel toroid magnet and the barrel calorimeters will be installed. This will keep the ATLAS team busy for the entire year 2004.
International Nuclear Information System (INIS)
Bussat, Jean-Marie
1998-01-01
The construction of the new particle accelerator, the LHC (Large Hadron Collider) at CERN is entails many research and development projects. It is the case in electronics where the problem of the acquisition of large dynamic range signals at high sampling frequencies occurs. Typically, the requirements are a dynamic range of about 65,000 (around 16 bits) at 40 MHz. Some solutions to this problem will be presented. One of them is using a commercial analog-to-digital converter. This case brings up the necessity of a signal conditioning equipment. This thesis describes a way of building such a system that will be called 'multi-gain system'. Then, an application of this method is presented. It involves the realization of an automatic gain switching integrated circuit. It is designed for the readout of the ATLAS electromagnetic calorimeter. The choice and the calculation of the components of this systems are described. They are followed by the results of some measurements done on a prototype made using the AMS 1.2μm BiCMOS foundry. Possible enhancements are also presented. We conclude on the feasibility of such a system and its various applications in a number of fields that are not restricted to particle physics. (author)
Taso, Manuel; Le Troter, Arnaud; Sdika, Michaël; Cohen-Adad, Julien; Arnoux, Pierre-Jean; Guye, Maxime; Ranjeva, Jean-Philippe; Callot, Virginie
2015-08-15
Recently, a T2*-weighted template and probabilistic atlas of the white and gray matter (WM, GM) of the spinal cord (SC) have been reported. Such template can be used as tissue-priors for automated WM/GM segmentation but can also provide a common reference and normalized space for group studies. Here, a new template has been created (AMU40), and accuracy of automatic template-based WM/GM segmentation was quantified. The feasibility of tensor-based morphometry (TBM) for studying voxel-wise morphological differences of SC between young and elderly healthy volunteers was also investigated. Sixty-five healthy subjects were divided into young (n=40, age50years old, mean age 57±5years old) groups and scanned at 3T using an axial high-resolution T2*-weighted sequence. Inhomogeneity correction and affine intensity normalization of the SC and cerebrospinal fluid (CSF) signal intensities across slices were performed prior to both construction of the AMU40 template and WM/GM template-based segmentation. The segmentation was achieved using non-linear spatial normalization of T2*-w MR images to the AMU40 template. Validation of WM/GM segmentations was performed with a leave-one-out procedure by calculating DICE similarity coefficients between manual and automated WM/GM masks. SC morphological differences between young and elderly healthy volunteers were assessed using the same non-linear spatial normalization of the subjects' MRI to a common template, derivation of the Jacobian determinant maps from the warping fields, and a TBM analysis. Results demonstrated robust WM/GM automated segmentation, with mean DICE values greater than 0.8. Concerning the TBM analysis, an anterior GM atrophy was highlighted in elderly volunteers, demonstrating thereby, for the first time, the feasibility of studying local structural alterations in the SC using tensor-based morphometry. This holds great promise for studies of morphological impairment occurring in several central nervous system
An introduction to tensors and group theory for physicists
Jeevanjee, Nadir
2015-01-01
The second edition of this highly praised textbook provides an introduction to tensors, group theory, and their applications in classical and quantum physics. Both intuitive and rigorous, it aims to demystify tensors by giving the slightly more abstract but conceptually much clearer definition found in the math literature, and then connects this formulation to the component formalism of physics calculations. New pedagogical features, such as new illustrations, tables, and boxed sections, as well as additional “invitation” sections that provide accessible introductions to new material, offer increased visual engagement, clarity, and motivation for students. Part I begins with linear algebraic foundations, follows with the modern component-free definition of tensors, and concludes with applications to physics through the use of tensor products. Part II introduces group theory, including abstract groups and Lie groups and their associated Lie algebras, then intertwines this material with that of Part...
International Nuclear Information System (INIS)
Smirnov, Yu.F.; Tolstoi, V.N.; Kharitonov, Yu.I.
1993-01-01
The tree technique for the quantum algebra su q (2) developed in an earlier study is used to construct the q analog of the algebra of irreducible tensor operators. The adjoint action of the algebra su q (2) on irreducible tensor operators is discussed, and the adjoint R matrix is introduced. A set of expressions is obtained for the matrix elements of various irreducible tensor operators and combinations of them. As an application, the recursion relations for the Clebsch-Gordan and Racah coefficients of the algebra su q (2) are derived. 16 refs
Oishi, Kenichi; Chang, Linda; Huang, Hao
2018-04-03
The baby brain is constantly changing due to its active neurodevelopment, and research into the baby brain is one of the frontiers in neuroscience. To help guide neuroscientists and clinicians in their investigation of this frontier, maps of the baby brain, which contain a priori knowledge about neurodevelopment and anatomy, are essential. "Brain atlas" in this review refers to a 3D-brain image with a set of reference labels, such as a parcellation map, as the anatomical reference that guides the mapping of the brain. Recent advancements in scanners, sequences, and motion control methodologies enable the creation of various types of high-resolution baby brain atlases. What is becoming clear is that one atlas is not sufficient to characterize the existing knowledge about the anatomical variations, disease-related anatomical alterations, and the variations in time-dependent changes. In this review, the types and roles of the human baby brain MRI atlases that are currently available are described and discussed, and future directions in the field of developmental neuroscience and its clinical applications are proposed. The potential use of disease-based atlases to characterize clinically relevant information, such as clinical labels, in addition to conventional anatomical labels, is also discussed. Copyright © 2018. Published by Elsevier Inc.
Typesafe Abstractions for Tensor Operations
Chen, Tongfei
2017-01-01
We propose a typesafe abstraction to tensors (i.e. multidimensional arrays) exploiting the type-level programming capabilities of Scala through heterogeneous lists (HList), and showcase typesafe abstractions of common tensor operations and various neural layers such as convolution or recurrent neural networks. This abstraction could lay the foundation of future typesafe deep learning frameworks that runs on Scala/JVM.
Indicial tensor manipulation on MACSYMA
International Nuclear Information System (INIS)
Bogen, R.A.; Pavelle, R.
1977-01-01
A new computational tool for physical calculations is described. It is the first computer system capable of performing indicial tensor calculus (as opposed to component tensor calculus). It is now operational on the symbolic manipulation system MACSYMA. The authors outline the capabilities of the system and describe some of the physical problems considered as well as others being examined at this time. (Auth.)
Topological b-hadron decay reconstruction and application for heavy-flavour jet tagging in ATLAS
Gilles, Geoffrey; The ATLAS collaboration
2017-01-01
The identification of jets originating from the hadronisation of heavy-flavour quarks represents a key ingredient in the physics program of the ATLAS experiment. Exploiting the topological structure of weak b- and c-hadron decays, the multi-vertex finder algorithm - JetFitter - tries to reconstruct the full b-hadron decay chain inside b-jets and provides a complementary approach to conventional secondary vertex finder algorithms. Based on the hypothesis that the primary and displaced b- and c-hadron decay vertices lie on a common line approximating the b-hadron flight direction, an extension of the Kalman Filter formalism for vertex reconstruction implemented in JetFitter allows to solve this pattern recognition problem. Detailed information on the reconstructed decay cascades is then used to identify and discriminate heavy-flavour jets. This poster presents the principle of this algorithm and its performance in the context of a recent optimization campaign performed in view of the 2017 LHC data-taking by the...
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
International Nuclear Information System (INIS)
Somogyi, A.J.
1976-09-01
The paper proves that it is possible to interpret the experimental results of the Musala experiment as being consequences of a vector anisotropy with maximum in the direction of the galactic centre and a tensor anisotropy with principal axes in the physically plausible directions of the galactic arm, the normal direction of the galactic plane and the direction perpendicular them, respectively. It is underlined that the interpretation is not the only possible one and, in addition to this, statistical errors are rather large. The results favour the galactic origin of the particles concerned (E=6x10 13 eV). (Sz.N.Z.)
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
Bates, R.; Berry, S.; Berthoud, J.; Bitadze, A.; Bonneau, P.; Botelho-Direito, J.; Bousson, N.; Boyd, G.; Bozza, G.; Da Riva, E.; Degeorge, C.; DiGirolamo, B.; Doubek, M.; Godlewski, J.; Hallewell, G.; Katunin, S.; Lombard, D.; Mathieu, M.; McMahon, S.; Nagai, K.; Perez-Rodriguez, E.; Rossi, C.; Rozanov, A.; Vacek, V.; Vitek, M.; Zwalinski, L.
2013-01-01
Precision sound velocity measurements can simultaneously determine binary gas composition and flow. We have developed an analyzer with custom electronics, currently in use in the ATLAS inner detector, with numerous potential applications. The instrument has demonstrated ~0.3% mixture precision for C3F8/C2F6 mixtures and < 10-4 resolution for N2/C3F8 mixtures. Moderate and high flow versions of the instrument have demonstrated flow resolutions of +/- 2% F.S. for flows up to 250 l.min-1, and +/- 1.9% F.S. for linear flow velocities up to 15 ms-1; the latter flow approaching that expected in the vapour return of the thermosiphon fluorocarbon coolant recirculator being built for the ATLAS silicon tracker.
Rajagopalan, Vidya; Scott, Julia; Habas, Piotr A; Kim, Kio; Rousseau, Francois; Glenn, Orit A; Barkovich, A James; Studholme, Colin
2012-11-01
Tensor based morphometry (TBM) is a powerful approach to analyze local structural changes in brain anatomy. However, conventional scalar TBM methods do not completely capture all direction specific volume changes required to model complex changes such as those during brain growth. In this paper, we describe novel TBM descriptors for studying direction-specific changes in a subject population which can be used in conjunction with scalar TBM to analyze local patterns in directionality of volume change during brain development. We also extend the methodology to provide a new approach to mapping directional asymmetry in deformation tensors associated with the emergence of structural asymmetry in the developing brain. We illustrate the use of these methods by studying developmental patterns in the human fetal brain, in vivo. Results show that fetal brain development exhibits a distinct spatial pattern of anisotropic growth. The most significant changes in the directionality of growth occur in the cortical plate at major sulci. Our analysis also detected directional growth asymmetry in the peri-Sylvian region and the medial frontal lobe of the fetal brain. Copyright © 2012 Elsevier Inc. All rights reserved.
Rodríguez Cardozo, Félix; Hjörleifsdóttir, Vala; Caló, Marco
2017-04-01
Moment tensor inversions for intermediate and small earthquakes (M. < 4.5) are challenging as they principally excite relatively short period seismic waves that interact strongly with local heterogeneities. Incorporating detailed regional 3D velocity models permits obtaining realistic synthetic seismograms and recover the seismic source parameters these smaller events. Two 3D regional velocity models have recently been developed for Mexico, using surface waves and seismic noise tomography (Spica et al., 2016; Gaite et al., 2015), which could be used to model the waveforms of intermediate magnitud earthquakes in this region. Such models are parameterized as layered velocity profiles and for some of the profiles, the velocity difference between two layers are considerable. The "jump" in velocities between two layers is inconvenient for some methods and algorithms that calculate synthetic waveforms, in particular for the method that we are using, the spectral element method (SPECFEM3D GLOBE, Komatitsch y Tromp, 2000), when the mesh does not follow the layer boundaries. In order to make the velocity models more easily implementec in SPECFEM3D GLOBE it is neccesary to apply a homogenization algorithm (Capdeville et al., 2015) such that the (now anisotropic) layer velocities are smoothly varying with depth. In this work, we apply a homogenization algorithm to the regional velocity models in México for implementing them in SPECFEM3D GLOBE, calculate synthetic waveforms for intermediate-magnitude earthquakes in México and invert them for the seismic moment tensor.
Directory of Open Access Journals (Sweden)
Dan Yang
2017-04-01
Full Text Available To solve the problem of multi-fault blind source separation (BSS in the case that the observed signals are under-determined, a novel approach for single channel blind source separation (SCBSS based on the improved tensor-based singular spectrum analysis (TSSA is proposed. As the most natural representation of high-dimensional data, tensor can preserve the intrinsic structure of the data to the maximum extent. Thus, TSSA method can be employed to extract the multi-fault features from the measured single-channel vibration signal. However, SCBSS based on TSSA still has some limitations, mainly including unsatisfactory convergence of TSSA in many cases and the number of source signals is hard to accurately estimate. Therefore, the improved TSSA algorithm based on canonical decomposition and parallel factors (CANDECOMP/PARAFAC weighted optimization, namely CP-WOPT, is proposed in this paper. CP-WOPT algorithm is applied to process the factor matrix using a first-order optimization approach instead of the original least square method in TSSA, so as to improve the convergence of this algorithm. In order to accurately estimate the number of the source signals in BSS, EMD-SVD-BIC (empirical mode decomposition—singular value decomposition—Bayesian information criterion method, instead of the SVD in the conventional TSSA, is introduced. To validate the proposed method, we applied it to the analysis of the numerical simulation signal and the multi-fault rolling bearing signals.
National Oceanic and Atmospheric Administration, Department of Commerce — Climatic atlas dated 1985, in Mongolian, with introductory material also in Russian and English. One hundred eight pages in single page PDFs.
Efficient tensor completion for color image and video recovery: Low-rank tensor train
Bengua, Johann A.; Phien, Ho N.; Tuan, Hoang D.; Do, Minh N.
2016-01-01
This paper proposes a novel approach to tensor completion, which recovers missing entries of data represented by tensors. The approach is based on the tensor train (TT) rank, which is able to capture hidden information from tensors thanks to its definition from a well-balanced matricization scheme. Accordingly, new optimization formulations for tensor completion are proposed as well as two new algorithms for their solution. The first one called simple low-rank tensor completion via tensor tra...
Random SU(2) invariant tensors
Li, Youning; Han, Muxin; Ruan, Dong; Zeng, Bei
2018-04-01
SU(2) invariant tensors are states in the (local) SU(2) tensor product representation but invariant under the global group action. They are of importance in the study of loop quantum gravity. A random tensor is an ensemble of tensor states. An average over the ensemble is carried out when computing any physical quantities. The random tensor exhibits a phenomenon known as ‘concentration of measure’, which states that for any bipartition the average value of entanglement entropy of its reduced density matrix is asymptotically the maximal possible as the local dimensions go to infinity. We show that this phenomenon is also true when the average is over the SU(2) invariant subspace instead of the entire space for rank-n tensors in general. It is shown in our earlier work Li et al (2017 New J. Phys. 19 063029) that the subleading correction of the entanglement entropy has a mild logarithmic divergence when n = 4. In this paper, we show that for n > 4 the subleading correction is not divergent but a finite number. In some special situation, the number could be even smaller than 1/2, which is the subleading correction of random state over the entire Hilbert space of tensors.
Motion Detection in Ultrasound Image-Sequences Using Tensor Voting
Inba, Masafumi; Yanagida, Hirotaka; Tamura, Yasutaka
2008-05-01
Motion detection in ultrasound image sequences using tensor voting is described. We have been developing an ultrasound imaging system adopting a combination of coded excitation and synthetic aperture focusing techniques. In our method, frame rate of the system at distance of 150 mm reaches 5000 frame/s. Sparse array and short duration coded ultrasound signals are used for high-speed data acquisition. However, many artifacts appear in the reconstructed image sequences because of the incompleteness of the transmitted code. To reduce the artifacts, we have examined the application of tensor voting to the imaging method which adopts both coded excitation and synthetic aperture techniques. In this study, the basis of applying tensor voting and the motion detection method to ultrasound images is derived. It was confirmed that velocity detection and feature enhancement are possible using tensor voting in the time and space of simulated ultrasound three-dimensional image sequences.
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...
A General Sparse Tensor Framework for Electronic Structure Theory.
Manzer, Samuel; Epifanovsky, Evgeny; Krylov, Anna I; Head-Gordon, Martin
2017-03-14
Linear-scaling algorithms must be developed in order to extend the domain of applicability of electronic structure theory to molecules of any desired size. However, the increasing complexity of modern linear-scaling methods makes code development and maintenance a significant challenge. A major contributor to this difficulty is the lack of robust software abstractions for handling block-sparse tensor operations. We therefore report the development of a highly efficient symbolic block-sparse tensor library in order to provide access to high-level software constructs to treat such problems. Our implementation supports arbitrary multi-dimensional sparsity in all input and output tensors. We avoid cumbersome machine-generated code by implementing all functionality as a high-level symbolic C++ language library and demonstrate that our implementation attains very high performance for linear-scaling sparse tensor contractions.
DEFF Research Database (Denmark)
Nielsen, Søren Føns Vind; Mørup, Morten
2014-01-01
Non-negative Tensor Factorization (NTF) has become a prominent tool for analyzing high dimensional multi-way structured data. In this paper we set out to analyze gene expression across brain regions in multiple subjects based on data from the Allen Human Brain Atlas [1] with more than 40 % data m...
Chin, Alex
Singlet fission (SF) is an ultrafast process in which a singlet exciton spontaneously converts into a pair of entangled triplet excitons on neighbouring organic molecules. As a mechanism of multiple exciton generation, it has been suggested as a way to increase the efficiency of organic photovoltaic devices, and its underlying photophysics across a wide range of molecules and materials has attracted significant theoretical attention. Recently, a number of studies using ultrafast nonlinear optics have underscored the importance of intramolecular vibrational dynamics in efficient SF systems, prompting a need for methods capable of simulating open quantum dynamics in the presence of highly structured and strongly coupled environments. Here, a combination of ab initio electronic structure techniques and a new tensor-network methodology for simulating open vibronic dynamics is presented and applied to a recently synthesised dimer of pentacene (DP-Mes). We show that ultrafast (300 fs) SF in this system is driven entirely by symmetry breaking vibrations, and our many-body approach enables the real-time identification and tracking of the ''functional' vibrational dynamics and the role of the ''bath''-like parts of the environment. Deeper analysis of the emerging wave functions points to interesting links between the time at which parts of the environment become relevant to the SF process and the optimal topology of the tensor networks, highlighting the additional insight provided by moving the problem into the natural language of correlated quantum states and how this could lead to simulations of much larger multichromophore systems Supported by The Winton Programme for the Physics of Sustainability.
Energy Technology Data Exchange (ETDEWEB)
Wang, Yuqing [Department of Radiology, West China Hospital, Sichuan University, Sichuan 610041 (China); CAS Key Laboratory for Biomedical Effects of Nanomaterials and Nanosafety, National Center for Nanoscience and Technology of China, Beijing 100190 (China); Cai, Wei [Department of Radiology, West China Hospital, Sichuan University, Sichuan 610041 (China); Department of Radiology, Beijing Jishuitan Hospital, 4th Clinical Medical College of Peking University, Beijing 100035 (China); Wang, Lei [Department of Radiology, West China Hospital, Sichuan University, Sichuan 610041 (China); Xia, Rui [Department of Radiology, West China Hospital, Sichuan University, Sichuan 610041 (China); Department of Radiology, The First Affiliated Hospital, Chongqing Medical University, Chongqing 400016 (China); Chen, Wei [Department of Radiology, West China Hospital, Sichuan University, Sichuan 610041 (China); Department of Radiology, The First Affiliated Hospital of Kunming Medical University, Yunnan 650032 (China); Zheng, Jie [Mallinckrodt Institute of Radiology, School of Medicine, Washington University, St. Louis, MO 63110 (United States); Gao, Fabao [Department of Radiology, West China Hospital, Sichuan University, Sichuan 610041 (China)
2016-11-01
To understand microstructural changes after myocardial infarction (MI), we evaluated myocardial fibers of rhesus monkeys during acute or chronic MI, and identified the differences of myocardial fibers between acute and chronic MI. Six fixed hearts of rhesus monkeys with left anterior descending coronary artery ligation for 1 hour or 84 days were scanned by diffusion tensor magnetic resonance imaging (MRI) to measure apparent diffusion coefficient (ADC), fractional anisotropy (FA) and helix angle (HA). Comparing with acute MI monkeys (FA: 0.59 ± 0.02; ADC: 5.0 ± 0.6 × 10{sup -4} mm{sup 2}/s; HA: 94.5 ± 4.4°), chronic MI monkeys showed remarkably decreased FA value (0.26 ± 0.03), increased ADC value (7.8 ± 0.8 × 10{sup -4}mm{sup 2}/s), decreased HA transmural range (49.5 ± 4.6°) and serious defects on endocardium in infarcted regions. The HA in infarcted regions shifted to more components of negative left-handed helix in chronic MI monkeys (-38.3 ± 5.0°–11.2 ± 4.3°) than in acute MI monkeys (-41.4 ± 5.1°–53.1 ± 3.7°), but the HA in remote regions shifted to more components of positive right-handed helix in chronic MI monkeys (-43.8 ± 2.7°–66.5 ± 4.9°) than in acute MI monkeys (-59.5 ± 3.4°–64.9 ± 4.3°). Diffusion tensor MRI method helps to quantify differences of mechanical microstructure and water diffusion of myocardial fibers between acute and chronic MI monkey's models.
Energy Technology Data Exchange (ETDEWEB)
Wang, Yu Qing; Cai, Wei; Wang, Lei; Xia, Rui; Chen, Wei; Zheng, Jie [Dept. of Radiology, West China Hospital, Sichuan University, Sichuan (China); Gao, Fabao [Mallinckrodt Institute of Radiology, School of Medicine, Washington University, St. Louis (United States)
2016-09-15
To understand microstructural changes after myocardial infarction (MI), we evaluated myocardial fibers of rhesus monkeys during acute or chronic MI, and identified the differences of myocardial fibers between acute and chronic MI. Six fixed hearts of rhesus monkeys with left anterior descending coronary artery ligation for 1 hour or 84 days were scanned by diffusion tensor magnetic resonance imaging (MRI) to measure apparent diffusion coefficient (ADC), fractional anisotropy (FA) and helix angle (HA). Comparing with acute MI monkeys (FA: 0.59 ± 0.02; ADC: 5.0 ± 0.6 × 10{sup -4} mm{sup 2}/s; HA: 94.5 ± 4.4°), chronic MI monkeys showed remarkably decreased FA value (0.26 ± 0.03), increased ADC value (7.8 ± 0.8 × 10{sup -4} mm{sup 2}/s), decreased HA transmural range (49.5 ± 4.6°) and serious defects on endocardium in infarcted regions. The HA in infarcted regions shifted to more components of negative left-handed helix in chronic MI monkeys (-38.3 ± 5.0°–11.2 ± 4.3°) than in acute MI monkeys (-41.4 ± 5.1°–53.1 ± 3.7°), but the HA in remote regions shifted to more components of positive right-handed helix in chronic MI monkeys (-43.8 ± 2.7°–66.5 ± 4.9°) than in acute MI monkeys (-59.5 ± 3.4°–64.9 ± 4.3°). Diffusion tensor MRI method helps to quantify differences of mechanical microstructure and water diffusion of myocardial fibers between acute and chronic MI monkey's models.
International Nuclear Information System (INIS)
Wang, Yu Qing; Cai, Wei; Wang, Lei; Xia, Rui; Chen, Wei; Zheng, Jie; Gao, Fabao
2016-01-01
To understand microstructural changes after myocardial infarction (MI), we evaluated myocardial fibers of rhesus monkeys during acute or chronic MI, and identified the differences of myocardial fibers between acute and chronic MI. Six fixed hearts of rhesus monkeys with left anterior descending coronary artery ligation for 1 hour or 84 days were scanned by diffusion tensor magnetic resonance imaging (MRI) to measure apparent diffusion coefficient (ADC), fractional anisotropy (FA) and helix angle (HA). Comparing with acute MI monkeys (FA: 0.59 ± 0.02; ADC: 5.0 ± 0.6 × 10 -4 mm 2 /s; HA: 94.5 ± 4.4°), chronic MI monkeys showed remarkably decreased FA value (0.26 ± 0.03), increased ADC value (7.8 ± 0.8 × 10 -4 mm 2 /s), decreased HA transmural range (49.5 ± 4.6°) and serious defects on endocardium in infarcted regions. The HA in infarcted regions shifted to more components of negative left-handed helix in chronic MI monkeys (-38.3 ± 5.0°–11.2 ± 4.3°) than in acute MI monkeys (-41.4 ± 5.1°–53.1 ± 3.7°), but the HA in remote regions shifted to more components of positive right-handed helix in chronic MI monkeys (-43.8 ± 2.7°–66.5 ± 4.9°) than in acute MI monkeys (-59.5 ± 3.4°–64.9 ± 4.3°). Diffusion tensor MRI method helps to quantify differences of mechanical microstructure and water diffusion of myocardial fibers between acute and chronic MI monkey's models
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
Colored Tensor Models - a Review
Directory of Open Access Journals (Sweden)
Razvan Gurau
2012-04-01
Full Text Available Colored tensor models have recently burst onto the scene as a promising conceptual and computational tool in the investigation of problems of random geometry in dimension three and higher. We present a snapshot of the cutting edge in this rapidly expanding research field. Colored tensor models have been shown to share many of the properties of their direct ancestor, matrix models, which encode a theory of fluctuating two-dimensional surfaces. These features include the possession of Feynman graphs encoding topological spaces, a 1/N expansion of graph amplitudes, embedded matrix models inside the tensor structure, a resumable leading order with critical behavior and a continuum large volume limit, Schwinger-Dyson equations satisfying a Lie algebra (akin to the Virasoro algebra in two dimensions, non-trivial classical solutions and so on. In this review, we give a detailed introduction of colored tensor models and pointers to current and future research directions.
Tensor 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.
Bayesian CP Factorization of Incomplete Tensors with Automatic Rank Determination.
Zhao, Qibin; Zhang, Liqing; Cichocki, Andrzej
2015-09-01
CANDECOMP/PARAFAC (CP) tensor factorization of incomplete data is a powerful technique for tensor completion through explicitly capturing the multilinear latent factors. The existing CP algorithms require the tensor rank to be manually specified, however, the determination of tensor rank remains a challenging problem especially for CP rank . In addition, existing approaches do not take into account uncertainty information of latent factors, as well as missing entries. To address these issues, we formulate CP factorization using a hierarchical probabilistic model and employ a fully Bayesian treatment by incorporating a sparsity-inducing prior over multiple latent factors and the appropriate hyperpriors over all hyperparameters, resulting in automatic rank determination. To learn the model, we develop an efficient deterministic Bayesian inference algorithm, which scales linearly with data size. Our method is characterized as a tuning parameter-free approach, which can effectively infer underlying multilinear factors with a low-rank constraint, while also providing predictive distributions over missing entries. Extensive simulations on synthetic data illustrate the intrinsic capability of our method to recover the ground-truth of CP rank and prevent the overfitting problem, even when a large amount of entries are missing. Moreover, the results from real-world applications, including image inpainting and facial image synthesis, demonstrate that our method outperforms state-of-the-art approaches for both tensor factorization and tensor completion in terms of predictive performance.
ATLAS Software Installation on Supercomputers
Undrus, Alexander; The ATLAS collaboration
2018-01-01
PowerPC and high performance computers (HPC) are important resources for computing in the ATLAS experiment. The future LHC data processing will require more resources than Grid computing, currently using approximately 100,000 cores at well over 100 sites, can provide. Supercomputers are extremely powerful as they use resources of hundreds of thousands CPUs joined together. However their architectures have different instruction sets. ATLAS binary software distributions for x86 chipsets do not fit these architectures, as emulation of these chipsets results in huge performance loss. This presentation describes the methodology of ATLAS software installation from source code on supercomputers. The installation procedure includes downloading the ATLAS code base as well as the source of about 50 external packages, such as ROOT and Geant4, followed by compilation, and rigorous unit and integration testing. The presentation reports the application of this procedure at Titan HPC and Summit PowerPC at Oak Ridge Computin...
Ambiguities and symmetry relations associated with fermionic tensor densities
International Nuclear Information System (INIS)
Dallabona, G.; Battistel, O. A.
2004-01-01
We consider the consistent evaluation of perturbative (divergent) Green functions associated with fermionic tensor densities and the derivation of symmetry relations for them. We show that, in spite of current algebra methods being not applicable, it is possible to derive symmetry properties analogous to the Ward identities of vector and axial-vector densities. The proposed method, which is applicable to any previously chosen order of perturbative calculation, gives the same results as those of current algebra when such a tool is applicable. By using a very general calculational strategy, concerning the manipulations and calculations involving divergent Feynman integrals, we evaluate the purely fermionic two-point functions containing tensor vertices and derive their symmetry properties. The present investigation is the first step in the study and characterization of possible anomalies involving fermionic tensor densities, particularly in purely fermionic three-point functions
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.
AGIS: Integration of new technologies used in ATLAS Distributed Computing
Anisenkov, Alexey; Di Girolamo, Alessandro; Alandes Pradillo, Maria
2017-01-01
The variety of the ATLAS Distributed Computing infrastructure requires a central information system to define the topology of computing resources and to store different parameters and configuration data which are needed by various ATLAS software components. The ATLAS Grid Information System (AGIS) is the system designed to integrate configuration and status information about resources, services and topology of the computing infrastructure used by ATLAS Distributed Computing applications and s...
AGIS: Evolution of Distributed Computing Information system for ATLAS
Anisenkov, Alexey; The ATLAS collaboration; Alandes Pradillo, Maria; Karavakis, Edward
2015-01-01
The variety of the ATLAS Computing Infrastructure requires a central information system to define the topology of computing resources and to store the different parameters and configuration data which are needed by the various ATLAS software components. The ATLAS Grid Information System is the system designed to integrate configuration and status information about resources, services and topology of the computing infrastructure used by ATLAS Distributed Computing applications and services.
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.
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.
Mastmeyer, Andre; Wilms, Matthias; Handels, Heinz
2018-03-01
Virtual reality (VR) training simulators of liver needle insertion in the hepatic area of breathing virtual patients often need 4D image data acquisitions as a prerequisite. Here, first a population-based breathing virtual patient 4D atlas is built and second the requirement of a dose-relevant or expensive acquisition of a 4D CT or MRI data set for a new patient can be mitigated by warping the mean atlas motion. The breakthrough contribution of this work is the construction and reuse of population-based, learned 4D motion models.
A system for managing information at ATLAS
International Nuclear Information System (INIS)
Tilbrook, I.R.
1993-01-01
In response to a need for better management of maintenance and document information at the Argonne Tandem-Linear Accelerating System (ATLAS), the ATLAS Information Management System (AIMS) has been created. The system is based on the relational database model. The system's applications use the Alpha-4 relational database management system, a commercially available software package. The system's function and design are described
International Nuclear Information System (INIS)
Kobashigawa, Yoshihiro; Saio, Tomohide; Ushio, Masahiro; Sekiguchi, Mitsuhiro; Yokochi, Masashi; Ogura, Kenji; Inagaki, Fuyuhiko
2012-01-01
Pseudo contact shifts (PCSs) induced by paramagnetic lanthanide ions fixed in a protein frame provide long-range distance and angular information, and are valuable for the structure determination of protein–protein and protein–ligand complexes. We have been developing a lanthanide-binding peptide tag (hereafter LBT) anchored at two points via a peptide bond and a disulfide bond to the target proteins. However, the magnetic susceptibility tensor displays symmetry, which can cause multiple degenerated solutions in a structure calculation based solely on PCSs. Here we show a convenient method for resolving this degeneracy by changing the spacer length between the LBT and target protein. We applied this approach to PCS-based rigid body docking between the FKBP12-rapamycin complex and the mTOR FRB domain, and demonstrated that degeneracy could be resolved using the PCS restraints obtained from two-point anchored LBT with two different spacer lengths. The present strategy will markedly increase the usefulness of two-point anchored LBT for protein complex structure determination.
Energy Technology Data Exchange (ETDEWEB)
Kobashigawa, Yoshihiro; Saio, Tomohide [Hokkaido University, Department of Structural Biology, Faculty of Advanced Life Science (Japan); Ushio, Masahiro [Hokkaido University, Graduate School of Life Science (Japan); Sekiguchi, Mitsuhiro [Astellas Pharma Inc., Analysis and Pharmacokinetics Research Labs, Department of Drug Discovery (Japan); Yokochi, Masashi; Ogura, Kenji; Inagaki, Fuyuhiko, E-mail: finagaki@pharm.hokudai.ac.jp [Hokkaido University, Department of Structural Biology, Faculty of Advanced Life Science (Japan)
2012-05-15
Pseudo contact shifts (PCSs) induced by paramagnetic lanthanide ions fixed in a protein frame provide long-range distance and angular information, and are valuable for the structure determination of protein-protein and protein-ligand complexes. We have been developing a lanthanide-binding peptide tag (hereafter LBT) anchored at two points via a peptide bond and a disulfide bond to the target proteins. However, the magnetic susceptibility tensor displays symmetry, which can cause multiple degenerated solutions in a structure calculation based solely on PCSs. Here we show a convenient method for resolving this degeneracy by changing the spacer length between the LBT and target protein. We applied this approach to PCS-based rigid body docking between the FKBP12-rapamycin complex and the mTOR FRB domain, and demonstrated that degeneracy could be resolved using the PCS restraints obtained from two-point anchored LBT with two different spacer lengths. The present strategy will markedly increase the usefulness of two-point anchored LBT for protein complex structure determination.
International Nuclear Information System (INIS)
2005-01-01
Magnetic Resonance Diffusion Tensor Imaging in the human cervical spinal cord, using an in-house developed DW-EPI sequence in the axial plane, was implemented on a 1.5 T SIGNA ECHO-PLUS GE system of the Silesian Imaging Centre HELIMED, tested on 30 volunteers to gather reference data, and used on patients with cervical spinal cord traumatic injury. Original software was developed to analyse data from DTI experiments. This work is performed in collaboration with Collegium Medicum UJ and Silesian Medical University. Special gradient coils capable of delivering gradients up 500 mT/m, a RF birdcage coil and a life-support system including temperature regulation and monitoring were designed and constructed to do MRI on transgenic mouse heart. A fast MRI cine-like FLASH sequence based on gradient echo was developed. Experiments are now under way, in collaboration with the Department of Pharmacology of the Collegium Medicum, Jagiellonian University to test heart-protecting drugs
Decorated tensor network renormalization for lattice gauge theories and spin foam models
International Nuclear Information System (INIS)
Dittrich, Bianca; Mizera, Sebastian; Steinhaus, Sebastian
2016-01-01
Tensor network techniques have proved to be powerful tools that can be employed to explore the large scale dynamics of lattice systems. Nonetheless, the redundancy of degrees of freedom in lattice gauge theories (and related models) poses a challenge for standard tensor network algorithms. We accommodate for such systems by introducing an additional structure decorating the tensor network. This allows to explicitly preserve the gauge symmetry of the system under coarse graining and straightforwardly interpret the fixed point tensors. We propose and test (for models with finite Abelian groups) a coarse graining algorithm for lattice gauge theories based on decorated tensor networks. We also point out that decorated tensor networks are applicable to other models as well, where they provide the advantage to give immediate access to certain expectation values and correlation functions. (paper)
Decorated tensor network renormalization for lattice gauge theories and spin foam models
Dittrich, Bianca; Mizera, Sebastian; Steinhaus, Sebastian
2016-05-01
Tensor network techniques have proved to be powerful tools that can be employed to explore the large scale dynamics of lattice systems. Nonetheless, the redundancy of degrees of freedom in lattice gauge theories (and related models) poses a challenge for standard tensor network algorithms. We accommodate for such systems by introducing an additional structure decorating the tensor network. This allows to explicitly preserve the gauge symmetry of the system under coarse graining and straightforwardly interpret the fixed point tensors. We propose and test (for models with finite Abelian groups) a coarse graining algorithm for lattice gauge theories based on decorated tensor networks. We also point out that decorated tensor networks are applicable to other models as well, where they provide the advantage to give immediate access to certain expectation values and correlation functions.
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.
Diffusion tensor and diffusion weighted imaging. Pictorial mathematics
Energy Technology Data Exchange (ETDEWEB)
Nakada, Tsutomu [California Univ., Davis, CA (United States)
1995-06-01
A new imaging algorithm for the treatment of a second order apparent diffusion tensor, D{sub app}{sup {xi}} is described. The method calls for only mathematics of images (pictorial mathematics) without necessity of eigenvalues/eigenvectors estimation. Nevertheless, it is capable of extracting properties of D{sub app}{sup {xi}} invariant to observation axes. While trace image is an example of images weighted by invariance of the tensor matrix, three dimensional anisotropy (3DAC) contrast represents the imaging method making use to anisotropic direction of tensor ellipsoid producing color coded contrast of exceptionally high anatomic resolution. Contrary to intuition, the processes require only a simple algorithm directly applicable to clinical magnetic resonance imaging (MRI). As a contrast method which precisely represents physical characteristics of a target tissue, invariant D{sub app}{sup {xi}} images produced by pictorial mathematics possess significant potential for a number of biological and clinical applications. (author).
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....
Simultaneous tensor decomposition and completion using factor priors.
Chen, Yi-Lei; Hsu, Chiou-Ting; Liao, Hong-Yuan Mark
2014-03-01
The success of research on matrix completion is evident in a variety of real-world applications. Tensor completion, which is a high-order extension of matrix completion, has also generated a great deal of research interest in recent years. Given a tensor with incomplete entries, existing methods use either factorization or completion schemes to recover the missing parts. However, as the number of missing entries increases, factorization schemes may overfit the model because of incorrectly predefined ranks, while completion schemes may fail to interpret the model factors. In this paper, we introduce a novel concept: complete the missing entries and simultaneously capture the underlying model structure. To this end, we propose a method called simultaneous tensor decomposition and completion (STDC) that combines a rank minimization technique with Tucker model decomposition. Moreover, as the model structure is implicitly included in the Tucker model, we use factor priors, which are usually known a priori in real-world tensor objects, to characterize the underlying joint-manifold drawn from the model factors. By exploiting this auxiliary information, our method leverages two classic schemes and accurately estimates the model factors and missing entries. We conducted experiments to empirically verify the convergence of our algorithm on synthetic data and evaluate its effectiveness on various kinds of real-world data. The results demonstrate the efficacy of the proposed method and its potential usage in tensor-based applications. It also outperforms state-of-the-art methods on multilinear model analysis and visual data completion tasks.
A locally convergent Jacobi iteration for the tensor singular value problem
Shekhawat, Hanumant Singh; Weiland, Siep
2018-01-01
Multi-linear functionals or tensors are useful in study and analysis multi-dimensional signal and system. Tensor approximation, which has various applications in signal processing and system theory, can be achieved by generalizing the notion of singular values and singular vectors of matrices to
Effect of cocaine on structural changes in brain: MRI volumetry using tensor-based morphometry.
Narayana, Ponnada A; Datta, Sushmita; Tao, Guozhi; Steinberg, Joel L; Moeller, F Gerard
2010-10-01
Magnetic resonance imaging (MRI) was performed in cocaine-dependent subjects to determine the structural changes in brain compared to non-drug using controls. Cocaine-dependent subjects and controls were carefully screened to rule out brain pathology of undetermined origin. Magnetic resonance images were analyzed using tensor-based morphometry (TBM) and voxel-based morphometry (VBM) without and with modulation to adjust for volume changes during normalization. For TBM analysis, unbiased atlases were generated using two different inverse consistent and diffeomorphic nonlinear registration techniques. Two different control groups were used for generating unbiased atlases. Independent of the nonlinear registration technique and normal cohorts used for creating the unbiased atlases, our analysis failed to detect any statistically significant effect of cocaine on brain volumes. These results show that cocaine-dependent subjects do not show differences in regional brain volumes compared to non-drug using controls. Copyright © 2010 Elsevier Ireland Ltd. All rights reserved.
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.
Complete algebraic reduction of one-loop tensor Feynman integrals
International Nuclear Information System (INIS)
Fleischer, J.; Riemann, T.
2011-01-01
We set up a new, flexible approach for the tensor reduction of one-loop Feynman integrals. The 5-point tensor integrals up to rank R=5 are expressed by 4-point tensor integrals of rank R-1, such that the appearance of the inverse 5-point Gram determinant is avoided. The 4-point tensor coefficients are represented in terms of 4-point integrals, defined in d dimensions, 4-2ε≤d≤4-2ε+2(R-1), with higher powers of the propagators. They can be further reduced to expressions which stay free of the inverse 4-point Gram determinants but contain higher-dimensional 4-point integrals with only the first power of scalar propagators, plus 3-point tensor coefficients. A direct evaluation of the higher-dimensional 4-point functions would avoid the appearance of inverse powers of the Gram determinants completely. The simplest approach, however, is to apply here dimensional recurrence relations in order to reduce them to the familiar 2- to 4-point functions in generic dimension d=4-2ε, introducing thereby coefficients with inverse 4-point Gram determinants up to power R for tensors of rank R. For small or vanishing Gram determinants--where this reduction is not applicable--we use analytic expansions in positive powers of the Gram determinants. Improving the convergence of the expansions substantially with Pade approximants we close up to the evaluation of the 4-point tensor coefficients for larger Gram determinants. Finally, some relations are discussed which may be useful for analytic simplifications of Feynman diagrams.
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||.
International Nuclear Information System (INIS)
Tabar, L.; Dean, P.B.
1985-01-01
The illustrated case reports in this teaching atlas cover practically the entire range of possible pathological changes and are based on in-patient case material and 80,000 screening documents. The two basic approaches, - detection and analysis of changes -, are taught comprehensively and in great detail. A systematic procedure for analysing the mammographies, in order to detect even the very least changes, and its practical application is explained using mammographies showing unclear findings at first sight. A system of coordinates is presented which allows precise localisation of the changes. Exercises for practising the technique of identifying the pathological changes round up the methodolical chapters. Additional imaging technical enhancements and detail enlargements are of great help in interpreting the findings. The specific approach adopted for this teaching atlas is a 'reverse procedure', which leaves the beaten track and starts with analysing the mammographies and evaluating the radiographic findings, in order to finally derive the diagnosis. (orig./CB) [de
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
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.
Vilanova, Anna; Burgeth, Bernhard; Visualization and Processing of Tensors and Higher Order Descriptors for Multi-Valued Data
2014-01-01
Arising from the fourth Dagstuhl conference entitled Visualization and Processing of Tensors and Higher Order Descriptors for Multi-Valued Data (2011), this book offers a broad and vivid view of current work in this emerging field. Topics covered range from applications of the analysis of tensor fields to research on their mathematical and analytical properties. Part I, Tensor Data Visualization, surveys techniques for visualization of tensors and tensor fields in engineering, discusses the current state of the art and challenges, and examines tensor invariants and glyph design, including an overview of common glyphs. The second Part, Representation and Processing of Higher-order Descriptors, describes a matrix representation of local phase, outlines mathematical morphological operations techniques, extended for use in vector images, and generalizes erosion to the space of diffusion weighted MRI. Part III, Higher Order Tensors and Riemannian-Finsler Geometry, offers powerful mathematical language to model and...
Development, deployment and operations of ATLAS databases
International Nuclear Information System (INIS)
Vaniachine, A. V.; von der Schmitt, J. G.
2008-01-01
In preparation for ATLAS data taking, a coordinated shift from development towards operations has occurred in ATLAS database activities. In addition to development and commissioning activities in databases, ATLAS is active in the development and deployment (in collaboration with the WLCG 3D project) of the tools that allow the worldwide distribution and installation of databases and related datasets, as well as the actual operation of this system on ATLAS multi-grid infrastructure. We describe development and commissioning of major ATLAS database applications for online and offline. We present the first scalability test results and ramp-up schedule over the initial LHC years of operations towards the nominal year of ATLAS running, when the database storage volumes are expected to reach 6.1 TB for the Tag DB and 1.0 TB for the Conditions DB. ATLAS database applications require robust operational infrastructure for data replication between online and offline at Tier-0, and for the distribution of the offline data to Tier-1 and Tier-2 computing centers. We describe ATLAS experience with Oracle Streams and other technologies for coordinated replication of databases in the framework of the WLCG 3D services
Reciprocal mass tensor : a general form
International Nuclear Information System (INIS)
Roy, C.L.
1978-01-01
Using the results of earlier treatment of wave packets, a general form of reciprocal mass tensor has been obtained. The elements of this tensor are seen to be dependent on momentum as well as space coordinates of the particle under consideration. The conditions under which the tensor would reduce to the usual space-independent form, are discussed and the impact of the space-dependence of this tensor on the motion of Bloch electrons, is examined. (author)
A new deteriorated energy-momentum tensor
International Nuclear Information System (INIS)
Duff, M.J.
1982-01-01
The stress-tensor of a scalar field theory is not unique because of the possibility of adding an 'improvement term'. In supersymmetric field theories the stress-tensor will appear in a super-current multiplet along with the sypersymmetry current. The general question of the supercurrent multiplet for arbitrary deteriorated stress tensors and their relationship to supercurrent multiplets for models with gauge antisymmetric tensors is answered for various models of N = 1, 2 and 4 supersymmetry. (U.K.)
Tensor-based spatiotemporal saliency detection
Dou, Hao; Li, Bin; Deng, Qianqian; Zhang, LiRui; Pan, Zhihong; Tian, Jinwen
2018-03-01
This paper proposes an effective tensor-based spatiotemporal saliency computation model for saliency detection in videos. First, we construct the tensor representation of video frames. Then, the spatiotemporal saliency can be directly computed by the tensor distance between different tensors, which can preserve the complete temporal and spatial structure information of object in the spatiotemporal domain. Experimental results demonstrate that our method can achieve encouraging performance in comparison with the state-of-the-art methods.
Akkerman, Erik M.
2010-01-01
Both in diffusion tensor imaging (DTI) and in generalized diffusion tensor imaging (GDTI) the relation between the diffusion tensor and the measured apparent diffusion coefficients is given by a tensorial equation, which needs to be inverted in order to solve the diffusion tensor. The traditional
International Nuclear Information System (INIS)
Sanchez, M.; Perez, J.; Martorell, S.; Carlos, S.; Villanueva, J. F.; Sanchez, F.; Queral, C.; Rebollo, M. J.; Rivas-Lewicky, J.; Verdu, G.; Gallardo, S.; Miro, R.; Querol, A.; Munoz-Cobo, J. L.; Escriva, A.; Berna, C.; Reventos, F.; Freixa, J.; Martinez, V.
2016-01-01
CSN involvement in different international NEA experimental TH programmes has outlined the scope for a new period of CAMP-Espana activities, currently focused on the: -Analysis, simulation and investigation of specific safety aspects of PKL3/OECD and ATLAS/OECD experiments. -Analysis of applicability and/or extension of the results in these projects to the safety, operation or availability of the Spanish nuclear power plants. Both objective are carried out by simulating experiments and plant application with the last available versions of NRC TH codes (RELAP5 or TRACE). A CAMP in kind contribution (NUREG/IA) is aimed as final result of both types of analyses. Five different national research groups (from Technical Universities of Madrid, Valencia and Cataluna) ate carrying out the development of these activities. (Author)
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.
Directory of Open Access Journals (Sweden)
Raúl Hernández-García
2015-07-01
Conclusion: The ATLAS score is a potentially useful tool for the routine evaluation of patients at the time of C. difficile infection diagnosis. At 30 days post-diagnosis, patients with a score of ≤3 points had 100% survival while all of those with scores ≥8 died. Patients with scores between 4 and 7 points had a greater probability of colectomy with an overall cure rate of 70.1%.
An efficient method for tensor voting using steerable filters
Franken, E.M.; Almsick, van M.A.; Rongen, P.M.J.; Florack, L.M.J.; Haar Romenij, ter B.M.; Leonardis, A.; Bischof, H; Pinz, A.
2006-01-01
In many image analysis applications there is a need to extract curves in noisy images. To achieve a more robust extraction, one can exploit correlations of oriented features over a spatial context in the image. Tensor voting is an existing technique to extract features in this way. In this paper, we
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
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.
Cheatham, Susan; The ATLAS collaboration
2016-01-01
The ATLAS outreach team is very active, promoting particle physics to a broad range of audiences including physicists, general public, policy makers, students and teachers, and media. A selection of current outreach activities and new projects will be presented. Recent highlights include the new ATLAS public website and ATLAS Open Data, the very recent public release of 1 fb-1 of ATLAS data.
Anthony, Katarina
2018-01-01
Winners of the ATLAS Thesis Award were presented with certificates and glass cubes during a ceremony on 22 February, 2018. They are pictured here with Karl Jakobs (ATLAS Spokesperson), Max Klein (ATLAS Collaboration Board Chair) and Katsuo Tokushuku (ATLAS Collaboration Board Deputy Chair).
Tensor Completion for Estimating Missing Values in Visual Data
Liu, Ji
2012-01-25
In this paper, we propose an algorithm to estimate missing values in tensors of visual data. The values can be missing due to problems in the acquisition process or because the user manually identified unwanted outliers. Our algorithm works even with a small amount of samples and it can propagate structure to fill larger missing regions. Our methodology is built on recent studies about matrix completion using the matrix trace norm. The contribution of our paper is to extend the matrix case to the tensor case by proposing the first definition of the trace norm for tensors and then by building a working algorithm. First, we propose a definition for the tensor trace norm that generalizes the established definition of the matrix trace norm. Second, similarly to matrix completion, the tensor completion is formulated as a convex optimization problem. Unfortunately, the straightforward problem extension is significantly harder to solve than the matrix case because of the dependency among multiple constraints. To tackle this problem, we developed three algorithms: simple low rank tensor completion (SiLRTC), fast low rank tensor completion (FaLRTC), and high accuracy low rank tensor completion (HaLRTC). The SiLRTC algorithm is simple to implement and employs a relaxation technique to separate the dependant relationships and uses the block coordinate descent (BCD) method to achieve a globally optimal solution; the FaLRTC algorithm utilizes a smoothing scheme to transform the original nonsmooth problem into a smooth one and can be used to solve a general tensor trace norm minimization problem; the HaLRTC algorithm applies the alternating direction method of multipliers (ADMMs) to our problem. Our experiments show potential applications of our algorithms and the quantitative evaluation indicates that our methods are more accurate and robust than heuristic approaches. The efficiency comparison indicates that FaLTRC and HaLRTC are more efficient than SiLRTC and between Fa
Tensor Completion for Estimating Missing Values in Visual Data
Liu, Ji; Musialski, Przemyslaw; Wonka, Peter; Ye, Jieping
2012-01-01
In this paper, we propose an algorithm to estimate missing values in tensors of visual data. The values can be missing due to problems in the acquisition process or because the user manually identified unwanted outliers. Our algorithm works even with a small amount of samples and it can propagate structure to fill larger missing regions. Our methodology is built on recent studies about matrix completion using the matrix trace norm. The contribution of our paper is to extend the matrix case to the tensor case by proposing the first definition of the trace norm for tensors and then by building a working algorithm. First, we propose a definition for the tensor trace norm that generalizes the established definition of the matrix trace norm. Second, similarly to matrix completion, the tensor completion is formulated as a convex optimization problem. Unfortunately, the straightforward problem extension is significantly harder to solve than the matrix case because of the dependency among multiple constraints. To tackle this problem, we developed three algorithms: simple low rank tensor completion (SiLRTC), fast low rank tensor completion (FaLRTC), and high accuracy low rank tensor completion (HaLRTC). The SiLRTC algorithm is simple to implement and employs a relaxation technique to separate the dependant relationships and uses the block coordinate descent (BCD) method to achieve a globally optimal solution; the FaLRTC algorithm utilizes a smoothing scheme to transform the original nonsmooth problem into a smooth one and can be used to solve a general tensor trace norm minimization problem; the HaLRTC algorithm applies the alternating direction method of multipliers (ADMMs) to our problem. Our experiments show potential applications of our algorithms and the quantitative evaluation indicates that our methods are more accurate and robust than heuristic approaches. The efficiency comparison indicates that FaLTRC and HaLRTC are more efficient than SiLRTC and between Fa
Tensor completion for estimating missing values in visual data.
Liu, Ji; Musialski, Przemyslaw; Wonka, Peter; Ye, Jieping
2013-01-01
In this paper, we propose an algorithm to estimate missing values in tensors of visual data. The values can be missing due to problems in the acquisition process or because the user manually identified unwanted outliers. Our algorithm works even with a small amount of samples and it can propagate structure to fill larger missing regions. Our methodology is built on recent studies about matrix completion using the matrix trace norm. The contribution of our paper is to extend the matrix case to the tensor case by proposing the first definition of the trace norm for tensors and then by building a working algorithm. First, we propose a definition for the tensor trace norm that generalizes the established definition of the matrix trace norm. Second, similarly to matrix completion, the tensor completion is formulated as a convex optimization problem. Unfortunately, the straightforward problem extension is significantly harder to solve than the matrix case because of the dependency among multiple constraints. To tackle this problem, we developed three algorithms: simple low rank tensor completion (SiLRTC), fast low rank tensor completion (FaLRTC), and high accuracy low rank tensor completion (HaLRTC). The SiLRTC algorithm is simple to implement and employs a relaxation technique to separate the dependent relationships and uses the block coordinate descent (BCD) method to achieve a globally optimal solution; the FaLRTC algorithm utilizes a smoothing scheme to transform the original nonsmooth problem into a smooth one and can be used to solve a general tensor trace norm minimization problem; the HaLRTC algorithm applies the alternating direction method of multipliers (ADMMs) to our problem. Our experiments show potential applications of our algorithms and the quantitative evaluation indicates that our methods are more accurate and robust than heuristic approaches. The efficiency comparison indicates that FaLTRC and HaLRTC are more efficient than SiLRTC and between FaLRTC an
The Next Generation ATLAS Production System
Borodin, Mikhail; The ATLAS collaboration; Golubkov, Dmitry; Klimentov, Alexei; Maeno, Tadashi; Mashinistov, Ruslan; Vaniachine, Alexandre
2015-01-01
The ATLAS experiment at LHC data processing and simulation grows continuously, as more data and more use cases emerge. For data processing the ATLAS experiment adopted the data transformation approach, where software applications transform the input data into outputs. In the ATLAS production system, each data transformation is represented by a task, a collection of many jobs, dynamically submitted by the ATLAS workload management system (PanDA/JEDI) and executed on the Grid, clouds and supercomputers. Patterns in ATLAS data transformation workflows composed of many tasks provided a scalable production system framework for template definitions of the many-tasks workflows. User interface and system logic of these workflows are being implemented in the Database Engine for Tasks (DEFT). Such development required using modern computing technologies and approaches. We report technical details of this development: database implementation, server logic and Web user interface technologies.
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.
ProstAtlas: A digital morphologic atlas of the prostate
International Nuclear Information System (INIS)
Betrouni, N.; Iancu, A.; Puech, P.; Mordon, S.; Makni, N.
2012-01-01
Computer-aided medical interventions and medical robotics for prostate cancer have known an increasing interest and research activity. However before the routine deployment of these procedures in clinical practice becomes a reality, in vivo and in silico validations must be undertaken. In this study, we developed a digital morphologic atlas of the prostate. We were interested by the gland, the peripheral zone and the central gland. Starting from an image base collected from 30 selected patients, a mean shape and most important deformations for each structure were deduced using principal component analysis. The usefulness of this atlas was highlighted in two applications: image simulation and physical phantom design
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...
Tensor Network Wavefunctions for Topological Phases
Ware, Brayden Alexander
intrinsically fermionic topological phases, i.e. topological phases contructed out of fermions with a nontrivial response to fermion parity defects. A zero correlation length wavefunction and a commuting projector Hamiltonian that realizes this wavefunction as its ground state are constructed. Using an appropriate generalization of the minimally entangled states method for extraction of topological order from the ground states on a torus to the intrinsically fermionic case, we fully characterize the corresponding topological order as Ising x (px - ipy). We argue that this phase can be captured using fermionic tensor networks, expanding the applicability of tensor network methods.
CSIR Research Space (South Africa)
Linzer, LM
2002-03-01
Full Text Available analysis of failure mechanisms, development of moment tensor inversion program and verification of the hybrid moment tensor inversion technique. Geomechanical and geotechnical analyses were undertaken to determine the rock mass condition of in situ... on the mine using the ISS software and then reprocessed using AURA, the seismogram processing analysis program written by CSIR Miningtek. It was found that the magnitudes computed using AURA were substantially larger than those computed using the ISS...
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.
Ghose, Ranajeet; Fushman, David; Cowburn, David
2001-04-01
In this paper we present a method for determining the rotational diffusion tensor from NMR relaxation data using a combination of approximate and exact methods. The approximate method, which is computationally less intensive, computes values of the principal components of the diffusion tensor and estimates the Euler angles, which relate the principal axis frame of the diffusion tensor to the molecular frame. The approximate values of the principal components are then used as starting points for an exact calculation by a downhill simplex search for the principal components of the tensor over a grid of the space of Euler angles relating the diffusion tensor frame to the molecular frame. The search space of Euler angles is restricted using the tensor orientations calculated using the approximate method. The utility of this approach is demonstrated using both simulated and experimental relaxation data. A quality factor that determines the extent of the agreement between the measured and predicted relaxation data is provided. This approach is then used to estimate the relative orientation of SH3 and SH2 domains in the SH(32) dual-domain construct of Abelson kinase complexed with a consolidated ligand.
Ghose, R; Fushman, D; Cowburn, D
2001-04-01
In this paper we present a method for determining the rotational diffusion tensor from NMR relaxation data using a combination of approximate and exact methods. The approximate method, which is computationally less intensive, computes values of the principal components of the diffusion tensor and estimates the Euler angles, which relate the principal axis frame of the diffusion tensor to the molecular frame. The approximate values of the principal components are then used as starting points for an exact calculation by a downhill simplex search for the principal components of the tensor over a grid of the space of Euler angles relating the diffusion tensor frame to the molecular frame. The search space of Euler angles is restricted using the tensor orientations calculated using the approximate method. The utility of this approach is demonstrated using both simulated and experimental relaxation data. A quality factor that determines the extent of the agreement between the measured and predicted relaxation data is provided. This approach is then used to estimate the relative orientation of SH3 and SH2 domains in the SH(32) dual-domain construct of Abelson kinase complexed with a consolidated ligand. Copyright 2001 Academic Press.
AGIS: Integration of new technologies used in ATLAS Distributed Computing
AUTHOR|(INSPIRE)INSPIRE-00291854; The ATLAS collaboration; Di Girolamo, Alessandro; Alandes Pradillo, Maria
2017-01-01
The variety of the ATLAS Distributed Computing infrastructure requires a central information system to define the topology of computing resources and to store different parameters and configuration data which are needed by various ATLAS software components. The ATLAS Grid Information System (AGIS) is the system designed to integrate configuration and status information about resources, services and topology of the computing infrastructure used by ATLAS Distributed Computing applications and services. Being an intermediate middleware system between clients and external information sources (like central BDII, GOCDB, MyOSG), AGIS defines the relations between experiment specific used resources and physical distributed computing capabilities. Being in production during LHC Runl AGIS became the central information system for Distributed Computing in ATLAS and it is continuously evolving to fulfil new user requests, enable enhanced operations and follow the extension of the ATLAS Computing model. The ATLAS Computin...
Extended vector-tensor theories
Energy Technology Data Exchange (ETDEWEB)
Kimura, Rampei; Naruko, Atsushi; Yoshida, Daisuke, E-mail: rampei@th.phys.titech.ac.jp, E-mail: naruko@th.phys.titech.ac.jp, E-mail: yoshida@th.phys.titech.ac.jp [Department of Physics, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, Tokyo 152-8551 (Japan)
2017-01-01
Recently, several extensions of massive vector theory in curved space-time have been proposed in many literatures. In this paper, we consider the most general vector-tensor theories that contain up to two derivatives with respect to metric and vector field. By imposing a degeneracy condition of the Lagrangian in the context of ADM decomposition of space-time to eliminate an unwanted mode, we construct a new class of massive vector theories where five degrees of freedom can propagate, corresponding to three for massive vector modes and two for massless tensor modes. We find that the generalized Proca and the beyond generalized Proca theories up to the quartic Lagrangian, which should be included in this formulation, are degenerate theories even in curved space-time. Finally, introducing new metric and vector field transformations, we investigate the properties of thus obtained theories under such transformations.
Scalar-tensor linear inflation
Energy Technology Data Exchange (ETDEWEB)
Artymowski, Michał [Institute of Physics, Jagiellonian University, Łojasiewicza 11, 30-348 Kraków (Poland); Racioppi, Antonio, E-mail: Michal.Artymowski@uj.edu.pl, E-mail: Antonio.Racioppi@kbfi.ee [National Institute of Chemical Physics and Biophysics, Rävala 10, 10143 Tallinn (Estonia)
2017-04-01
We investigate two approaches to non-minimally coupled gravity theories which present linear inflation as attractor solution: a) the scalar-tensor theory approach, where we look for a scalar-tensor theory that would restore results of linear inflation in the strong coupling limit for a non-minimal coupling to gravity of the form of f (φ) R /2; b) the particle physics approach, where we motivate the form of the Jordan frame potential by loop corrections to the inflaton field. In both cases the Jordan frame potentials are modifications of the induced gravity inflationary scenario, but instead of the Starobinsky attractor they lead to linear inflation in the strong coupling limit.
Yiu, Chang-li; Wilde, Carroll O.
Vector analysis is viewed to play a key role in many branches of engineering and the physical sciences. This unit is geared towards deriving identities and establishing "machinery" to make derivations a routine task. It is noted that the module is not an applications unit, but has as its primary objective the goal of providing science,…
The Atlas Experiment On-Line Monitoring And Filtering As An Example Of Real-Time Application
Directory of Open Access Journals (Sweden)
K. Korcyl
2008-01-01
Full Text Available The ATLAS detector, recording LHC particles’ interactions, produces events with rate of40 MHz and size of 1.6 MB. The processes with new and interesting physics phenomena arevery rare, thus an efficient on-line filtering system (trigger is necessary. The asynchronouspart of that system relays on few thousands of computing nodes running the filtering software.Applying refined filtering criteria results in increase of processing times what may lead tolack of processing resources installed on CERN site. We propose extension to this part ofthe system based on submission of the real-time filtering tasks into the Grid.
International Nuclear Information System (INIS)
Mace, R.L.
1996-01-01
We report on a new form for the dielectric tensor for a plasma containing superthermal particles. The individual particle components are modelled by 3-dimensional isotropic kappa, or generalized Lorentzian, distributions with arbitrary real-valued index κ. The new dielectric tensor is valid for arbitrary wavevectors. The dielectric tensor, which resembles Trubnikov's dielectric tensor for a relativistic plasma, is compared with the familiar Maxwellian form. When the dielectric tensor is used in the plasma dispersion relation for waves propagating parallel to the magnetic field it reproduces previously derived dispersion relations for various electromagnetic and electrostatic waves in plasmas modelled by Lorentzian particle distributions. Within the constraints of propagation parallel to the ambient magnetic field, we extend the above results to incorporate loss-cone Lorentzian particle distributions, which have important applications in laboratory mirror devices, as well as in space and astrophysical environments. (orig.)
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.
Teh, Irvin; McClymont, Darryl; Zdora, Marie-Christine; Whittington, Hannah J; Davidoiu, Valentina; Lee, Jack; Lygate, Craig A; Rau, Christoph; Zanette, Irene; Schneider, Jürgen E
2017-03-10
Diffusion tensor imaging (DTI) is widely used to assess tissue microstructure non-invasively. Cardiac DTI enables inference of cell and sheetlet orientations, which are altered under pathological conditions. However, DTI is affected by many factors, therefore robust validation is critical. Existing histological validation is intrinsically flawed, since it requires further tissue processing leading to sample distortion, is routinely limited in field-of-view and requires reconstruction of three-dimensional volumes from two-dimensional images. In contrast, synchrotron radiation imaging (SRI) data enables imaging of the heart in 3D without further preparation following DTI. The objective of the study was to validate DTI measurements based on structure tensor analysis of SRI data. One isolated, fixed rat heart was imaged ex vivo with DTI and X-ray phase contrast SRI, and reconstructed at 100 μm and 3.6 μm isotropic resolution respectively. Structure tensors were determined from the SRI data and registered to the DTI data. Excellent agreement in helix angles (HA) and transverse angles (TA) was observed between the DTI and structure tensor synchrotron radiation imaging (STSRI) data, where HA DTI-STSRI = -1.4° ± 23.2° and TA DTI-STSRI = -1.4° ± 35.0° (mean ± 1.96 standard deviation across all voxels in the left ventricle). STSRI confirmed that the primary eigenvector of the diffusion tensor corresponds with the cardiomyocyte long-axis across the whole myocardium. We have used STSRI as a novel and high-resolution gold standard for the validation of DTI, allowing like-with-like comparison of three-dimensional tissue structures in the same intact heart free of distortion. This represents a critical step forward in independently verifying the structural basis and informing the interpretation of cardiac DTI data, thereby supporting the further development and adoption of DTI in structure-based electro-mechanical modelling and routine clinical
Tensor categories and the mathematics of rational and logarithmic conformal field theory
International Nuclear Information System (INIS)
Huang, Yi-Zhi; Lepowsky, James
2013-01-01
We review the construction of braided tensor categories and modular tensor categories from representations of vertex operator algebras, which correspond to chiral algebras in physics. The extensive and general theory underlying this construction also establishes the operator product expansion for intertwining operators, which correspond to chiral vertex operators, and more generally, it establishes the logarithmic operator product expansion for logarithmic intertwining operators. We review the main ideas in the construction of the tensor product bifunctors and the associativity isomorphisms. For rational and logarithmic conformal field theories, we review the precise results that yield braided tensor categories, and in the rational case, modular tensor categories as well. In the case of rational conformal field theory, we also briefly discuss the construction of the modular tensor categories for the Wess–Zumino–Novikov–Witten models and, especially, a recent discovery concerning the proof of the fundamental rigidity property of the modular tensor categories for this important special case. In the case of logarithmic conformal field theory, we mention suitable categories of modules for the triplet W-algebras as an example of the applications of our general construction of the braided tensor category structure. (review)
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.
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.
Hernández-García, Raúl; Garza-González, Elvira; Miller, Mark; Arteaga-Muller, Giovanna; Galván-de los Santos, Alejandra María; Camacho-Ortiz, Adrián
2015-01-01
For clinicians, a practical bedside tool for severity assessment and prognosis of patients with Clostridium difficile infection is a highly desirable unmet medical need. Two general teaching hospitals in northeast Mexico. Adult patients with C. difficile infection. Prospective observational study. Patients included had a median of 48 years of age, 54% of male gender and an average of 24.3 days length of hospital stay. Third generation cephalosporins were the antibiotics most commonly used prior to C. difficile infection diagnosis. Patients diagnosed with C. difficile infection had a median ATLAS score of 4 and 56.7% of the subjects had a score between 4 and 7 points. Patients with a score of 8 through 10 points had 100% mortality. The ATLAS score is a potentially useful tool for the routine evaluation of patients at the time of C. difficile infection diagnosis. At 30 days post-diagnosis, patients with a score of ≤3 points had 100% survival while all of those with scores ≥8 died. Patients with scores between 4 and 7 points had a greater probability of colectomy with an overall cure rate of 70.1%. Copyright © 2015 Elsevier Editora Ltda. All rights reserved.
Wind Energy Resource Atlas of Oaxaca
Energy Technology Data Exchange (ETDEWEB)
Elliott, D.; Schwartz, M.; Scott, G.; Haymes, S.; Heimiller, D.; George, R.
2003-08-01
The Oaxaca Wind Resource Atlas, produced by the National Renewable Energy Laboratory's (NREL's) wind resource group, is the result of an extensive mapping study for the Mexican State of Oaxaca. This atlas identifies the wind characteristics and distribution of the wind resource in Oaxaca. The detailed wind resource maps and other information contained in the atlas facilitate the identification of prospective areas for use of wind energy technologies, both for utility-scale power generation and off-grid wind energy applications.
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...
Production of the Finnish Wind Atlas
DEFF Research Database (Denmark)
Tammelin, Bengt; Vihma, Timo; Atlaskin, Evgeny
2013-01-01
) the parameterization method for gust factor was extended to be applicable at higher altitudes; and (vii) the dissemination of the Wind Atlas was based on new technical solutions. The AROME results were calculated for the heights of 50, 75, 100, 125, 150, 200, 300 and 400 m, and the WAsP results for the heights of 50......, 75, 100, 125 and 150 m. In addition to the wind speed, the results included the values of the Weibull distribution parameters, the gust factor, wind power content and the potential power production, which was calculated for three turbine sizes. The Wind Atlas data are available for each grid point......The Finnish Wind Atlas was prepared applying the mesoscale model AROME with 2.5 km horizontal resolution and the diagnostic downscaling method Wind Atlas Analysis and Application Programme (WAsP) with 250 m resolution. The latter was applied for areas most favourable for wind power production: a 30...
Fullea, J.; Fernàndez, M.; Zeyen, H.; Vergés, J.
2007-02-01
We present a method based on the combination of elevation and geoid anomaly data together with thermal field to map crustal and lithospheric thickness. The main assumptions are local isostasy and a four-layered model composed of crust, lithospheric mantle, sea water and the asthenosphere. We consider a linear density gradient for the crust and a temperature dependent density for the lithospheric mantle. We perform sensitivity tests to evaluate the effect of the variation of the model parameters and the influence of RMS error of elevation and geoid anomaly databases. The application of this method to the Gibraltar Arc System, Atlas Mountains and adjacent zones reveals the presence of a lithospheric thinning zone, SW-NE oriented. This zone affects the High and Middle Atlas and extends from the Canary Islands to the eastern Alboran Basin and is probably linked with a similarly trending zone of thick lithosphere constituting the western Betics, eastern Rif, Rharb Basin, and Gulf of Cadiz. A number of different, even mutually opposite, geodynamic models have been proposed to explain the origin and evolution of the study area. Our results suggest that a plausible slab-retreating model should incorporate tear and asymmetric roll-back of the subducting slab to fit the present-day observed lithosphere geometry. In this context, the lithospheric thinning would be caused by lateral asthenospheric flow. An alternative mechanism responsible for lithospheric thinning is the presence of a hot magmatic reservoir derived from a deep ancient plume centred in the Canary Island, and extending as far as Central Europe.
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...
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.
Directory of Open Access Journals (Sweden)
Gonzalo M Rojas
2014-11-01
Full Text Available Effective visualization is central to the exploration and comprehension of brain imaging data. While MRI data are acquired in three-dimensional space, the methods for visualizing such data have rarely taken advantage of three-dimensional stereoscopic technologies. We present here results of stereoscopic visualization of clinical data, as well as an atlas of whole-brain functional connectivity. In comparison with traditional 3D rendering techniques, we demonstrate the utility of stereoscopic visualizations to provide an intuitive description of the exact location and the relative sizes of various brain landmarks, structures and lesions. In the case of resting state fMRI, stereoscopic 3D visualization facilitated comprehension of the anatomical position of complex large-scale functional connectivity patterns. Overall, stereoscopic visualization improves the intuitive visual comprehension of image contents, and brings increased dimensionality to visualization of traditional MRI data, as well as patterns of functional connectivity.
DEFF Research Database (Denmark)
Ólafsdóttir, Hildur; Darvann, Tron Andre; Hermann, Nuno V.
2007-01-01
Crouzon syndrome is characterised by premature fusion of sutures and synchondroses. Recently the first mouse model of the syndrome was generated, having the mutation Cys342Tyr in Fgfr2c, equivalent to the most common human Crouzon/Pfeiffer syndrome mutation. In this study, a set of Micro CT scann....... Furthermore, the nonrigid approach is essential when it comes to analysing local, nonlinear shape differences.......Crouzon syndrome is characterised by premature fusion of sutures and synchondroses. Recently the first mouse model of the syndrome was generated, having the mutation Cys342Tyr in Fgfr2c, equivalent to the most common human Crouzon/Pfeiffer syndrome mutation. In this study, a set of Micro CT....... Subsequently, the atlas was deformed to match each subject from the two groups of mice. The accuracy of these registrations was measured by a comparison of manually placed landmarks from two different observers and automatically assessed landmarks. Both of the automatic approaches were within the inter...
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...
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.
Structural equations for Killing tensors of order two. II
International Nuclear Information System (INIS)
Hauser, I.; Malhiot, R.J.
1975-01-01
In a preceding paper, a new form of the structural equations for any Killing tensor of order two have been derived; these equations constitute a system analogous to the Killing vector equations Nabla/sub alpha/ K/sub beta/ = ω/sub alpha beta/ = -ω/sub beta alpha/ and Nabla/sub gamma/ ω/sub alpha beta = R/sub alpha beta gamma delta/ K/sup delta/. The first integrability condition for the Killing tensor structural equations is now derived. The structural equations and the integrability condition have forms which can readily be expressed in terms of a null tetrad to furnish a Killing tensor parallel of the Newman--Penrose equations; this is briefly described. The integrability condition implies the new result, for any given space--time, that the dimension of the set of second-order Killing tensors attains its maximum possible value of 50 only if the space--time is of constant curvature. Potential applications of the structural equations are discussed
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.)
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...
International Nuclear Information System (INIS)
Kang, Keon Wook; Lee, Dong Soo; Cho, Jae Hoon; Lee, Jae Sung; Yeo, Jeong Seok; Lee, Sang Gun; Chung, June Key; Lee, Myung Chul
2000-01-01
A probabilistic atlas of the human brain (Statistical Probability Anatomical Maps: SPAM) was developed by the international consortium for brain mapping (ICBM). After calculating the counts in volume of interest (VOI) using the product of probability of SPAM images and counts in FDG images, asymmetric indexes(AI) were calculated and used for finding epileptogenic zones in temporal lobe epilepsy (TLE). FDG PET images from 28 surgically confirmed TLE patients and 12 age-matched controls were spatially normalized to the averaged brain MRI atlas of ICBM. The counts from normalized PET images were multiplied with the probability of 12 VOIs (superior temporal gyrus, middle temporal gyrus, inferior temporal gyrus, hippocampus, parahippocampal gyrus, and amygdala in each hemisphere) of SPAM images of Montreal Neurological Institute. Finally AI was calculated on each pair of VOI, and compared with visual assessment. If AI was deviated more than 2 standard deviation of normal controls, we considered epileptogenic zones were found successfully. The counts of VOIs in normal controls were symmetric (AI 0.05) except those of inferior temporal gyrus (p<0.01). AIs in 5 pairs of VOI excluding inferior temporal gyrus were deviated to one side in TLE (p<0.05). Lateralization was correct in 23/28 of patients by AI, but all of 28 were consistent with visual inspection. In 3 patients with normal AI was symmetric on visual inspection. In 2 patients falsely lateralized using AI, metabolism was also decreased visually on contra-lateral side. Asymmetric index obtained by the product of statistical probability anatomical map and FDG PET correlated well with visual assessment in TLE patients. SPAM is useful for quantification of VOIs in functional images
Energy Technology Data Exchange (ETDEWEB)
Kang, Keon Wook; Lee, Dong Soo; Cho, Jae Hoon; Lee, Jae Sung; Yeo, Jeong Seok; Lee, Sang Gun; Chung, June Key; Lee, Myung Chul [Seoul National Univ., Seoul (Korea, Republic of)
2000-07-01
A probabilistic atlas of the human brain (Statistical Probability Anatomical Maps: SPAM) was developed by the international consortium for brain mapping (ICBM). After calculating the counts in volume of interest (VOI) using the product of probability of SPAM images and counts in FDG images, asymmetric indexes(AI) were calculated and used for finding epileptogenic zones in temporal lobe epilepsy (TLE). FDG PET images from 28 surgically confirmed TLE patients and 12 age-matched controls were spatially normalized to the averaged brain MRI atlas of ICBM. The counts from normalized PET images were multiplied with the probability of 12 VOIs (superior temporal gyrus, middle temporal gyrus, inferior temporal gyrus, hippocampus, parahippocampal gyrus, and amygdala in each hemisphere) of SPAM images of Montreal Neurological Institute. Finally AI was calculated on each pair of VOI, and compared with visual assessment. If AI was deviated more than 2 standard deviation of normal controls, we considered epileptogenic zones were found successfully. The counts of VOIs in normal controls were symmetric (AI <6%, paired t-test p>0.05) except those of inferior temporal gyrus (p<0.01). AIs in 5 pairs of VOI excluding inferior temporal gyrus were deviated to one side in TLE (p<0.05). Lateralization was correct in 23/28 of patients by AI, but all of 28 were consistent with visual inspection. In 3 patients with normal AI was symmetric on visual inspection. In 2 patients falsely lateralized using AI, metabolism was also decreased visually on contra-lateral side. Asymmetric index obtained by the product of statistical probability anatomical map and FDG PET correlated well with visual assessment in TLE patients. SPAM is useful for quantification of VOIs in functional images.
Directory of Open Access Journals (Sweden)
Olena G. Filatova
2018-04-01
Full Text Available Better insight into white matter (WM alterations after stroke onset could help to understand the underlying recovery mechanisms and improve future interventions. MR diffusion imaging enables to assess such changes. Our goal was to investigate the relation of WM diffusion characteristics derived from diffusion models of increasing complexity with the motor function of the upper limb. Moreover, we aimed to evaluate the variation of such characteristics across different WM structures of chronic stroke patients in comparison to healthy subjects. Subjects were scanned with a two b-value diffusion-weighted MRI protocol to exploit multiple diffusion models: single tensor, single tensor with isotropic compartment, bi-tensor model, bi-tensor with isotropic compartment. From each model we derived the mean tract fractional anisotropy (FA, mean (MD, radial (RD and axial (AD diffusivities outside the lesion site based on a WM tracts atlas. Asymmetry of these measures was correlated with the Fugl-Meyer upper extremity assessment (FMA score and compared between patient and control groups. Eighteen chronic stroke patients and eight age-matched healthy individuals participated in the study. Significant correlation of the outcome measures with the clinical scores of stroke recovery was found. The lowest correlation of the corticospinal tract FAasymmetry and FMA was with the single tensor model (r = −0.3, p = 0.2 whereas the other models reported results in the range of r = −0.79 ÷ −0.81 and p = 4E-5 ÷ 8E-5. The corticospinal tract and superior longitudinal fasciculus showed most alterations in our patient group relative to controls. Multiple compartment models yielded superior correlation of the diffusion measures and FMA compared to the single tensor model.
City and County of Durham, North Carolina — This EnviroAtlas web service supports research and online mapping activities related to EnviroAtlas (https://www.epa.gov/enviroatlas). The layers in this web...
The tensor network theory library
Al-Assam, S.; Clark, S. R.; Jaksch, D.
2017-09-01
In this technical paper we introduce the tensor network theory (TNT) library—an open-source software project aimed at providing a platform for rapidly developing robust, easy to use and highly optimised code for TNT calculations. The objectives of this paper are (i) to give an overview of the structure of TNT library, and (ii) to help scientists decide whether to use the TNT library in their research. We show how to employ the TNT routines by giving examples of ground-state and dynamical calculations of one-dimensional bosonic lattice system. We also discuss different options for gaining access to the software available at www.tensornetworktheory.org.
Dirac tensor with heavy photon
Energy Technology Data Exchange (ETDEWEB)
Bytev, V.V.; Kuraev, E.A. [Joint Institute of Nuclear Research, Moscow (Russian Federation). Bogoliubov Lab. of Theoretical Physics; Scherbakova, E.S. [Hamburg Univ. (Germany). 1. Inst. fuer Theoretische Physik
2012-01-15
For the large-angles hard photon emission by initial leptons in process of high energy annihilation of e{sup +}e{sup -} {yields} to hadrons the Dirac tensor is obtained, taking into account the lowest order radiative corrections. The case of large-angles emission of two hard photons by initial leptons is considered. This result is being completed by the kinematics case of collinear hard photons emission as well as soft virtual and real photons and can be used for construction of Monte-Carlo generators. (orig.)
The Scalar, Vector and Tensor Fields in Theory of Elasticity and Plasticity
Directory of Open Access Journals (Sweden)
František FOJTÍK
2014-06-01
Full Text Available This article is devoted to an analysis of scalar, vector and tensor fields, which occur in the loaded and deformed bodies. The aim of this article is to clarify and simplify the creation of an understandable idea of some elementary concepts and quantities in field theories, such as, for example equiscalar levels, scalar field gradient, Hamilton operator, divergence, rotation and gradient of vector or tensor and others. Applications of those mathematical terms are shown in simple elasticity and plasticity tasks. We hope that content of our article might help technicians to make their studies of necessary mathematical chapters of vector and tensor analysis and field theories easier.
Multi-atlas pancreas segmentation: Atlas selection based on vessel structure.
Karasawa, Ken'ichi; Oda, Masahiro; Kitasaka, Takayuki; Misawa, Kazunari; Fujiwara, Michitaka; Chu, Chengwen; Zheng, Guoyan; Rueckert, Daniel; Mori, Kensaku
2017-07-01
Automated organ segmentation from medical images is an indispensable component for clinical applications such as computer-aided diagnosis (CAD) and computer-assisted surgery (CAS). We utilize a multi-atlas segmentation scheme, which has recently been used in different approaches in the literature to achieve more accurate and robust segmentation of anatomical structures in computed tomography (CT) volume data. Among abdominal organs, the pancreas has large inter-patient variability in its position, size and shape. Moreover, the CT intensity of the pancreas closely resembles adjacent tissues, rendering its segmentation a challenging task. Due to this, conventional intensity-based atlas selection for pancreas segmentation often fails to select atlases that are similar in pancreas position and shape to those of the unlabeled target volume. In this paper, we propose a new atlas selection strategy based on vessel structure around the pancreatic tissue and demonstrate its application to a multi-atlas pancreas segmentation. Our method utilizes vessel structure around the pancreas to select atlases with high pancreatic resemblance to the unlabeled volume. Also, we investigate two types of applications of the vessel structure information to the atlas selection. Our segmentations were evaluated on 150 abdominal contrast-enhanced CT volumes. The experimental results showed that our approach can segment the pancreas with an average Jaccard index of 66.3% and an average Dice overlap coefficient of 78.5%. Copyright © 2017 Elsevier B.V. All rights reserved.
Forbes, Jessica L; Kim, Regina E Y; Paulsen, Jane S; Johnson, Hans J
2016-01-01
The creation of high-quality medical imaging reference atlas datasets with consistent dense anatomical region labels is a challenging task. Reference atlases have many uses in medical image applications and are essential components of atlas-based segmentation tools commonly used for producing personalized anatomical measurements for individual subjects. The process of manual identification of anatomical regions by experts is regarded as a so-called gold standard; however, it is usually impractical because of the labor-intensive costs. Further, as the number of regions of interest increases, these manually created atlases often contain many small inconsistently labeled or disconnected regions that need to be identified and corrected. This project proposes an efficient process to drastically reduce the time necessary for manual revision in order to improve atlas label quality. We introduce the LabelAtlasEditor tool, a SimpleITK-based open-source label atlas correction tool distributed within the image visualization software 3D Slicer. LabelAtlasEditor incorporates several 3D Slicer widgets into one consistent interface and provides label-specific correction tools, allowing for rapid identification, navigation, and modification of the small, disconnected erroneous labels within an atlas. The technical details for the implementation and performance of LabelAtlasEditor are demonstrated using an application of improving a set of 20 Huntingtons Disease-specific multi-modal brain atlases. Additionally, we present the advantages and limitations of automatic atlas correction. After the correction of atlas inconsistencies and small, disconnected regions, the number of unidentified voxels for each dataset was reduced on average by 68.48%.
Berliner Philarmoniker ATLAS visit
ATLAS Collaboration
2017-01-01
The Berliner Philarmoniker in on tour through Europe. They stopped on June 27th in Geneva, for a concert at the Victoria Hall. An ATLAS visit was organised the morning after, lead by the ATLAS spokesperson Karl Jakobs (welcome and overview talk) and two ATLAS guides (AVC visit and 3D movie).
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).
Generalized Tensor Analysis Model for Multi-Subcarrier Analog Optical Systems
DEFF Research Database (Denmark)
Zhao, Ying; Yu, Xianbin; Zheng, Xiaoping
2011-01-01
We propose and develop a general tensor analysis framework for a subcarrier multiplex analog optical fiber link for applications in microwave photonics. The goal of this work is to construct an uniform method to address nonlinear distortions of a discrete frequency transmission system. We employ....... In addition, it is demonstrated that each corresponding tensor is formally determined by device structures, which allows for a synthesized study of device combinations more systematically. For implementing numerical methods, the practical significance of the tensor model is it simplifies the derivation...... details compared with series-based approaches by hiding the underlying multi-fold summation and index operation. The integrity of the proposed methodology is validated by investigating the classical intensity modulated system. Furthermore, to give an application model of the tensor formalism, we make...
The geosystems of complex geographical atlases
Directory of Open Access Journals (Sweden)
Jovanović Jasmina
2012-01-01
Full Text Available Complex geographical atlases represent geosystems of different hierarchical rank, complexity and diversity, scale and connection. They represent a set of large number of different pieces of information about geospace. Also, they contain systematized, correlative and in the apparent form represented pieces of information about space. The degree of information revealed in the atlas is precisely explained by its content structure and the form of presentation. The quality of atlas depends on the method of visualization of data and the quality of geodata. Cartographic visualization represents cognitive process. The analysis converts geospatial data into knowledge. A complex geographical atlas represents information complex of spatial - temporal coordinated database on geosystems of different complexity and territorial scope. Each geographical atlas defines a concrete geosystem. Systemic organization (structural and contextual determines its complexity and concreteness. In complex atlases, the attributes of geosystems are modeled and pieces of information are given in systematized, graphically unique form. The atlas can be considered as a database. In composing a database, semantic analysis of data is important. The result of semantic modeling is expressed in structuring of data information, in emphasizing logic connections between phenomena and processes and in defining their classes according to the degree of similarity. Accordingly, the efficiency of research of needed pieces of information in the process of the database use is enabled. An atlas map has a special power to integrate sets of geodata and present information contents in user - friendly and understandable visual and tactile way using its visual ability. Composing an atlas by systemic cartography requires the pieces of information on concrete - defined geosystems of different hierarchical level, the application of scientific methods and making of adequate number of analytical, synthetic
Tensor Fields for Use in Fractional-Order Viscoelasticity
Freed, Alan D.; Diethelm, Kai
2003-01-01
To be able to construct viscoelastic material models from fractional0order differentegral equations that are applicable for 3D finite-strain analysis requires definitions for fractional derivatives and integrals for symmetric tensor fields, like stress and strain. We define these fields in the body manifold. We then map them ito spatial fields expressed in terms of an Eulerian or Lagrangian reference frame where most analysts prefer to solve boundary problems.
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...
Local transformations of units in scalar-tensor cosmology
International Nuclear Information System (INIS)
Catena, R.; Pietroni, M.; Scarabello, L.; Padua Univ.
2006-10-01
The physical equivalence of Einstein and Jordan frame in Scalar Tensor theories has been explained by Dicke in 1962: they are related by a local transformation of units. We discuss this point in a cosmological framework. Our main result is the construction of a formalism in which all the physical observables are frame-invariant. The application of this approach to CMB codes is at present under analysis. (orig.)
Algebraic classification of the Weyl tensor in higher dimensions based on its 'superenergy' tensor
International Nuclear Information System (INIS)
Senovilla, Jose M M
2010-01-01
The algebraic classification of the Weyl tensor in the arbitrary dimension n is recovered by means of the principal directions of its 'superenergy' tensor. This point of view can be helpful in order to compute the Weyl aligned null directions explicitly, and permits one to obtain the algebraic type of the Weyl tensor by computing the principal eigenvalue of rank-2 symmetric future tensors. The algebraic types compatible with states of intrinsic gravitational radiation can then be explored. The underlying ideas are general, so that a classification of arbitrary tensors in the general dimension can be achieved. (fast track communication)
Gravitational Metric Tensor Exterior to Rotating Homogeneous ...
African Journals Online (AJOL)
The covariant and contravariant metric tensors exterior to a homogeneous spherical body rotating uniformly about a common φ axis with constant angular velocity ω is constructed. The constructed metric tensors in this gravitational field have seven non-zero distinct components.The Lagrangian for this gravitational field is ...
Tensor Network Quantum Virtual Machine (TNQVM)
Energy Technology Data Exchange (ETDEWEB)
2016-11-18
There is a lack of state-of-the-art quantum computing simulation software that scales on heterogeneous systems like Titan. Tensor Network Quantum Virtual Machine (TNQVM) provides a quantum simulator that leverages a distributed network of GPUs to simulate quantum circuits in a manner that leverages recent results from tensor network theory.
Tensor product varieties and crystals. GL case
Malkin, Anton
2001-01-01
The role of Spaltenstein varieties in the tensor product for GL is explained. In particular a direct (non-combinatorial) proof of the fact that the number of irreducible components of a Spaltenstein variety is equal to a Littlewood-Richardson coefficient (i.e. certain tensor product multiplicity) is obtained.
An EM System with Dynamic Multi-Axis Transmitter and Tensor Gradiometer Receiver
2011-06-01
main difference between the spatial behavior of target anomalies measured with a magnetometer and those we measured with an EM system is in the nature...environmental and UXO applications, current efforts include the development of tensor magnetic gradiometers based on triaxial fluxgate technology by the USGS...Superconducting gradiometer/ Magnetometer Arrays and a Novel Signal Processing Technique. IEEE Trans. on Magnetics, MAG-11(2), 701-707. EM Tensor
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
Superconducting rf development at ATLAS
Energy Technology Data Exchange (ETDEWEB)
Shepard, K.W.; Kedzie, M.; Clifft, B.E. [Argonne National Lab., IL (United States); Roy, A.; Potukuchi, P. [Nuclear Science Centre, New Delhi (India); Givens, J.; Potter, J.; Crandall, K. [AccSys Technology, Inc., Pleasanton, CA (United States); Added, N. [Sao Paulo Univ., SP (Brazil)
1993-12-31
The ATLAS superconducting heavy-ion linac began operation in 1978 and has operated nearly continuously since that time, while undergoing a series of upgrades and expansions, the most recent being the ``uranium upgrade`` completed earlier this year and described below. In its present configuration the ATLAS linac consists of an array of 64 resonant cavities operating from 48 to 145 MHz, which match a range of particle velocities .007 < {beta} = v/c < .2. The linac provides approximately 50 MV of effective accelerating potential for ions of q/m > 1/10 over the entire periodic table. Delivered beams include 5 {minus} 7 pnA of {sup 238}U{sup 39+} at 1535 MeV. At present more than 10{sup 6} cavity-hours of operation at surface electric fields of 15 MV/m have been accumulated. Superconducting structure development at ATLAS is aimed at improving the cost/performance of existing low velocity structures both for possible future ATLAS upgrades, and also for heavy-ion linacs at other institutions. An application of particular current interest is to develop structures suitable for accelerating radioactive ion beams. Such structures must accelerate very low charge to mass ratio beams and must also have very large transverse acceptance.
ATLAS job monitoring in the Dashboard Framework
Sargsyan, L; The ATLAS collaboration; Campana, S; Karavakis, E; Kokoszkiewicz, L; Saiz, P; Schovancova, J; Tuckett, D
2012-01-01
Monitoring of the large-scale data processing of the ATLAS experiment includes monitoring of production and user analysis jobs. The Experiment Dashboard provides a common job monitoring solution, which is shared by ATLAS and CMS experiments. This includes an accounting portal as well as real-time monitoring. Dashboard job monitoring for ATLAS combines information from PanDA job processing database, Production system database and monitoring information from jobs submitted through GANGA to Workload Management System (WMS) or local batch systems. Usage of Dashboard-based job monitoring applications will decrease load on the PanDA database and overcome scale limitations in PanDA monitoring caused by the short job rotation cycle in the PanDA database. Aggregation of the task/job metrics from different sources provides complete view of job processing activity in ATLAS scope.
ATLAS job monitoring in the Dashboard Framework
International Nuclear Information System (INIS)
Andreeva, J; Campana, S; Karavakis, E; Kokoszkiewicz, L; Saiz, P; Tuckett, D; Sargsyan, L; Schovancova, J
2012-01-01
Monitoring of the large-scale data processing of the ATLAS experiment includes monitoring of production and user analysis jobs. The Experiment Dashboard provides a common job monitoring solution, which is shared by ATLAS and CMS experiments. This includes an accounting portal as well as real-time monitoring. Dashboard job monitoring for ATLAS combines information from the PanDA job processing database, Production system database and monitoring information from jobs submitted through GANGA to Workload Management System (WMS) or local batch systems. Usage of Dashboard-based job monitoring applications will decrease load on the PanDA database and overcome scale limitations in PanDA monitoring caused by the short job rotation cycle in the PanDA database. Aggregation of the task/job metrics from different sources provides complete view of job processing activity in ATLAS scope.
Anisotropic Conductivity Tensor Imaging of In Vivo Canine Brain Using DT-MREIT.
Jeong, Woo Chul; Sajib, Saurav Z K; Katoch, Nitish; Kim, Hyung Joong; Kwon, Oh In; Woo, Eung Je
2017-01-01
We present in vivo images of anisotropic electrical conductivity tensor distributions inside canine brains using diffusion tensor magnetic resonance electrical impedance tomography (DT-MREIT). The conductivity tensor is represented as a product of an ion mobility tensor and a scale factor of ion concentrations. Incorporating directional mobility information from water diffusion tensors, we developed a stable process to reconstruct anisotropic conductivity tensor images from measured magnetic flux density data using an MRI scanner. Devising a new image reconstruction algorithm, we reconstructed anisotropic conductivity tensor images of two canine brains with a pixel size of 1.25 mm. Though the reconstructed conductivity values matched well in general with those measured by using invasive probing methods, there were some discrepancies as well. The degree of white matter anisotropy was 2 to 4.5, which is smaller than previous findings of 5 to 10. The reconstructed conductivity value of the cerebrospinal fluid was about 1.3 S/m, which is smaller than previous measurements of about 1.8 S/m. Future studies of in vivo imaging experiments with disease models should follow this initial trial to validate clinical significance of DT-MREIT as a new diagnostic imaging modality. Applications in modeling and simulation studies of bioelectromagnetic phenomena including source imaging and electrical stimulation are also promising.
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)
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
International Nuclear Information System (INIS)
Ahmad, I.; Glagola, B.
1995-05-01
This report contains discussing in the following areas: Status of the Atlas accelerator; highlights of recent research at Atlas; concept for an advanced exotic beam facility based on Atlas; program advisory committee; Atlas executive committee; and Atlas and ANL physics division on the world wide web
J. Herr
As reported in the September 2004 ATLAS eNews, the Web Lecture Archive Project is a system for the archiving and publishing of multimedia presentations, using the Web as medium. We list here newly available WLAP items relating to ATLAS: Atlas Physics Workshop 6-11 June 2005 June 2005 ATLAS Week Plenary Session Click here to browse WLAP for all ATLAS lectures.
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.
Pajevic, Sinisa; Aldroubi, Akram; Basser, Peter J
2002-01-01
The effective diffusion tensor of water, D, measured by diffusion tensor MRI (DT-MRI), is inherently a discrete, noisy, voxel-averaged sample of an underlying macroscopic effective diffusion tensor field, D(x). Within fibrous tissues this field is presumed to be continuous and smooth at a gross anatomical length scale. Here a new, general mathematical framework is proposed that uses measured DT-MRI data to produce a continuous approximation to D(x). One essential finding is that the continuous tensor field representation can be constructed by repeatedly performing one-dimensional B-spline transforms of the DT-MRI data. The fidelity and noise-immunity of this approximation are tested using a set of synthetically generated tensor fields to which background noise is added via Monte Carlo methods. Generally, these tensor field templates are reproduced faithfully except at boundaries where diffusion properties change discontinuously or where the tensor field is not microscopically homogeneous. Away from such regions, the tensor field approximation does not introduce bias in useful DT-MRI parameters, such as Trace(D(x)). It also facilitates the calculation of several new parameters, particularly differential quantities obtained from the tensor of spatial gradients of D(x). As an example, we show that they can identify tissue boundaries across which diffusion properties change rapidly using in vivo human brain data. One important application of this methodology is to improve the reliability and robustness of DT-MRI fiber tractography.
Bengt Lund-Jensen
2007-01-01
On December 9, the former ATLAS physicist Christer Fuglesang was launched into space onboard the STS-116 Space Shuttle flight from Kennedy Space Center in Florida. Christer worked on the development of the accordion-type liquid argon calorimeter and SUSY simulations in what eventually became ATLAS until summer 1992 when he became one out of six astronaut trainees with the European Space Agency (ESA). His selection out of a very large number of applicants from all over the ESA member states involved a number of tests in order to choose the most suitable candidates. As ESA astronaut Christer trained with the Russian Soyuz programme in Star City outside of Moscow from 1993 until 1996, when he moved to Houston to train for space shuttle missions with NASA. Christer belonged to the backup crew for the Euromir95 mission. After additional training in Russia, Christer qualified as âSoyuz return commanderâ in 1998. Christer rerouting cables during his second space walk. (Photo: courtesy NASA) During...
ATLAS DBM Module Qualification
Energy Technology Data Exchange (ETDEWEB)
Soha, Aria [Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States); Gorisek, Andrej [J. Stefan Inst., Ljubljana (Slovenia); Zavrtanik, Marko [J. Stefan Inst., Ljubljana (Slovenia); Sokhranyi, Grygorii [J. Stefan Inst., Ljubljana (Slovenia); McGoldrick, Garrin [Univ. of Toronto, ON (Canada); Cerv, Matevz [European Organization for Nuclear Research (CERN), Geneva (Switzerland)
2014-06-18
This is a technical scope of work (TSW) between the Fermi National Accelerator Laboratory (Fermilab) and the experimenters of Jozef Stefan Institute, CERN, and University of Toronto who have committed to participate in beam tests to be carried out during the 2014 Fermilab Test Beam Facility program. Chemical Vapour Deposition (CVD) diamond has a number of properties that make it attractive for high energy physics detector applications. Its large band-gap (5.5 eV) and large displacement energy (42 eV/atom) make it a material that is inherently radiation tolerant with very low leakage currents and high thermal conductivity. CVD diamond is being investigated by the RD42 Collaboration for use very close to LHC interaction regions, where the most extreme radiation conditions are found. This document builds on that work and proposes a highly spatially segmented diamond-based luminosity monitor to complement the time-segmented ATLAS Beam Conditions Monitor (BCM) so that, when Minimum Bias Trigger Scintillators (MTBS) and LUCID (LUminosity measurement using a Cherenkov Integrating Detector) have difficulty functioning, the ATLAS luminosity measurement is not compromised.
Di Simone, A; Di Ciaccio, A
2005-01-01
In the muon spectrometer different detectors are used to provide trigger functionality and precision momentum measurements. In the pseudorapidity range |eta|<1 the first level muon trigger is based on Resistive Plate Chambers, gas ionization detectors which are characterized by a fast response and an excellent time resolution (<1.5ns). The working principles of the Resistive Plate Chambers will be illustrated in chapter 3. Given the long time of operation expected for the ATLAS experiment (~10 years), ageing phenomena have been carefully studied, in order to ensure stable long-term operation of all the subdetectors. Concerning Resistive Plate Chambers, a very extensive ageing test has been performed at CERN's Gamma Irradiation Facility on three production chambers. The results of this test are presented in chapter 4. One of the most commonly used gases in RPCs operation is C2H2F4, which during the gas discharge can produce fluorine ions. Being F one of the most aggressive elements in nature, the presenc...
ATLAS Distributed Computing Automation
Schovancova, J; The ATLAS collaboration; Borrego, C; Campana, S; Di Girolamo, A; Elmsheuser, J; Hejbal, J; Kouba, T; Legger, F; Magradze, E; Medrano Llamas, R; Negri, G; Rinaldi, L; Sciacca, G; Serfon, C; Van Der Ster, D C
2012-01-01
The ATLAS Experiment benefits from computing resources distributed worldwide at more than 100 WLCG sites. The ATLAS Grid sites provide over 100k CPU job slots, over 100 PB of storage space on disk or tape. Monitoring of status of such a complex infrastructure is essential. The ATLAS Grid infrastructure is monitored 24/7 by two teams of shifters distributed world-wide, by the ATLAS Distributed Computing experts, and by site administrators. In this paper we summarize automation efforts performed within the ATLAS Distributed Computing team in order to reduce manpower costs and improve the reliability of the system. Different aspects of the automation process are described: from the ATLAS Grid site topology provided by the ATLAS Grid Information System, via automatic site testing by the HammerCloud, to automatic exclusion from production or analysis activities.
Nowinski, Wieslaw L; Belov, Dmitry
2003-09-01
The article introduces an atlas-assisted method and a tool called the Cerefy Neuroradiology Atlas (CNA), available over the Internet for neuroradiology and human brain mapping. The CNA contains an enhanced, extended, and fully segmented and labeled electronic version of the Talairach-Tournoux brain atlas, including parcelated gyri and Brodmann's areas. To our best knowledge, this is the first online, publicly available application with the Talairach-Tournoux atlas. The process of atlas-assisted neuroimage analysis is done in five steps: image data loading, Talairach landmark setting, atlas normalization, image data exploration and analysis, and result saving. Neuroimage analysis is supported by a near-real-time, atlas-to-data warping based on the Talairach transformation. The CNA runs on multiple platforms; is able to process simultaneously multiple anatomical and functional data sets; and provides functions for a rapid atlas-to-data registration, interactive structure labeling and annotating, and mensuration. It is also empowered with several unique features, including interactive atlas warping facilitating fine tuning of atlas-to-data fit, navigation on the triplanar formed by the image data and the atlas, multiple-images-in-one display with interactive atlas-anatomy-function blending, multiple label display, and saving of labeled and annotated image data. The CNA is useful for fast atlas-assisted analysis of neuroimage data sets. It increases accuracy and reduces time in localization analysis of activation regions; facilitates to communicate the information on the interpreted scans from the neuroradiologist to other clinicians and medical students; increases the neuroradiologist's confidence in terms of anatomy and spatial relationships; and serves as a user-friendly, public domain tool for neuroeducation. At present, more than 700 users from five continents have subscribed to the CNA.
International Nuclear Information System (INIS)
Pott, G.; Schrameyer, B.
1989-01-01
Endoscopic-retrograde cholangio-pancreatography is a diagnostic tool that has become a routine method also in medical centres other than those specializing in the field of gastroenterology. It is estimated that there are about 1000 hospitals in the Federal Republic of Germany applying cholangio-pancreatography as a diagnostic method. Frequently, data interpretation is difficult, because imaging of subsequently detected lesions is found to have been insufficiently differential, or incomplete. The experienced examiner, who knows the pathological processes involved and hence to be expected, will perform the ERCP examination in a specific manner, i.e. purposefully. The ERCP atlas now presents a selection of typical, frequently found conditions, and of rarely encountered lesions. The material has been chosen from a total of 15 000 retrograde cholangio-pancreatographies. The introductory text is relatively short, as it is not so much intended to enhance experienced readers' skill in endoscopic diagnostics, - there is other literature for this purpose -, but rather as a brief survey for less experienced readers. (orig./MG) With 280 figs [de
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.
International Nuclear Information System (INIS)
Limbach, Christian
2015-05-01
This thesis presents a new method for the reconstruction and classification of hadronically decaying tau leptons in the ATLAS detector at the LHC. It also presents a possible application of the new methods. The new reconstruction method follows the energy flow approach, which aims at reconstructing every single particle in a collision, and applies it to hadronically decaying tau leptons. This provides access to the tau decay mode and also improves the energy and spatial resolution of the tau. The new classification method makes use of so-called kinematic tau variables, which capture the kinematics of the tau decay. By combining several of these variables, it is possible to further improve the decay mode classification of the tau leptons. By taking into account the decay mode, the new classification method is also capable of improving the spatial and energy resolution of reconstructed tau leptons. In a simulation-based study, it is shown that the new reconstruction and classification methods are also capable of measuring the mean tau polarisation in the decays of a Z-Boson into two taus.
Making tensor factorizations robust to non-gaussian noise.
Energy Technology Data Exchange (ETDEWEB)
Chi, Eric C. (Rice University, Houston, TX); Kolda, Tamara Gibson
2011-03-01
Tensors are multi-way arrays, and the CANDECOMP/PARAFAC (CP) tensor factorization has found application in many different domains. The CP model is typically fit using a least squares objective function, which is a maximum likelihood estimate under the assumption of independent and identically distributed (i.i.d.) Gaussian noise. We demonstrate that this loss function can be highly sensitive to non-Gaussian noise. Therefore, we propose a loss function based on the 1-norm because it can accommodate both Gaussian and grossly non-Gaussian perturbations. We also present an alternating majorization-minimization (MM) algorithm for fitting a CP model using our proposed loss function (CPAL1) and compare its performance to the workhorse algorithm for fitting CP models, CP alternating least squares (CPALS).
Abelian tensor hierarchy in 4D, N=1 superspace
International Nuclear Information System (INIS)
Becker, Katrin; Becker, Melanie; III, William D. Linch; Robbins, Daniel
2016-01-01
With the goal of constructing the supersymmetric action for all fields, massless and massive, obtained by Kaluza-Klein compactification from type II theory or M-theory in a closed form, we embed the (Abelian) tensor hierarchy of p-forms in four-dimensional, N=1 superspace and construct its Chern-Simons-like invariants. When specialized to the case in which the tensors arise from a higher-dimensional theory, the invariants may be interpreted as higher-dimensional Chern-Simons forms reduced to four dimensions. As an application of the formalism, we construct the eleven-dimensional Chern-Simons form in terms of four-dimensional, N=1 superfields.
Abelian tensor hierarchy in 4D, N=1 superspace
Energy Technology Data Exchange (ETDEWEB)
Becker, Katrin; Becker, Melanie; III, William D. Linch; Robbins, Daniel [George P. and Cynthia W. Mitchell Institute for Fundamental Physics and Astronomy,Texas A& M University, College Station, TX 77843 (United States)
2016-03-09
With the goal of constructing the supersymmetric action for all fields, massless and massive, obtained by Kaluza-Klein compactification from type II theory or M-theory in a closed form, we embed the (Abelian) tensor hierarchy of p-forms in four-dimensional, N=1 superspace and construct its Chern-Simons-like invariants. When specialized to the case in which the tensors arise from a higher-dimensional theory, the invariants may be interpreted as higher-dimensional Chern-Simons forms reduced to four dimensions. As an application of the formalism, we construct the eleven-dimensional Chern-Simons form in terms of four-dimensional, N=1 superfields.
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.
MULTISCALE TENSOR ANISOTROPIC FILTERING OF FLUORESCENCE MICROSCOPY FOR DENOISING MICROVASCULATURE.
Prasath, V B S; Pelapur, R; Glinskii, O V; Glinsky, V V; Huxley, V H; Palaniappan, K
2015-04-01
Fluorescence microscopy images are contaminated by noise and improving image quality without blurring vascular structures by filtering is an important step in automatic image analysis. The application of interest here is to automatically extract the structural components of the microvascular system with accuracy from images acquired by fluorescence microscopy. A robust denoising process is necessary in order to extract accurate vascular morphology information. For this purpose, we propose a multiscale tensor with anisotropic diffusion model which progressively and adaptively updates the amount of smoothing while preserving vessel boundaries accurately. Based on a coherency enhancing flow with planar confidence measure and fused 3D structure information, our method integrates multiple scales for microvasculature preservation and noise removal membrane structures. Experimental results on simulated synthetic images and epifluorescence images show the advantage of our improvement over other related diffusion filters. We further show that the proposed multiscale integration approach improves denoising accuracy of different tensor diffusion methods to obtain better microvasculature segmentation.
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.
Evidence of tensor correlations in the nuclear many-body system using a modern NN potential
International Nuclear Information System (INIS)
Fiase, J.O.; Nkoma, J.S.; Sharmaand, L.K.; Hosaka, A.
2003-01-01
In this paper we show evidence of the importance of tensor correlations in the nuclear many-body system by calculating the effective two-body nuclear matrix elements in the frame work of the Lowest-Order Constrained Variational (LOCV) technique with two-body correlation functions using the Reid93 potential. We have achieved this by switching on and off the strength of the tensor correlations, α k . We have found that in order to obtain reasonable agreement with earlier calculations based on the G-matrix theory, we must turn on the strength of the tensor correlations especially in the triplet even (TE) and tensor even (TNE) channels to take the value of approximately, 0.05. As an application, we have estimated the value of the Landau - Migdal parameter, g' NN which we found to be g' NN = 0.65. This compares favorably with the G-matrix calculated value of g' NN = 0.54. (author)
An introduction to tensor calculus, relativity and cosmology /3rd edition/
Lawden, D. F.
This textbook introduction to the principles of special relativity proceeds within the context of cartesian tensors. Newton's laws of motion are reviewed, as are the Lorentz transformations, Minkowski space-time, and the Fitzgerald contraction. Orthogonal transformations are described, and invariants, gradients, tensor derivatives, contraction, scalar products, divergence, pseudotensors, vector products, and curl are defined. Special relativity mechanics are explored in terms of mass, momentum, the force vector, the Lorentz transformation equations for force, calculations for photons and neutrinos, the development of the Lagrange and Hamilton equations, and the energy-momentum tensor. Electrodynamics is investigated, together with general tensor calculus and Riemmanian space. The General Theory of Relativity is presented, along with applications to astrophysical phenomena such as black holes and gravitational waves. Finally, analytical discussions of cosmological problems are reviewed, particularly Einstein, de Sitter, and Friedmann universes, redshifts, event horizons, and the redshift.
Energy Technology Data Exchange (ETDEWEB)
Orús, Román, E-mail: roman.orus@uni-mainz.de
2014-10-15
This is a partly non-technical introduction to selected topics on tensor network methods, based on several lectures and introductory seminars given on the subject. It should be a good place for newcomers to get familiarized with some of the key ideas in the field, specially regarding the numerics. After a very general introduction we motivate the concept of tensor network and provide several examples. We then move on to explain some basics about Matrix Product States (MPS) and Projected Entangled Pair States (PEPS). Selected details on some of the associated numerical methods for 1d and 2d quantum lattice systems are also discussed. - Highlights: • A practical introduction to selected aspects of tensor network methods is presented. • We provide analytical examples of MPS and 2d PEPS. • We provide basic aspects on several numerical methods for MPS and 2d PEPS. • We discuss a number of applications of tensor network methods from a broad perspective.
Probabilistic liver atlas construction.
Dura, Esther; Domingo, Juan; Ayala, Guillermo; Marti-Bonmati, Luis; Goceri, E
2017-01-13
Anatomical atlases are 3D volumes or shapes representing an organ or structure of the human body. They contain either the prototypical shape of the object of interest together with other shapes representing its statistical variations (statistical atlas) or a probability map of belonging to the object (probabilistic atlas). Probabilistic atlases are mostly built with simple estimations only involving the data at each spatial location. A new method for probabilistic atlas construction that uses a generalized linear model is proposed. This method aims to improve the estimation of the probability to be covered by the liver. Furthermore, all methods to build an atlas involve previous coregistration of the sample of shapes available. The influence of the geometrical transformation adopted for registration in the quality of the final atlas has not been sufficiently investigated. The ability of an atlas to adapt to a new case is one of the most important quality criteria that should be taken into account. The presented experiments show that some methods for atlas construction are severely affected by the previous coregistration step. We show the good performance of the new approach. Furthermore, results suggest that extremely flexible registration methods are not always beneficial, since they can reduce the variability of the atlas and hence its ability to give sensible values of probability when used as an aid in segmentation of new cases.
Classification of materials for conducting spheroids based on the first order polarization tensor
Khairuddin, TK Ahmad; Mohamad Yunos, N.; Aziz, ZA; Ahmad, T.; Lionheart, WRB
2017-09-01
Polarization tensor is an old terminology in mathematics and physics with many recent industrial applications including medical imaging, nondestructive testing and metal detection. In these applications, it is theoretically formulated based on the mathematical modelling either in electrics, electromagnetics or both. Generally, polarization tensor represents the perturbation in the electric or electromagnetic fields due to the presence of conducting objects and hence, it also desribes the objects. Understanding the properties of the polarization tensor is necessary and important in order to apply it. Therefore, in this study, when the conducting object is a spheroid, we show that the polarization tensor is positive-definite if and only if the conductivity of the object is greater than one. In contrast, we also prove that the polarization tensor is negative-definite if and only if the conductivity of the object is between zero and one. These features categorize the conductivity of the spheroid based on in its polarization tensor and can then help to classify the material of the spheroid.
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...
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...
Amir Farbin
The ATLAS Analysis Model is a continually developing vision of how to reconcile physics analysis requirements with the ATLAS offline software and computing model constraints. In the past year this vision has influenced the evolution of the ATLAS Event Data Model, the Athena software framework, and physics analysis tools. These developments, along with the October Analysis Model Workshop and the planning for CSC analyses have led to a rapid refinement of the ATLAS Analysis Model in the past few months. This article introduces some of the relevant issues and presents the current vision of the future ATLAS Analysis Model. Event Data Model The ATLAS Event Data Model (EDM) consists of several levels of details, each targeted for a specific set of tasks. For example the Event Summary Data (ESD) stores calorimeter cells and tracking system hits thereby permitting many calibration and alignment tasks, but will be only accessible at particular computing sites with potentially large latency. In contrast, the Analysis...
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
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
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...
Energy Technology Data Exchange (ETDEWEB)
Watson, R [Univ. College Dublin, Dept. of Electronic and Electrical Engineering, Dublin (Ireland); Landberg, L [Risoe National Lab., Meteorology and Wind Energy Dept., Roskilde (Denmark)
1999-03-01
The development work on the Irish Wind Atlas is nearing completion. The Irish Wind Atlas is an updated improved version of the Irish section of the European Wind Atlas. A map of the irish wind resource based on a WA{sup s}P analysis of the measured data and station description of 27 measuring stations is presented. The results of previously presented WA{sup s}P/KAMM runs show good agreement with these results. (au)
Smart, Ben; The ATLAS collaboration
2017-01-01
The High-Luminosity LHC will prove a challenging environment to work in, with for example $=200$ expected. It will however also provide great opportunities for advancing studies of the Higgs boson. The ATLAS detector will be upgraded, and Higgs prospects analyses have been performed to assess the reach of ATLAS Higgs studies in the HL-LHC era. These analyses are presented, as are Run-2 ATLAS di-Higgs analyses for comparison.
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
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.
Potentials for transverse trace-free tensors
International Nuclear Information System (INIS)
Conboye, Rory; Murchadha, Niall Ó
2014-01-01
In constructing and understanding initial conditions in the 3 + 1 formalism for numerical relativity, the transverse and trace-free (TT) part of the extrinsic curvature plays a key role. We know that TT tensors possess two degrees of freedom per space point. However, finding an expression for a TT tensor depending on only two scalar functions is a non-trivial task. Assuming either axial or translational symmetry, expressions depending on two scalar potentials alone are derived here for all TT tensors in flat 3-space. In a more general spatial slice, only one of these potentials is found, the same potential given in (Baker and Puzio 1999 Phys. Rev. D 59 044030) and (Dain 2001 Phys. Rev. D 64 124002), with the remaining equations reduced to a partial differential equation, depending on boundary conditions for a solution. As an exercise, we also derive the potentials which give the Bowen-York curvature tensor in flat space. (paper)
Loop optimization for tensor network renormalization
Yang, Shuo; Gu, Zheng-Cheng; Wen, Xiao-Gang
We introduce a tensor renormalization group scheme for coarse-graining a two-dimensional tensor network, which can be successfully applied to both classical and quantum systems on and off criticality. The key idea of our scheme is to deform a 2D tensor network into small loops and then optimize tensors on each loop. In this way we remove short-range entanglement at each iteration step, and significantly improve the accuracy and stability of the renormalization flow. We demonstrate our algorithm in the classical Ising model and a frustrated 2D quantum model. NSF Grant No. DMR-1005541 and NSFC 11274192, BMO Financial Group, John Templeton Foundation, Government of Canada through Industry Canada, Province of Ontario through the Ministry of Economic Development & Innovation.
An introduction to linear algebra and tensors
Akivis, M A; Silverman, Richard A
1978-01-01
Eminently readable, completely elementary treatment begins with linear spaces and ends with analytic geometry, covering multilinear forms, tensors, linear transformation, and more. 250 problems, most with hints and answers. 1972 edition.
Algebraic classification of the conformal tensor
International Nuclear Information System (INIS)
Ares de Parga, Gonzalo; Chavoya, O.; Lopez B, J.L.; Ovando Z, Gerardo
1989-01-01
Starting from the Petrov matrix method, we deduce a new algorithm (adaptable to computers), within the Newman-Penrose formalism, to obtain the algebraic type of the Weyl tensor in general relativity. (author)
Effects of tensor forces in nuclei
International Nuclear Information System (INIS)
Tanihata, Isao
2013-01-01
Recent studies of nuclei far from the stability line have revealed drastic changes in nuclear orbitals and reported the appearance of new magic numbers and the disappearance of magic numbers observed at the stability line. One of the important reasons for such changes is considered to be because of the effect of tensor forces on nuclear structure. Although the role of tensor forces in binding very light nuclei such as deuterons and 4 He has been known, direct experimental evidence for the effect on nuclear structure is scarce. In this paper, I review known effects of tensor forces in nuclei and then discuss the recently raised question of s–p wave mixing in a halo nucleus of 11 Li. Following these reviews, the development of a new experiment to see the high-momentum components due to the tensor forces is discussed and some of the new data are presented. (paper)
The energy–momentum tensor(s in classical gauge theories
Directory of Open Access Journals (Sweden)
Daniel N. Blaschke
2016-11-01
Full Text Available We give an introduction to, and review of, the energy–momentum tensors in classical gauge field theories in Minkowski space, and to some extent also in curved space–time. For the canonical energy–momentum tensor of non-Abelian gauge fields and of matter fields coupled to such fields, we present a new and simple improvement procedure based on gauge invariance for constructing a gauge invariant, symmetric energy–momentum tensor. The relationship with the Einstein–Hilbert tensor following from the coupling to a gravitational field is also discussed.
Geometric decomposition of the conformation tensor in viscoelastic turbulence
Hameduddin, Ismail; Meneveau, Charles; Zaki, Tamer A.; Gayme, Dennice F.
2018-05-01
This work introduces a mathematical approach to analysing the polymer dynamics in turbulent viscoelastic flows that uses a new geometric decomposition of the conformation tensor, along with associated scalar measures of the polymer fluctuations. The approach circumvents an inherent difficulty in traditional Reynolds decompositions of the conformation tensor: the fluctuating tensor fields are not positive-definite and so do not retain the physical meaning of the tensor. The geometric decomposition of the conformation tensor yields both mean and fluctuating tensor fields that are positive-definite. The fluctuating tensor in the present decomposition has a clear physical interpretation as a polymer deformation relative to the mean configuration. Scalar measures of this fluctuating conformation tensor are developed based on the non-Euclidean geometry of the set of positive-definite tensors. Drag-reduced viscoelastic turbulent channel flow is then used an example case study. The conformation tensor field, obtained using direct numerical simulations, is analysed using the proposed framework.
Estimation of Uncertainties of Full Moment Tensors
2017-10-06
For our moment tensor inversions, we use the ‘cut-and-paste’ ( CAP ) code of Zhu and Helmberger (1996) and Zhu and Ben-Zion (2013), with some...modifications. For the misfit function we use an L1 norm Silwal and Tape (2016), and we incorporate the number of misfitting polarities into the waveform... norm of the eigenvalue triple provides the magnitude of the moment tensor, leaving two free parameters to define the source type. In the same year
Superconformal tensor calculus in five dimensions
International Nuclear Information System (INIS)
Fujita, Tomoyuki; Ohashi, Keisuke
2001-01-01
We present a full superconformal tensor calculus in five spacetime dimensions in which the Weyl multiplet has 32 Bose plus 32 Fermi degrees of freedom. It is derived using dimensional reduction from the 6D superconformal tensor calculus. We present two types of 32+32 Weyl multiplets, a vector multiplet, linear multiplet, hypermultiplet and nonlinear multiplet. Their superconformal transformation laws and the embedding and invariant action formulas are given. (author)
Goldsborough, Peter
2016-01-01
Deep learning is a branch of artificial intelligence employing deep neural network architectures that has significantly advanced the state-of-the-art in computer vision, speech recognition, natural language processing and other domains. In November 2015, Google released $\\textit{TensorFlow}$, an open source deep learning software library for defining, training and deploying machine learning models. In this paper, we review TensorFlow and put it in context of modern deep learning concepts and ...
Geometrical foundations of tensor calculus and relativity
Schuller , Frédéric; Lorent , Vincent
2006-01-01
Manifolds, particularly space curves: basic notions 1 The first groundform, the covariant metric tensor 11 The second groundform, Meusnier's theorem 19 Transformation groups in the plane 28 Co- and contravariant components for a special affine transformation in the plane 29 Surface vectors 32 Elements of tensor calculus 36 Generalization of the first groundform to the space 46 The covariant (absolute) derivation 57 Examples from elasticity theory 61 Geodesic lines 63 Main curvatur...
Smartphone dependence classification using tensor factorization
Kim, Yejin; Yook, In Hye; Yu, Hwanjo; Kim, Dai-Jin
2017-01-01
Excessive smartphone use causes personal and social problems. To address this issue, we sought to derive usage patterns that were directly correlated with smartphone dependence based on usage data. This study attempted to classify smartphone dependence using a data-driven prediction algorithm. We developed a mobile application to collect smartphone usage data. A total of 41,683 logs of 48 smartphone users were collected from March 8, 2015, to January 8, 2016. The participants were classified into the control group (SUC) or the addiction group (SUD) using the Korean Smartphone Addiction Proneness Scale for Adults (S-Scale) and a face-to-face offline interview by a psychiatrist and a clinical psychologist (SUC = 23 and SUD = 25). We derived usage patterns using tensor factorization and found the following six optimal usage patterns: 1) social networking services (SNS) during daytime, 2) web surfing, 3) SNS at night, 4) mobile shopping, 5) entertainment, and 6) gaming at night. The membership vectors of the six patterns obtained a significantly better prediction performance than the raw data. For all patterns, the usage times of the SUD were much longer than those of the SUC. From our findings, we concluded that usage patterns and membership vectors were effective tools to assess and predict smartphone dependence and could provide an intervention guideline to predict and treat smartphone dependence based on usage data. PMID:28636614
Smartphone dependence classification using tensor factorization.
Directory of Open Access Journals (Sweden)
Jingyun Choi
Full Text Available Excessive smartphone use causes personal and social problems. To address this issue, we sought to derive usage patterns that were directly correlated with smartphone dependence based on usage data. This study attempted to classify smartphone dependence using a data-driven prediction algorithm. We developed a mobile application to collect smartphone usage data. A total of 41,683 logs of 48 smartphone users were collected from March 8, 2015, to January 8, 2016. The participants were classified into the control group (SUC or the addiction group (SUD using the Korean Smartphone Addiction Proneness Scale for Adults (S-Scale and a face-to-face offline interview by a psychiatrist and a clinical psychologist (SUC = 23 and SUD = 25. We derived usage patterns using tensor factorization and found the following six optimal usage patterns: 1 social networking services (SNS during daytime, 2 web surfing, 3 SNS at night, 4 mobile shopping, 5 entertainment, and 6 gaming at night. The membership vectors of the six patterns obtained a significantly better prediction performance than the raw data. For all patterns, the usage times of the SUD were much longer than those of the SUC. From our findings, we concluded that usage patterns and membership vectors were effective tools to assess and predict smartphone dependence and could provide an intervention guideline to predict and treat smartphone dependence based on usage data.
Smartphone dependence classification using tensor factorization.
Choi, Jingyun; Rho, Mi Jung; Kim, Yejin; Yook, In Hye; Yu, Hwanjo; Kim, Dai-Jin; Choi, In Young
2017-01-01
Excessive smartphone use causes personal and social problems. To address this issue, we sought to derive usage patterns that were directly correlated with smartphone dependence based on usage data. This study attempted to classify smartphone dependence using a data-driven prediction algorithm. We developed a mobile application to collect smartphone usage data. A total of 41,683 logs of 48 smartphone users were collected from March 8, 2015, to January 8, 2016. The participants were classified into the control group (SUC) or the addiction group (SUD) using the Korean Smartphone Addiction Proneness Scale for Adults (S-Scale) and a face-to-face offline interview by a psychiatrist and a clinical psychologist (SUC = 23 and SUD = 25). We derived usage patterns using tensor factorization and found the following six optimal usage patterns: 1) social networking services (SNS) during daytime, 2) web surfing, 3) SNS at night, 4) mobile shopping, 5) entertainment, and 6) gaming at night. The membership vectors of the six patterns obtained a significantly better prediction performance than the raw data. For all patterns, the usage times of the SUD were much longer than those of the SUC. From our findings, we concluded that usage patterns and membership vectors were effective tools to assess and predict smartphone dependence and could provide an intervention guideline to predict and treat smartphone dependence based on usage data.
One-loop tensor Feynman integral reduction with signed minors
International Nuclear Information System (INIS)
Fleischer, J.; Yundin, V.
2011-12-01
We present an algebraic approach to one-loop tensor integral reduction. The integrals are presented in terms of scalar one- to four-point functions. The reduction is worked out explicitly until five-point functions of rank five. The numerical C++ package PJFry evaluates tensor coefficients in terms of a basis of scalar integrals, which is provided by an external library, e.g. QCDLoop. We shortly describe installation and use of PJFry. Examples for numerical results are shown, including a special treatment for small or vanishing inverse four-point Gram determinants. An extremely efficient application of the formalism is the immediate evaluation of complete contractions of the tensor integrals with external momenta. This leads to the problem of evaluating sums over products of signed minors with scalar products of chords. Chords are differences of external momenta. These sums may be evaluated analytically in a systematic way. The final expressions for the numerical evaluation are then compact combinations of the contributing basic scalar functions. (orig.)
One-loop tensor Feynman integral reduction with signed minors
Energy Technology Data Exchange (ETDEWEB)
Fleischer, J. [Bielefeld Univ. (Germany). Fakultaet fuer Physik; Riemann, T. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Yundin, V. [Copenhagen Univ. (Denmark). Niels Bohr International Academy and Discovery Center
2011-12-15
We present an algebraic approach to one-loop tensor integral reduction. The integrals are presented in terms of scalar one- to four-point functions. The reduction is worked out explicitly until five-point functions of rank five. The numerical C++ package PJFry evaluates tensor coefficients in terms of a basis of scalar integrals, which is provided by an external library, e.g. QCDLoop. We shortly describe installation and use of PJFry. Examples for numerical results are shown, including a special treatment for small or vanishing inverse four-point Gram determinants. An extremely efficient application of the formalism is the immediate evaluation of complete contractions of the tensor integrals with external momenta. This leads to the problem of evaluating sums over products of signed minors with scalar products of chords. Chords are differences of external momenta. These sums may be evaluated analytically in a systematic way. The final expressions for the numerical evaluation are then compact combinations of the contributing basic scalar functions. (orig.)
Calibrating a tensor magnetic gradiometer using spin data
Bracken, Robert E.; Smith, David V.; Brown, Philip J.
2005-01-01
Scalar magnetic data are often acquired to discern characteristics of geologic source materials and buried objects. It is evident that a great deal can be done with scalar data, but there are significant advantages to direct measurement of the magnetic gradient tensor in applications with nearby sources, such as unexploded ordnance (UXO). To explore these advantages, we adapted a prototype tensor magnetic gradiometer system (TMGS) and successfully implemented a data-reduction procedure. One of several critical reduction issues is the precise determination of a large group of calibration coefficients for the sensors and sensor array. To resolve these coefficients, we devised a spin calibration method, after similar methods of calibrating space-based magnetometers (Snare, 2001). The spin calibration procedure consists of three parts: (1) collecting data by slowly revolving the sensor array in the Earth?s magnetic field, (2) deriving a comprehensive set of coefficients from the spin data, and (3) applying the coefficients to the survey data. To show that the TMGS functions as a tensor gradiometer, we conducted an experimental survey that verified that the reduction procedure was effective (Bracken and Brown, in press). Therefore, because it was an integral part of the reduction, it can be concluded that the spin calibration was correctly formulated with acceptably small errors.
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.
Measuring Nematic Susceptibilities from the Elastoresistivity Tensor
Hristov, A. T.; Shapiro, M. C.; Hlobil, Patrick; Maharaj, Akash; Chu, Jiun-Haw; Fisher, Ian
The elastoresistivity tensor mijkl relates changes in resistivity to the strain on a material. As a fourth-rank tensor, it contains considerably more information about the material than the simpler (second-rank) resistivity tensor; in particular, certain elastoresistivity coefficients can be related to thermodynamic susceptibilities and serve as a direct probe of symmetry breaking at a phase transition. The aim of this talk is twofold. First, we enumerate how symmetry both constrains the structure of the elastoresistivity tensor into an easy-to-understand form and connects tensor elements to thermodynamic susceptibilities. In the process, we generalize previous studies of elastoresistivity to include the effects of magnetic field. Second, we describe an approach to measuring quantities in the elastoresistivity tensor with a novel transverse measurement, which is immune to relative strain offsets. These techniques are then applied to BaFe2As2 in a proof of principle measurement. This work is supported by the Department of Energy, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division, under Contract DE-AC02-76SF00515.
On the concircular curvature tensor of Riemannian manifolds
International Nuclear Information System (INIS)
Rahman, M.S.; Lal, S.
1990-06-01
Definition of the concircular curvature tensor, Z hijk , along with Z-tensor, Z ij , is given and some properties of Z hijk are described. Tensors identical with Z hijk are shown. A necessary and sufficient condition that a Riemannian V n has zero Z-tensor is found. A number of theorems on concircular symmetric space, concircular recurrent space (Z n -space) and Z n -space with zero Z-tensor are deduced. (author). 6 refs
(Ln-bar, g)-spaces. Special tensor fields
International Nuclear Information System (INIS)
Manoff, S.; Dimitrov, B.
1998-01-01
The Kronecker tensor field, the contraction tensor field, as well as the multi-Kronecker and multi-contraction tensor fields are determined and the action of the covariant differential operator, the Lie differential operator, the curvature operator, and the deviation operator on these tensor fields is established. The commutation relations between the operators Sym and Asym and the covariant and Lie differential operators are considered acting on symmetric and antisymmetric tensor fields over (L n bar, g)-spaces
Eigenvector of gravity gradient tensor for estimating fault dips considering fault type
Kusumoto, Shigekazu
2017-12-01
The dips of boundaries in faults and caldera walls play an important role in understanding their formation mechanisms. The fault dip is a particularly important parameter in numerical simulations for hazard map creation as the fault dip affects estimations of the area of disaster occurrence. In this study, I introduce a technique for estimating the fault dip using the eigenvector of the observed or calculated gravity gradient tensor on a profile and investigating its properties through numerical simulations. From numerical simulations, it was found that the maximum eigenvector of the tensor points to the high-density causative body, and the dip of the maximum eigenvector closely follows the dip of the normal fault. It was also found that the minimum eigenvector of the tensor points to the low-density causative body and that the dip of the minimum eigenvector closely follows the dip of the reverse fault. It was shown that the eigenvector of the gravity gradient tensor for estimating fault dips is determined by fault type. As an application of this technique, I estimated the dip of the Kurehayama Fault located in Toyama, Japan, and obtained a result that corresponded to conventional fault dip estimations by geology and geomorphology. Because the gravity gradient tensor is required for this analysis, I present a technique that estimates the gravity gradient tensor from the gravity anomaly on a profile.
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.
Estimate of the neutron fields in ATLAS based on ATLAS-MPX detectors data
Energy Technology Data Exchange (ETDEWEB)
Bouchami, J; Dallaire, F; Gutierrez, A; Idarraga, J; Leroy, C; Picard, S; Scallon, O [Universite de Montreal, Montreal, Quebec H3C 3J7 (Canada); Kral, V; PospIsil, S; Solc, J; Suk, M; Turecek, D; Vykydal, Z; Zemlieka, J, E-mail: scallon@lps.umontreal.ca [Institute of Experimental and Applied Physics of the CTU in Prague, Horska 3a/22, CZ-12800 Praha2 - Albertov (Czech Republic)
2011-01-15
The ATLAS-MPX detectors are based on Medipix2 silicon devices designed by CERN for the detection of different types of radiation. These detectors are covered with converting layers of {sup 6}LiF and polyethylene (PE) to increase their sensitivity to thermal and fast neutrons, respectively. These devices allow the measurement of the composition and spectroscopic characteristics of the radiation field in ATLAS, particularly of neutrons. These detectors can operate in low or high preset energy threshold mode. The signature of particles interacting in a ATLAS-MPX detector at low threshold are clusters of adjacent pixels with different size and form depending on their type, energy and incidence angle. The classification of particles into different categories can be done using the geometrical parameters of these clusters. The Medipix analysis framework (MAFalda) - based on the ROOT application - allows the recognition of particle tracks left in ATLAS-MPX devices located at various positions in the ATLAS detector and cavern. The pattern recognition obtained from the application of MAFalda was configured to distinguish the response of neutrons from other radiation. The neutron response at low threshold is characterized by clusters of adjoining pixels (heavy tracks and heavy blobs) left by protons and heavy ions resulting from neutron interactions in the converting layers of the ATLAS-MPX devices. The neutron detection efficiency of ATLAS-MPX devices has been determined by the exposure of two detectors of reference to radionuclide sources of neutrons ({sup 252}Cf and {sup 241}AmBe). With these results, an estimate of the neutrons fields produced at the devices locations during ATLAS operation was done.
Estimate of the neutron fields in ATLAS based on ATLAS-MPX detectors data
International Nuclear Information System (INIS)
Bouchami, J; Dallaire, F; Gutierrez, A; Idarraga, J; Leroy, C; Picard, S; Scallon, O; Kral, V; PospIsil, S; Solc, J; Suk, M; Turecek, D; Vykydal, Z; Zemlieka, J
2011-01-01
The ATLAS-MPX detectors are based on Medipix2 silicon devices designed by CERN for the detection of different types of radiation. These detectors are covered with converting layers of 6 LiF and polyethylene (PE) to increase their sensitivity to thermal and fast neutrons, respectively. These devices allow the measurement of the composition and spectroscopic characteristics of the radiation field in ATLAS, particularly of neutrons. These detectors can operate in low or high preset energy threshold mode. The signature of particles interacting in a ATLAS-MPX detector at low threshold are clusters of adjacent pixels with different size and form depending on their type, energy and incidence angle. The classification of particles into different categories can be done using the geometrical parameters of these clusters. The Medipix analysis framework (MAFalda) - based on the ROOT application - allows the recognition of particle tracks left in ATLAS-MPX devices located at various positions in the ATLAS detector and cavern. The pattern recognition obtained from the application of MAFalda was configured to distinguish the response of neutrons from other radiation. The neutron response at low threshold is characterized by clusters of adjoining pixels (heavy tracks and heavy blobs) left by protons and heavy ions resulting from neutron interactions in the converting layers of the ATLAS-MPX devices. The neutron detection efficiency of ATLAS-MPX devices has been determined by the exposure of two detectors of reference to radionuclide sources of neutrons ( 252 Cf and 241 AmBe). With these results, an estimate of the neutrons fields produced at the devices locations during ATLAS operation was done.
Estimate of the neutron fields in ATLAS based on ATLAS-MPX detectors data
Bouchami, J.; Dallaire, F.; Gutiérrez, A.; Idarraga, J.; Král, V.; Leroy, C.; Picard, S.; Pospíšil, S.; Scallon, O.; Solc, J.; Suk, M.; Turecek, D.; Vykydal, Z.; Žemlièka, J.
2011-01-01
The ATLAS-MPX detectors are based on Medipix2 silicon devices designed by CERN for the detection of different types of radiation. These detectors are covered with converting layers of 6LiF and polyethylene (PE) to increase their sensitivity to thermal and fast neutrons, respectively. These devices allow the measurement of the composition and spectroscopic characteristics of the radiation field in ATLAS, particularly of neutrons. These detectors can operate in low or high preset energy threshold mode. The signature of particles interacting in a ATLAS-MPX detector at low threshold are clusters of adjacent pixels with different size and form depending on their type, energy and incidence angle. The classification of particles into different categories can be done using the geometrical parameters of these clusters. The Medipix analysis framework (MAFalda) — based on the ROOT application — allows the recognition of particle tracks left in ATLAS-MPX devices located at various positions in the ATLAS detector and cavern. The pattern recognition obtained from the application of MAFalda was configured to distinguish the response of neutrons from other radiation. The neutron response at low threshold is characterized by clusters of adjoining pixels (heavy tracks and heavy blobs) left by protons and heavy ions resulting from neutron interactions in the converting layers of the ATLAS-MPX devices. The neutron detection efficiency of ATLAS-MPX devices has been determined by the exposure of two detectors of reference to radionuclide sources of neutrons (252Cf and 241AmBe). With these results, an estimate of the neutrons fields produced at the devices locations during ATLAS operation was done.
International Nuclear Information System (INIS)
Ahmad, I.; Glagola, B.
1996-06-01
This report contains the following topics: Status of the ATLAS Accelerator; Highlights of Recent Research at ATLAS; Program Advisory Committee; ATLAS User Group Executive Committee; FMA Information Available On The World Wide Web; Conference on Nuclear Structure at the Limits; and Workshop on Experiments with Gammasphere at ATLAS
2012-06-15
... Mid-Continent WestTex, LLC; Pioneer Natural Resources USA, Inc.; Notice of Application Take notice that on May 30, 2012, Atlas Pipeline Mid-Continent WestTex, LLC (Atlas) and Pioneer Natural Resources... President and General Counsel, Atlas Pipeline Mid-Continent, LLC, 110 W. 7th Street, Suite 2300, Tulsa, OK...
Energy Technology Data Exchange (ETDEWEB)
Bussat, Jean-Marie [Universite de Paris Sud, 91 - Orsay (France)
1998-06-05
The construction of the new particle accelerator, the LHC (Large Hadron Collider) at CERN is entails many research and development projects. It is the case in electronics where the problem of the acquisition of large dynamic range signals at high sampling frequencies occurs. Typically, the requirements are a dynamic range of about 65,000 (around 16 bits) at 40 MHz. Some solutions to this problem will be presented. One of them is using a commercial analog-to-digital converter. This case brings up the necessity of a signal conditioning equipment. This thesis describes a way of building such a system that will be called `multi-gain system`. Then, an application of this method is presented. It involves the realization of an automatic gain switching integrated circuit. It is designed for the readout of the ATLAS electromagnetic calorimeter. The choice and the calculation of the components of this systems are described. They are followed by the results of some measurements done on a prototype made using the AMS 1.2{mu}m BiCMOS foundry. Possible enhancements are also presented. We conclude on the feasibility of such a system and its various applications in a number of fields that are not restricted to particle physics. (author) 33 refs., 132 figs., 22 tabs.
Goldfarb, S
2005-01-01
As reported in the September 2004 ATLAS eNews, the Web Lecture Archive Project is a system for the archiving and publishing of multimedia presentations, using the Web as medium. We list here newly available WLAP items relating to ATLAS: Atlas Software Week Plenary 6-10 December 2004 North American ATLAS Physics Workshop (Tucson) 20-21 December 2004 (17 talks) Physics Analysis Tools Tutorial (Tucson) 19 December 2004 Full Chain Tutorial 21 September 2004 ATLAS Plenary Sessions, 17-18 February 2005 (17 talks) Coming soon: ATLAS Tutorial on Electroweak Physics, 14 Feb. 2005 Software Workshop, 21-22 February 2005 Click here to browse WLAP for all ATLAS lectures.
Marin Quintero, Maider J.
2013-01-01
The structure tensor for vector valued images is most often defined as the average of the scalar structure tensors in each band. The problem with this definition is the assumption that all bands provide the same amount of edge information giving them the same weights. As a result non-edge pixels can be reinforced and edges can be weakened…
Lepore, N; Brun, C; Chou, Y Y; Chiang, M C; Dutton, R A; Hayashi, K M; Luders, E; Lopez, O L; Aizenstein, H J; Toga, A W; Becker, J T; Thompson, P M
2008-01-01
This paper investigates the performance of a new multivariate method for tensor-based morphometry (TBM). Statistics on Riemannian manifolds are developed that exploit the full information in deformation tensor fields. In TBM, multiple brain images are warped to a common neuroanatomical template via 3-D nonlinear registration; the resulting deformation fields are analyzed statistically to identify group differences in anatomy. Rather than study the Jacobian determinant (volume expansion factor) of these deformations, as is common, we retain the full deformation tensors and apply a manifold version of Hotelling's $T(2) test to them, in a Log-Euclidean domain. In 2-D and 3-D magnetic resonance imaging (MRI) data from 26 HIV/AIDS patients and 14 matched healthy subjects, we compared multivariate tensor analysis versus univariate tests of simpler tensor-derived indices: the Jacobian determinant, the trace, geodesic anisotropy, and eigenvalues of the deformation tensor, and the angle of rotation of its eigenvectors. We detected consistent, but more extensive patterns of structural abnormalities, with multivariate tests on the full tensor manifold. Their improved power was established by analyzing cumulative p-value plots using false discovery rate (FDR) methods, appropriately controlling for false positives. This increased detection sensitivity may empower drug trials and large-scale studies of disease that use tensor-based morphometry.
Tensor network state correspondence and holography
Singh, Sukhwinder
2018-01-01
In recent years, tensor network states have emerged as a very useful conceptual and simulation framework to study quantum many-body systems at low energies. In this paper, we describe a particular way in which any given tensor network can be viewed as a representation of two different quantum many-body states. The two quantum many-body states are said to correspond to each other by means of the tensor network. We apply this "tensor network state correspondence"—a correspondence between quantum many-body states mediated by tensor networks as we describe—to the multi-scale entanglement renormalization ansatz (MERA) representation of ground states of one dimensional (1D) quantum many-body systems. Since the MERA is a 2D hyperbolic tensor network (the extra dimension is identified as the length scale of the 1D system), the two quantum many-body states obtained from the MERA, via tensor network state correspondence, are seen to live in the bulk and on the boundary of a discrete hyperbolic geometry. The bulk state so obtained from a MERA exhibits interesting features, some of which caricature known features of the holographic correspondence of String theory. We show how (i) the bulk state admits a description in terms of "holographic screens", (ii) the conformal field theory data associated with a critical ground state can be obtained from the corresponding bulk state, in particular, how pointlike boundary operators are identified with extended bulk operators. (iii) We also present numerical results to illustrate that bulk states, dual to ground states of several critical spin chains, have exponentially decaying correlations, and that the bulk correlation length generally decreases with increase in central charge for these spin chains.
ATLAS Brochure (English version)
Lefevre, Christiane
2011-01-01
ATLAS is the largest detector at the LHC, the most powerful particle accelerator in the world, which will start up in 2008. ATLAS is a multi-purpose detector, designed to throw light on fundamental questions such as the origin of mass and the nature of the Universe's dark matter.
ATLAS brochure (Italian version)
Lefevre, C
2010-01-01
ATLAS is the largest detector at the LHC, the most powerful particle accelerator in the world. ATLAS is a multi-purpose detector, designed to throw light on fundamental questions such as the origin of mass and the nature of the Universe's dark matter.
ATLAS brochure (French version)
Lefevre, C
2012-01-01
ATLAS is the largest detector at the LHC, the most powerful particle accelerator in the world. ATLAS is a multi-purpose detector, designed to throw light on fundamental questions such as the origin of mass and the nature of the Universe's dark matter.
ATLAS brochure (German version)
Lefevre, C
2012-01-01
ATLAS is the largest detector at the LHC, the most powerful particle accelerator in the world. ATLAS is a multi-purpose detector, designed to throw light on fundamental questions such as the origin of mass and the nature of the Universe's dark matter.
ATLAS brochure (Danish version)
Lefevre, C
2010-01-01
ATLAS is the largest detector at the LHC, the most powerful particle accelerator in the world. ATLAS is a multi-purpose detector, designed to throw light on fundamental questions such as the origin of mass and the nature of the Universe's dark matter.
Biondi, Silvia
2016-01-01
Winners of the ATLAS Thesis Award were presented with certificates and glass cubes during a ceremony on Thursday 25 February. The winners also presented their work in front of members of the ATLAS Collaboration. Winners: Javier Montejo Berlingen, Barcelona (Spain), Ruth Pöttgen, Mainz (Germany), Nils Ruthmann, Freiburg (Germany), and Steven Schramm, Toronto (Canada).
M Ed Uwe Krause
2008-01-01
Uwe Krause: Atlas of Eurpean Values De Atlas of European Values is een samenwerkingsproject met bijbehorende website van de Universiteit van Tilburg en Fontys Lerarenopleiding in Tilburg, waarbij de wetenschappelijke data van de European Values Study (EVS) voor het onderwijs toegankelijk worden
Claudia Marcelloni de Oliveira; Pauline Gagnon
It must be all the training we are getting every day, running around trying to get everything ready for the start of the LHC next year. This year, the ATLAS runners were in fine form and came in force. Nine ATLAS teams signed up for the 37th Annual CERN Relay Race with six runners per team. Under a blasting sun on Wednesday 23rd May 2007, each team covered the distances of 1000m, 800m, 800m, 500m, 500m and 300m taking the runners around the whole Meyrin site, hills included. A small reception took place in the ATLAS secretariat a week later to award the ATLAS Cup to the best ATLAS team. For the details on this complex calculation which takes into account the age of each runner, their gender and the color of their shoes, see the July 2006 issue of ATLAS e-news. The ATLAS Running Athena Team, the only all-women team enrolled this year, won the much coveted ATLAS Cup for the second year in a row. In fact, they are so good that Peter Schmid and Patrick Fassnacht are wondering about reducing the women's bonus in...
Anthony, Katarina
2016-01-01
The ATLAS Experiment Colouring Book is a free-to-download educational book, ideal for kids aged 5-9. It aims to introduce children to the field of High-Energy Physics, as well as the work being carried out by the ATLAS Collaboration.
ATLAS brochure (Catalan version)
Lefevre, C
2008-01-01
ATLAS is the largest detector at the LHC, the most powerful particle accelerator in the world, which will start up in 2008. ATLAS is a multi-purpose detector, designed to throw light on fundamental questions such as the origin of mass and the nature of the Universe's dark matter.
ATLAS Brochure (french version)
Marcastel, F
2007-01-01
ATLAS is the largest detector at the LHC, the most powerful particle accelerator in the world, which will start up in 2008. ATLAS is a multi-purpose detector, designed to throw light on fundamental questions such as the origin of mass and the nature of the Universe's dark matter.
ATLAS brochure (Polish version)
Lefevre, C
2007-01-01
ATLAS is the largest detector at the LHC, the most powerful particle accelerator in the world, which will start up in 2008. ATLAS is a multi-purpose detector, designed to throw light on fundamental questions such as the origin of mass and the nature of the Universe's dark matter.
ATLAS brochure (Norwegian version)
Lefevre, C
2009-01-01
ATLAS is the largest detector at the LHC, the most powerful particle accelerator in the world. ATLAS is a multi-purpose detector, designed to throw light on fundamental questions such as the origin of mass and the nature of the Universe's dark matter. Français
ATLAS Brochure (german version)
Marcastel, F
2007-01-01
ATLAS is the largest detector at the LHC, the most powerful particle accelerator in the world, which will start up in 2008. ATLAS is a multi-purpose detector, designed to throw light on fundamental questions such as the origin of mass and the nature of the Universe's dark matter.
ATLAS Brochure (english version)
Marcastel, F
2007-01-01
ATLAS is the largest detector at the LHC, the most powerful particle accelerator in the world, which will start up in 2008. ATLAS is a multi-purpose detector, designed to throw light on fundamental questions such as the origin of mass and the nature of the Universe's dark matter.
ATLAS brochure (Spanish version)
Lefevre, C
2008-01-01
ATLAS is the largest detector at the LHC, the most powerful particle accelerator in the world, which will start up in 2008. ATLAS is a multi-purpose detector, designed to throw light on fundamental questions such as the origin of mass and the nature of the Universe's dark matter.
claudia Marcelloni
2009-01-01
ATLAS Visitors Centre has opened its shiny new doors to the public. Officially launched on Monday February 23rd, 2009, the permanent exhibition at Point 1 was conceived as a tour resource for ATLAS guides, and as a way to preserve the public’s opportunity to get a close-up look at the experiment in action when the cavern is sealed.
2004-01-01
An entire section of the ATLAS detector is being assembled at Prévessin. Since May the components have been tested using a beam from the SPS, giving the ATLAS team valuable experience of operating the detector as well as an opportunity to debug the system.
Maximilien Brice
2006-01-01
For contributing vital pieces to the ATLAS puzzle, three industries were recognized on Friday 5 May during a supplier awards ceremony. After a welcome and overview of the ATLAS experiment by spokesperson Peter Jenni, CERN Secretary-General Maximilian Metzger stressed the importance of industry to CERN's scientific goals. Picture 30 : representatives of the three award-wining companies after the ceremony
AGIS: Evolution of Distributed Computing information system for ATLAS
Anisenkov, A.; Di Girolamo, A.; Alandes, M.; Karavakis, E.
2015-12-01
ATLAS, a particle physics experiment at the Large Hadron Collider at CERN, produces petabytes of data annually through simulation production and tens of petabytes of data per year from the detector itself. The ATLAS computing model embraces the Grid paradigm and a high degree of decentralization of computing resources in order to meet the ATLAS requirements of petabytes scale data operations. It has been evolved after the first period of LHC data taking (Run-1) in order to cope with new challenges of the upcoming Run- 2. In this paper we describe the evolution and recent developments of the ATLAS Grid Information System (AGIS), developed in order to integrate configuration and status information about resources, services and topology of the computing infrastructure used by the ATLAS Distributed Computing applications and services.
European Wind Atlas and Wind Resource Research in Denmark
DEFF Research Database (Denmark)
Mortensen, Niels Gylling
to estimate the actual wind climate at any specific site and height within this region. The Danish and European Wind Atlases are examples of how the wind atlas methodology can be employed to estimate the wind resource potential for a country or a sub-continent. Recently, the methodology has also been used...... - from wind measurements at prospective sites to wind tunnel simulations and advanced flow modelling. Among these approaches, the wind atlas methodology - developed at Ris0 National Laboratory over the last 25 years - has gained widespread recognition and is presently considered by many as the industry......-standard tool for wind resource assessment and siting of wind turbines. The PC-implementation of the methodology, the Wind Atlas Analysis and Application Program (WAsP), has been applied in more than 70 countries and territories world-wide. The wind atlas methodology is based on physical descriptions and models...
Toward the holistic, reference, and extendable atlas of the human brain, head, and neck.
Nowinski, Wieslaw L
2015-06-01
Despite numerous efforts, a fairly complete (holistic) anatomical model of the whole, normal, adult human brain, which is required as the reference in brain studies and clinical applications, has not yet been constructed. Our ultimate objective is to build this kind of atlas from advanced in vivo imaging. This work presents the taxonomy of our currently developed brain atlases and addresses the design, content, functionality, and current results in the holistic atlas development as well as atlas usefulness and future directions. We have developed to date 35 commercial brain atlases (along with numerous research prototypes), licensed to 63 companies and institutions, and made available to medical societies, organizations, medical schools, and individuals. These atlases have been applied in education, research, and clinical applications. Hundreds of thousands of patients have been treated by using our atlases. Based on this experience, the first version of the holistic and reference atlas of the brain, head, and neck has been developed and made available. The atlas has been created from multispectral 3 and 7 Tesla and high-resolution CT in vivo scans. It is fully 3D, scalable, interactive, and highly detailed with about 3,000 labeled components. This atlas forms a foundation for the development of a multi-level molecular, cellular, anatomical, physiological, and behavioral brain atlas platform.
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)
The ATLAS collaboration
2018-01-01
The current ATLAS model of Open Access to recorded and simulated data offers the opportunity to access datasets with a focus on education, training and outreach. This mandate supports the creation of platforms, projects, software, and educational products used all over the planet. We describe the overall status of ATLAS Open Data (http://opendata.atlas.cern) activities, from core ATLAS activities and releases to individual and group efforts, as well as educational programs, and final web or software-based (and hard-copy) products that have been produced or are under development. The relatively large number and heterogeneous use cases currently documented is driving an upcoming release of more data and resources for the ATLAS Community and anyone interested to explore the world of experimental particle physics and the computer sciences through data analysis.
PH Department
2008-01-01
We are collecting old pairs of glasses to take out to Mali, where they can be re-used by people there. The price for a pair of glasses can often exceed 3 months salary, so they are prohibitively expensive for many people. If you have any old spectacles you can donate, please put them in the special box in the ATLAS secretariat, bldg.40-4-D01 before the Christmas closure on 19 December so we can take them with us when we leave for Africa at the end of the month. (more details in ATLAS e-news edition of 29 September 2008: http://atlas-service-enews.web.cern.ch/atlas-service-enews/news/news_mali.php) many thanks! Katharine Leney co-driver of the ATLAS car on the Charity Run to Mali
DEFF Research Database (Denmark)
The results of a comprehensive, 8-year wind resource assessment programme in Egypt are presented. The objective has been to provide reliable and accurate wind atlas data sets for evaluating the potential wind power output from large electricityproducing wind turbine installations. The regional wind...... climates of Egypt have been determined by two independent methods: a traditional wind atlas based on observations from more than 30 stations all over Egypt, and a numerical wind atlas based on long-term reanalysis data and a mesoscale model (KAMM). The mean absolute error comparing the two methods is about...... 10% for two large-scale KAMM domains covering all of Egypt, and typically about 5% for several smaller-scale regional domains. The numerical wind atlas covers all of Egypt, whereas the meteorological stations are concentrated in six regions. The Wind Atlas for Egypt represents a significant step...
International Nuclear Information System (INIS)
Hodgkinson, Mark; Seuster, Rolf; Simmons, Brinick; Sherwood, Peter; Rousseau, David
2012-01-01
The ATLAS collaboration operates an extensive set of protocols to validate the quality of the offline software in a timely manner. This is essential in order to process the large amounts of data being collected by the ATLAS detector in 2011 without complications on the offline software side. We will discuss a number of different strategies used to validate the ATLAS offline software; running the ATLAS framework software, Athena, in a variety of configurations daily on each nightly build via the ATLAS Nightly System (ATN) and Run Time Tester (RTT) systems; the monitoring of these tests and checking the compilation of the software via distributed teams of rotating shifters; monitoring of and follow up on bug reports by the shifter teams and periodic software cleaning weeks to improve the quality of the offline software further.