WorldWideScience

Sample records for totally antisymmetric tensor

  1. Antisymmetric tensor generalizations of affine vector fields.

    Science.gov (United States)

    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.

  2. Aspects of the Antisymmetric Tensor Field

    Science.gov (United States)

    Lahiri, Amitabha

    1991-02-01

    With the possible exception of gravitation, fundamental interactions are generally described by theories of point particles interacting via massless gauge fields. Since the advent of string theories the picture of physical interaction has changed to accommodate one in which extended objects interact with each other. The generalization of the gauge theories to extended objects leads to theories of antisymmetric tensor fields. At scales corresponding to present-day laboratory experiments one expects to see only point particles, their interactions modified by the presence of antisymmetric tensor fields in the theory. Therefore, in order to establish the validity of any theory with antisymmetric tensor fields one needs to look for manifestations of these fields at low energies. The principal problem of gauge theories is the failure to provide a suitable explanation for the generation of masses for the fields in the theory. While there is a known mechanism (spontaneous symmetry breaking) for generating masses for both the matter fields and the gauge fields, the lack of experimental evidence in support of an elementary scalar field suggests that one look for alternative ways of generating masses for the fields. The interaction of gauge fields with an antisymmetric tensor field seems to be an attractive way of doing so, especially since all indications point to the possibility that there will be no remnant degrees of freedom. On the other hand the interaction of such a field with black holes suggest an independent way of verifying the existence of such fields. In this dissertation the origins of the antisymmetric tensor field are discussed in terms of string theory. The interaction of black holes with such a field is discussed next. The last chapter discusses the effects of an antisymmetric tensor field on quantum electrodynamics when the fields are minimally coupled.

  3. Relativistic particles with spin and antisymmetric tensor fields

    International Nuclear Information System (INIS)

    Sandoval Junior, L.

    1990-09-01

    A study is made on antisymmetric tensor fields particularly on second order tensor field as far as his equivalence to other fields and quantization through the path integral are concerned. Also, a particle model is studied which has been recently proposed and reveals to be equivalent to antisymmetric tensor fields of any order. (L.C.J.A.)

  4. Composite antisymmetric tensor bosons in a four-fermion interaction model

    International Nuclear Information System (INIS)

    Dmitrasinovic, V.

    2000-01-01

    We discuss the phenomenological consequences of the U A (1) symmetry-breaking two-flavour four-fermion antisymmetric (AS) Lorentz tensor interaction Lagrangians. We use the recently developed methods that respect the 'duality' symmetry of this interaction. Starting from the Fierz transform of the two-flavour 't Hooft interaction (a four-fermion Lagrangian with AS tensor interaction terms augmented by Nambu and Jona-Lasinio (NJL)-type Lorentz scalar interaction responsible for dynamical symmetry breaking and quark mass generation), we find the following. (a) Four antisymmetric tensor and four AS pseudotensor bosons exist which satisfy a mass relation previously derived for scalar and pseudoscalar mesons from the 't Hooft interaction. (b) Antisymmetric tensor bosons mix with vector bosons via one-fermion-loop effective couplings so that both kinds of bosons have their masses shifted and the fermions (quarks) acquire anomalous magnetic moment form factors that explicitly violate chiral symmetry. (c) The mixing of massive AS tensor fields with vector fields leads to two sets of spin-1 states. The second set of spin-1 mesons is heavy and has not been observed. Moreover, at least one member of this second set is tachyonic, under standard assumptions about the source and strength of the AS tensor interaction. The tachyonic state also shows up as a pole in the space-like region of the electromagnetic form factors. (d) The mixing of axial-vector fields with antisymmetric tensor bosons is proportional to the (small) isospin-breaking up-down quark mass difference, so the mixing-induced mass shift is negligible. (e) The AS tensor version of the Veneziano-Witten U A (1) symmetry-breaking interaction does not lead to tachyons, or any AS tensor field propagation to leading order in N C . (author)

  5. Anti-symmetric rank-two tensor matter field on superspace for NT=2

    International Nuclear Information System (INIS)

    Spalenza, Wesley; Ney, Wander G.; Helayel-Neto, J.A.

    2004-01-01

    In this work, we discuss the interaction between anti-symmetric rank-two tensor matter and topological Yang-Mills fields. The matter field considered here is the rank-2 Avdeev-Chizhov tensor matter field in a suitably extended N T =2 SUSY. We start off from the N T =2, D=4 superspace formulation and we go over to Riemannian manifolds. The matter field is coupled to the topological Yang-Mills field. We show that both actions are obtained as Q-exact forms, which allows us to express the energy-momentum tensor as Q-exact observables

  6. New topological invariants for non-abelian antisymmetric tensor fields from extended BRS algebra

    International Nuclear Information System (INIS)

    Boukraa, S.; Maillet, J.M.; Nijhoff, F.

    1988-09-01

    Extended non-linear BRS and Gauge transformations containing Lie algebra cocycles, and acting on non-abelian antisymmetric tensor fields are constructed in the context of free differential algebras. New topological invariants are given in this framework. 6 refs

  7. Detection of antisymmetric tensor contribution to the magnetic screening of 13C nuclei

    International Nuclear Information System (INIS)

    Kuhn, W.

    1983-01-01

    In the present thesis for the first time a practicable way for the detection of antisymmetric contributions to the tensor of the magnetic screening of atomic nuclei is indicated. The detection is based on the relaxation efficiency of the antisymmetric screening. The measurements were performed on the 13 C nuclei of phthalic acid anhydride. Measured were the spin-lattice relaxation times of all 13 C nuclei of the molecule at field strengths between 4.69 T and 11.74 T, this corresponds to 1 H resonance frequencies in the range from 200 MHz to 500 MHz. From this the interaction-specific relaxation rates could be determined without problems. The space-group of the crystal and the molecule geometry were determined by X-ray structure analysis. For the accurate determination of the hydrogen position on a deuterated monocrystal by means of deuterium nuclear resonance measurements the electric field gradient tensors were measured and from the orientation of the main axes of these tensors the bonding angles calculated. On a monocrystal enriched in the C(7) respectively C(8) position with 13 C the symmetric part of the tensor of the magnetic screening of these two nuclei was measured. With these values and the relaxation rates of the 13 C nuclei by an iterative procedure from the equations for the theoretical relaxation rates of all 13 C nuclei of the molecule the main values of the rotation-diffusion tensor could be determined. On the base of the plane molecule geometry from this the tensor element sigmasub(xz)sup(A) could be explicety detected according to an amount of 11.7 ppm. (orig.) [de

  8. Anti-symmetric rank-two tensor matter field on superspace for N{sub T}=2

    Energy Technology Data Exchange (ETDEWEB)

    Spalenza, Wesley; Ney, Wander G; Helayel-Neto, J A

    2004-05-06

    In this work, we discuss the interaction between anti-symmetric rank-two tensor matter and topological Yang-Mills fields. The matter field considered here is the rank-2 Avdeev-Chizhov tensor matter field in a suitably extended N{sub T}=2 SUSY. We start off from the N{sub T}=2, D=4 superspace formulation and we go over to Riemannian manifolds. The matter field is coupled to the topological Yang-Mills field. We show that both actions are obtained as Q-exact forms, which allows us to express the energy-momentum tensor as Q-exact observables.

  9. Tensor-optimized antisymmetrized molecular dynamics as a successive variational method in nuclear many-body system

    Energy Technology Data Exchange (ETDEWEB)

    Myo, Takayuki, E-mail: takayuki.myo@oit.ac.jp [General Education, Faculty of Engineering, Osaka Institute of Technology, Osaka 535-8585 (Japan); Research Center for Nuclear Physics (RCNP), Osaka University, Ibaraki 567-0047 (Japan); Toki, Hiroshi [Research Center for Nuclear Physics (RCNP), Osaka University, Ibaraki 567-0047 (Japan); Ikeda, Kiyomi [RIKEN Nishina Center, Wako, Saitama 351-0198 (Japan); Horiuchi, Hisashi [Research Center for Nuclear Physics (RCNP), Osaka University, Ibaraki 567-0047 (Japan); Suhara, Tadahiro [Matsue College of Technology, Matsue 690-8518 (Japan)

    2017-06-10

    We study the tensor-optimized antisymmetrized molecular dynamics (TOAMD) as a successive variational method in many-body systems with strong interaction for nuclei. In TOAMD, the correlation functions for the tensor force and the short-range repulsion and their multiples are operated to the AMD state as the variational wave function. The total wave function is expressed as the sum of all the components and the variational space can be increased successively with the multiple correlation functions to achieve convergence. All the necessary matrix elements of many-body operators, consisting of the multiple correlation functions and the Hamiltonian, are expressed analytically using the Gaussian integral formula. In this paper we show the results of TOAMD with up to the double products of the correlation functions for the s-shell nuclei, {sup 3}H and {sup 4}He, using the nucleon–nucleon interaction AV8′. It is found that the energies and Hamiltonian components of two nuclei converge rapidly with respect to the multiple of correlation functions. This result indicates the efficiency of TOAMD for the power series expansion in terms of the tensor and short-range correlation functions.

  10. Scalar potential for the gauged Heisenberg algebra and a non-polynomial antisymmetric tensor theory

    International Nuclear Information System (INIS)

    D'Auria, R.; Ferrara, S.; Trigiante, M.; Vaula, S.

    2005-01-01

    We study some issues related to the effective theory of Calabi-Yau compactifications with fluxes in type II theories. At first the scalar potential for a generic electric Abelian gauging of the Heisenberg algebra, underlying all possible gaugings of R-R isometries, is presented and shown to exhibit, in some circumstances, a 'dual' no-scale structure under the interchange of hypermultiplets and vector multiplets. Subsequently a new setting of such theories, when all R-R scalars are dualized into antisymmetric tensors, is discussed. This formulation falls in the class of non-polynomial tensor theories considered long ago by Freedman and Townsend and it may be relevant for the introduction of both electric and magnetic charges

  11. Antisymmetric tensor Zp gauge symmetries in field theory and string theory

    International Nuclear Information System (INIS)

    Berasaluce-González, Mikel; Ramírez, Guillermo; Uranga, Angel M.

    2014-01-01

    We consider discrete gauge symmetries in D dimensions arising as remnants of broken continuous gauge symmetries carried by general antisymmetric tensor fields, rather than by standard 1-forms. The lagrangian for such a general Z p gauge theory can be described in terms of a r-form gauge field made massive by a (r−1)-form, or other dual realizations, that we also discuss. The theory contains charged topological defects of different dimensionalities, generalizing the familiar charged particles and strings in D=4. We describe realizations in string theory compactifications with torsion cycles, or with background field strength fluxes. We also provide examples of non-abelian discrete groups, for which the group elements are associated with charged objects of different dimensionality

  12. Gauge theories of Yang-Mills vector fields coupled to antisymmetric tensor fields

    International Nuclear Information System (INIS)

    Anco, Stephen C.

    2003-01-01

    A non-Abelian class of massless/massive nonlinear gauge theories of Yang-Mills vector potentials coupled to Freedman-Townsend antisymmetric tensor potentials is constructed in four space-time dimensions. These theories involve an extended Freedman-Townsend-type coupling between the vector and tensor fields, and a Chern-Simons mass term with the addition of a Higgs-type coupling of the tensor fields to the vector fields in the massive case. Geometrical, field theoretic, and algebraic aspects of the theories are discussed in detail. In particular, the geometrical structure mixes and unifies features of Yang-Mills theory and Freedman-Townsend theory formulated in terms of Lie algebra valued curvatures and connections associated to the fields and nonlinear field strengths. The theories arise from a general determination of all possible geometrical nonlinear deformations of linear Abelian gauge theory for one-form fields and two-form fields with an Abelian Chern-Simons mass term in four dimensions. For this type of deformation (with typical assumptions on the allowed form considered for terms in the gauge symmetries and field equations), an explicit classification of deformation terms at first-order is obtained, and uniqueness of deformation terms at all higher orders is proven. This leads to a uniqueness result for the non-Abelian class of theories constructed here

  13. New perspectives in the PAW/GIPAW approach: J(P-O-Si) coupling constants, antisymmetric parts of shift tensors and NQR predictions.

    Science.gov (United States)

    Bonhomme, Christian; Gervais, Christel; Coelho, Cristina; Pourpoint, Frédérique; Azaïs, Thierry; Bonhomme-Coury, Laure; Babonneau, Florence; Jacob, Guy; Ferrari, Maude; Canet, Daniel; Yates, Jonathan R; Pickard, Chris J; Joyce, Siân A; Mauri, Francesco; Massiot, Dominique

    2010-12-01

    In 2001, Pickard and Mauri implemented the gauge including projected augmented wave (GIPAW) protocol for first-principles calculations of NMR parameters using periodic boundary conditions (chemical shift anisotropy and electric field gradient tensors). In this paper, three potentially interesting perspectives in connection with PAW/GIPAW in solid-state NMR and pure nuclear quadrupole resonance (NQR) are presented: (i) the calculation of J coupling tensors in inorganic solids; (ii) the calculation of the antisymmetric part of chemical shift tensors and (iii) the prediction of (14)N and (35)Cl pure NQR resonances including dynamics. We believe that these topics should open new insights in the combination of GIPAW, NMR/NQR crystallography, temperature effects and dynamics. Points (i), (ii) and (iii) will be illustrated by selected examples: (i) chemical shift tensors and heteronuclear (2)J(P-O-Si) coupling constants in the case of silicophosphates and calcium phosphates [Si(5)O(PO(4))(6), SiP(2)O(7) polymorphs and α-Ca(PO(3))(2)]; (ii) antisymmetric chemical shift tensors in cyclopropene derivatives, C(3)X(4) (X = H, Cl, F) and (iii) (14)N and (35)Cl NQR predictions in the case of RDX (C(3)H(6)N(6)O(6)), β-HMX (C(4)H(8)N(8)O(8)), α-NTO (C(2)H(2)N(4)O(3)) and AlOPCl(6). RDX, β-HMX and α-NTO are explosive compounds. Copyright © 2010 John Wiley & Sons, Ltd.

  14. Algebraic Rainich theory and antisymmetrization in higher dimensions

    International Nuclear Information System (INIS)

    Bergqvist, G; Hoeglund, A

    2002-01-01

    The classical Rainich(-Misner-Wheeler) theory gives necessary and sufficient conditions on an energy-momentum tensor T to be that of a Maxwell field (a 2-form) in four dimensions. Via Einstein's equations, these conditions can be expressed in terms of the Ricci tensor, thus providing conditions for a spacetime geometry to be an Einstein-Maxwell spacetime. One of the conditions is that T 2 is proportional to the metric, and it has previously been shown in arbitrary dimension that any tensor satisfying this condition is a superenergy tensor of a simple p-form. Here we examine algebraic Rainich conditions for general p-forms in higher dimensions and their relations to identities by antisymmetrization. Using antisymmetrization techniques we find new identities for superenergy tensors of these general (non-simple) forms, and we also prove in some cases the converse: that the identities are sufficient to determine the form. As an example we obtain the complete generalization of the classical Rainich theory to five dimensions

  15. Hybridization of tensor-optimized and high-momentum antisymmetrized molecular dynamics for light nuclei with bare interaction

    Science.gov (United States)

    Lyu, Mengjiao; Isaka, Masahiro; Myo, Takayuki; Toki, Hiroshi; Ikeda, Kiyomi; Horiuchi, Hisashi; Suhara, Tadahiro; Yamada, Taiichi

    2018-01-01

    Many-body correlations play an essential role in the ab initio description of nuclei with nuclear bare interactions. We propose a new framework to describe light nuclei by the hybridization of the tensor-optimized antisymmetrized molecular dynamics (TOAMD) and the high-momentum AMD (HM-AMD), which we call "HM-TOAMD." In this framework, we describe the many-body correlations in terms of not only the correlation functions in TOAMD, but also the high-momentum pairs in the AMD wave function. With the bare nucleon-nucleon interaction AV8^', we sufficiently reproduce the energy and radius of the {^3}H nucleus in HM-TOAMD. The effects of tensor force and short-range repulsion in the bare interaction are nicely described in this new framework. We also discuss the convergence in calculation and flexibility of the model space for this new method.

  16. New successive variational method of tensor-optimized antisymmetrized molecular dynamics for nuclear many-body systems

    Science.gov (United States)

    Myo, Takayuki; Toki, Hiroshi; Ikeda, Kiyomi; Horiuchi, Hisashi; Suhara, Tadahiro

    2017-07-01

    We recently proposed a new variational theory of “tensor-optimized antisymmetrized molecular dynamics” (TOAMD), which treats the strong interaction explicitly for finite nuclei [T. Myo et al., Prog. Theor. Exp. Phys. 2015, 073D02 (2015)]. In TOAMD, the correlation functions for the tensor force and the short-range repulsion and their multiple products are successively operated to the AMD state. The correlated Hamiltonian is expanded into many-body operators by using the cluster expansion and all the resulting operators are taken into account in the calculation without any truncation. We show detailed results for TOAMD with the nucleon-nucleon interaction AV8‧ for s-shell nuclei. The binding energy and the Hamiltonian components are successively converged to exact values of the few-body calculations. We also apply TOAMD to the Malfliet-Tjon central potential having a strong short-range repulsion. TOAMD can treat the short-range correlation and provided accurate energies of s-shell nuclei, reproducing the results of few-body calculations. It turns out that the numerical accuracy of TOAMD with double products of the correlation functions is beyond the variational Monte Carlo method with Jastrow's product-type correlation functions.

  17. Current density tensors

    Science.gov (United States)

    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.

  18. (Ln-bar, g)-spaces. Ordinary and tensor differentials

    International Nuclear Information System (INIS)

    Manoff, S.; Dimitrov, B.

    1998-01-01

    Different types of differentials as special cases of differential operators acting on tensor fields over (L n bar, g)-spaces are considered. The ordinary differential, the covariant differential as a special case of the covariant differential operator, and the Lie differential as a special case of the Lie differential operator are investigated. The tensor differential and its special types (Covariant tensor differential, and Lie tensor differential) are determined and their properties are discussed. Covariant symmetric and antisymmetric (external) tensor differentials, Lie symmetric, and Lie antisymmetric (external) tensor differentials are determined and considered over (L n bar, g)-spaces

  19. On the large N limit, Wilson Loops, Confinement and Composite Antisymmetric Tensor Field theories

    CERN Document Server

    Castro, C

    2004-01-01

    A novel approach to evaluate the Wilson loops asociated with a $ SU ( \\infty )$ gauge theory in terms of pure string degrees of freedom is presented. It is based on the Guendelman-Nissimov-Pacheva formulation of composite antisymmetric tensor field theories of area (volume ) preserving diffeomorphisms which admit $p$-brane solutions and which provide a $new$ route to scale symmetry breaking and confinement in Yang-Mills theory. The quantum effects are discussed and we evaluate the vacuum expectation values (vev) of the Wilson loops in the large $N$ limit of the $quenched$ reduced $SU(N)$ Yang-Mills theory in terms of a path integral involving pure string degrees of freedom. The $quenched$ approximation is necessary to avoid a crumpling of the string world-sheet giving rise to very large Hausdorff dimensions as pointed out by Olesen. The approach is also consistent with the recent results based on the AdS/CFT correspondence and dual QCD models (dual Higgs model with dual Dirac strings ). More general Loop wav...

  20. Dynamical compactification of D-dimensional gravity coupled to antisymmetric tensors in a 1/D expansion

    International Nuclear Information System (INIS)

    Foda, O.

    1984-12-01

    The effective potential of components of the curl of an antisymmetric tensor coupled to gravity in D dimensions is evaluated in a 1/D expansion. For large D, only highest-rank propagators contribute to leading order, while multiloop diagrams are suppressed by phase-space factors. Divergences are regulated by a cut-off LAMBDA, that we interpret as the mass-breaking scale of a larger theory that is finite. As an application we consider the bosonic sector of D=11, N=1 supergravity. If the full theory is finite, then LAMBDA is msub(SUSY): the scale below which the fermion sector decouples. For m 9 sub(SUSY)>1/akappa 2 , (kappa 2 : the D=11 Newton's coupling, a approx.= O(1)) the 11-dimensional symmetric vacuum is unstable under compactification. For m 9 sub(SUSY) 2 , it is metastable. To leading order in 1/D, all gauge dependence cancels identically, while ghosts as well as the graviton decouple. (author)

  1. Antisymmetric Orbit Functions

    Directory of Open Access Journals (Sweden)

    Anatoliy Klimyk

    2007-02-01

    Full Text Available In the paper, properties of antisymmetric orbit functions are reviewed and further developed. Antisymmetric orbit functions on the Euclidean space $E_n$ are antisymmetrized exponential functions. Antisymmetrization is fulfilled by a Weyl group, corresponding to a Coxeter-Dynkin diagram. Properties of such functions are described. These functions are closely related to irreducible characters of a compact semisimple Lie group $G$ of rank $n$. Up to a sign, values of antisymmetric orbit functions are repeated on copies of the fundamental domain $F$ of the affine Weyl group (determined by the initial Weyl group in the entire Euclidean space $E_n$. Antisymmetric orbit functions are solutions of the corresponding Laplace equation in $E_n$, vanishing on the boundary of the fundamental domain $F$. Antisymmetric orbit functions determine a so-called antisymmetrized Fourier transform which is closely related to expansions of central functions in characters of irreducible representations of the group $G$. They also determine a transform on a finite set of points of $F$ (the discrete antisymmetric orbit function transform. Symmetric and antisymmetric multivariate exponential, sine and cosine discrete transforms are given.

  2. Tensor Excitations in Nambu - Jona-Lasinio Model

    CERN Document Server

    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.

  3. 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.)

  4. (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

  5. Couplings of self-dual tensor multiplet in six dimensions

    NARCIS (Netherlands)

    Bergshoeff, E.; Sezgin, E.; Sokatchev, E.

    1996-01-01

    The (1, 0) supersymmetry in six dimensions admits a tensor multiplet which contains a second-rank antisymmetric tensor field with a self-dual field strength and a dilaton. We describe the fully supersymmetric coupling of this multiplet to a Yang–Mills multiplet, in the absence of supergravity. The

  6. Antisymmetrized four-body wave function and coexistence of single particle and cluster structures

    International Nuclear Information System (INIS)

    Sasakawa, T.

    1979-01-01

    It is shown that each Yakubovski component of the totally antisymmetric four-body wave function satisfies the same equation as the unantisymmetric wave function. In the antisymmetric total wave function, the wave functions belonging to the same kind of partition are totally antisymmetric among themselves. This leads to the coexistence of cluster models, including the single particle model as a special case of the cluster model, as a sum

  7. Mass generation for Abelian spin-1 particles via a symmetric tensor

    International Nuclear Information System (INIS)

    Dalmazi, D.; Mendonça, E.L.

    2012-01-01

    In the topologically massive BF model (TMBF) the photon becomes massive via coupling to an antisymmetric tensor, without breaking the U(1) gauge symmetry. There is no need of a Higgs field. The TMBF model is dual to a first-order (in derivatives) formulation of the Maxwell-Proca theory where the antisymmetric field plays the role of an auxiliary field. Since the Maxwell-Proca theory also admits a first-order version which makes use of an auxiliary symmetric tensor, we investigate here a possible generalization of the TMBF model where the photon acquires mass via coupling to a symmetric tensor. We show that it is indeed possible to build up dual models to the Maxwell-Proca theory where the U(1) gauge symmetry is manifest without Higgs field, but after a local field redefinition the vector field eats up the trace of the symmetric tensor and becomes massive. So the explicit U(1) symmetry can be removed unlike the TMBF model.

  8. Renormalization of nonabelian gauge theories with tensor matter fields

    International Nuclear Information System (INIS)

    Lemes, Vitor; Renan, Ricardo; Sorella, Silvio Paolo

    1996-03-01

    The renormalizability of a nonabelian model describing the coupling between antisymmetric second rank tensor matter fields and Yang-Mills gauge fields is discussed within the BRS algebraic framework. (author). 12 refs

  9. Radiative corrections in a vector-tensor model

    International Nuclear Information System (INIS)

    Chishtie, F.; Gagne-Portelance, M.; Hanif, T.; Homayouni, S.; McKeon, D.G.C.

    2006-01-01

    In a recently proposed model in which a vector non-Abelian gauge field interacts with an antisymmetric tensor field, it has been shown that the tensor field possesses no physical degrees of freedom. This formal demonstration is tested by computing the one-loop contributions of the tensor field to the self-energy of the vector field. It is shown that despite the large number of Feynman diagrams in which the tensor field contributes, the sum of these diagrams vanishes, confirming that it is not physical. Furthermore, if the tensor field were to couple with a spinor field, it is shown at one-loop order that the spinor self-energy is not renormalizable, and hence this coupling must be excluded. In principle though, this tensor field does couple to the gravitational field

  10. Canonical forms of tensor representations and spontaneous symmetry breaking

    International Nuclear Information System (INIS)

    Cummins, C.J.

    1986-01-01

    An algorithm for constructing canonical forms for any tensor representation of the classical compact Lie groups is given. This method is used to find a complete list of the symmetry breaking patterns produced by Higgs fields in the third-rank antisymmetric representations of U(n), SU(n) and SO(n) for n<=7. A simple canonical form is also given for kth-rank symmetric tensor representations. (author)

  11. Symmetry rules for the indirect nuclear spin-spin coupling tensor revisited

    Science.gov (United States)

    Buckingham, A. D.; Pyykkö, P.; Robert, J. B.; Wiesenfeld, L.

    The symmetry rules of Buckingham and Love (1970), relating the number of independent components of the indirect spin-spin coupling tensor J to the symmetry of the nuclear sites, are shown to require modification if the two nuclei are exchanged by a symmetry operation. In that case, the anti-symmetric part of J does not transform as a second-rank polar tensor under symmetry operations that interchange the coupled nuclei and may be called an anti-tensor. New rules are derived and illustrated by simple molecular models.

  12. The total position-spread tensor: Spin partition

    International Nuclear Information System (INIS)

    El Khatib, Muammar; Evangelisti, Stefano; Leininger, Thierry; Brea, Oriana; Fertitta, Edoardo; Bendazzoli, Gian Luigi

    2015-01-01

    The Total Position Spread (TPS) tensor, defined as the second moment cumulant of the position operator, is a key quantity to describe the mobility of electrons in a molecule or an extended system. In the present investigation, the partition of the TPS tensor according to spin variables is derived and discussed. It is shown that, while the spin-summed TPS gives information on charge mobility, the spin-partitioned TPS tensor becomes a powerful tool that provides information about spin fluctuations. The case of the hydrogen molecule is treated, both analytically, by using a 1s Slater-type orbital, and numerically, at Full Configuration Interaction (FCI) level with a V6Z basis set. It is found that, for very large inter-nuclear distances, the partitioned tensor growths quadratically with the distance in some of the low-lying electronic states. This fact is related to the presence of entanglement in the wave function. Non-dimerized open chains described by a model Hubbard Hamiltonian and linear hydrogen chains H n (n ≥ 2), composed of equally spaced atoms, are also studied at FCI level. The hydrogen systems show the presence of marked maxima for the spin-summed TPS (corresponding to a high charge mobility) when the inter-nuclear distance is about 2 bohrs. This fact can be associated to the presence of a Mott transition occurring in this region. The spin-partitioned TPS tensor, on the other hand, has a quadratical growth at long distances, a fact that corresponds to the high spin mobility in a magnetic system

  13. The total energy-momentum tensor for electromagnetic fields in a dielectric

    Science.gov (United States)

    Crenshaw, Michael E.

    2017-08-01

    mv. Newtonian fluids can behave very much like dust with the same energy-momentum tensor. The energy and momentum conservation properties of light propagating in the vacuum were long-ago cast in the energy-momentum tensor formalism in terms of the electromagnetic energy density and electromagnetic momentum density. However, extrapolating the tensor theory of energy-momentum conservation for propagation of light in the vacuum to propagation of light in a simple linear dielectric medium has proven to be problematic and controversial. A dielectric medium is not "otherwise empty" and it is typically assumed that optically induced forces accelerate and decelerate nanoscopic material constituents of the dielectric. The corresponding material energy-momentum tensor is added to the electromagnetic energy-momentum tensor to form the total energy-momentum tensor, thereby ensuring that the total energy and the total momentum of the thermodynamically closed system remain constant in time.

  14. Quark antisymmetrization and deep-inelastic scattering. Pt. 2

    International Nuclear Information System (INIS)

    Meyer, H.; Mulders, P.J.; Spit, W.F.M.

    1994-01-01

    We consider the effects of quark antisymmetrization for nuclear structure functions. Antisymmetrizing the naive folding of nuclear wave functions in terms of nucleons and the nucleon wave function in terms of quarks, introduces additional contributions. Using the calculated results on quark three-momentum distributions, we calculate the effects on the deep-inelastic structure functions for s- and p-wave nuclei. The effects of quark antisymmetrization turn out to be small. (orig.)

  15. Tridiagonal realization of the antisymmetric Gaussian β-ensemble

    International Nuclear Information System (INIS)

    Dumitriu, Ioana; Forrester, Peter J.

    2010-01-01

    The Householder reduction of a member of the antisymmetric Gaussian unitary ensemble gives an antisymmetric tridiagonal matrix with all independent elements. The random variables permit the introduction of a positive parameter β, and the eigenvalue probability density function of the corresponding random matrices can be computed explicitly, as can the distribution of (q i ), the first components of the eigenvectors. Three proofs are given. One involves an inductive construction based on bordering of a family of random matrices which are shown to have the same distributions as the antisymmetric tridiagonal matrices. This proof uses the Dixon-Anderson integral from Selberg integral theory. A second proof involves the explicit computation of the Jacobian for the change of variables between real antisymmetric tridiagonal matrices, its eigenvalues, and (q i ). The third proof maps matrices from the antisymmetric Gaussian β-ensemble to those realizing particular examples of the Laguerre β-ensemble. In addition to these proofs, we note some simple properties of the shooting eigenvector and associated Pruefer phases of the random matrices.

  16. Computations of the chirality-sensitive effect induced by an antisymmetric indirect spin–spin coupling

    Science.gov (United States)

    Garbacz, Piotr

    2018-05-01

    Results of quantum mechanical computations of the antisymmetric part of the indirect spin-spin coupling tensor, ?, performed using the coupled-cluster method, the second-order polarisation propagator approximation, and the density functional theory for 25 molecules and nearly 100 spin-spin couplings are reported. These results are used for an estimation of the magnitude of the recently proposed liquid-state nuclear magnetic resonance chirality-sensitive effect, which allows to determine the molecular chirality directly, i.e. without the need for the application of any chiral agent. The following were found: (i) the antisymmetry J⋆ is usually larger for the coupling between spins separated by two chemical bonds in comparison with the coupling through one bond, (ii) promising samples are those which contain fluorine, and (iii) the antisymmetry of the spin-spin coupling tensor is of the order of a few hertz for commercially available chemical compounds. Therefore, the relevant property of the experiment, the pseudoscalar Jc, for them is of the order of 1 nHz m/V.

  17. Coleman-Weinberg symmetry breaking in SU(8) induced by a third rank antisymmetric tensor scalar field II: the fermion spectrum

    Science.gov (United States)

    Adler, Stephen L.

    2017-07-01

    We continue our study of Coleman-Weinberg symmetry breaking induced by a third rank antisymmetric tensor scalar, in the context of the SU(8) model (Adler 2014 Int. J. Mod. Phys. A 29 1450130) we proposed earlier. We focus in this paper on qualitative features that will determine whether the model can make contact with the observed particle spectrum. We discuss the mechanism for giving the spin \\frac{3}{2} field a mass by the BEH mechanism, and analyze the remaining massless spin \\frac{1}{2} fermions, the global chiral symmetries, and the running couplings after symmetry breaking. We note that the smallest gluon mass matrix eigenvalue has an eigenvector suggestive of U(1) B-L , and conjecture that the theory runs to an infrared fixed point at which there is a massless gluon with 3 to  -1 ratios in generator components. Assuming this, we discuss a mechanism for making contact with the standard model, based on a conjectured asymmetric breaking of Sp(4) to SU(2) subgroups, one of which is the electroweak SU(2), and the other of which is a ‘technicolor’ group that binds the original SU(8) model fermions, which play the role of ‘preons’, into composites. Quarks can emerge as 5 preon composites and leptons as 3 preon composites, with consequent stability of the proton against decay to a single lepton plus a meson. A composite Higgs boson can emerge as a two preon composite. Since anomaly matching for the relevant conserved global symmetry current is not obeyed by three fermion families, emergence of three composite families requires formation of a Goldstone boson with quantum numbers matching this current, which can be a light dark matter candidate.

  18. Symmetry properties of second harmonics generated by antisymmetric Lamb waves

    Science.gov (United States)

    Zhu, Wujun; Xiang, Yanxun; Liu, Chang-Jun; Deng, Mingxi; Xuan, Fu-Zhen

    2018-03-01

    Symmetry properties of second harmonics generated by antisymmetric primary Lamb waves are systematically studied in this work. In theory, the acoustic field of second harmonic Lamb waves is obtained by using the perturbation approximation and normal modal method, and the energy flux transfer from the primary Lamb waves to second harmonics is mainly explored. Symmetry analyses indicate that either the symmetric or antisymmetric Lamb waves can merely generate the symmetric second harmonics. Finite element simulations are performed on the nonlinear Lamb wave propagation of the antisymmetric A0 mode in the low frequency region. The signals of the second harmonics and the symmetric second harmonic s0 mode are found to be exactly equivalent in the time domain. The relative acoustic nonlinearity parameter A2/A12 oscillates with the propagation distance, and the oscillation amplitude and spatial period are well consistent with the theoretical prediction of the A0-s0 mode pair, which means that only the second harmonic s0 mode is generated by the antisymmetric primary A0 mode. Experiments are further conducted to examine the cumulative generation of symmetric second harmonics for the antisymmetric-symmetric mode pair A3-s6. Results show that A2/A12 increases linearly with the propagation distance, which means that the symmetric second harmonic s6 mode is generated cumulatively by the antisymmetric primary A3 mode. The present investigation systematically corroborates the proposed theory that only symmetric second harmonics can be generated accompanying the propagation of antisymmetric primary Lamb waves in a plate.

  19. Orbital floor reconstruction using a tensor fascia lata sling after total maxillectomy.

    Science.gov (United States)

    Jung, Bok Ki; Yun, In Sik; Lee, Won Jai; Lew, Dae Hyun; Choi, Eun Chang; Lee, Dong Won

    2016-05-01

    Reconstruction after total maxillectomy with extensive orbital floor defects poses a significant challenge for the reconstruction. The aim of this study is to present the outcomes of orbital floor reconstruction using tensor fascia lata slings after total maxillectomy and to compare these results to orbital floor reconstruction using alloplastic implants. This was a retrospective analysis of 19 consecutive patients who underwent tumor resection with orbital floor removal for malignancies. Reconstructions were performed using either tensor fascia lata slings (Group A) or alloplastic implants (Group B). The early and late postoperative outcomes such as wound infection, plate exposure, ectropion, diplopia, and enophthalmos, were analyzed and compared between the two groups. Patients in group A had significantly less wound complication than in group B (p < 0.05). In group A, there were no early or late wound complications after the operation. However, in group B, five patients had infection, the plate was exposed in eight of fourteen patients, and three patients had enophthalmos. Eight patients in group B underwent reoperation to correct their complications. Reconstruction of the orbital floor with a tensor fascia lata sling offers reliable support to the globe and prevents the ophthalmic complications associated with loss of orbital support. Copyright © 2016 European Association for Cranio-Maxillo-Facial Surgery. Published by Elsevier Ltd. All rights reserved.

  20. (Anti)symmetric multivariate exponential functions and corresponding Fourier transforms

    International Nuclear Information System (INIS)

    Klimyk, A U; Patera, J

    2007-01-01

    We define and study symmetrized and antisymmetrized multivariate exponential functions. They are defined as determinants and antideterminants of matrices whose entries are exponential functions of one variable. These functions are eigenfunctions of the Laplace operator on the corresponding fundamental domains satisfying certain boundary conditions. To symmetric and antisymmetric multivariate exponential functions there correspond Fourier transforms. There are three types of such Fourier transforms: expansions into the corresponding Fourier series, integral Fourier transforms and multivariate finite Fourier transforms. Eigenfunctions of the integral Fourier transforms are found

  1. Total magnitude of diffusion tensor imaging as an effective tool for the differentiation of glioma

    Energy Technology Data Exchange (ETDEWEB)

    Smitha, Karavallil A., E-mail: mithamahesh@gmail.com [Department of Imaging Sciences and Interventional Radiology, Sree Chitra Tirunal Institute for Medical Sciences and Technology, Thiruvananthapuram (India); Gupta, Arun kumar, E-mail: gupta209@gmail.com [Department of Neuroimaging and Interventional Radiology, National Institute of Mental Health and Neuro Sciences, Bangalore (India); Jayasree, Ramapurath S., E-mail: jayashreemenon@gmail.com [Biophotonics and Imaging Laboratory, Biomedical Technology Wing, Sree Chitra Tirunal Institute for Medical Sciences and Technology, Thiruvananthapuram (India)

    2013-05-15

    Objectives: The study aims to evaluate the difference in diffusion properties between high grade glioma and low grade glioma by measuring the total magnitude of diffusion tensor (L), and its isotropic (p) and anisotropic (q) components. Methods: The diffusion tensor parameters p, q, L and FA from the tumor area, adjacent area to the tumor and corresponding contra lateral normal area of 30 high grade glioma and 49 low grade glioma were calculated. Chi square analysis was done to find the changes in age and sex. One Way ANOVA was performed to compare the mean and ROC curve analysis to confirm the discriminative sensitivity. Results: Major variation in the mean values of p, L and FA was observed in different brain areas considered. Variation in the p and L values between low grade and high grade glioma were statistically significant (p < 0.001) and their ROC curve analysis yielded 93.9% and 91.8% sensitivity and 53.3% specificity respectively. Conclusion: Measurement of the isotropic component p and the total value of diffusion tensor L can be effectively correlated with different grades of glioma and can be used to study the diffusion properties of tumor affected brain.

  2. An antisymmetric psychometric function on a logarithmic scale

    NARCIS (Netherlands)

    Bergmann Tiest, W.M.; Kappers, A.M.L.

    2011-01-01

    This very brief report introduces a psychometric function, very suitable for psychophysical data that displays Weber-like behaviour, because it is antisymmetric on a logarithmic scale. © 2011 a Pion publication.

  3. TensorLy: Tensor Learning in Python

    NARCIS (Netherlands)

    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.

  4. Electromagnetic wave propagation in time-dependent media with antisymmetric magnetoelectric coupling

    International Nuclear Information System (INIS)

    Lin, Shi-Rong; Zhang, Ruo-Yang; Ma, Yi-Rong; Jia, Wei; Zhao, Qing

    2016-01-01

    Highlights: • Time-dependent permittivity combined with antisymmetric magnetoelectric coupling will yield a novel linear birefringence. • Distinct dynamical behaviors of these two birefringent modes are analyzed. • As a new nonlinear optical effect, a scheme utilizing optical Kerr effect in moving media is proposed. - Abstract: This paper deals with electromagnetic wave propagation in time-dependent media with an antisymmetric magnetoelectric coupling and an isotropic time-dependent permittivity. We identify a new mechanism of linear birefringence, originated from the combined action of the time-dependent permittivity and the antisymmetric magnetoelectric coupling. Permittivity with linear and exponential temporal variations exemplifies the creation and control of these two distinct types of linear birefringent modes. As a novel nonlinear optical effect, a scheme utilizing optical Kerr effect in moving media is proposed for the realization of the predicted birefringence.

  5. Electromagnetic wave propagation in time-dependent media with antisymmetric magnetoelectric coupling

    Energy Technology Data Exchange (ETDEWEB)

    Lin, Shi-Rong [School of Physics, Beijing Institute of Technology, Beijing 100081 (China); Zhang, Ruo-Yang [Theoretical Physics Division, Chern Institute of Mathematics, Nankai University, Tianjin 300071 (China); Ma, Yi-Rong; Jia, Wei [School of Physics, Beijing Institute of Technology, Beijing 100081 (China); Zhao, Qing, E-mail: qzhaoyuping@bit.edu.cn [School of Physics, Beijing Institute of Technology, Beijing 100081 (China)

    2016-07-29

    Highlights: • Time-dependent permittivity combined with antisymmetric magnetoelectric coupling will yield a novel linear birefringence. • Distinct dynamical behaviors of these two birefringent modes are analyzed. • As a new nonlinear optical effect, a scheme utilizing optical Kerr effect in moving media is proposed. - Abstract: This paper deals with electromagnetic wave propagation in time-dependent media with an antisymmetric magnetoelectric coupling and an isotropic time-dependent permittivity. We identify a new mechanism of linear birefringence, originated from the combined action of the time-dependent permittivity and the antisymmetric magnetoelectric coupling. Permittivity with linear and exponential temporal variations exemplifies the creation and control of these two distinct types of linear birefringent modes. As a novel nonlinear optical effect, a scheme utilizing optical Kerr effect in moving media is proposed for the realization of the predicted birefringence.

  6. Relativistic analysis of the dielectric Einstein box: Abraham, Minkowski and total energy-momentum tensors

    International Nuclear Information System (INIS)

    Ramos, Tomas; Rubilar, Guillermo F.; Obukhov, Yuri N.

    2011-01-01

    Highlights: → The definition of the momentum of light inside matter is studied. → Fully relativistic analysis of the dielectric 'Einstein box' thought experiment. → Minkowski, Abraham and the total energy-momentum tensors are derived in detail. → Some assumptions hidden in the usual Einstein box argument are identified. → The Abraham momentum is not uniquely selected as the momentum of light in this case. - Abstract: We analyse the 'Einstein box' thought experiment and the definition of the momentum of light inside matter. We stress the importance of the total energy-momentum tensor of the closed system (electromagnetic field plus material medium) and derive in detail the relativistic expressions for the Abraham and Minkowski momenta, together with the corresponding balance equations for an isotropic and homogeneous medium. We identify some assumptions hidden in the Einstein box argument, which make it weaker than it is usually recognized. In particular, we show that the Abraham momentum is not uniquely selected as the momentum of light in this case.

  7. TensorLy: Tensor Learning in Python

    OpenAIRE

    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...

  8. Non abelian Chern-Simons topological coupling from self-interaction

    International Nuclear Information System (INIS)

    Aragone, C.; Stephany, R.J.E.

    1986-01-01

    It is shown that the self-interaction mechanism drives in one step the topologically coupled-Maxwell-second rank antisymmetric tensor system into the Chern-Simons coupled -non abelian- (second rank) antisymmetric tensor action. Only one step is required to saturate the process because the action for the initial Maxwell-antisymmetric tensor system is given in its first-order form. The self-interaction mechanism works both for the original Chapline-Manton form of the action and for the dual form. (Author) [pt

  9. A RENORMALIZATION PROCEDURE FOR TENSOR MODELS AND SCALAR-TENSOR THEORIES OF GRAVITY

    OpenAIRE

    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...

  10. Is there a cosmological evidence for additional particles

    International Nuclear Information System (INIS)

    Kirilova, D.P.; Chizhov, M.V.

    1998-05-01

    An extended cosmological model of the early Universe with additional antisymmetric tensor particles is described. The cosmological effects of the additional particles, namely additional interactions of the early Universe plasma with the tensor particles, a shift of the early Universe temperature-time dependence and the total energy density increase are discussed. The efficiency of the tensor particles interactions with the early Universe plasma components and their corresponding cosmological time and temperature are determined. (author)

  11. On the geometry of mixed states and the Fisher information tensor

    Energy Technology Data Exchange (ETDEWEB)

    Contreras, I., E-mail: icontrer@illinois.edu [Department of Mathematics, University of Illinois at Urbana-Champaign, 1409 W. Green Street, Urbana, Illinois 61801 (United States); Ercolessi, E., E-mail: ercolessi@bo.infn.it [Dipartimento di Fisica e Astronomia, Università di Bologna and INFN, V. Irnerio 46, 40127 Bologna (Italy); Schiavina, M., E-mail: michele.schiavina@math.uzh.ch [Institut für Mathematik, Winterthurerstrasse 190, 8057 Zürich (Switzerland)

    2016-06-15

    In this paper, we will review the co-adjoint orbit formulation of finite dimensional quantum mechanics, and in this framework, we will interpret the notion of quantum Fisher information index (and metric). Following previous work of part of the authors, who introduced the definition of Fisher information tensor, we will show how its antisymmetric part is the pullback of the natural Kostant–Kirillov–Souriau symplectic form along some natural diffeomorphism. In order to do this, we will need to understand the symmetric logarithmic derivative as a proper 1-form, settling the issues about its very definition and explicit computation. Moreover, the fibration of co-adjoint orbits, seen as spaces of mixed states, is also discussed.

  12. Kinetics of Interactions of Matter, Antimatter and Radiation Consistent with Antisymmetric (CPT-Invariant Thermodynamics

    Directory of Open Access Journals (Sweden)

    A.Y. Klimenko

    2017-05-01

    Full Text Available This work investigates the influence of directional properties of decoherence on kinetics rate equations. The physical reality is understood as a chain of unitary and decoherence events. The former are quantum-deterministic, while the latter introduce uncertainty and increase entropy. For interactions of matter and antimatter, two approaches are considered: symmetric decoherence, which corresponds to conventional symmetric (CP-invariant thermodynamics, and antisymmetric decoherence, which corresponds to antisymmetric (CPT-invariant thermodynamics. Radiation, in its interactions with matter and antimatter, is shown to be decoherence-neutral. The symmetric and antisymmetric assumptions result in different interactions of radiation with matter and antimatter. The theoretical predictions for these differences are testable by comparing absorption (emission of light by thermodynamic systems made of matter and antimatter. Canonical typicality for quantum mixtures is briefly discussed in Appendix A.

  13. Four-body correlation embedded in antisymmetrized geminal power wave function.

    Science.gov (United States)

    Kawasaki, Airi; Sugino, Osamu

    2016-12-28

    We extend the Coleman's antisymmetrized geminal power (AGP) to develop a wave function theory that can incorporate up to four-body correlation in a region of strong correlation. To facilitate the variational determination of the wave function, the total energy is rewritten in terms of the traces of geminals. This novel trace formula is applied to a simple model system consisting of one dimensional Hubbard ring with a site of strong correlation. Our scheme significantly improves the result obtained by the AGP-configuration interaction scheme of Uemura et al. and also achieves more efficient compression of the degrees of freedom of the wave function. We regard the result as a step toward a first-principles wave function theory for a strongly correlated point defect or adsorbate embedded in an AGP-based mean-field medium.

  14. The Riemann-Lovelock Curvature Tensor

    OpenAIRE

    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

  15. Weakly Interacting Symmetric and Anti-Symmetric States in the Bilayer Systems

    Science.gov (United States)

    Marchewka, M.; Sheregii, E. M.; Tralle, I.; Tomaka, G.; Ploch, D.

    We have studied the parallel magneto-transport in DQW-structures of two different potential shapes: quasi-rectangular and quasi-triangular. The quantum beats effect was observed in Shubnikov-de Haas (SdH) oscillations for both types of the DQW structures in perpendicular magnetic filed arrangement. We developed a special scheme for the Landau levels energies calculation by means of which we carried out the necessary simulations of beating effect. In order to obtain the agreement between our experimental data and the results of simulations, we introduced two different quasi-Fermi levels which characterize symmetric and anti-symmetric states in DQWs. The existence of two different quasi Fermi-Levels simply means, that one can treat two sub-systems (charge carriers characterized by symmetric and anti-symmetric wave functions) as weakly interacting and having their own rate of establishing the equilibrium state.

  16. Optical detection of symmetric and antisymmetric states in double quantum wells at room temperature

    Science.gov (United States)

    Marchewka, M.; Sheregii, E. M.; Tralle, I.; Marcelli, A.; Piccinini, M.; Cebulski, J.

    2009-09-01

    We studied the optical reflectivity of a specially grown double quantum well (DQW) structure characterized by a rectangular shape and a high electron density at room temperature. Assuming that the QWs depth is known, reflectivity spectra in the mid-IR range allow to carry out the precise measurements of the SAS-gap values (the energy gap between the symmetric and anti-symmetric states) and the absolute energies of both symmetric and antisymmetric electron states. The results of our experiments are in favor of the existence of the SAS splitting in the DQWs at room temperature. Here we have shown that the SAS gap increases proportionally to the subband quantum number and the optical electron transitions between symmetric and antisymmetric states belonging to different subbands are allowed. These results were used for interpretation of the beating effect in the Shubnikov-de Haas (SdH) oscillations at low temperatures (0.6 and 4.2 K). The approach to the calculation of the Landau-levels energies for DQW structures developed earlier [D. Ploch , Phys. Rev. B 79, 195434 (2009)] is used for the analysis and interpretation of the experimental data related to the beating effect. We also argue that in order to explain the beating effect in the SdH oscillations, one should introduce two different quasi-Fermi levels characterizing the two electron subsystems regarding symmetry properties of their wave functions, symmetric and antisymmetric ones. These states are not mixed neither by electron-electron interaction nor probably by electron-phonon interaction.

  17. Numerical correction of anti-symmetric aberrations in single HRTEM images of weakly scattering 2D-objects

    International Nuclear Information System (INIS)

    Lehtinen, Ossi; Geiger, Dorin; Lee, Zhongbo; Whitwick, Michael Brian; Chen, Ming-Wei; Kis, Andras; Kaiser, Ute

    2015-01-01

    Here, we present a numerical post-processing method for removing the effect of anti-symmetric residual aberrations in high-resolution transmission electron microscopy (HRTEM) images of weakly scattering 2D-objects. The method is based on applying the same aberrations with the opposite phase to the Fourier transform of the recorded image intensity and subsequently inverting the Fourier transform. We present the theoretical justification of the method, and its verification based on simulated images in the case of low-order anti-symmetric aberrations. Ultimately the method is applied to experimental hardware aberration-corrected HRTEM images of single-layer graphene and MoSe 2 resulting in images with strongly reduced residual low-order aberrations, and consequently improved interpretability. Alternatively, this method can be used to estimate by trial and error the residual anti-symmetric aberrations in HRTEM images of weakly scattering objects

  18. Tensor rank is not multiplicative under the tensor product

    NARCIS (Netherlands)

    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

  19. Tensor rank is not multiplicative under the tensor product

    NARCIS (Netherlands)

    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

  20. Tensor rank is not multiplicative under the tensor product

    OpenAIRE

    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...

  1. Tensor surgery and tensor rank

    NARCIS (Netherlands)

    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

  2. Tensor surgery and tensor rank

    NARCIS (Netherlands)

    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

  3. 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...

  4. Tensor Factorization for Low-Rank Tensor Completion.

    Science.gov (United States)

    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.

  5. Notes on Translational and Rotational Properties of Tensor Fields in Relativistic Quantum Mechanics

    Science.gov (United States)

    Dvoeglazov, V. V.

    Recently, several discussions on the possible observability of 4-vector fields have been published in literature. Furthermore, several authors recently claimed existence of the helicity=0 fundamental field. We re-examine the theory of antisymmetric tensor fields and 4-vector potentials. We study the massless limits. In fact, a theoretical motivation for this venture is the old papers of Ogievetskiĭ and Polubarinov, Hayashi, and Kalb and Ramond. Ogievetskiĭ and Polubarinov proposed the concept of the notoph, whose helicity properties are complementary to those of the photon. We analyze the quantum field theory with taking into account mass dimensions of the notoph and the photon. It appears to be possible to describe both photon and notoph degrees of freedom on the basis of the modified Bargmann-Wigner formalism for the symmetric second-rank spinor. Next, we proceed to derive equations for the symmetric tensor of the second rank on the basis of the Bargmann-Wigner formalism in a straightforward way. The symmetric multispinor of the fourth rank is used. Due to serious problems with the interpretation of the results obtained on using the standard procedure we generalize it and obtain the spin-2 relativistic equations, which are consistent with the general relativity. Thus, in fact we deduced the gravitational field equations from relativistic quantum mechanics. The relations of this theory with the scalar-tensor theories of gravitation and f(R) are discussed. Particular attention has been paid to the correct definitions of the energy-momentum tensor and other Nöther currents in the electromagnetic theory, the relativistic theory of gravitation, the general relativity, and their generalizations. We estimate possible interactions, fermion-notoph, graviton-notoph, photon-notoph, and we conclude that they can probably be seen in experiments in the next few years.

  6. A Review of Tensors and Tensor Signal Processing

    Science.gov (United States)

    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.

  7. Gauged N=8 d=5 supergravity

    International Nuclear Information System (INIS)

    Pernici, M.; Pilch, K.; Van Nieuwenhuizen, P.

    1985-01-01

    The complete gauged nonlinear N=8 d=5 supergravity action and supersymmetry transformation laws (without four- and three-fermion terms) are presented. They are obtained from the ungauged model by reinterpreting part of the field strengths of the abelian vector fields as real self-dual second-rank antisymmetric tensors. The complete set of T-tensor indentities are given and their validity is checked numerically. The model has a local Yang-Mills SO(6) and a local composite USp(8) symmetry. The self-duality is essential for the consistent coupling of the antisymmetric tensors to the nonabelian gauge fields. (orig.)

  8. Statistical properties of anti-symmetrized molecular dynamics

    International Nuclear Information System (INIS)

    Ohnishi, A.; Randrup, J.

    1993-01-01

    We study the statistical equilibrium properties of the recently developed anti-symmetrized molecular dynamics model for heavy-ion reactions. We consider A non-interacting fermions in one dimension, either bound in a common harmonic potential or moving freely within an interval, and perform a Metropolis sampling of the corresponding parameter space. Generally the average excitation and the specific heat, considered as functions of the imposed temperature, behave in a classical manner when the canonical weight is calculated in the mean-field approximation. However, it is possible to obtain results that are much closer to the quantal behavior by modifying the weight to take approximate account of the energy fluctuations within the individual wave packets. (orig.)

  9. Tensor gauge condition and tensor field decomposition

    Science.gov (United States)

    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.

  10. 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

  11. Poynting Theorem, Relativistic Transformation of Total Energy-Momentum and Electromagnetic Energy-Momentum Tensor

    Science.gov (United States)

    Kholmetskii, Alexander; Missevitch, Oleg; Yarman, Tolga

    2016-02-01

    We address to the Poynting theorem for the bound (velocity-dependent) electromagnetic field, and demonstrate that the standard expressions for the electromagnetic energy flux and related field momentum, in general, come into the contradiction with the relativistic transformation of four-vector of total energy-momentum. We show that this inconsistency stems from the incorrect application of Poynting theorem to a system of discrete point-like charges, when the terms of self-interaction in the product {\\varvec{j}} \\cdot {\\varvec{E}} (where the current density {\\varvec{j}} and bound electric field {\\varvec{E}} are generated by the same source charge) are exogenously omitted. Implementing a transformation of the Poynting theorem to the form, where the terms of self-interaction are eliminated via Maxwell equations and vector calculus in a mathematically rigorous way (Kholmetskii et al., Phys Scr 83:055406, 2011), we obtained a novel expression for field momentum, which is fully compatible with the Lorentz transformation for total energy-momentum. The results obtained are discussed along with the novel expression for the electromagnetic energy-momentum tensor.

  12. Linear Invariant Tensor Interpolation Applied to Cardiac Diffusion Tensor MRI

    Science.gov (United States)

    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

  13. Tensor network method for reversible classical computation

    Science.gov (United States)

    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.

  14. Palatini approach to Born-Infeld-Einstein theory and a geometric description of electrodynamics

    International Nuclear Information System (INIS)

    Vollick, Dan N.

    2004-01-01

    The field equations associated with the Born-Infeld-Einstein action are derived using the Palatini variational technique. In this approach the metric and connection are varied independently and the Ricci tensor is generally not symmetric. For sufficiently small curvatures the resulting field equations can be divided into two sets. One set, involving the antisymmetric part of the Ricci tensor R or μν , consists of the field equation for a massive vector field. The other set consists of the Einstein field equations with an energy momentum tensor for the vector field plus additional corrections. In a vacuum with R or μν =0 the field equations are shown to be the usual Einstein vacuum equations. This extends the universality of the vacuum Einstein equations, discussed by Ferraris et al., to the Born-Infeld-Einstein action. In the simplest version of the theory there is a single coupling constant and by requiring that the Einstein field equations hold to a good approximation in neutron stars it is shown that mass of the vector field exceeds the lower bound on the mass of the photon. Thus, in this case the vector field cannot represent the electromagnetic field and would describe a new geometrical field. In a more general version in which the symmetric and antisymmetric parts of the Ricci tensor have different coupling constants it is possible to satisfy all of the observational constraints if the antisymmetric coupling is much larger than the symmetric coupling. In this case the antisymmetric part of the Ricci tensor can describe the electromagnetic field

  15. The mirror transform of type I vacua in six dimensions

    International Nuclear Information System (INIS)

    Sen, A.; Sethi, S.

    1997-01-01

    We study certain compactifications of the type I string on K3. The three topologically distinct choices of gauge bundles for the type I theory are shown to be equivalent to type IIB orientifolds with different choices of background anti-symmetric tensor field flux. Using a mirror transformation we relate these models to orientifolds with fixed seven planes, and without any anti-symmetric tensor field flux. This map allows us to relate these type I vacua to particular six-dimensional F-theory and heterotic string compactifications. (orig.)

  16. Skewons and gravitons

    International Nuclear Information System (INIS)

    Soleng, H.H.; Eeg, J.O.

    1991-04-01

    A gravitational theory based on the generalised affine geometry is presented. It contains an antisymmetric torsion potensial in addition to the metric. The coupling to matter is derived by the minimal coupling principle, implying that the metric couples to a symmetrised energy-momentum tensor, and the antisymmetric field couples to the canonical spin tensor of matter. The coupling constant for both cases is Newton's constant G. Phenomenological consequences of the linearised theory for quantum processes at the tree level are explored. 110 refs., 10 figs

  17. The Color Antisymmetric Ghost Propagator and One-Loop Vertex Renormalization

    OpenAIRE

    Furui, Sadataka

    2007-01-01

    The color matrix elements of the ghost triangle diagram that appears in the triple gluon vertex and the ghost-ghost-gluon triangle diagram that appears in the ghost-gluon-ghost vertex are calculated. The ghost-ghost-gluon triangle contains a loop consisting of two color diagonal ghosts and one gluon and a loop consisting of two color antisymmetric ghosts and one gluon. Consequently, the pQCD argument in the infrared region based on the one particle irreducible diagram should be modified. Impl...

  18. Diffusion tensor image registration using hybrid connectivity and tensor features.

    Science.gov (United States)

    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.

  19. Comparison of Magnetic Susceptibility Tensor and Diffusion Tensor of the Brain.

    Science.gov (United States)

    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.

  20. 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

  1. Tensors for physics

    CERN Document Server

    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-...

  2. Hypertrophy of the tensor fascia lata muscle as a complication of total hip arthroplasty.

    Science.gov (United States)

    Rodríguez-Roiz, Juan Miguel; Bori, Guillem; Tomas, Xavier; Fernández-Valencia, Jenaro A; García-Díez, Ana Isabel; Pomés, Jaume; Garcia, Sebastián

    2017-02-01

    Hypertrophy of the tensor fascia lata muscle (HTFLM) is a rare complication after total hip arthroplasty (THA) and is a potential source of pain, palpable mass, or both. We retrospectively analyzed 1285 primary THAs and 482 THA revisions (THAR) performed at our center from 2008 to 2014. Among these, five patients had HTFLM (average age 68.8 years). The type of surgery and symptoms were evaluated, as were imaging studies (CT or MRI) of both hips (10 hips), and functional outcomes with the Merle d'Aubigné score. The suspected diagnosis was established at an average of 30.2 months after surgery. Four cases occurred after THA and one case after THAR. A modified Hardinge approach was used in four cases and a Röttinger approach in one case. Two cases had pain and palpable mass in the trochanteric region and three cases only pain. The asymmetric HTFLM of the THA side against the nonsurgical side was confirmed by measuring the cross section of the tensor fascia lata muscle on imaging. The sartorius muscle was measured for reference in each case. The Merle d'Aubigne scale had a mean value of 16.6 (range 13-18) at 38 months after the procedure. HTFLM after THA is a benign condition that could be mistaken for a tumor when presenting as a palpable mass. We propose that it should be considered in the differential diagnosis of pain in the lateral aspect of hips that have previously undergone THA.

  3. The Riemann-Lovelock curvature tensor

    International Nuclear Information System (INIS)

    Kastor, David

    2012-01-01

    In order to study the properties of Lovelock gravity theories in low dimensions, we define the kth-order Riemann-Lovelock tensor as a certain quantity having a total 4k-indices, which is kth order in the Riemann curvature tensor and shares its basic algebraic and differential properties. We show that the kth-order Riemann-Lovelock tensor is determined by its traces in dimensions 2k ≤ D < 4k. In D = 2k + 1 this identity implies that all solutions of pure kth-order Lovelock gravity are 'Riemann-Lovelock' flat. It is verified that the static, spherically symmetric solutions of these theories, which are missing solid angle spacetimes, indeed satisfy this flatness property. This generalizes results from Einstein gravity in D = 3, which corresponds to the k = 1 case. We speculate about some possible further consequences of Riemann-Lovelock curvature. (paper)

  4. The 1/ N Expansion of Tensor Models with Two Symmetric Tensors

    Science.gov (United States)

    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.

  5. Field-theoretical investigations in nonlinear realizations of gauge symmetry

    International Nuclear Information System (INIS)

    Lee, Chenhan.

    1989-01-01

    A review of both linear realization and non-linear realization of gauge symmetries is given and the connection between the two recipes is carefully examined. The author then constructs both linear and non-linear realizations for of supersymmetric theories. The supermultiplets of the Goldstone modes contain Goldstone bosons, quasi-Goldstone bosons and quasi-Goldstone fermions. He makes an attempt to construct a specific model of a supersymmetric non-linear realization for the Nambu-Goldstone superfields and the quasi-Goldstone fermions are identified with the quarks and leptons. Further, he discusses a mechanism by which the components of the Nambu-Goldstone supermultiplets are given non-zero mass splittings by the coupling to a hidden sector. Next, he turns to anti-symmetric tensor gauge theories, which are shown to be classically equivalent to the non-linear models describing the complete symmetry breakdown. To study the quantum mechanical equivalence of these two models, he carries out the tensor gauge fixing and the quantization procedures for the anti-symmetric tensor theories and establish the global symmetry currents which connect the two models. He then builds the supersymmetric extensions of the anti-symmetric tensor gauge theories in both abelian and non-abelian versions. Such super-tensor gauge theories are shown, by using the superfield equations of motion, to be equivalent to the fully doubled supersymmetric non-linear models of complete symmetry breakdown

  6. Propagation of symmetric and anti-symmetric surface waves in aself-gravitating magnetized dusty plasma layer with generalized (r, q) distribution

    Science.gov (United States)

    Lee, Myoung-Jae; Jung, Young-Dae

    2018-05-01

    The dispersion properties of surface dust ion-acoustic waves in a self-gravitating magnetized dusty plasma layer with the (r, q) distribution are investigated. The result shows that the wave frequency of the symmetric mode in the plasma layer decreases with an increase in the wave number. It is also shown that the wave frequency of the symmetric mode decreases with an increase in the spectral index r. However, the wave frequency of the anti-symmetric mode increases with an increase in the wave number. It is also found that the anti-symmetric mode wave frequency increases with an increase in the spectral index r. In addition, it is found that the influence of the self-gravitation on the symmetric mode wave frequency decreases with increasing scaled Jeans frequency. Moreover, it is found that the wave frequency of the symmetric mode increases with an increase in the dust charge; however, the anti-symmetric mode shows opposite behavior.

  7. The "Fermi hole" and the correlation introduced by the symmetrization or the anti-symmetrization of the wave function.

    Science.gov (United States)

    Giner, Emmanuel; Tenti, Lorenzo; Angeli, Celestino; Malrieu, Jean-Paul

    2016-09-28

    The impact of the antisymmetrization is often addressed as a local property of the many-electron wave function, namely that the wave function should vanish when two electrons with parallel spins are in the same position in space. In this paper, we emphasize that this presentation is unduly restrictive: we illustrate the strong non-local character of the antisymmetrization principle, together with the fact that it is a matter of spin symmetry rather than spin parallelism. To this aim, we focus our attention on the simplest representation of various states of two-electron systems, both in atomic (helium atom) and molecular (H 2 and the π system of the ethylene molecule) cases. We discuss the non-local property of the nodal structure of some two-electron wave functions, both using analytical derivations and graphical representations of cuttings of the nodal hypersurfaces. The attention is then focussed on the impact of the antisymmetrization on the maxima of the two-body density, and we show that it introduces strong correlation effects (radial and/or angular) with a non-local character. These correlation effects are analyzed in terms of inflation and depletion zones, which are easily identifiable, thanks to the nodes of the orbitals composing the wave function. Also, we show that the correlation effects induced by the antisymmetrization occur also for anti-parallel spins since all M s components of a given spin state have the same N-body densities. Finally, we illustrate that these correlation effects occur also for the singlet states, but they have strictly opposite impacts: the inflation zones in the triplet become depletion zones in the singlet and vice versa.

  8. Roles of the color antisymmetric ghost propagator in the Infrared QCD

    International Nuclear Information System (INIS)

    Furui, S.

    2009-01-01

    The results of Coulomb gauge and Landau gauge lattice QCD simulation do not agree completely with continuum theory. There are indications that the ghost propagator in the infrared region has strong fluctuation whose modulus is compatible with that of the color diagonal ghost propagator. After presenting lattice simulation of configurations produced with Kogut-Susskind fermion (MILC collaboration) and those with domain wall fermion (RBC/UKQCD collaboration), I investigate in triple gluon vertex and the ghost-gluon-ghost vertex how the square of the color antisymmetric ghost contributes. Then the effect of the vertex correction to the gluon propagator and the ghost propagator is investigated. Recent Dyson-Schwinger equation analysis suggests the ghost dressing function G(0) = finite and no infrared enhancement or a G = 0. But the ghost propagator renormalized by the loop containing a product of color antisymmetric ghost is expected to behave as [cc] r = - (G(q 2 ))/(q 2 ) with G(q 2 ) ∝ q -2aG with a G = 0.5, if the fixed point scenario is valid. I interpret the a G = 0 solution should contain a vertex correction. The infrared exponent of our lattice Landau gauge gluon propagator of the RBC/UKQCD is a D = - 0.5 and that of MILC is about - 0.7. A possible interpretation of the origin of the fluctuation is given. (author)

  9. Complex vector triads in spinor theory in Minkowski space

    International Nuclear Information System (INIS)

    Zhelnorovich, V.A.

    1990-01-01

    It is shown that tensor equations corresponding to the spinor Dirac equations represent a three-dimensional part of four-dimensional vector equations. The equations are formulated in an evidently invariant form in antisymmetric tensor components and in the corresponding components of a complex vector triad. A complete system of relativistically invariant tensor equations is ascertained

  10. MathGR: a tensor and GR computation package to keep it simple

    OpenAIRE

    Wang, Yi

    2013-01-01

    We introduce the MathGR package, written in Mathematica. The package can manipulate tensor and GR calculations with either abstract or explicit indices, simplify tensors with permutational symmetries, decompose tensors from abstract indices to partially or completely explicit indices and convert partial derivatives into total derivatives. Frequently used GR tensors and a model of FRW universe with ADM type perturbations are predefined. The package is built around the philosophy to "keep it si...

  11. 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.

  12. Mixed symmetry tensors in the worldline formalism

    Energy Technology Data Exchange (ETDEWEB)

    Corradini, Olindo [Dipartimento di Scienze Fisiche, Informatiche e Matematiche,Università degli Studi di Modena e Reggio Emilia, via Campi 213/A, I-41125 Modena (Italy); INFN - Sezione di Bologna,via Irnerio 46, I-40126 Bologna (Italy); Edwards, James P. [Department of Mathematical Sciences, University of Bath,Claverton Down, Bath BA2 7AY (United Kingdom)

    2016-05-10

    We consider the first quantised approach to quantum field theory coupled to a non-Abelian gauge field. Representing the colour degrees of freedom with a single family of auxiliary variables the matter field transforms in a reducible representation of the gauge group which — by adding a suitable Chern-Simons term to the particle action — can be projected onto a chosen fully (anti-)symmetric representation. By considering F families of auxiliary variables, we describe how to extend the model to arbitrary tensor products of F reducible representations, which realises a U(F) “flavour” symmetry on the worldline particle model. Gauging this symmetry allows the introduction of constraints on the Hilbert space of the colour fields which can be used to project onto an arbitrary irreducible representation, specified by a certain Young tableau. In particular the occupation numbers of the wavefunction — i.e. the lengths of the columns (rows) of the Young tableau — are fixed through the introduction of Chern-Simons terms. We verify this projection by calculating the number of colour degrees of freedom associated to the matter field. We suggest that, using the worldline approach to quantum field theory, this mechanism will allow the calculation of one-loop scattering amplitudes with the virtual particle in an arbitrary representation of the gauge group.

  13. Efficient tensor completion for color image and video recovery: Low-rank tensor train

    OpenAIRE

    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...

  14. The color antisymmetric ghost propagator and one-loop vertex renormalization

    International Nuclear Information System (INIS)

    Furui, Sadataka

    2008-01-01

    The color matrix elements of the ghost triangle diagram that appears in the triple gluon vertex and the ghost-ghost-gluon triangle diagram that appears in the ghost-gluon-ghost vertex are calculated. The ghost-ghost-gluon triangle contains a loop consisting of two color diagonal ghosts and one gluon and a loop consisting of two color antisymmetric ghosts and one gluon. Consequently, the pQCD argument in the infrared region based on the one particle irreducible diagram should be modified. Implications for the Kugo-Ojima color confinement and the QCD running coupling are discussed. (author)

  15. 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

  16. Tensor eigenvalues and their applications

    CERN Document Server

    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.

  17. Tensor Transpose and Its Properties

    OpenAIRE

    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.

  18. Nucleation of (4)R brane universes

    International Nuclear Information System (INIS)

    Cordero, Ruben; Rojas, EfraIn

    2004-01-01

    The creation of brane universes induced by a totally antisymmetric tensor living in a fixed background spacetime is presented, where a term involving the intrinsic curvature of the brane is considered. A canonical quantum mechanical approach employing the Wheeler-DeWitt equation is used. The probability nucleation for the brane is calculated by means of the corresponding instanton and the WKB approximation. Some cosmological implications from the model are presented

  19. Nucleation of {sup (4)}R brane universes

    Energy Technology Data Exchange (ETDEWEB)

    Cordero, Ruben [Departamento de FIsica, Escuela Superior de FIsica y Matematicas del IPN, Unidad Adolfo Lopez Mateos, Edificio 9, 07738 Mexico, DF (Mexico); Rojas, EfraIn [Facultad de FIsica e Inteligencia Artificial, Universidad Veracruzana, Sebastian Camacho 5, Xalapa, Veracruz, 91000 (Mexico)

    2004-09-07

    The creation of brane universes induced by a totally antisymmetric tensor living in a fixed background spacetime is presented, where a term involving the intrinsic curvature of the brane is considered. A canonical quantum mechanical approach employing the Wheeler-DeWitt equation is used. The probability nucleation for the brane is calculated by means of the corresponding instanton and the WKB approximation. Some cosmological implications from the model are presented.

  20. Role of antisymmetric spin-orbit component in effective interactions in the sd-shell

    International Nuclear Information System (INIS)

    Yoshinada, K.

    1981-10-01

    The antisymmetric spin-orbit interaction (ALS) proposed for sd-shell nuclei is investigated. It is shown that the centroid energy of the d sub(5/2) - d sub(3/2) interactions plays a crucial role in reproducing the excited band spectra of A = 18 - 24 nuclei. An empirical effective interaction without ALS component is proposed to reproduce the observed spectra of light sd-shell nuclei. (author)

  1. Physical states in the canonical tensor model from the perspective of random tensor networks

    Energy Technology Data Exchange (ETDEWEB)

    Narain, Gaurav [The Institute for Fundamental Study “The Tah Poe Academia Institute”,Naresuan University, Phitsanulok 65000 (Thailand); Sasakura, Naoki [Yukawa Institute for Theoretical Physics,Kyoto University, Kyoto 606-8502 (Japan); Sato, Yuki [National Institute for Theoretical Physics,School of Physics and Centre for Theoretical Physics,University of the Witwartersrand, WITS 2050 (South Africa)

    2015-01-07

    Tensor models, generalization of matrix models, are studied aiming for quantum gravity in dimensions larger than two. Among them, the canonical tensor model is formulated as a totally constrained system with first-class constraints, the algebra of which resembles the Dirac algebra of general relativity. When quantized, the physical states are defined to be vanished by the quantized constraints. In explicit representations, the constraint equations are a set of partial differential equations for the physical wave-functions, which do not seem straightforward to be solved due to their non-linear character. In this paper, after providing some explicit solutions for N=2,3, we show that certain scale-free integration of partition functions of statistical systems on random networks (or random tensor networks more generally) provides a series of solutions for general N. Then, by generalizing this form, we also obtain various solutions for general N. Moreover, we show that the solutions for the cases with a cosmological constant can be obtained from those with no cosmological constant for increased N. This would imply the interesting possibility that a cosmological constant can always be absorbed into the dynamics and is not an input parameter in the canonical tensor model. We also observe the possibility of symmetry enhancement in N=3, and comment on an extension of Airy function related to the solutions.

  2. Antisymmetric Amino-Wagging Band of Hydrazine up toK‧ = 13 Levels

    Science.gov (United States)

    Gulaczyk, Iwona; Kre, Marek; Valentin, Alain

    1997-12-01

    A newly recorded high-resolution infrared spectrum of hydrazine has been studied in the 729-1198 cm-1region (the ν12antisymmetric wagging band) with a resolution of 0.002 cm-1. About 1350 transitions withK‧ from 7 to 13 have been newly assigned and about 2350 transitions with lower values ofK‧ reanalyzed with the improved precision. The effective parameters have been calculated separately for each value ofK‧ using the Hougen-Ohashi hamiltonian for hydrazine. The extended assignment completes the analysis of the ν12band of hydrazine.

  3. The tensor rank of tensor product of two three-qubit W states is eight

    OpenAIRE

    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.

  4. Efficient Tensor Completion for Color Image and Video Recovery: Low-Rank Tensor Train.

    Science.gov (United States)

    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.

  5. Bowen-York tensors

    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

  6. Harmonic d-tensors

    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.

  7. Enhanced Sensitivity of Anti-Symmetrically Structured Surface Plasmon Resonance Sensors with Zinc Oxide Intermediate Layers

    Directory of Open Access Journals (Sweden)

    Nan-Fu Chiu

    2013-12-01

    Full Text Available We report a novel design wherein high-refractive-index zinc oxide (ZnO intermediary layers are used in anti-symmetrically structured surface plasmon resonance (SPR devices to enhance signal quality and improve the full width at half maximum (FWHM of the SPR reflectivity curve. The surface plasmon (SP modes of the ZnO intermediary layer were excited by irradiating both sides of the Au film, thus inducing a high electric field at the Au/ZnO interface. We demonstrated that an improvement in the ZnO (002 crystal orientation led to a decrease in the FWHM of the SPR reflectivity curves. We optimized the design of ZnO thin films using different parameters and performed analytical comparisons of the ZnO with conventional chromium (Cr and indium tin oxide (ITO intermediary layers. The present study is based on application of the Fresnel equation, which provides an explanation and verification for the observed narrow SPR reflectivity curve and optical transmittance spectra exhibited by (ZnO/Au, (Cr/Au, and (ITO/Au devices. On exposure to ethanol, the anti-symmetrically structured showed a huge electric field at the Au/ZnO interface and a 2-fold decrease in the FWHM value and a 1.3-fold larger shift in angle interrogation and a 4.5-fold high-sensitivity shift in intensity interrogation. The anti-symmetrically structured of ZnO intermediate layers exhibited a wider linearity range and much higher sensitivity. It also exhibited a good linear relationship between the incident angle and ethanol concentration in the tested range. Thus, we demonstrated a novel and simple method for fabricating high-sensitivity, high-resolution SPR biosensors that provide high accuracy and precision over relevant ranges of analyte measurement.

  8. TensorFlow Agents: Efficient Batched Reinforcement Learning in TensorFlow

    OpenAIRE

    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...

  9. Correlator of fundamental and anti-symmetric Wilson loops in AdS/CFT correspondence

    International Nuclear Information System (INIS)

    Tai, T.-S.; Yamaguchi, Satoshi

    2007-01-01

    We study the two circular Wilson loop correlator in which one is of anti-symmetric representation, while the other is of fundamental representation in 4-dimensional N = 4 super Yang-Mills theory. This correlator has a good AdS dual, which is a system of a D5-brane and a fundamental string. We calculated the on-shell action of the string, and clarified the Gross-Ooguri transition in this correlator. Some limiting cases are also examined

  10. Time integration of tensor trains

    OpenAIRE

    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...

  11. Tensor spaces and exterior algebra

    CERN Document Server

    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.

  12. The direct tensor solution and higher-order acquisition schemes for generalized diffusion tensor imaging

    NARCIS (Netherlands)

    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

  13. 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.)

  14. Tensor structure for Nori motives

    OpenAIRE

    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.

  15. Tensor SOM and tensor GTM: Nonlinear tensor analysis by topographic mappings.

    Science.gov (United States)

    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.

  16. Physical and Geometric Interpretations of the Riemann Tensor, Ricci Tensor, and Scalar Curvature

    OpenAIRE

    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.

  17. Generalized tensor-based morphometry of HIV/AIDS using multivariate statistics on deformation tensors.

    Science.gov (United States)

    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.

  18. Development of the Tensoral Computer Language

    Science.gov (United States)

    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.

  19. Kronecker-Basis-Representation Based Tensor Sparsity and Its Applications to Tensor Recovery.

    Science.gov (United States)

    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.

  20. 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

  1. A multivector derivative approach to Lagrangian field theory

    International Nuclear Information System (INIS)

    Lasenby, A.; Gull, S.; Doran, C.

    1993-01-01

    A new calculus, based upon the multivector derivative, is developed for Lagrangian mechanics and field theory, providing streamlined and rigorous derivations of the Euler-Lagrange equations. A more general form of Noether's theorem is found which is appropriate to both discrete and continuous symmetries. This is used to find the conjugate currents of the Dirac theory, where it improves on techniques previously used for analyses of local observables. General formulas for the canonical stress-energy and angular-momentum tensors are derived, with spinors and vectors treated in a unified way. It is demonstrated that the antisymmetric terms in the stress-energy tensor are crucial to the correct treatment of angular momentum. The multivector derivative is extended to provide a functional calculus for linear functions which is more compact and more powerful than previous formalisms. This is demonstrated in a reformulation of the functional derivative with respect to the metric, which is then used to recover the full canonical stress-energy tensor. Unlike conventional formalisms, which result in a symmetric stress-energy tensor, this reformulation retains the potentially important antisymmetric contribution. 23 refs

  2. 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.

  3. Tensor Permutation Matrices in Finite Dimensions

    OpenAIRE

    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...

  4. 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...

  5. A queer reduction of degrees of freedom

    International Nuclear Information System (INIS)

    Avdeev, L.V.; Chizhov, M.V.

    2005-01-01

    The classical dynamics of antisymmetric second-rank tensor matter fields is analyzed. The conformally invariant action for the tensor field leads to a positive-definite Hamiltonian on the class of the solutions that are bounded at the time infinity (plane waves). Only the longitudinal waves contribute to the energy and momentum. The helicity proves to be equal to zero

  6. 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)

  7. Surface waves at the interface with an antisymmetric gain/loss profile

    International Nuclear Information System (INIS)

    Ctyroky, Jiri; Kuzmiak, Vladimir; Eyderman, Sergey

    2010-01-01

    We studied properties of strongly guiding two-mode waveguides with antisymmetric gain/loss profile which constitute photonic analogues of quantum mechanical structures with parity-time symmetry breaking. For both TE and TM polarizations, the dependences of effective indices of the guided modes vs. gain/loss coefficient exhibit a degenerate critical point that defines two regimes with profoundly different behavior. In addition, we have shown that the interface between the two media supports propagation of a strongly confined non-attenuated TM polarized surface wave. We examined the properties of the surface wave obtained by both the modal and FDTD method and discuss the differences between the results obtained by both techniques as both the material and geometrical parameters are varied.

  8. 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....

  9. Full magnetic gradient tensor from triaxial aeromagnetic gradient measurements: Calculation and application

    Science.gov (United States)

    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.

  10. Massive and massless gauge fields of any spin and symmetry

    International Nuclear Information System (INIS)

    Hussain, F.; Jarvis, P.D.

    1988-05-01

    An analysis of the BRST approach to massive and massless gauge fields of any spin and symmetry is presented. Previous results on massless gauge fields are extended to totally antisymmetric massless tensors and Kaehler-Dirac particles. Two methods for arriving at a BRST invariant, massive theory from the corresponding massless one are discussed. The first allows for an interpretation in terms of dimensional reduction, while the second keeps the BRST operator of the massless theory, but employs gauge invariant fields. (author). 10 refs

  11. Performance Optimization of Tensor Contraction Expressions for Many Body Methods in Quantum Chemistry

    International Nuclear Information System (INIS)

    Hartono, Albert; Lu, Qingda; Henretty, Thomas; Krishnamoorthy, Sriram; Zhang, Huaijian; Baumgartner, Gerald; Bernholdt, David E.; Nooijen, Marcel; Pitzer, Russell M.; Ramanujam, J.; Sadayappan, Ponnuswamy

    2009-01-01

    Complex tensor contraction expressions arise in accurate electronic structure models in quantum chemistry, such as the coupled cluster method. This paper addresses two complementary aspects of performance optimization of such tensor contraction expressions. Transformations using algebraic properties of commutativity and associativity can be used to significantly decrease the number of arithmetic operations required for evaluation of these expressions. The identification of common subexpressions among a set of tensor contraction expressions can result in a reduction of the total number of operations required to evaluate the tensor contractions. The first part of the paper describes an effective algorithm for operation minimization with common subexpression identification and demonstrates its effectiveness on tensor contraction expressions for coupled cluster equations. The second part of the paper highlights the importance of data layout transformation in the optimization of tensor contraction computations on modern processors. A number of considerations such as minimization of cache misses and utilization of multimedia vector instructions are discussed. A library for efficient index permutation of multi-dimensional tensors is described and experimental performance data is provided that demonstrates its effectiveness.

  12. Performance Optimization of Tensor Contraction Expressions for Many Body Methods in Quantum Chemistry

    International Nuclear Information System (INIS)

    Krishnamoorthy, Sriram; Bernholdt, David E.; Pitzer, R.M.; Sadayappan, Ponnuswamy

    2009-01-01

    Complex tensor contraction expressions arise in accurate electronic structure models in quantum chemistry, such as the coupled cluster method. This paper addresses two complementary aspects of performance optimization of such tensor contraction expressions. Transformations using algebraic properties of commutativity and associativity can be used to significantly decrease the number of arithmetic operations required for evaluation of these expressions. The identification of common subexpressions among a set of tensor contraction expressions can result in a reduction of the total number of operations required to evaluate the tensor contractions. The first part of the paper describes an effective algorithm for operation minimization with common subexpression identification and demonstrates its effectiveness on tensor contraction expressions for coupled cluster equations. The second part of the paper highlights the importance of data layout transformation in the optimization of tensor contraction computations on modern processors. A number of considerations, such as minimization of cache misses and utilization of multimedia vector instructions, are discussed. A library for efficient index permutation of multidimensional tensors is described, and experimental performance data is provided that demonstrates its effectiveness.

  13. Monograph On Tensor Notations

    Science.gov (United States)

    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.

  14. Thermodynamical inequivalence of quantum stress-energy and spin tensors

    International Nuclear Information System (INIS)

    Becattini, F.; Tinti, L.

    2011-01-01

    It is shown that different couples of stress-energy and spin tensors of quantum-relativistic fields, which would be otherwise equivalent, are in fact inequivalent if the second law of thermodynamics is taken into account. The proof of the inequivalence is based on the analysis of a macroscopic system at full thermodynamical equilibrium with a macroscopic total angular momentum and a specific instance is given for the free Dirac field, for which we show that the canonical and Belinfante stress-energy tensors are not equivalent. For this particular case, we show that the difference between the predicted angular momentum densities for a rotating system at full thermodynamical equilibrium is a quantum effect, persisting in the nonrelativistic limit, corresponding to a polarization of particles of the order of (ℎ/2π)ω/KT (ω being the angular velocity) and could in principle be measured experimentally. This result implies that specific stress-energy and spin tensors are physically meaningful even in the absence of gravitational coupling and raises the issue of finding the thermodynamically right (or the right class of) tensors. We argue that the maximization of the thermodynamic potential theoretically allows us to discriminate between two different couples, yet for the present we are unable to provide a theoretical method to single out the best couple of tensors in a given quantum field theory. The existence of a nonvanishing spin tensor would have major consequences in hydrodynamics, gravity and cosmology.

  15. Cartesian tensors an introduction

    CERN Document Server

    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

  16. Effect of antisymmetric C–H stretching excitation on the dynamics of O({sup 1}D) + CH{sub 4} → OH + CH{sub 3}

    Energy Technology Data Exchange (ETDEWEB)

    Pan, Huilin; Yang, Jiayue; Zhang, Dong; Shuai, Quan; Jiang, Bo [State Key Laboratory of Molecular Reaction Dynamics, Dalian Institute of Chemical Physics, Chinese Academy of Sciences, Dalian, Liaoning 116023 (China); Dai, Dongxu; Wu, Guorong, E-mail: wugr@dicp.ac.cn, E-mail: xmyang@dicp.ac.cn; Yang, Xueming, E-mail: wugr@dicp.ac.cn, E-mail: xmyang@dicp.ac.cn [State Key Laboratory of Molecular Reaction Dynamics, Dalian Institute of Chemical Physics, Chinese Academy of Sciences, Dalian, Liaoning 116023 (China); Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026 (China)

    2014-04-21

    The effect of antisymmetric C–H stretching excitation of CH{sub 4} on the dynamics and reactivity of the O({sup 1}D) + CH{sub 4} → OH + CD{sub 3} reaction at the collision energy of 6.10 kcal/mol has been investigated using the crossed-beam and time-sliced velocity map imaging techniques. The antisymmetric C–H stretching mode excited CH{sub 4} molecule was prepared by direct infrared excitation. From the measured images of the CH{sub 3} products with the infrared laser on and off, the product translational energy and angular distributions were derived for both the ground and vibrationally excited reactions. Experimental results show that the vibrational energy of the antisymmetric stretching excited CH{sub 4} reagent is channeled exclusively into the vibrational energy of the OH co-products and, hence, the OH products from the excited-state reaction are about one vibrational quantum hotter than those from the ground-state reaction, and the product angular distributions are barely affected by the vibrational excitation of the CH{sub 4} reagent. The reactivity was found to be suppressed by the antisymmetric stretching excitation of CH{sub 4} for all observed CH{sub 3} vibrational states. The degree of suppression is different for different CH{sub 3} vibrational states: the suppression is about 40%–60% for the ground state and the umbrella mode excited CH{sub 3} products, while for the CH{sub 3} products with one quantum symmetric stretching mode excitation, the suppression is much less pronounced. In consequence, the vibrational state distribution of the CH{sub 3} product from the excited-state reaction is considerably different from that of the ground-state reaction.

  17. 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.

  18. Density matrix embedding in an antisymmetrized geminal power bath

    International Nuclear Information System (INIS)

    Tsuchimochi, Takashi; Welborn, Matthew; Van Voorhis, Troy

    2015-01-01

    Density matrix embedding theory (DMET) has emerged as a powerful tool for performing wave function-in-wave function embedding for strongly correlated systems. In traditional DMET, an accurate calculation is performed on a small impurity embedded in a mean field bath. Here, we extend the original DMET equations to account for correlation in the bath via an antisymmetrized geminal power (AGP) wave function. The resulting formalism has a number of advantages. First, it allows one to properly treat the weak correlation limit of independent pairs, which DMET is unable to do with a mean-field bath. Second, it associates a size extensive correlation energy with a given density matrix (for the models tested), which AGP by itself is incapable of providing. Third, it provides a reasonable description of charge redistribution in strongly correlated but non-periodic systems. Thus, AGP-DMET appears to be a good starting point for describing electron correlation in molecules, which are aperiodic and possess both strong and weak electron correlation

  19. 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)

  20. 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)

  1. A note on the Deser-Tekin charges

    International Nuclear Information System (INIS)

    Petrov, A N

    2005-01-01

    Perturbed equations for an arbitrary metric theory of gravity in D dimensions are constructed in the vacuum of this theory. The nonlinear part together with matter fields are a source for the linear part and are treated as a total energy-momentum tensor. A generalized family of conserved currents expressed through divergences of anti-symmetrical tensor densities (superpotentials) linear in perturbations is constructed. The new family generalizes the Deser and Tekin currents and superpotentials in quadratic curvature gravity theories generating Killing charges in dS and AdS vacua. As an example, the mass of a D-dimensional Schwarzschild black hole in an effective AdS spacetime (a solution in the Einstein-Gauss-Bonnet theory) is examined. (letter to the editor)

  2. Cerebral perfusion computed tomography deconvolution via structure tensor total variation regularization

    Energy Technology Data Exchange (ETDEWEB)

    Zeng, Dong; Zhang, Xinyu; Bian, Zhaoying, E-mail: zybian@smu.edu.cn, E-mail: jhma@smu.edu.cn; Huang, Jing; Zhang, Hua; Lu, Lijun; Lyu, Wenbing; Feng, Qianjin; Chen, Wufan; Ma, Jianhua, E-mail: zybian@smu.edu.cn, E-mail: jhma@smu.edu.cn [Department of Biomedical Engineering, Southern Medical University, Guangzhou, Guangdong 510515, China and Guangdong Provincial Key Laboratory of Medical Image Processing, Southern Medical University, Guangzhou, Guangdong 510515 (China); Zhang, Jing [Department of Radiology, Tianjin Medical University General Hospital, Tianjin 300052 (China)

    2016-05-15

    Purpose: Cerebral perfusion computed tomography (PCT) imaging as an accurate and fast acute ischemic stroke examination has been widely used in clinic. Meanwhile, a major drawback of PCT imaging is the high radiation dose due to its dynamic scan protocol. The purpose of this work is to develop a robust perfusion deconvolution approach via structure tensor total variation (STV) regularization (PD-STV) for estimating an accurate residue function in PCT imaging with the low-milliampere-seconds (low-mAs) data acquisition. Methods: Besides modeling the spatio-temporal structure information of PCT data, the STV regularization of the present PD-STV approach can utilize the higher order derivatives of the residue function to enhance denoising performance. To minimize the objective function, the authors propose an effective iterative algorithm with a shrinkage/thresholding scheme. A simulation study on a digital brain perfusion phantom and a clinical study on an old infarction patient were conducted to validate and evaluate the performance of the present PD-STV approach. Results: In the digital phantom study, visual inspection and quantitative metrics (i.e., the normalized mean square error, the peak signal-to-noise ratio, and the universal quality index) assessments demonstrated that the PD-STV approach outperformed other existing approaches in terms of the performance of noise-induced artifacts reduction and accurate perfusion hemodynamic maps (PHM) estimation. In the patient data study, the present PD-STV approach could yield accurate PHM estimation with several noticeable gains over other existing approaches in terms of visual inspection and correlation analysis. Conclusions: This study demonstrated the feasibility and efficacy of the present PD-STV approach in utilizing STV regularization to improve the accuracy of residue function estimation of cerebral PCT imaging in the case of low-mAs.

  3. Nonminimal description of spin 3/2

    International Nuclear Information System (INIS)

    Tybor, W.

    1988-01-01

    The nonminimal description (with the help of the antisymmetric tensor-bispinor) of the spin 3/2, equivalent to the Rarita-Schwinger theory, is given. The variational principle is formulated. 5 refs. (author)

  4. Tensor-based spatiotemporal saliency detection

    Science.gov (United States)

    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.

  5. Dynamical correlations in finite nuclei: A simple method to study tensor effects

    International Nuclear Information System (INIS)

    Dellagiacoma, F.; Orlandini, G.; Traini, M.

    1983-01-01

    Dynamical correlations are introduced in finite nuclei by changing the two-body density through a phenomenological method. The role of tensor and short-range correlations in nuclear momentum distribution, electric form factor and two-body density of 4 He is investigated. The importance of induced tensor correlations in the total photonuclear cross section is reinvestigated providing a successful test of the method proposed here. (orig.)

  6. 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

  7. Tensor analysis for physicists

    CERN Document Server

    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...

  8. Sparse alignment for robust tensor learning.

    Science.gov (United States)

    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.

  9. TensorPack: a Maple-based software package for the manipulation of algebraic expressions of tensors in general relativity

    International Nuclear Information System (INIS)

    Huf, P A; Carminati, J

    2015-01-01

    In this paper we: (1) introduce TensorPack, a software package for the algebraic manipulation of tensors in covariant index format in Maple; (2) briefly demonstrate the use of the package with an orthonormal tensor proof of the shearfree conjecture for dust. TensorPack is based on the Riemann and Canon tensor software packages and uses their functions to express tensors in an indexed covariant format. TensorPack uses a string representation as input and provides functions for output in index form. It extends the functionality to basic algebra of tensors, substitution, covariant differentiation, contraction, raising/lowering indices, symmetry functions and other accessory functions. The output can be merged with text in the Maple environment to create a full working document with embedded dynamic functionality. The package offers potential for manipulation of indexed algebraic tensor expressions in a flexible software environment. (paper)

  10. Some torsion potentials

    Energy Technology Data Exchange (ETDEWEB)

    Grundberg, J; Lindstrom, U

    1986-10-01

    Using the notion of torsion potentials, the duality between antisymmetric tensor fields and scalar fields is discussed. First-order actions with these fields, the connection and the metric as independent variables are presented.

  11. 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

  12. Tensor Product of Polygonal Cell Complexes

    OpenAIRE

    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.

  13. Mean template for tensor-based morphometry using deformation tensors.

    Science.gov (United States)

    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.

  14. 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.

  15. Anti-symmetrized molecular dynamics: a new insight into the structure of nuclei

    International Nuclear Information System (INIS)

    Yoshiko, Kanada-En'yo; Masaaki, Kimura; Hisashi, Horiuchi

    2003-01-01

    The AMD (anti-symmetrized molecular dynamics) theory for nuclear structure is explained by showing its actual applications. First the formulation of AMD including various refined versions is briefly presented and its characteristics are discussed, putting a stress on its nature as an 'ab initio' theory. Then we demonstrate fruitful applications to various structure problems in stable nuclei, in order to explicitly verify the 'ab initio' nature of AMD, especially the ability to describe both mean-field-type structure and cluster structure. Finally, we show the results of applications of AMD to unstable nuclei, from which we see that AMD is powerful in elucidating and understanding various types of nuclear structure of unstable nuclei. (authors)

  16. Tensor Train Neighborhood Preserving Embedding

    Science.gov (United States)

    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.

  17. The Topology of Symmetric Tensor Fields

    Science.gov (United States)

    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.

  18. Extension of Hartree-Fock theory including tensor correlation in nuclear matter

    Science.gov (United States)

    Hu, Jinniu; Toki, Hiroshi; Ogawa, Yoko

    2013-10-01

    We study the properties of nuclear matter in the extension of Hartree-Fock theory including tensor correlation using a realistic nucleon-nucleon (NN) interaction. The nuclear wave function consists of the Hartree-Fock and two-particle-two-hole (2p-2h) states, following the concept of the tensor-optimized shell model (TOSM) for light nuclei. The short range repulsion and strong tensor force of realistic NN interaction provide high momentum components, which are taken into account in a many-body framework by introducing 2p-2h states. Single particle states are determined by the variational principle of the total energy with respect to 2p-2h amplitudes and Hartree-Fock (HF) single-particle states. The resulting differential equation is almost identical with that of Brueckner-Hartree-Fock (BHF) theory by taking two-body scattering terms only. We calculate the equation of state (EOS) of nuclear matter in this framework with the Bonn potential as a realistic NN interaction. We found similar results to BHF theory with slightly repulsive effects in the total energy. The relativistic effect is discussed for the EOSs of nuclear matter in both non-relativistic and relativistic frameworks. The momentum distribution has large components at high momenta due to 2p-2h excitations. We also obtain the EOSs of pure neutron matter, where the tensor effect is small in the iso-vector channel.

  19. Random SU(2) invariant tensors

    Science.gov (United States)

    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.

  20. Spherical Tensor Calculus for Local Adaptive Filtering

    Science.gov (United States)

    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.

  1. Improved tensor multiplets

    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.)

  2. 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

  3. Tensor algebra and tensor analysis for engineers with applications to continuum mechanics

    CERN Document Server

    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.

  4. Tensor Calculus: Unlearning Vector Calculus

    Science.gov (United States)

    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…

  5. 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....

  6. Energy-momentum tensor of the electromagnetic field

    International Nuclear Information System (INIS)

    Horndeski, G.W.; Wainwright, J.

    1977-01-01

    In this paper we investigate the energy-momentum tensor of the most general second-order vector-tensor theory of gravitation and electromagnetism which has field equations which are (i) derivable from a variational principle, (ii) consistent with the notion of conservation of charge, and (iii) compatible with Maxwell's equations in a flat space. This energy-momentum tensor turns out to be quadratic in the first partial derivatives of the electromagnetic field tensor and depends upon the curvature tensor. The asymptotic behavior of this energy-momentum tensor is examined for solutions to Maxwell's equations in Minkowski space, and it is demonstrated that this energy-momentum tensor predicts regions of negative energy density in the vicinity of point sources

  7. Anti-symmetrically fused model and non-linear integral equations in the three-state Uimin-Sutherland model

    International Nuclear Information System (INIS)

    Fujii, Akira; Kluemper, Andreas

    1999-01-01

    We derive the non-linear integral equations determining the free energy of the three-state pure bosonic Uimin-Sutherland model. In order to find a complete set of auxiliary functions, the anti-symmetric fusion procedure is utilized. We solve the non-linear integral equations numerically and see that the low-temperature behavior coincides with that predicted by conformal field theory. The magnetization and magnetic susceptibility are also calculated by means of the non-linear integral equation

  8. Behavior of the Position-Spread Tensor in Diatomic Systems.

    Science.gov (United States)

    Brea, Oriana; El Khatib, Muammar; Angeli, Celestino; Bendazzoli, Gian Luigi; Evangelisti, Stefano; Leininger, Thierry

    2013-12-10

    The behavior of the Position-Spread Tensor (Λ) in a series of light diatomic molecules (either neutral or negative ions) is investigated at a Full Configuration Interaction level. This tensor, which is the second moment cumulant of the total position operator, is invariant with respect to molecular translations, while its trace is also rotationally invariant. Moreover, the tensor is additive in the case of noninteracting subsystems and can be seen as an intrinsic property of a molecule. In the present work, it is shown that the longitudinal component of the tensor, Λ∥, which is small for internuclear distances close to the equilibrium, tends to grow if the bond is stretched. A maximum is reached in the region of the bond breaking, then Λ∥ decreases and converges toward the isolated-atom value. The degenerate transversal components, Λ⊥, on the other hand, usually have a monotonic growth toward the atomic value. The Position Spread is extremely sensitive to reorganization of the molecular wave function, and it becomes larger in the case of an increase of the electron mobility, as illustrated by the neutral-ionic avoided crossing in LiF. For these reasons, the Position Spread can be an extremely useful property that characterizes the nature of the wave function in a molecular system.

  9. A new Weyl-like tensor of geometric origin

    Science.gov (United States)

    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.

  10. Tensor calculus for physics a concise guide

    CERN Document Server

    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...

  11. 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...

  12. Tensor norms and operator ideals

    CERN Document Server

    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

  13. Shape anisotropy: tensor distance to anisotropy measure

    Science.gov (United States)

    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.

  14. Tensors and their applications

    CERN Document Server

    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

  15. Tensor Completion Algorithms in Big Data Analytics

    OpenAIRE

    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...

  16. Deep Into the Fibers! Postmortem Diffusion Tensor Imaging in Forensic Radiology.

    Science.gov (United States)

    Flach, Patricia Mildred; Schroth, Sarah; Schweitzer, Wolf; Ampanozi, Garyfalia; Slotboom, Johannes; Kiefer, Claus; Germerott, Tanja; Thali, Michael J; El-Koussy, Marwan

    2015-09-01

    In traumatic brain injury, diffusion-weighted and diffusion tensor imaging of the brain are essential techniques for determining the pathology sustained and the outcome. Postmortem cross-sectional imaging is an established adjunct to forensic autopsy in death investigation. The purpose of this prospective study was to evaluate postmortem diffusion tensor imaging in forensics for its feasibility, influencing factors and correlation to the cause of death compared with autopsy. Postmortem computed tomography, magnetic resonance imaging, and diffusion tensor imaging with fiber tracking were performed in 10 deceased subjects. The Likert scale grading of colored fractional anisotropy maps was correlated to the body temperature and intracranial pathology to assess the diagnostic feasibility of postmortem diffusion tensor imaging and fiber tracking. Optimal fiber tracking (>15,000 fiber tracts) was achieved with a body temperature at 10°C. Likert scale grading showed no linear correlation (P > 0.7) to fiber tract counts. No statistically significant correlation between total fiber count and postmortem interval could be observed (P = 0.122). Postmortem diffusion tensor imaging and fiber tracking allowed for radiological diagnosis in cases with shearing injuries but was impaired in cases with pneumencephalon and intracerebral mass hemorrhage. Postmortem diffusion tensor imaging with fiber tracking provides an exceptional in situ insight "deep into the fibers" of the brain with diagnostic benefit in traumatic brain injury and axonal injuries in the assessment of the underlying cause of death, considering influencing factors for optimal imaging technique.

  17. Efficient MATLAB computations with sparse and factored tensors.

    Energy Technology Data Exchange (ETDEWEB)

    Bader, Brett William; Kolda, Tamara Gibson (Sandia National Lab, Livermore, CA)

    2006-12-01

    In this paper, the term tensor refers simply to a multidimensional or N-way array, and we consider how specially structured tensors allow for efficient storage and computation. First, we study sparse tensors, which have the property that the vast majority of the elements are zero. We propose storing sparse tensors using coordinate format and describe the computational efficiency of this scheme for various mathematical operations, including those typical to tensor decomposition algorithms. Second, we study factored tensors, which have the property that they can be assembled from more basic components. We consider two specific types: a Tucker tensor can be expressed as the product of a core tensor (which itself may be dense, sparse, or factored) and a matrix along each mode, and a Kruskal tensor can be expressed as the sum of rank-1 tensors. We are interested in the case where the storage of the components is less than the storage of the full tensor, and we demonstrate that many elementary operations can be computed using only the components. All of the efficiencies described in this paper are implemented in the Tensor Toolbox for MATLAB.

  18. The dual formulation of cosmic strings and vortices

    CERN Document Server

    Lee, Ki-Myeong

    1993-01-01

    We study four dimensional systems of global, axionic and local strings. By using the path integral formalism, we derive the dual formulation of these systems, where Goldstone bosons, axions and missive vector bosons are described by antisymmetric tensor fields, and strings appear as a source for these tensor fields. We show also how magnetic monopoles attached to local strings are described in the dual formulation. We conclude with some remarks.

  19. Communication: Equivalence between symmetric and antisymmetric stretching modes of NH3 in promoting H + NH3 → H2 + NH2 reaction

    Science.gov (United States)

    Song, Hongwei; Yang, Minghui; Guo, Hua

    2016-10-01

    Vibrational excitations of reactants sometimes promote reactions more effectively than the same amount of translational energy. Such mode specificity provides insights into the transition-state modulation of reactivity and might be used to control chemical reactions. We report here a state-of-the-art full-dimensional quantum dynamical study of the hydrogen abstraction reaction H + NH3 → H2 + NH2 on an accurate ab initio based global potential energy surface. This reaction serves as an ideal candidate to study the relative efficacies of symmetric and degenerate antisymmetric stretching modes. Strong mode specificity, particularly for the NH3 stretching modes, is demonstrated. It is further shown that nearly identical efficacies of the symmetric and antisymmetric stretching modes of NH3 in promoting the reaction can be understood in terms of local-mode stretching vibrations of the reactant molecule.

  20. 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)

  1. Irreducible Representations of Oscillatory and Swirling Flows in Active Soft Matter

    Science.gov (United States)

    Ghose, Somdeb; Adhikari, R.

    2014-03-01

    Recent experiments imaging fluid flow around swimming microorganisms have revealed complex time-dependent velocity fields that differ qualitatively from the stresslet flow commonly employed in theoretical descriptions of active matter. Here we obtain the most general flow around a finite sized active particle by expanding the surface stress in irreducible Cartesian tensors. This expansion, whose first term is the stresslet, must include, respectively, third-rank polar and axial tensors to minimally capture crucial features of the active oscillatory flow around translating Chlamydomonas and the active swirling flow around rotating Volvox. The representation provides explicit expressions for the irreducible symmetric, antisymmetric, and isotropic parts of the continuum active stress. Antisymmetric active stresses do not conserve orbital angular momentum and our work thus shows that spin angular momentum is necessary to restore angular momentum conservation in continuum hydrodynamic descriptions of active soft matter.

  2. Dual double field theory

    Energy Technology Data Exchange (ETDEWEB)

    Bergshoeff, Eric A. [Centre for Theoretical Physics, University of Groningen,Nijenborgh 4, 9747 AG Groningen (Netherlands); Hohm, Olaf [Simons Center for Geometry and Physics, Stony Brook University,Stony Brook, NY 11794-3636 (United States); Penas, Victor A. [Centre for Theoretical Physics, University of Groningen,Nijenborgh 4, 9747 AG Groningen (Netherlands); Riccioni, Fabio [INFN - Sezione di Roma, Dipartimento di Fisica, Università di Roma “La Sapienza”,Piazzale Aldo Moro 2, 00185 Roma (Italy)

    2016-06-06

    We present the dual formulation of double field theory at the linearized level. This is a classically equivalent theory describing the duals of the dilaton, the Kalb-Ramond field and the graviton in a T-duality or O(D,D) covariant way. In agreement with previous proposals, the resulting theory encodes fields in mixed Young-tableau representations, combining them into an antisymmetric 4-tensor under O(D,D). In contrast to previous proposals, the theory also requires an antisymmetric 2-tensor and a singlet, which are not all pure gauge. The need for these additional fields is analogous to a similar phenomenon for “exotic' dualizations, and we clarify this by comparing with the dualizations of the component fields. We close with some speculative remarks on the significance of these observations for the full non-linear theory yet to be constructed.

  3. TensorCalculator: exploring the evolution of mechanical stress in the CCMV capsid

    Science.gov (United States)

    Kononova, Olga; Maksudov, Farkhad; Marx, Kenneth A.; Barsegov, Valeri

    2018-01-01

    A new computational methodology for the accurate numerical calculation of the Cauchy stress tensor, stress invariants, principal stress components, von Mises and Tresca tensors is developed. The methodology is based on the atomic stress approach which permits the calculation of stress tensors, widely used in continuum mechanics modeling of materials properties, using the output from the MD simulations of discrete atomic and C_α -based coarse-grained structural models of biological particles. The methodology mapped into the software package TensorCalculator was successfully applied to the empty cowpea chlorotic mottle virus (CCMV) shell to explore the evolution of mechanical stress in this mechanically-tested specific example of a soft virus capsid. We found an inhomogeneous stress distribution in various portions of the CCMV structure and stress transfer from one portion of the virus structure to another, which also points to the importance of entropic effects, often ignored in finite element analysis and elastic network modeling. We formulate a criterion for elastic deformation using the first principal stress components. Furthermore, we show that von Mises and Tresca stress tensors can be used to predict the onset of a viral capsid’s mechanical failure, which leads to total structural collapse. TensorCalculator can be used to study stress evolution and dynamics of defects in viral capsids and other large-size protein assemblies.

  4. The Physical Interpretation of the Lanczos Tensor

    OpenAIRE

    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...

  5. Real-time object recognition in multidimensional images based on joined extended structural tensor and higher-order tensor decomposition methods

    Science.gov (United States)

    Cyganek, Boguslaw; Smolka, Bogdan

    2015-02-01

    In this paper a system for real-time recognition of objects in multidimensional video signals is proposed. Object recognition is done by pattern projection into the tensor subspaces obtained from the factorization of the signal tensors representing the input signal. However, instead of taking only the intensity signal the novelty of this paper is first to build the Extended Structural Tensor representation from the intensity signal that conveys information on signal intensities, as well as on higher-order statistics of the input signals. This way the higher-order input pattern tensors are built from the training samples. Then, the tensor subspaces are built based on the Higher-Order Singular Value Decomposition of the prototype pattern tensors. Finally, recognition relies on measurements of the distance of a test pattern projected into the tensor subspaces obtained from the training tensors. Due to high-dimensionality of the input data, tensor based methods require high memory and computational resources. However, recent achievements in the technology of the multi-core microprocessors and graphic cards allows real-time operation of the multidimensional methods as is shown and analyzed in this paper based on real examples of object detection in digital images.

  6. 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

  7. Open BRST algebras, ghost unification and string field theory

    NARCIS (Netherlands)

    Baulieu, Laurent; Bergshoeff, Eric; Sezgin, Ergin

    1988-01-01

    Geometrical aspects of the BRST quantization of charged antisymmetric tensor fields and string fields are studied within the framework of the Batalin and Vilkovisky method. In both cases, candidate anomalies which obey the Wess-Zumino consistency conditions are given.

  8. Probing white-matter microstructure with higher-order diffusion tensors and susceptibility tensor MRI

    Science.gov (United States)

    Liu, Chunlei; Murphy, Nicole E.; Li, Wei

    2012-01-01

    Diffusion MRI has become an invaluable tool for studying white matter microstructure and brain connectivity. The emergence of quantitative susceptibility mapping and susceptibility tensor imaging (STI) has provided another unique tool for assessing the structure of white matter. In the highly ordered white matter structure, diffusion MRI measures hindered water mobility induced by various tissue and cell membranes, while susceptibility sensitizes to the molecular composition and axonal arrangement. Integrating these two methods may produce new insights into the complex physiology of white matter. In this study, we investigated the relationship between diffusion and magnetic susceptibility in the white matter. Experiments were conducted on phantoms and human brains in vivo. Diffusion properties were quantified with the diffusion tensor model and also with the higher order tensor model based on the cumulant expansion. Frequency shift and susceptibility tensor were measured with quantitative susceptibility mapping and susceptibility tensor imaging. These diffusion and susceptibility quantities were compared and correlated in regions of single fiber bundles and regions of multiple fiber orientations. Relationships were established with similarities and differences identified. It is believed that diffusion MRI and susceptibility MRI provide complementary information of the microstructure of white matter. Together, they allow a more complete assessment of healthy and diseased brains. PMID:23507987

  9. Non-Newtonian stress tensor and thermal conductivity tensor in granular plane shear flow

    Science.gov (United States)

    Alam, Meheboob; Saha, Saikat

    2014-11-01

    The non-Newtonian stress tensor and the heat flux in the plane shear flow of smooth inelastic disks are analysed from the Grad-level moment equations using the anisotropic Gaussian as a reference. Closed-form expressions for shear viscosity, pressure, first normal stress difference (N1) and the dissipation rate are given as functions of (i) the density or the area fraction (ν), (ii) the restitution coefficient (e), (iii) the dimensionless shear rate (R), (iv) the temperature anisotropy [ η, the difference between the principal eigenvalues of the second moment tensor] and (v) the angle (ϕ) between the principal directions of the shear tensor and the second moment tensor. Particle simulation data for a sheared hard-disk system is compared with theoretical results, with good agreement for p, μ and N1 over a large range of density. In contrast, the predictions from a Navier-Stokes order constitutive model are found to deviate significantly from both the simulation and the moment theory even at moderate values of e. We show that the gradient of the deviatoric part of the kinetic stress drives a heat current and the thermal conductivity is characterized by an anisotropic 2nd rank tensor for which explicit expressions are derived.

  10. 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

  11. Tensor voting for robust color edge detection

    OpenAIRE

    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 ...

  12. Geometrically nonlinear transient vibrations of actively damped anti-symmetric angle ply laminated composite shallow shell using active fibre composite (AFC) actuators

    Science.gov (United States)

    Ashok, M. H.; Shivakumar, J.; Nandurkar, Santosh; Khadakbhavi, Vishwanath; Pujari, Sanjay

    2018-02-01

    In present work, the thin laminated composite shallow shell as smart structure with AFC material’s ACLD treatment is analyzed for geometrically nonlinear transient vibrations. The AFC material is used to make the constraining layer of the ACLD treatment. Golla-Hughes-McTavish (GHM) is used to model the constrained viscoelastic layer of the ACLD treatment in time domain. Along with a simple first-order shear deformation theory the Von Kármán type non-linear strain displacement relations are used for deriving this electromechanical coupled problem. A 3-dimensional finite element model of smart composite panels integrated with the ACLD treated patches has been modelled to reveal the performance of ACLD treated patches on improving the damping properties of slender anti-symmetric angle-ply laminated shallow shell, in controlling the transient vibrations which are geometrically nonlinear. The mathematical results explain that the ACLD treated patches considerably enhance the damping properties of anti-symmetric angle-ply panels undergoing geometrically nonlinear transient vibrations.

  13. Magnetospectroscopy of symmetric and anti-symmetric states in double quantum wells

    Science.gov (United States)

    Marchewka, M.; Sheregii, E. M.; Tralle, I.; Ploch, D.; Tomaka, G.; Furdak, M.; Kolek, A.; Stadler, A.; Mleczko, K.; Zak, D.; Strupinski, W.; Jasik, A.; Jakiela, R.

    2008-02-01

    The experimental results obtained for magnetotransport in the InGaAs/InAlAs double quantum well (DQW) structures of two different shapes of wells are reported. A beating effect occurring in the Shubnikov-de Haas (SdH) oscillations was observed for both types of structures at low temperatures in the parallel transport when the magnetic field was perpendicular to the layers. An approach for the calculation of the Landau level energies for DQW structures was developed and then applied to the analysis and interpretation of the experimental data related to the beating effect. We also argue that in order to account for the observed magnetotransport phenomena (SdH and integer quantum Hall effect), one should introduce two different quasi-Fermi levels characterizing two electron subsystems regarding the symmetry properties of their states, symmetric and anti-symmetric ones, which are not mixed by electron-electron interaction.

  14. Thick-walled anisotropic elliptic tube analyzed via curvilinear tensor calculus

    Directory of Open Access Journals (Sweden)

    Mareš T.

    2007-10-01

    Full Text Available After a brief introduction into the tensor calculus, the thick-walled anisotropic elliptic tube is analyzed. A procedure of the analysis is described in a stepwise manner. A choice of the appropriate coordinate systems is the first step. The second step consists of the determination of corresponding metric tensors. Then the elasticity tensor of a local orthotropy is transformed into a global computational coordinate system. Next the appropriate Christoffel symbols of the second kind are determined and the total potential energy of the system is expressed. At the end the solution is approximated by a Fourier series and for given geometrical values and loading the numerical results are obtained and graphically represented.It must be said that throughout the calculation the free software only was used and for the numerical operations an old laptop is sufficient. The author regards both the former and the latter as a great advantage of the demonstrated method.

  15. A theoretical high energy physics program

    International Nuclear Information System (INIS)

    Clark, T.E.; Kuo, T.K.; Love, S.T.

    1989-01-01

    This report briefly describes the following research topics: aspects of dynamical symmetry breaking in gauge field theory; supersymmetric quantum electrodynamics and dynamical chiral symmetry breaking; anti-symmetric tensor gauge theories; extensions of the standard model; and neutrino oscillations in matter

  16. Should I use TensorFlow

    OpenAIRE

    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,...

  17. Dictionary-Based Tensor Canonical Polyadic Decomposition

    Science.gov (United States)

    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.

  18. 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...

  19. Energy-momentum tensor in the fermion-pairing model

    International Nuclear Information System (INIS)

    Kawati, S.; Miyata, H.

    1980-01-01

    The symmetric energy-momentum tensor for the self-interacting fermion theory (psi-barpsi) 2 is expressed in terms of the collective mode within the Hartree approximation. The divergent part of the energy-momentum tensor for the fermion theory induces an effective energy-momentum tensor for the collective mode, and this effective energy-momentum tensor automatically has the Callan-Coleman-Jackiw improved form. The renormalized energy-momentum tensor is structurally equivalent to the Callan-Coleman-Jackiw improved tensor for the Yukawa theory

  20. Time-optimized high-resolution readout-segmented diffusion tensor imaging.

    Directory of Open Access Journals (Sweden)

    Gernot Reishofer

    Full Text Available Readout-segmented echo planar imaging with 2D navigator-based reacquisition is an uprising technique enabling the sampling of high-resolution diffusion images with reduced susceptibility artifacts. However, low signal from the small voxels and long scan times hamper the clinical applicability. Therefore, we introduce a regularization algorithm based on total variation that is applied directly on the entire diffusion tensor. The spatially varying regularization parameter is determined automatically dependent on spatial variations in signal-to-noise ratio thus, avoiding over- or under-regularization. Information about the noise distribution in the diffusion tensor is extracted from the diffusion weighted images by means of complex independent component analysis. Moreover, the combination of those features enables processing of the diffusion data absolutely user independent. Tractography from in vivo data and from a software phantom demonstrate the advantage of the spatially varying regularization compared to un-regularized data with respect to parameters relevant for fiber-tracking such as Mean Fiber Length, Track Count, Volume and Voxel Count. Specifically, for in vivo data findings suggest that tractography results from the regularized diffusion tensor based on one measurement (16 min generates results comparable to the un-regularized data with three averages (48 min. This significant reduction in scan time renders high resolution (1 × 1 × 2.5 mm(3 diffusion tensor imaging of the entire brain applicable in a clinical context.

  1. Dilaton and second-rank tensor fields as supersymmetric compensators

    International Nuclear Information System (INIS)

    Nishino, Hitoshi; Rajpoot, Subhash

    2007-01-01

    We formulate a supersymmetric theory in which both a dilaton and a second-rank tensor play roles of compensators. The basic off-shell multiplets are a linear multiplet (B μν ,χ,φ) and a vector multiplet (A μ ,λ;C μνρ ), where φ and B μν are, respectively, a dilaton and a second-rank tensor. The third-rank tensor C μνρ in the vector multiplet is ''dual'' to the conventional D field with 0 on-shell or 1 off-shell degree of freedom. The dilaton φ is absorbed into one longitudinal component of A μ , making it massive. Initially, B μν has 1 on-shell or 3 off-shell degrees of freedom, but it is absorbed into the longitudinal components of C μνρ . Eventually, C μνρ with 0 on-shell or 1 off-shell degree of freedom acquires in total 1 on-shell or 4 off-shell degrees of freedom, turning into a propagating massive field. These basic multiplets are also coupled to chiral multiplets and a supersymmetric Dirac-Born-Infeld action. Some of these results are also reformulated in superspace. The proposed mechanism may well provide a solution to the long-standing puzzle of massless dilatons and second-rank tensors in supersymmetric models inspired by string theory

  2. Diffusion tensor imaging tensor shape analysis for assessment of regional white matter differences.

    Science.gov (United States)

    Middleton, Dana M; Li, Jonathan Y; Lee, Hui J; Chen, Steven; Dickson, Patricia I; Ellinwood, N Matthew; White, Leonard E; Provenzale, James M

    2017-08-01

    Purpose The purpose of this study was to investigate a novel tensor shape plot analysis technique of diffusion tensor imaging data as a means to assess microstructural differences in brain tissue. We hypothesized that this technique could distinguish white matter regions with different microstructural compositions. Methods Three normal canines were euthanized at seven weeks old. Their brains were imaged using identical diffusion tensor imaging protocols on a 7T small-animal magnetic resonance imaging system. We examined two white matter regions, the internal capsule and the centrum semiovale, each subdivided into an anterior and posterior region. We placed 100 regions of interest in each of the four brain regions. Eigenvalues for each region of interest triangulated onto tensor shape plots as the weighted average of three shape metrics at the plot's vertices: CS, CL, and CP. Results The distribution of data on the plots for the internal capsule differed markedly from the centrum semiovale data, thus confirming our hypothesis. Furthermore, data for the internal capsule were distributed in a relatively tight cluster, possibly reflecting the compact and parallel nature of its fibers, while data for the centrum semiovale were more widely distributed, consistent with the less compact and often crossing pattern of its fibers. This indicates that the tensor shape plot technique can depict data in similar regions as being alike. Conclusion Tensor shape plots successfully depicted differences in tissue microstructure and reflected the microstructure of individual brain regions. This proof of principle study suggests that if our findings are reproduced in larger samples, including abnormal white matter states, the technique may be useful in assessment of white matter diseases.

  3. 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

  4. Exact solutions for an oscillator with anti-symmetric quadratic nonlinearity

    Science.gov (United States)

    Beléndez, A.; Martínez, F. J.; Beléndez, T.; Pascual, C.; Alvarez, M. L.; Gimeno, E.; Arribas, E.

    2018-04-01

    Closed-form exact solutions for an oscillator with anti-symmetric quadratic nonlinearity are derived from the first integral of the nonlinear differential equation governing the behaviour of this oscillator. The mathematical model is an ordinary second order differential equation in which the sign of the quadratic nonlinear term changes. Two parameters characterize this oscillator: the coefficient of the linear term and the coefficient of the quadratic term. Not only the common case in which both coefficients are positive but also all possible combinations of positive and negative signs of these coefficients which provide periodic motions are considered, giving rise to four different cases. Three different periods and solutions are obtained, since the same result is valid in two of these cases. An interesting feature is that oscillatory motions whose equilibrium points are not at x = 0 are also considered. The periods are given in terms of an incomplete or complete elliptic integral of the first kind, and the exact solutions are expressed as functions including Jacobi elliptic cosine or sine functions.

  5. Transposes, L-Eigenvalues and Invariants of Third Order Tensors

    OpenAIRE

    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...

  6. Joint Tensor Feature Analysis For Visual Object Recognition.

    Science.gov (United States)

    Wong, Wai Keung; Lai, Zhihui; Xu, Yong; Wen, Jiajun; Ho, Chu Po

    2015-11-01

    Tensor-based object recognition has been widely studied in the past several years. This paper focuses on the issue of joint feature selection from the tensor data and proposes a novel method called joint tensor feature analysis (JTFA) for tensor feature extraction and recognition. In order to obtain a set of jointly sparse projections for tensor feature extraction, we define the modified within-class tensor scatter value and the modified between-class tensor scatter value for regression. The k-mode optimization technique and the L(2,1)-norm jointly sparse regression are combined together to compute the optimal solutions. The convergent analysis, computational complexity analysis and the essence of the proposed method/model are also presented. It is interesting to show that the proposed method is very similar to singular value decomposition on the scatter matrix but with sparsity constraint on the right singular value matrix or eigen-decomposition on the scatter matrix with sparse manner. Experimental results on some tensor datasets indicate that JTFA outperforms some well-known tensor feature extraction and selection algorithms.

  7. Graded tensor calculus

    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.)

  8. Robust estimation of adaptive tensors of curvature by tensor voting.

    Science.gov (United States)

    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.

  9. Quasicomplex N=2, d=1 Supersymmetric Sigma Models

    Directory of Open Access Journals (Sweden)

    Evgeny A. Ivanov

    2013-11-01

    Full Text Available We derive and discuss a new type of N=2 supersymmetric quantum mechanical sigma models which appear when the superfield action of the (1,2,1 multiplets is modified by adding an imaginary antisymmetric tensor to the target space metric, thus completing the latter to a non-symmetric Hermitian metric. These models are not equivalent to the standard de Rham sigma models, but are related to them through a certain special similarity transformation of the supercharges. On the other hand, they can be obtained by a Hamiltonian reduction from the complex supersymmetric N=2 sigma models built on the multiplets (2,2,0 and describing the Dolbeault complex on the manifolds with proper isometries. We study in detail the extremal two-dimensional case, when the target space metric is defined solely by the antisymmetric tensor, and show that the corresponding quantum systems reveal a hidden N=4 supersymmetry.

  10. 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

  11. Glyph-Based Comparative Visualization for Diffusion Tensor Fields.

    Science.gov (United States)

    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.

  12. Tensoral for post-processing users and simulation authors

    Science.gov (United States)

    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.

  13. Geometric decomposition of the conformation tensor in viscoelastic turbulence

    Science.gov (United States)

    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.

  14. 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)

  15. Tensor interaction in heavy-ion scattering. Pt. 1

    International Nuclear Information System (INIS)

    Nishioka, H.; Johnson, R.C.

    1985-01-01

    The Heidelberg shape-effect model for heavy-ion tensor interactions is reformulated and generalized using the Hooton-Johnson formulation. The generalized semiclassical model (the turning-point model) predicts that the components of the tensor analysing power anti Tsub(2q) have certain relations with each other for each type of tensor interaction (Tsub(R), Tsub(P) and Tsub(L) types). The predicted relations between the anti Tsub(2q) are very simple and have a direct connection with the properties of the tensor interaction at the turning point. The model predictions are satisfied in quantum-mechanical calculations for 7 Li and 23 Na elastic scattering from 58 Ni in the Fresnel-diffraction energy region. As a consequence of this model, it becomes possible to single out effects from a Tsub(P)- or Tsub(L)-type tensor interaction in polarized heavy-ion scattering. The presence of a Tsub(P)-type tensor interaction is suggested by measured anti T 20 /anti T 22 ratios for 7 Li + 58 Ni scattering. In the turning-point model the three types of tensor operator are not independent, and this is found to be true also in a quantum-mechanical calculation. The model also predicts relations between the components of higher-rank tensor analysing power in the presence of a higher-rank tensor interaction. The rank-3 tensor case is discussed in detail. (orig.)

  16. On Lovelock analogs of the Riemann tensor

    Science.gov (United States)

    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.

  17. The simplicial Ricci tensor

    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.

  18. The simplicial Ricci tensor

    Science.gov (United States)

    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.

  19. Beyond Low Rank: A Data-Adaptive Tensor Completion Method

    OpenAIRE

    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...

  20. Exploring the tensor networks/AdS correspondence

    Energy Technology Data Exchange (ETDEWEB)

    Bhattacharyya, Arpan [Department of Physics and Center for Field Theory and Particle Physics, Fudan University,220 Handan Road, 200433 Shanghai (China); Centre For High Energy Physics, Indian Institute of Science,560012 Bangalore (India); Gao, Zhe-Shen [Department of Physics and Center for Field Theory and Particle Physics, Fudan University,220 Handan Road, 200433 Shanghai (China); Hung, Ling-Yan [Department of Physics and Center for Field Theory and Particle Physics, Fudan University,220 Handan Road, 200433 Shanghai (China); State Key Laboratory of Surface Physics and Department of Physics, Fudan University,220 Handan Road, 200433 Shanghai (China); Collaborative Innovation Center of Advanced Microstructures, Nanjing University,Nanjing, 210093 (China); Liu, Si-Nong [Department of Physics and Center for Field Theory and Particle Physics, Fudan University,220 Handan Road, 200433 Shanghai (China)

    2016-08-11

    In this paper we study the recently proposed tensor networks/AdS correspondence. We found that the Coxeter group is a useful tool to describe tensor networks in a negatively curved space. Studying generic tensor network populated by perfect tensors, we find that the physical wave function generically do not admit any connected correlation functions of local operators. To remedy the problem, we assume that wavefunctions admitting such semi-classical gravitational interpretation are composed of tensors close to, but not exactly perfect tensors. Computing corrections to the connected two point correlation functions, we find that the leading contribution is given by structures related to geodesics connecting the operators inserted at the boundary physical dofs. Such considerations admit generalizations at least to three point functions. This is highly suggestive of the emergence of the analogues of Witten diagrams in the tensor network. The perturbations alone however do not give the right entanglement spectrum. Using the Coxeter construction, we also constructed the tensor network counterpart of the BTZ black hole, by orbifolding the discrete lattice on which the network resides. We found that the construction naturally reproduces some of the salient features of the BTZ black hole, such as the appearance of RT surfaces that could wrap the horizon, depending on the size of the entanglement region A.

  1. 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.

  2. Classical theory of radiating strings

    Science.gov (United States)

    Copeland, Edmund J.; Haws, D.; Hindmarsh, M.

    1990-01-01

    The divergent part of the self force of a radiating string coupled to gravity, an antisymmetric tensor and a dilaton in four dimensions are calculated to first order in classical perturbation theory. While this divergence can be absorbed into a renormalization of the string tension, demanding that both it and the divergence in the energy momentum tensor vanish forces the string to have the couplings of compactified N = 1 D = 10 supergravity. In effect, supersymmetry cures the classical infinities.

  3. Open BRST algebras, ghost unification and string field theory

    International Nuclear Information System (INIS)

    Baulieu, L.; Bergshoeff, E.; Sezgin, E.

    1988-01-01

    Geometrical aspects of the BRST quantization of charged antisymmetric tensor fields and string fields are studied within the framework of the Batalin and Vilkovisky method. In both cases, candidate anomalies which obey the Wess-Zumino consistency conditions are given. (author). 18 refs, 1 fig

  4. 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)

  5. 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

  6. Calculus of tensors and differential forms

    CERN Document Server

    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.

  7. Tensor Galileons and gravity

    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.

  8. Algebraic and computational aspects of real tensor ranks

    CERN Document Server

    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...

  9. Self-adaptive tensor network states with multi-site correlators

    Science.gov (United States)

    Kovyrshin, Arseny; Reiher, Markus

    2017-12-01

    We introduce the concept of self-adaptive tensor network states (SATNSs) based on multi-site correlators. The SATNS ansatz gradually extends its variational space incorporating the most important next-order correlators into the ansatz for the wave function. The selection of these correlators is guided by entanglement-entropy measures from quantum information theory. By sequentially introducing variational parameters and adjusting them to the system under study, the SATNS ansatz achieves keeping their number significantly smaller than the total number of full-configuration interaction parameters. The SATNS ansatz is studied for manganocene in its lowest-energy sextet and doublet states; the latter of which is known to be difficult to describe. It is shown that the SATNS parametrization solves the convergence issues found for previous correlator-based tensor network states.

  10. Decomposition of a symmetric second-order tensor

    Science.gov (United States)

    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.

  11. Efficient Low Rank Tensor Ring Completion

    OpenAIRE

    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...

  12. 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.

  13. 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.

  14. 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.

  15. On improving the efficiency of tensor voting.

    Science.gov (United States)

    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.

  16. 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

  17. 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.

  18. Loop optimization for tensor network renormalization

    Science.gov (United States)

    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.

  19. The Twist Tensor Nuclear Norm for Video Completion.

    Science.gov (United States)

    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.

  20. 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

  1. Generalized Tensor-Based Morphometry of HIV/AIDS Using Multivariate Statistics on Deformation Tensors

    OpenAIRE

    Lepore, Natasha; Brun, Caroline; Chou, Yi-Yu; Chiang, Ming-Chang; Dutton, Rebecca A.; Hayashi, Kiralee M.; Luders, Eileen; Lopez, Oscar L.; Aizenstein, Howard J.; Toga, Arthur W.; Becker, James T.; Thompson, Paul M.

    2008-01-01

    This paper investigates the performance of a new multivariate method for tensor-based morphometry (TBM). Statistics on Riemannian manifolds are developed that exploit the full information in deformation tensor fields. In TBM, multiple brain images are warped to a common neuroanatomical template via 3-D nonlinear registration; the resulting deformation fields are analyzed statistically to identify group differences in anatomy. Rather than study the Jacobian determinant (volume expansion factor...

  2. Tensors, relativity, and cosmology

    CERN Document Server

    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...

  3. The modified indeterminate couple stress model: Why Yang et al.'s arguments motivating a symmetric couple stress tensor contain a gap and why the couple stress tensor may be chosen symmetric nevertheless

    OpenAIRE

    Münch, Ingo; Neff, Patrizio; Madeo, Angela; Ghiba, Ionel-Dumitrel

    2015-01-01

    We show that the reasoning in favor of a symmetric couple stress tensor in Yang et al.'s introduction of the modified couple stress theory contains a gap, but we present a reasonable physical hypothesis, implying that the couple stress tensor is traceless and may be symmetric anyway. To this aim, the origin of couple stress is discussed on the basis of certain properties of the total stress itself. In contrast to classical continuum mechanics, the balance of linear momentum and the balance of...

  4. Combined Tensor Fitting and TV Regularization in Diffusion Tensor Imaging Based on a Riemannian Manifold Approach.

    Science.gov (United States)

    Baust, Maximilian; Weinmann, Andreas; Wieczorek, Matthias; Lasser, Tobias; Storath, Martin; Navab, Nassir

    2016-08-01

    In this paper, we consider combined TV denoising and diffusion tensor fitting in DTI using the affine-invariant Riemannian metric on the space of diffusion tensors. Instead of first fitting the diffusion tensors, and then denoising them, we define a suitable TV type energy functional which incorporates the measured DWIs (using an inverse problem setup) and which measures the nearness of neighboring tensors in the manifold. To approach this functional, we propose generalized forward- backward splitting algorithms which combine an explicit and several implicit steps performed on a decomposition of the functional. We validate the performance of the derived algorithms on synthetic and real DTI data. In particular, we work on real 3D data. To our knowledge, the present paper describes the first approach to TV regularization in a combined manifold and inverse problem setup.

  5. Measuring Nematic Susceptibilities from the Elastoresistivity Tensor

    Science.gov (United States)

    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.

  6. Congruences of totally geodesic surfaces

    International Nuclear Information System (INIS)

    Plebanski, J.F.; Rozga, K.

    1989-01-01

    A general theory of congruences of totally geodesic surfaces is presented. In particular their classification, based on the properties of induced affine connections, is provided. In the four-dimensional case canonical forms of the metric tensor admitting congruences of two-dimensional totally geodesic surfaces of rank one are given. Finally, congruences of two-dimensional extremal surfaces are studied. (author)

  7. Tucker tensor analysis of Matern functions in spatial statistics

    KAUST Repository

    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

  8. Observation of vector and tensor light shifts in 87Rb using near-resonant, stimulated Raman spectroscopy

    Science.gov (United States)

    Hu, Qing-Qing; Freier, Christian; Sun, Yuan; Leykauf, Bastian; Schkolnik, Vladimir; Yang, Jun; Krutzik, Markus; Peters, Achim

    2018-01-01

    We present the derivation of the frequency-dependent scalar, vector, and tensor dynamical polarizabilities for the two hyperfine levels of the 87Rb atom 5 s ground state. Based on the characterization of the dynamical polarizabilities, we analyze and measure the differential vector and tensor light shift between the 5 s ground-state sublevels with near-resonant, stimulated Raman transitions. These results clarify that the tensor polarizabilities for the ground states of alkali atoms are absent when the light field is far detuned from the atomic resonance and the total electronic angular momentum J is a good quantum number. In the near-resonant case, the light shifts are nontrivial and the determination of the frequency-dependent vector and tensor dynamic polarizabilities will help to achieve higher fidelities for applications of neutral atoms in quantum information and precision measurements.

  9. M2- and M5-branes in E11 current algebra formulation of M-theory

    Science.gov (United States)

    Shiba, Shotaro; Sugawara, Hirotaka

    2018-03-01

    Equations of motion for M2- and M5-branes are written down in the E11 current algebra formulation of M-theory. These branes correspond to currents of the second and the fifth rank antisymmetric tensors in the E11 representation, whereas the electric and magnetic fields (coupled to M2- and M5-branes) correspond to currents of the third and the sixth rank antisymmetric tensors, respectively. We show that these equations of motion have solutions in terms of the coordinates on M2- and M5-branes. We also discuss the geometric equations, and show that there are static solutions when M2- or M5-brane exists alone and also when M5-brane wraps around M2-brane. This situation is realized because our Einstein-like equation contains an extra term which can be interpreted as gravitational energy contributing to the curvature, thus avoiding the usual intersection rule.

  10. Duality invariant class of exact string backgrounds

    CERN Document Server

    Klimcík, C

    1994-01-01

    We consider a class of $2+D$ - dimensional string backgrounds with a target space metric having a covariantly constant null Killing vector and flat `transverse' part. The corresponding sigma models are invariant under $D$ abelian isometries and are transformed by $O(D,D)$ duality into models belonging to the same class. The leading-order solutions of the conformal invariance equations (metric, antisymmetric tensor and dilaton), as well as the action of $O(D,D)$ duality transformations on them, are exact, i.e. are not modified by $\\a'$-corrections. This makes a discussion of different space-time representations of the same string solution (related by $O(D,D|Z)$ duality subgroup) rather explicit. We show that the $O(D,D)$ duality may connect curved $2+D$-dimensional backgrounds with solutions having flat metric but, in general, non-trivial antisymmetric tensor and dilaton. We discuss several particular examples including the $2+D=4$ - dimensional background that was recently interpreted in terms of a WZW model.

  11. Order α'(two-loop) equivalence of the string equations of motion and the σ-model Weyl invariance conditions

    International Nuclear Information System (INIS)

    Metsaev, R.R.; Tseytlin, A.A.

    1987-01-01

    We prove the on-shell equivalence of the order α' terms in the string effective equations (for the graviton, dilaton and the antisymmetric tensor) to the vanishing of the corresponding (two-loop) terms in the Weyl anomaly coefficients for the general bosonic σ-model. We first determine the α' term in the string effective action starting with the known expression for the 3- and 4-point string amplitudes. Then we compute the two-loop β-function in the general σ-model with the antisymmetric tensor coupling. Special emphasis is made on the renormalization scheme dependence of the β-function. Our result disagrees with the previously known one and cannot be manifestly expressed in terms of the generalized curvature for the connection with torsion. We also prove (to the order α' 2 ) that the parallelizable spaces are solutions of the string equations of motion and establish the complete 3-loop expression for the 'central charge' coefficient. (orig.)

  12. 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....

  13. 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....

  14. [An Improved Spectral Quaternion Interpolation Method of Diffusion Tensor Imaging].

    Science.gov (United States)

    Xu, Yonghong; Gao, Shangce; Hao, Xiaofei

    2016-04-01

    Diffusion tensor imaging(DTI)is a rapid development technology in recent years of magnetic resonance imaging.The diffusion tensor interpolation is a very important procedure in DTI image processing.The traditional spectral quaternion interpolation method revises the direction of the interpolation tensor and can preserve tensors anisotropy,but the method does not revise the size of tensors.The present study puts forward an improved spectral quaternion interpolation method on the basis of traditional spectral quaternion interpolation.Firstly,we decomposed diffusion tensors with the direction of tensors being represented by quaternion.Then we revised the size and direction of the tensor respectively according to different situations.Finally,we acquired the tensor of interpolation point by calculating the weighted average.We compared the improved method with the spectral quaternion method and the Log-Euclidean method by the simulation data and the real data.The results showed that the improved method could not only keep the monotonicity of the fractional anisotropy(FA)and the determinant of tensors,but also preserve the tensor anisotropy at the same time.In conclusion,the improved method provides a kind of important interpolation method for diffusion tensor image processing.

  15. 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.)

  16. Joint eigenvector estimation from mutually anisotropic tensors improves susceptibility tensor imaging of the brain, kidney, and heart.

    Science.gov (United States)

    Dibb, Russell; Liu, Chunlei

    2017-06-01

    To develop a susceptibility-based MRI technique for probing microstructure and fiber architecture of magnetically anisotropic tissues-such as central nervous system white matter, renal tubules, and myocardial fibers-in three dimensions using susceptibility tensor imaging (STI) tools. STI can probe tissue microstructure, but is limited by reconstruction artifacts because of absent phase information outside the tissue and noise. STI accuracy may be improved by estimating a joint eigenvector from mutually anisotropic susceptibility and relaxation tensors. Gradient-recalled echo image data were simulated using a numerical phantom and acquired from the ex vivo mouse brain, kidney, and heart. Susceptibility tensor data were reconstructed using STI, regularized STI, and the proposed algorithm of mutually anisotropic and joint eigenvector STI (MAJESTI). Fiber map and tractography results from each technique were compared with diffusion tensor data. MAJESTI reduced the estimated susceptibility tensor orientation error by 30% in the phantom, 36% in brain white matter, 40% in the inner medulla of the kidney, and 45% in myocardium. This improved the continuity and consistency of susceptibility-based fiber tractography in each tissue. MAJESTI estimation of the susceptibility tensors yields lower orientation errors for susceptibility-based fiber mapping and tractography in the intact brain, kidney, and heart. Magn Reson Med 77:2331-2346, 2017. © 2016 International Society for Magnetic Resonance in Medicine. © 2016 International Society for Magnetic Resonance in Medicine.

  17. Weak field approximation of new general relativity

    International Nuclear Information System (INIS)

    Fukui, Masayasu; Masukawa, Junnichi

    1985-01-01

    In the weak field approximation, gravitational field equations of new general relativity with arbitrary parameters are examined. Assuming a conservation law delta sup(μ)T sub(μν) = 0 of the energy-momentum tensor T sub(μν) for matter fields in addition to the usual one delta sup(ν)T sub(μν) = 0, we show that the linearized gravitational field equations are decomposed into equations for a Lorentz scalar field and symmetric and antisymmetric Lorentz tensor fields. (author)

  18. Quantum stress tensor in Schwarzschild space-time

    International Nuclear Information System (INIS)

    Howard, K.W.; Candelas, P.

    1984-01-01

    The vacuum expectation value of the stress-energy tensor for the Hartle-Hawking state in Schwartzschild space-time has been calculated for the conformal scalar field. separates naturally into the sum of two terms. The first coincides with an approximate expression suggested by Page. The second term is a ''remainder'' that may be evaluated numerically. The total expression is in good qualitative agreement with Page's approximation. These results are at variance with earlier results given by Fawcett whose error is explained

  19. Tensor-based Dictionary Learning for Spectral CT Reconstruction

    Science.gov (United States)

    Zhang, Yanbo; Wang, Ge

    2016-01-01

    Spectral computed tomography (CT) produces an energy-discriminative attenuation map of an object, extending a conventional image volume with a spectral dimension. In spectral CT, an image can be sparsely represented in each of multiple energy channels, and are highly correlated among energy channels. According to this characteristics, we propose a tensor-based dictionary learning method for spectral CT reconstruction. In our method, tensor patches are extracted from an image tensor, which is reconstructed using the filtered backprojection (FBP), to form a training dataset. With the Candecomp/Parafac decomposition, a tensor-based dictionary is trained, in which each atom is a rank-one tensor. Then, the trained dictionary is used to sparsely represent image tensor patches during an iterative reconstruction process, and the alternating minimization scheme is adapted for optimization. The effectiveness of our proposed method is validated with both numerically simulated and real preclinical mouse datasets. The results demonstrate that the proposed tensor-based method generally produces superior image quality, and leads to more accurate material decomposition than the currently popular popular methods. PMID:27541628

  20. Tensor-Based Dictionary Learning for Spectral CT Reconstruction.

    Science.gov (United States)

    Zhang, Yanbo; Mou, Xuanqin; Wang, Ge; Yu, Hengyong

    2017-01-01

    Spectral computed tomography (CT) produces an energy-discriminative attenuation map of an object, extending a conventional image volume with a spectral dimension. In spectral CT, an image can be sparsely represented in each of multiple energy channels, and are highly correlated among energy channels. According to this characteristics, we propose a tensor-based dictionary learning method for spectral CT reconstruction. In our method, tensor patches are extracted from an image tensor, which is reconstructed using the filtered backprojection (FBP), to form a training dataset. With the Candecomp/Parafac decomposition, a tensor-based dictionary is trained, in which each atom is a rank-one tensor. Then, the trained dictionary is used to sparsely represent image tensor patches during an iterative reconstruction process, and the alternating minimization scheme is adapted for optimization. The effectiveness of our proposed method is validated with both numerically simulated and real preclinical mouse datasets. The results demonstrate that the proposed tensor-based method generally produces superior image quality, and leads to more accurate material decomposition than the currently popular popular methods.

  1. Typesafe Abstractions for Tensor Operations

    OpenAIRE

    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.

  2. Tensor network state correspondence and holography

    Science.gov (United States)

    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.

  3. 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

  4. Representation of dislocation cores using Nye tensor distributions

    International Nuclear Information System (INIS)

    Hartley, Craig S.; Mishin, Y.

    2005-01-01

    This paper demonstrates how the cores of atomistically simulated dislocations in Cu and Al can be represented by a distribution of infinitesimal dislocations described by appropriate components of the Nye tensor. Components calculated from atomic positions in the dislocated crystal are displayed as contour plots on the plane normal to the dislocation line. The method provides an accurate and instructive means for characterizing dislocation core structures and calculating the total Burgers vector

  5. Concatenated image completion via tensor augmentation and completion

    OpenAIRE

    Bengua, Johann A.; Tuan, Hoang D.; Phien, Ho N.; Do, Minh N.

    2016-01-01

    This paper proposes a novel framework called concatenated image completion via tensor augmentation and completion (ICTAC), which recovers missing entries of color images with high accuracy. Typical images are second- or third-order tensors (2D/3D) depending if they are grayscale or color, hence tensor completion algorithms are ideal for their recovery. The proposed framework performs image completion by concatenating copies of a single image that has missing entries into a third-order tensor,...

  6. 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

  7. 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)

  8. Tensor estimation for double-pulsed diffusional kurtosis imaging.

    Science.gov (United States)

    Shaw, Calvin B; Hui, Edward S; Helpern, Joseph A; Jensen, Jens H

    2017-07-01

    Double-pulsed diffusional kurtosis imaging (DP-DKI) represents the double diffusion encoding (DDE) MRI signal in terms of six-dimensional (6D) diffusion and kurtosis tensors. Here a method for estimating these tensors from experimental data is described. A standard numerical algorithm for tensor estimation from conventional (i.e. single diffusion encoding) diffusional kurtosis imaging (DKI) data is generalized to DP-DKI. This algorithm is based on a weighted least squares (WLS) fit of the signal model to the data combined with constraints designed to minimize unphysical parameter estimates. The numerical algorithm then takes the form of a quadratic programming problem. The principal change required to adapt the conventional DKI fitting algorithm to DP-DKI is replacing the three-dimensional diffusion and kurtosis tensors with the 6D tensors needed for DP-DKI. In this way, the 6D diffusion and kurtosis tensors for DP-DKI can be conveniently estimated from DDE data by using constrained WLS, providing a practical means for condensing DDE measurements into well-defined mathematical constructs that may be useful for interpreting and applying DDE MRI. Data from healthy volunteers for brain are used to demonstrate the DP-DKI tensor estimation algorithm. In particular, representative parametric maps of selected tensor-derived rotational invariants are presented. Copyright © 2017 John Wiley & Sons, Ltd.

  9. Tensor network decompositions in the presence of a global symmetry

    International Nuclear Information System (INIS)

    Singh, Sukhwinder; Pfeifer, Robert N. C.; Vidal, Guifre

    2010-01-01

    Tensor network decompositions offer an efficient description of certain many-body states of a lattice system and are the basis of a wealth of numerical simulation algorithms. We discuss how to incorporate a global symmetry, given by a compact, completely reducible group G, in tensor network decompositions and algorithms. This is achieved by considering tensors that are invariant under the action of the group G. Each symmetric tensor decomposes into two types of tensors: degeneracy tensors, containing all the degrees of freedom, and structural tensors, which only depend on the symmetry group. In numerical calculations, the use of symmetric tensors ensures the preservation of the symmetry, allows selection of a specific symmetry sector, and significantly reduces computational costs. On the other hand, the resulting tensor network can be interpreted as a superposition of exponentially many spin networks. Spin networks are used extensively in loop quantum gravity, where they represent states of quantum geometry. Our work highlights their importance in the context of tensor network algorithms as well, thus setting the stage for cross-fertilization between these two areas of research.

  10. An Adaptive Spectrally Weighted Structure Tensor Applied to Tensor Anisotropic Nonlinear Diffusion for Hyperspectral Images

    Science.gov (United States)

    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…

  11. 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.)

  12. Tensor based structure estimation in multi-channel images

    DEFF Research Database (Denmark)

    Schou, Jesper; Dierking, Wolfgang; Skriver, Henning

    2000-01-01

    . In the second part tensors are used for representing the structure information. This approach has the advantage, that tensors can be averaged either spatially or by applying several images, and the resulting tensor provides information of the average strength as well as orientation of the structure...

  13. On energy-momentum tensors of gravitational field

    International Nuclear Information System (INIS)

    Nikishov, A.I.

    2001-01-01

    The phenomenological approach to gravitation is discussed in which the 3-graviton interaction is reduced to the interaction of each graviton with the energy-momentum tensor of two others. If this is so, (and in general relativity this is not so), then the problem of choosing the correct energy-momentum tensor comes to finding the right 3-graviton vertex. Several energy-momentum tensors od gravitational field are considered and compared in the lowest approximation. Each of them together with the energy-momentum tensor of point-like particles satisfies the conservation laws when equations of motion of particles are the same as in general relativity. It is shown that in Newtonian approximation the considered tensors differ one from other in the way their energy density is distributed between energy density of interaction (nonzero only at locations of particles) and energy density of gravitational field. Stating from Lorentz invariance, the Lagrangians for spin-2, mass-0 field are considered [ru

  14. 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)

  15. 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/)....

  16. Free Vibration Study of Anti-Symmetric Angle-Ply Laminated Plates under Clamped Boundary Conditions

    Science.gov (United States)

    Viswanathan, K. K.; Karthik, K.; Sanyasiraju, Y. V. S. S.; Aziz, Z. A.

    2016-11-01

    Two type of numerical approach namely, Radial Basis Function and Spline approximation, used to analyse the free vibration of anti-symmetric angle-ply laminated plates under clamped boundary conditions. The equations of motion are derived using YNS theory under first order shear deformation. By assuming the solution in separable form, coupled differential equations obtained in term of mid-plane displacement and rotational functions. The coupled differential is then approximated using Spline function and radial basis function to obtain the generalize eigenvalue problem and parametric studies are made to investigate the effect of aspect ratio, length-to-thickness ratio, number of layers, fibre orientation and material properties with respect to the frequency parameter. Some results are compared with the existing literature and other new results are given in tables and graphs.

  17. Spin and charge controlled by antisymmetric spin-orbit coupling in a triangular-triple-quantum-dot Kondo system

    Science.gov (United States)

    Koga, M.; Matsumoto, M.; Kusunose, H.

    2018-05-01

    We study a local antisymmetric spin-orbit (ASO) coupling effect on a triangular-triple-quantum-dot (TTQD) system as a theoretical proposal for a new application of the Kondo physics to nanoscale devices. The electric polarization induced by the Kondo effect is strongly correlated with the spin configurations and molecular orbital degrees of freedom in the TTQD. In particular, an abrupt sign reversal of the emergent electric polarization is associated with a quantum critical point in a magnetic field, which can also be controlled by the ASO coupling that changes the mixing weight of different orbital components in the TTQD ground state.

  18. 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...

  19. 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...

  20. Charge- and parity-projected Hartree-Fock method for the strong tensor correlation and its application to the alpha particle

    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

  1. On improving the efficiency of tensor voting

    OpenAIRE

    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...

  2. The effects of noise over the complete space of diffusion tensor shape.

    Science.gov (United States)

    Gahm, Jin Kyu; Kindlmann, Gordon; Ennis, Daniel B

    2014-01-01

    Diffusion tensor magnetic resonance imaging (DT-MRI) is a technique used to quantify the microstructural organization of biological tissues. Multiple images are necessary to reconstruct the tensor data and each acquisition is subject to complex thermal noise. As such, measures of tensor invariants, which characterize components of tensor shape, derived from the tensor data will be biased from their true values. Previous work has examined this bias, but over a narrow range of tensor shape. Herein, we define the mathematics for constructing a tensor from tensor invariants, which permits an intuitive and principled means for building tensors with a complete range of tensor shape and salient microstructural properties. Thereafter, we use this development to evaluate by simulation the effects of noise on characterizing tensor shape over the complete space of tensor shape for three encoding schemes with different SNR and gradient directions. We also define a new framework for determining the distribution of the true values of tensor invariants given their measures, which provides guidance about the confidence the observer should have in the measures. Finally, we present the statistics of tensor invariant estimates over the complete space of tensor shape to demonstrate how the noise sensitivity of tensor invariants varies across the space of tensor shape as well as how the imaging protocol impacts measures of tensor invariants. Copyright © 2013 Elsevier B.V. All rights reserved.

  3. 3D Inversion of SQUID Magnetic Tensor Data

    DEFF Research Database (Denmark)

    Zhdanov, Michael; Cai, Hongzhu; Wilson, Glenn

    2012-01-01

    Developments in SQUID-based technology have enabled direct measurement of magnetic tensor data for geophysical exploration. For quantitative interpretation, we introduce 3D regularized inversion for magnetic tensor data. For mineral exploration-scale targets, our model studies show that magnetic...... tensor data have significantly improved resolution compared to magnetic vector data for the same model. We present a case study for the 3D regularized inversion of magnetic tensor data acquired over a magnetite skarn at Tallawang, Australia. The results obtained from our 3D regularized inversion agree...

  4. Tensor Rank Preserving Discriminant Analysis for Facial Recognition.

    Science.gov (United States)

    Tao, Dapeng; Guo, Yanan; Li, Yaotang; Gao, Xinbo

    2017-10-12

    Facial recognition, one of the basic topics in computer vision and pattern recognition, has received substantial attention in recent years. However, for those traditional facial recognition algorithms, the facial images are reshaped to a long vector, thereby losing part of the original spatial constraints of each pixel. In this paper, a new tensor-based feature extraction algorithm termed tensor rank preserving discriminant analysis (TRPDA) for facial image recognition is proposed; the proposed method involves two stages: in the first stage, the low-dimensional tensor subspace of the original input tensor samples was obtained; in the second stage, discriminative locality alignment was utilized to obtain the ultimate vector feature representation for subsequent facial recognition. On the one hand, the proposed TRPDA algorithm fully utilizes the natural structure of the input samples, and it applies an optimization criterion that can directly handle the tensor spectral analysis problem, thereby decreasing the computation cost compared those traditional tensor-based feature selection algorithms. On the other hand, the proposed TRPDA algorithm extracts feature by finding a tensor subspace that preserves most of the rank order information of the intra-class input samples. Experiments on the three facial databases are performed here to determine the effectiveness of the proposed TRPDA algorithm.

  5. The tensor bi-spectrum in a matter bounce

    Energy Technology Data Exchange (ETDEWEB)

    Chowdhury, Debika; Sreenath, V.; Sriramkumar, L., E-mail: debika@physics.iitm.ac.in, E-mail: sreenath@lsu.edu, E-mail: sriram@physics.iitm.ac.in [Department of Physics, Indian Institute of Technology Madras, Chennai 600036 (India)

    2015-11-01

    Matter bounces are bouncing scenarios wherein the universe contracts as in a matter dominated phase at early times. Such scenarios are known to lead to a scale invariant spectrum of tensor perturbations, just as de Sitter inflation does. In this work, we examine if the tensor bi-spectrum can discriminate between the inflationary and the bouncing scenarios. Using the Maldacena formalism, we analytically evaluate the tensor bi-spectrum in a matter bounce for an arbitrary triangular configuration of the wavevectors. We show that, over scales of cosmological interest, the non-Gaussianity parameter h{sub NL} that characterizes the amplitude of the tensor bi-spectrum is quite small when compared to the corresponding values in de Sitter inflation. During inflation, the amplitude of the tensor perturbations freeze on super-Hubble scales, a behavior that results in the so-called consistency condition relating the tensor bi-spectrum and the power spectrum in the squeezed limit. In contrast, in the bouncing scenarios, the amplitude of the tensor perturbations grow strongly as one approaches the bounce, which suggests that the consistency condition will not be valid in such situations. We explicitly show that the consistency relation is indeed violated in the matter bounce. We discuss the implications of the results.

  6. Endoscopic Anatomy of the Tensor Fold and Anterior Attic.

    Science.gov (United States)

    Li, Bin; Doan, Phi; Gruhl, Robert R; Rubini, Alessia; Marchioni, Daniele; Fina, Manuela

    2018-02-01

    Objectives The objectives of the study were to (1) study the anatomical variations of the tensor fold and its anatomic relation with transverse crest, supratubal recess, and anterior epitympanic space and (2) explore the most appropriate endoscopic surgical approach to each type of the tensor fold variants. Study Design Cadaver dissection study. Setting Temporal bone dissection laboratory. Subjects and Methods Twenty-eight human temporal bones (26 preserved and 2 fresh) were dissected through an endoscopic transcanal approach between September 2016 and June 2017. The anatomical variations of the tensor fold, transverse crest, supratubal recess, and anterior epitympanic space were studied before and after removing ossicles. Results Three different tensor fold orientations were observed: vertical (type A, 11/28, 39.3%) with attachment to the transverse crest, oblique (type B, 13/28, 46.4%) with attachment to the anterior tegmen tympani, and horizontal (type C, 4/28, 14.3%) with attachment to the tensor tympani canal. The tensor fold was a complete membrane in 20 of 28 (71.4%) specimens, preventing direct ventilation between the supratubal recess and anterior epitympanic space. We identified 3 surgical endoscopic approaches, which allowed visualization of the tensor fold without removing the ossicles. Conclusions The orientation of the tensor fold is the determining structure that dictates the conformation and limits of the epitympanic space. We propose a classification of the tensor fold based on 3 anatomical variants. We also describe 3 different minimally invasive endoscopic approaches to identify the orientation of the tensor fold while maintaining ossicular chain continuity.

  7. Global diffusion tensor imaging derived metrics differentiate glioblastoma multiforme vs. normal brains by using discriminant analysis: introduction of a novel whole-brain approach.

    Science.gov (United States)

    Roldan-Valadez, Ernesto; Rios, Camilo; Cortez-Conradis, David; Favila, Rafael; Moreno-Jimenez, Sergio

    2014-06-01

    Histological behavior of glioblastoma multiforme suggests it would benefit more from a global rather than regional evaluation. A global (whole-brain) calculation of diffusion tensor imaging (DTI) derived tensor metrics offers a valid method to detect the integrity of white matter structures without missing infiltrated brain areas not seen in conventional sequences. In this study we calculated a predictive model of brain infiltration in patients with glioblastoma using global tensor metrics. Retrospective, case and control study; 11 global DTI-derived tensor metrics were calculated in 27 patients with glioblastoma multiforme and 34 controls: mean diffusivity, fractional anisotropy, pure isotropic diffusion, pure anisotropic diffusion, the total magnitude of the diffusion tensor, linear tensor, planar tensor, spherical tensor, relative anisotropy, axial diffusivity and radial diffusivity. The multivariate discriminant analysis of these variables (including age) with a diagnostic test evaluation was performed. The simultaneous analysis of 732 measures from 12 continuous variables in 61 subjects revealed one discriminant model that significantly differentiated normal brains and brains with glioblastoma: Wilks' λ = 0.324, χ(2) (3) = 38.907, p tensor and linear tensor. These metrics might be clinically applied for diagnosis, follow-up, and the study of other neurological diseases.

  8. 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)

  9. Gauge theories, duality relations and the tensor hierarchy

    International Nuclear Information System (INIS)

    Bergshoeff, Eric A.; Hohm, Olaf; Hartong, Jelle; Huebscher, Mechthild; OrtIn, Tomas

    2009-01-01

    We compute the complete 3- and 4-dimensional tensor hierarchies, i.e. sets of p-form fields, with 1 ≤ p ≤ D, which realize an off-shell algebra of bosonic gauge transformations. We show how these tensor hierarchies can be put on-shell by introducing a set of duality relations, thereby introducing additional scalars and a metric tensor. These so-called duality hierarchies encode the equations of motion of the bosonic part of the most general gauged supergravity theories in those dimensions, including the (projected) scalar equations of motion. We construct gauge-invariant actions that include all the fields in the tensor hierarchies. We elucidate the relation between the gauge transformations of the p-form fields in the action and those of the same fields in the tensor hierarchy.

  10. 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....

  11. Direct diffusion tensor estimation using a model-based method with spatial and parametric constraints.

    Science.gov (United States)

    Zhu, Yanjie; Peng, Xi; Wu, Yin; Wu, Ed X; Ying, Leslie; Liu, Xin; Zheng, Hairong; Liang, Dong

    2017-02-01

    To develop a new model-based method with spatial and parametric constraints (MB-SPC) aimed at accelerating diffusion tensor imaging (DTI) by directly estimating the diffusion tensor from highly undersampled k-space data. The MB-SPC method effectively incorporates the prior information on the joint sparsity of different diffusion-weighted images using an L1-L2 norm and the smoothness of the diffusion tensor using a total variation seminorm. The undersampled k-space datasets were obtained from fully sampled DTI datasets of a simulated phantom and an ex-vivo experimental rat heart with acceleration factors ranging from 2 to 4. The diffusion tensor was directly reconstructed by solving a minimization problem with a nonlinear conjugate gradient descent algorithm. The reconstruction performance was quantitatively assessed using the normalized root mean square error (nRMSE) of the DTI indices. The MB-SPC method achieves acceptable DTI measures at an acceleration factor up to 4. Experimental results demonstrate that the proposed method can estimate the diffusion tensor more accurately than most existing methods operating at higher net acceleration factors. The proposed method can significantly reduce artifact, particularly at higher acceleration factors or lower SNRs. This method can easily be adapted to MR relaxometry parameter mapping and is thus useful in the characterization of biological tissue such as nerves, muscle, and heart tissue. © 2016 American Association of Physicists in Medicine.

  12. Detecting brain growth patterns in normal children using tensor-based morphometry.

    Science.gov (United States)

    Hua, Xue; Leow, Alex D; Levitt, Jennifer G; Caplan, Rochelle; Thompson, Paul M; Toga, Arthur W

    2009-01-01

    Previous magnetic resonance imaging (MRI)-based volumetric studies have shown age-related increases in the volume of total white matter and decreases in the volume of total gray matter of normal children. Recent adaptations of image analysis strategies enable the detection of human brain growth with improved spatial resolution. In this article, we further explore the spatio-temporal complexity of adolescent brain maturation with tensor-based morphometry. By utilizing a novel non-linear elastic intensity-based registration algorithm on the serial structural MRI scans of 13 healthy children, individual Jacobian growth maps are generated and then registered to a common anatomical space. Statistical analyses reveal significant tissue growth in cerebral white matter, contrasted with gray matter loss in parietal, temporal, and occipital lobe. In addition, a linear regression with age and gender suggests a slowing down of the growth rate in regions with the greatest white matter growth. We demonstrate that a tensor-based Jacobian map is a sensitive and reliable method to detect regional tissue changes during development. (c) 2007 Wiley-Liss, Inc.

  13. Prescribed curvature tensor in locally conformally flat manifolds

    Science.gov (United States)

    Pina, Romildo; Pieterzack, Mauricio

    2018-01-01

    A global existence theorem for the prescribed curvature tensor problem in locally conformally flat manifolds is proved for a special class of tensors R. Necessary and sufficient conditions for the existence of a metric g ¯ , conformal to Euclidean g, are determined such that R ¯ = R, where R ¯ is the Riemannian curvature tensor of the metric g ¯ . The solution to this problem is given explicitly for special cases of the tensor R, including the case where the metric g ¯ is complete on Rn. Similar problems are considered for locally conformally flat manifolds.

  14. Algebraic Rainich conditions for the fourth rank tensor V

    International Nuclear Information System (INIS)

    So, Lau Loi

    2011-01-01

    Algebraic conditions on the Ricci tensor in the Rainich-Misner-Wheeler unified field theory are known as the Rainich conditions. Penrose and more recently Bergqvist and Lankinen made an analogy from the Ricci tensor to the Bel-Robinson tensor B αβμν , a certain fourth rank tensor quadratic in the Weyl curvature, which also satisfies algebraic Rainich-like conditions. However, we found that not only does the tensor B αβμν fulfill these conditions, but so also does our recently proposed tensor V αβμν , which has many of the desirable properties of B αβμν . For the quasilocal small sphere limit restriction, we found that there are only two fourth rank tensors, B αβμν and V αβμν , which form a basis for good energy expressions. Both of them have the completely trace free and causal properties, these two form necessary and sufficient conditions. Surprisingly either completely traceless or causal is enough to fulfill the algebraic Rainich conditions.

  15. On the skew-symmetric character of the couple-stress tensor

    OpenAIRE

    Hadjesfandiari, Ali R.

    2013-01-01

    In this paper, the skew-symmetric character of the couple-stress tensor is established as the result of arguments from tensor analysis. Consequently, the couple-stress pseudo-tensor has a true vectorial character. The fundamental step in this development is that the isotropic couple-stress tensor cannot exist.

  16. Tensor products of higher almost split sequences

    OpenAIRE

    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...

  17. 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

  18. 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...

  19. A General Expression for the Quartic Lovelock Tensor

    OpenAIRE

    Briggs, C. C.

    1997-01-01

    A general expression is given for the quartic Lovelock tensor in terms of the Riemann-Christoffel and Ricci curvature tensors and the Riemann curvature scalar for n-dimensional differentiable manifolds having a general linear connection. In addition, expressions are given (in the appendix) for the coefficient of the quartic Lovelock Lagrangian as well as for lower-order Lovelock tensors and Lovelock Lagrangian coefficients.

  20. Tensor-GMRES method for large sparse systems of nonlinear equations

    Science.gov (United States)

    Feng, Dan; Pulliam, Thomas H.

    1994-01-01

    This paper introduces a tensor-Krylov method, the tensor-GMRES method, for large sparse systems of nonlinear equations. This method is a coupling of tensor model formation and solution techniques for nonlinear equations with Krylov subspace projection techniques for unsymmetric systems of linear equations. Traditional tensor methods for nonlinear equations are based on a quadratic model of the nonlinear function, a standard linear model augmented by a simple second order term. These methods are shown to be significantly more efficient than standard methods both on nonsingular problems and on problems where the Jacobian matrix at the solution is singular. A major disadvantage of the traditional tensor methods is that the solution of the tensor model requires the factorization of the Jacobian matrix, which may not be suitable for problems where the Jacobian matrix is large and has a 'bad' sparsity structure for an efficient factorization. We overcome this difficulty by forming and solving the tensor model using an extension of a Newton-GMRES scheme. Like traditional tensor methods, we show that the new tensor method has significant computational advantages over the analogous Newton counterpart. Consistent with Krylov subspace based methods, the new tensor method does not depend on the factorization of the Jacobian matrix. As a matter of fact, the Jacobian matrix is never needed explicitly.

  1. 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.

  2. A Tour of TensorFlow

    OpenAIRE

    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 ...

  3. Feature Surfaces in Symmetric Tensor Fields Based on Eigenvalue Manifold.

    Science.gov (United States)

    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.

  4. 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)

  5. Theoretical study of lithium clusters by electronic stress tensor

    International Nuclear Information System (INIS)

    Ichikawa, Kazuhide; Nozaki, Hiroo; Komazawa, Naoya; Tachibana, Akitomo

    2012-01-01

    We study the electronic structure of small lithium clusters Li_n (n = 2 ∼ 8) using the electronic stress tensor. We find that the three eigenvalues of the electronic stress tensor of the Li clusters are negative and degenerate, just like the stress tensor of liquid. This leads us to propose that we may characterize a metallic bond in terms of the electronic stress tensor. Our proposal is that in addition to the negativity of the three eigenvalues of the electronic stress tensor, their degeneracy characterizes some aspects of the metallic nature of chemical bonding. To quantify the degree of degeneracy, we use the differential eigenvalues of the electronic stress tensor. By comparing the Li clusters and hydrocarbon molecules, we show that the sign of the largest eigenvalue and the differential eigenvalues could be useful indices to evaluate the metallicity or covalency of a chemical bond.

  6. Tensor hypercontraction. II. Least-squares renormalization

    Science.gov (United States)

    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.

  7. Vacuum stress tensor of a scalar field in a rectangular waveguide

    International Nuclear Information System (INIS)

    Rodrigues, R.B.; Svaiter, N.F.; Paola, R.D.M. de

    2001-11-01

    Using the heat Kernel method and the analytical continuation of the zeta function, we calculate the canonical and improved vacuum stress tensors, {T μν (vector x)} and {Θ μν (vector x)}, associated with a massless scalar field confined in the interior of an infinity long rectangular waveguide. The local depence of the renormalized energy for two special configurations when the total energy is positive and negative are presented using {T 00 (vector x)} and {Θ 00 (vector x)}. From the stress tensors we obtain the local casimir forces in all walls by introducing a particular external configuration. It is hown that this external configuration cannot give account of the edge divergences of the local forces. The local form of the forces is obtained for three special configurations. (author)

  8. Ryu-Takayanagi formula for symmetric random tensor networks

    Science.gov (United States)

    Chirco, Goffredo; Oriti, Daniele; Zhang, Mingyi

    2018-06-01

    We consider the special case of random tensor networks (RTNs) endowed with gauge symmetry constraints on each tensor. We compute the Rényi entropy for such states and recover the Ryu-Takayanagi (RT) formula in the large-bond regime. The result provides first of all an interesting new extension of the existing derivations of the RT formula for RTNs. Moreover, this extension of the RTN formalism brings it in direct relation with (tensorial) group field theories (and spin networks), and thus provides new tools for realizing the tensor network/geometry duality in the context of background-independent quantum gravity, and for importing quantum gravity tools into tensor network research.

  9. The Topology of Three-Dimensional Symmetric Tensor Fields

    Science.gov (United States)

    Lavin, Yingmei; Levy, Yuval; Hesselink, Lambertus

    1994-01-01

    We study the topology of 3-D symmetric tensor fields. The goal is to represent their complex structure by a simple set of carefully chosen points and lines analogous to vector field topology. The basic constituents of tensor topology are the degenerate points, or points where eigenvalues are equal to each other. First, we introduce a new method for locating 3-D degenerate points. We then extract the topological skeletons of the eigenvector fields and use them for a compact, comprehensive description of the tensor field. Finally, we demonstrate the use of tensor field topology for the interpretation of the two-force Boussinesq problem.

  10. Visualizing Tensor Normal Distributions at Multiple Levels of Detail.

    Science.gov (United States)

    Abbasloo, Amin; Wiens, Vitalis; Hermann, Max; Schultz, Thomas

    2016-01-01

    Despite the widely recognized importance of symmetric second order tensor fields in medicine and engineering, the visualization of data uncertainty in tensor fields is still in its infancy. A recently proposed tensorial normal distribution, involving a fourth order covariance tensor, provides a mathematical description of how different aspects of the tensor field, such as trace, anisotropy, or orientation, vary and covary at each point. However, this wealth of information is far too rich for a human analyst to take in at a single glance, and no suitable visualization tools are available. We propose a novel approach that facilitates visual analysis of tensor covariance at multiple levels of detail. We start with a visual abstraction that uses slice views and direct volume rendering to indicate large-scale changes in the covariance structure, and locations with high overall variance. We then provide tools for interactive exploration, making it possible to drill down into different types of variability, such as in shape or orientation. Finally, we allow the analyst to focus on specific locations of the field, and provide tensor glyph animations and overlays that intuitively depict confidence intervals at those points. Our system is demonstrated by investigating the effects of measurement noise on diffusion tensor MRI, and by analyzing two ensembles of stress tensor fields from solid mechanics.

  11. Energy-momentum tensor in quantum field theory

    International Nuclear Information System (INIS)

    Fujikawa, K.

    1981-01-01

    The definition of the energy-momentum tensor as a source current coupled to the background gravitational field receives an important modification in quantum theory. In the path-integral approach, the manifest covariance of the integral measure under general coordinate transformations dictates that field variables with weight 1/2 should be used as independent integration variables. An improved energy-momentum tensor is then generated by the variational derivative, and it gives rise to well-defined gravitational conformal (Weyl) anomalies. In the flat--space-time limit, all the Ward-Takahashi identities associated with space-time transformations including the global dilatation become free from anomalies in terms of this energy-momentum tensor, reflecting the general covariance of the integral measure; the trace of this tensor is thus finite at zero momentum transfer for renormalizable theories. The Jacobian for the local conformal transformation, however, becomes nontrivial, and it gives rise to an anomaly for the conformal identity. All the familiar anomalies are thus reduced to either chiral or conformal anomalies. The consistency of the dilatation and conformal identities at vanishing momentum transfer determines the trace anomaly of this energy-momentum tensor in terms of the renormalization-group b function and other parameters. In contrast, the trace of the conventional energy-momentum tensor generally diverges even at vanishing momentum transfer depending on the regularization scheme, and it is subtractively renormalized. We also explain how the apparently different renormalization properties of the chiral and trace anomalies arise

  12. Tensor and non-tensor tractography for the assessment of the corticospinal tract of children with motor disorders: a comparative study.

    Science.gov (United States)

    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.

  13. 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...

  14. Exact tensor network ansatz for strongly interacting systems

    Science.gov (United States)

    Zaletel, Michael P.

    It appears that the tensor network ansatz, while not quite complete, is an efficient coordinate system for the tiny subset of a many-body Hilbert space which can be realized as a low energy state of a local Hamiltonian. However, we don't fully understand precisely which phases are captured by the tensor network ansatz, how to compute their physical observables (even numerically), or how to compute a tensor network representation for a ground state given a microscopic Hamiltonian. These questions are algorithmic in nature, but their resolution is intimately related to understanding the nature of quantum entanglement in many-body systems. For this reason it is useful to compute the tensor network representation of various `model' wavefunctions representative of different phases of matter; this allows us to understand how the entanglement properties of each phase are expressed in the tensor network ansatz, and can serve as test cases for algorithm development. Condensed matter physics has many illuminating model wavefunctions, such as Laughlin's celebrated wave function for the fractional quantum Hall effect, the Bardeen-Cooper-Schrieffer wave function for superconductivity, and Anderson's resonating valence bond ansatz for spin liquids. This thesis presents some results on exact tensor network representations of these model wavefunctions. In addition, a tensor network representation is given for the time evolution operator of a long-range one-dimensional Hamiltonian, which allows one to numerically simulate the time evolution of power-law interacting spin chains as well as two-dimensional strips and cylinders.

  15. The normal conformal Cartan connection and the Bach tensor

    International Nuclear Information System (INIS)

    Korzynski, Mikolaj; Lewandowski, Jerzy

    2003-01-01

    The goal of this paper is to express the Bach tensor of a four-dimensional conformal geometry of an arbitrary signature by the Cartan normal conformal (CNC) connection. We show that the Bach tensor can be identified with the Yang-Mills current of the connection. It follows from that result that a conformal geometry whose CNC connection is reducible in an appropriate way has a degenerate Bach tensor. As an example we study the case of a CNC connection which admits a twisting covariantly constant twistor field. This class of conformal geometries of this property is known as given by the Fefferman metric tensors. We use our result to calculate the Bach tensor of an arbitrary Fefferman metric and show that it is proportional to the tensorial square of the four-fold eigenvector of the Weyl tensor. Finally, we solve the Yang-Mills equations imposed on the CNC connection for all the homogeneous Fefferman metrics. The only solution is the Nurowski-Plebanski metric

  16. An introduction to tensors and group theory for physicists

    CERN Document Server

    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...

  17. Phase transitions and topological excitations in hypergauge theories

    International Nuclear Information System (INIS)

    Nencka-Ficek, H.

    1985-01-01

    The problems connected with the phase structure of antisymmetric tensor gauge fields are investigated. (s+1)-dimensional hyperloops cannot be constructed in (s+1)-dimensional lattices. This is the cause of a lack of phase transitions in the U(1) theories with fields being sth-kind gauge invariant in the (s+1)-dimensional lattice

  18. On the energy-momentum tensor in Moyal space

    International Nuclear Information System (INIS)

    Balasin, Herbert; Schweda, Manfred; Blaschke, Daniel N.; Gieres, Francois

    2015-01-01

    We study the properties of the energy-momentum tensor of gauge fields coupled to matter in non-commutative (Moyal) space. In general, the non-commutativity affects the usual conservation law of the tensor as well as its transformation properties (gauge covariance instead of gauge invariance). It is well known that the conservation of the energy-momentum tensor can be achieved by a redefinition involving another star-product. Furthermore, for a pure gauge theory it is always possible to define a gauge invariant energy-momentum tensor by means of a Wilson line. We show that the last two procedures are incompatible with each other if couplings of gauge fields to matter fields (scalars or fermions) are considered: The gauge invariant tensor (constructed via Wilson line) does not allow for a redefinition assuring its conservation, and vice versa the introduction of another star-product does not allow for gauge invariance by means of a Wilson line. (orig.)

  19. Coordinate independent expression for transverse trace-free tensors

    International Nuclear Information System (INIS)

    Conboye, Rory

    2016-01-01

    The transverse and trace-free (TT) part of the extrinsic curvature represents half of the dynamical degrees of freedom of the gravitational field in the 3 + 1 formalism. As such, it is part of the freely specifiable initial data for numerical relativity. Though TT tensors in three-space possess only two component degrees of freedom, they cannot ordinarily be given solely by two scalar potentials. Such expressions have been derived, however, in coordinate form, for all TT tensors in flat space which are also translationally or axially symmetric (Conboye and Murchadha 2014 Class. Quantum Grav. 31 085019). Since TT tensors are conformally covariant, these also give TT tensors in conformally flat space. In this article, the work above has been extended by giving a coordinate-independent expression for these TT tensors. The translational and axial symmetry conditions have also been generalized to invariance along any hypersurface orthogonal Killing vector. (paper)

  20. Antisymmetric-Symmetric Mode Conversion of Ultrasonic Lamb Waves and Negative Refraction on Thin Steel Plate

    International Nuclear Information System (INIS)

    Kim, Young H.; Sung, Jin Woo

    2013-01-01

    In this study, focusing of ultrasonic Lamb wave by negative refraction with mode conversion from antisymmetric to symmetric mode was investigated. When a wave propagates backward by negative refraction, the energy flux is antiparallel to the phase velocity. Backward propagation of Lamb wave is quite well known, but the behavior of backward Lamb wave at an interface has rarely been investigated. A pin-type transducer is used to detect Lamb wave propagating on a steel plate with a step change in thickness. Conversion from forward to backward propagating mode leads to negative refraction and thus wave focusing. By comparing the amplitudes of received Lamb waves at a specific frequency measured at different distance between transmitter and interface, the focusing of Lamb wave due to negative refraction was confirmed.

  1. The tree technique and irreducible tensor operators for the quantum algebra suq (2). The algebra of irreducible tensor operators

    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

  2. Role(s) of anti-symmetrical background field in string theory

    International Nuclear Information System (INIS)

    Fidanza, St.

    2003-11-01

    In the first chapter (titled: non-commutative D-branes), we show that the B anti-symmetrical background fields can be embedded in the non-commutativity of branes and can distort gauge theories that branes convey. We know how to describe this transformation in the Abelian case thanks to the Kontsevic quantification formula. Moreover this formula combined to the Seiberg-Witter transformation allows one to compute more rapidly the explicit terms. For the non-Abelian case the situation is less clear. In the chapter 2 (titled: non-Abelian M5-branes), we have tackled the issue of the fields of a packet of N M5-branes. The direct approach based on a 6 dimensional super-symmetric multiplets has led to a stunning dead end, we have not been able to reproduce the expected anomaly in N 3 . We have presented in a unified manner different gauge theories. We have shown that we can get a number of freedom degrees in the magnitude order of N 3 from computations based on geometrical configurations of M2 membranes. In the chapter 3 (titled: systematizing mirror symmetry) we have shown that if the presence of a non-trivial Neveu-Schwarz flux constrains the compactification manifold geometry to shift from the Calabi-Yau case, we can yet specify a mirror symmetry that mixes geometry and background fields. (A.C.)

  3. 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

  4. OPERATOR NORM INEQUALITIES BETWEEN TENSOR UNFOLDINGS ON THE PARTITION LATTICE.

    Science.gov (United States)

    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.

  5. Tensor meson dominance and e+e--physics

    International Nuclear Information System (INIS)

    Genz, H.; Karlsruhe Univ.; Mallik, S.

    1983-01-01

    The phenomenological status of tensor meson dominance is reported. Some new results concerning hadronic decays of the 2 ++ -meson chi 2 (3.55) and the heavy lepton tau are also included. Considering experimental errors, tensor meson dominance is in agreement with experiment. (author)

  6. The nonabelian tensor square of a bieberbach group with ...

    African Journals Online (AJOL)

    The main objective of this paper is to compute the nonabelian tensor square of one Bieberbach group with elementary abelian 2-group point group of dimension three by using the computational method of the nonabelian tensor square for polycyclic groups. The finding of the computation showed that the nonabelian tensor ...

  7. Holographic stress tensor for non-relativistic theories

    International Nuclear Information System (INIS)

    Ross, Simon F.; Saremi, Omid

    2009-01-01

    We discuss the calculation of the field theory stress tensor from the dual geometry for two recent proposals for gravity duals of non-relativistic conformal field theories. The first of these has a Schroedinger symmetry including Galilean boosts, while the second has just an anisotropic scale invariance (the Lifshitz case). For the Lifshitz case, we construct an appropriate action principle. We propose a definition of the non-relativistic stress tensor complex for the field theory as an appropriate variation of the action in both cases. In the Schroedinger case, we show that this gives physically reasonable results for a simple black hole solution and agrees with an earlier proposal to determine the stress tensor from the familiar AdS prescription. In the Lifshitz case, we solve the linearised equations of motion for a general perturbation around the background, showing that our stress tensor is finite on-shell.

  8. Unsupervised Tensor Mining for Big Data Practitioners.

    Science.gov (United States)

    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.

  9. 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.

  10. 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.

  11. Superconformal tensor calculus and matter couplings in six dimensions

    International Nuclear Information System (INIS)

    Bergshoeff, E.; Sezgin, E.; Proeyen, A. van

    1986-01-01

    Using superconformal tensor calculus we construct general interactions of N = 2, d = 6 supergravity with a tensor multiplet and a number of scalar, vector and linear multiplets. We start from the superconformal algebra which we realize on a 40 + 40 Weyl multiplet and on several matter multiplets. A special role is played by the tensor multiplet, which cannot be treated as an ordinary matter multiplet, but leads to a second 40 + 40 version of the Weyl multiplet. We also obtain a 48 + 48 off-shell formulation of Poincare supergravity coupled to a tensor multiplet. (orig.)

  12. 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.

  13. A tensor-based dictionary learning approach to tomographic image reconstruction

    DEFF Research Database (Denmark)

    Soltani, Sara; Kilmer, Misha E.; Hansen, Per Christian

    2016-01-01

    We consider tomographic reconstruction using priors in the form of a dictionary learned from training images. The reconstruction has two stages: first we construct a tensor dictionary prior from our training data, and then we pose the reconstruction problem in terms of recovering the expansion...... coefficients in that dictionary. Our approach differs from past approaches in that (a) we use a third-order tensor representation for our images and (b) we recast the reconstruction problem using the tensor formulation. The dictionary learning problem is presented as a non-negative tensor factorization problem...... with sparsity constraints. The reconstruction problem is formulated in a convex optimization framework by looking for a solution with a sparse representation in the tensor dictionary. Numerical results show that our tensor formulation leads to very sparse representations of both the training images...

  14. Dark energy in scalar-tensor theories

    International Nuclear Information System (INIS)

    Moeller, J.

    2007-12-01

    We investigate several aspects of dynamical dark energy in the framework of scalar-tensor theories of gravity. We provide a classification of scalar-tensor coupling functions admitting cosmological scaling solutions. In particular, we recover that Brans-Dicke theory with inverse power-law potential allows for a sequence of background dominated scaling regime and scalar field dominated, accelerated expansion. Furthermore, we compare minimally and non-minimally coupled models, with respect to the small redshift evolution of the dark energy equation of state. We discuss the possibility to discriminate between different models by a reconstruction of the equation-of-state parameter from available observational data. The non-minimal coupling characterizing scalar-tensor models can - in specific cases - alleviate fine tuning problems, which appear if (minimally coupled) quintessence is required to mimic a cosmological constant. Finally, we perform a phase-space analysis of a family of biscalar-tensor models characterized by a specific type of σ-model metric, including two examples from recent literature. In particular, we generalize an axion-dilaton model of Sonner and Townsend, incorporating a perfect fluid background consisting of (dark) matter and radiation. (orig.)

  15. Dark energy in scalar-tensor theories

    Energy Technology Data Exchange (ETDEWEB)

    Moeller, J.

    2007-12-15

    We investigate several aspects of dynamical dark energy in the framework of scalar-tensor theories of gravity. We provide a classification of scalar-tensor coupling functions admitting cosmological scaling solutions. In particular, we recover that Brans-Dicke theory with inverse power-law potential allows for a sequence of background dominated scaling regime and scalar field dominated, accelerated expansion. Furthermore, we compare minimally and non-minimally coupled models, with respect to the small redshift evolution of the dark energy equation of state. We discuss the possibility to discriminate between different models by a reconstruction of the equation-of-state parameter from available observational data. The non-minimal coupling characterizing scalar-tensor models can - in specific cases - alleviate fine tuning problems, which appear if (minimally coupled) quintessence is required to mimic a cosmological constant. Finally, we perform a phase-space analysis of a family of biscalar-tensor models characterized by a specific type of {sigma}-model metric, including two examples from recent literature. In particular, we generalize an axion-dilaton model of Sonner and Townsend, incorporating a perfect fluid background consisting of (dark) matter and radiation. (orig.)

  16. Ultrasound elastic tensor imaging: comparison with MR diffusion tensor imaging in the myocardium

    Science.gov (United States)

    Lee, Wei-Ning; Larrat, Benoît; Pernot, Mathieu; Tanter, Mickaël

    2012-08-01

    We have previously proven the feasibility of ultrasound-based shear wave imaging (SWI) to non-invasively characterize myocardial fiber orientation in both in vitro porcine and in vivo ovine hearts. The SWI-estimated results were in good correlation with histology. In this study, we proposed a new and robust fiber angle estimation method through a tensor-based approach for SWI, coined together as elastic tensor imaging (ETI), and compared it with magnetic resonance diffusion tensor imaging (DTI), a current gold standard and extensively reported non-invasive imaging technique for mapping fiber architecture. Fresh porcine (n = 5) and ovine (n = 5) myocardial samples (20 × 20 × 30 mm3) were studied. ETI was firstly performed to generate shear waves and to acquire the wave events at ultrafast frame rate (8000 fps). A 2.8 MHz phased array probe (pitch = 0.28 mm), connected to a prototype ultrasound scanner, was mounted on a customized MRI-compatible rotation device, which allowed both the rotation of the probe from -90° to 90° at 5° increments and co-registration between two imaging modalities. Transmural shear wave speed at all propagation directions realized was firstly estimated. The fiber angles were determined from the shear wave speed map using the least-squares method and eigen decomposition. The test myocardial sample together with the rotation device was then placed inside a 7T MRI scanner. Diffusion was encoded in six directions. A total of 270 diffusion-weighted images (b = 1000 s mm-2, FOV = 30 mm, matrix size = 60 × 64, TR = 6 s, TE = 19 ms, 24 averages) and 45 B0 images were acquired in 14 h 30 min. The fiber structure was analyzed by the fiber-tracking module in software, MedINRIA. The fiber orientation in the overlapped myocardial region which both ETI and DTI accessed was therefore compared, thanks to the co-registered imaging system. Results from all ten samples showed good correlation (r2 = 0.81, p 0.05, unpaired, one-tailed t-test, N = 10). In

  17. Comparing a diffusion tensor and non-tensor approach to white matter fiber tractography in chronic stroke.

    Science.gov (United States)

    Auriat, A M; Borich, M R; Snow, N J; Wadden, K P; Boyd, L A

    2015-01-01

    Diffusion tensor imaging (DTI)-based tractography has been used to demonstrate functionally relevant differences in white matter pathway status after stroke. However, it is now known that the tensor model is insensitive to the complex fiber architectures found in the vast majority of voxels in the human brain. The inability to resolve intra-voxel fiber orientations may have important implications for the utility of standard DTI-based tract reconstruction methods. Intra-voxel fiber orientations can now be identified using novel, tensor-free approaches. Constrained spherical deconvolution (CSD) is one approach to characterize intra-voxel diffusion behavior. In the current study, we performed DTI- and CSD-based tract reconstruction of the corticospinal tract (CST) and corpus callosum (CC) to test the hypothesis that characterization of complex fiber orientations may improve the robustness of fiber tract reconstruction and increase the sensitivity to identify functionally relevant white matter abnormalities in individuals with chronic stroke. Diffusion weighted magnetic resonance imaging was performed in 27 chronic post-stroke participants and 12 healthy controls. Transcallosal pathways and the CST bilaterally were reconstructed using DTI- and CSD-based tractography. Mean fractional anisotropy (FA), apparent diffusion coefficient (ADC), axial diffusivity (AD), and radial diffusivity (RD) were calculated across the tracts of interest. The total number and volume of reconstructed tracts was also determined. Diffusion measures were compared between groups (Stroke, Control) and methods (CSD, DTI). The relationship between post-stroke motor behavior and diffusion measures was evaluated. Overall, CSD methods identified more tracts than the DTI-based approach for both CC and CST pathways. Mean FA, ADC, and RD differed between DTI and CSD for CC-mediated tracts. In these tracts, we discovered a difference in FA for the CC between stroke and healthy control groups using CSD but

  18. Comparing a diffusion tensor and non-tensor approach to white matter fiber tractography in chronic stroke

    Directory of Open Access Journals (Sweden)

    A.M. Auriat

    2015-01-01

    Full Text Available Diffusion tensor imaging (DTI-based tractography has been used to demonstrate functionally relevant differences in white matter pathway status after stroke. However, it is now known that the tensor model is insensitive to the complex fiber architectures found in the vast majority of voxels in the human brain. The inability to resolve intra-voxel fiber orientations may have important implications for the utility of standard DTI-based tract reconstruction methods. Intra-voxel fiber orientations can now be identified using novel, tensor-free approaches. Constrained spherical deconvolution (CSD is one approach to characterize intra-voxel diffusion behavior. In the current study, we performed DTI- and CSD-based tract reconstruction of the corticospinal tract (CST and corpus callosum (CC to test the hypothesis that characterization of complex fiber orientations may improve the robustness of fiber tract reconstruction and increase the sensitivity to identify functionally relevant white matter abnormalities in individuals with chronic stroke. Diffusion weighted magnetic resonance imaging was performed in 27 chronic post-stroke participants and 12 healthy controls. Transcallosal pathways and the CST bilaterally were reconstructed using DTI- and CSD-based tractography. Mean fractional anisotropy (FA, apparent diffusion coefficient (ADC, axial diffusivity (AD, and radial diffusivity (RD were calculated across the tracts of interest. The total number and volume of reconstructed tracts was also determined. Diffusion measures were compared between groups (Stroke, Control and methods (CSD, DTI. The relationship between post-stroke motor behavior and diffusion measures was evaluated. Overall, CSD methods identified more tracts than the DTI-based approach for both CC and CST pathways. Mean FA, ADC, and RD differed between DTI and CSD for CC-mediated tracts. In these tracts, we discovered a difference in FA for the CC between stroke and healthy control groups

  19. Tensor completion for PDEs with uncertain coefficients and Bayesian Update

    KAUST Repository

    Litvinenko, Alexander

    2017-03-05

    In this work, we tried to show connections between Bayesian update and tensor completion techniques. Usually, only a small/sparse vector/tensor of measurements is available. The typical measurement is a function of the solution. The solution of a stochastic PDE is a tensor, the measurement as well. The idea is to use completion techniques to compute all "missing" values of the measurement tensor and only then apply the Bayesian technique.

  20. Tensor completion for PDEs with uncertain coefficients and Bayesian Update

    KAUST Repository

    Litvinenko, Alexander

    2017-01-01

    In this work, we tried to show connections between Bayesian update and tensor completion techniques. Usually, only a small/sparse vector/tensor of measurements is available. The typical measurement is a function of the solution. The solution of a stochastic PDE is a tensor, the measurement as well. The idea is to use completion techniques to compute all "missing" values of the measurement tensor and only then apply the Bayesian technique.

  1. The Role of Antisymmetric Exchange on the Quantum Interference between States of Different Spin Length in a dimeric Molecular Nanomagnet.

    Science.gov (United States)

    Del Barco, Enrique

    2009-03-01

    We report direct evidence of quantum oscillations of the total spin length of a dimeric molecular nanomagnet through the observation of quantum interference associated with tunneling trajectories between states having different spin quantum numbers. As we outline, this is a consequence of the unique characteristics of a molecular Mn12 wheel which behaves as a (weak) ferromagnetic exchange-coupled molecular dimer: each half of the molecule acts as a single-molecule magnet (SMM), while the weak coupling between the two halves gives rise to an additional internal spin degree of freedom within the molecule, namely that its total spin may fluctuate. This extra degree of freedom accounts for several magnetization tunneling resonances that cannot be explained within the usual giant spin approximation. More importantly, the observation of quantum interference provides unambiguous evidence for the quantum mechanical superposition involving entangled states of both halves of the wheel. Magnetization results obtained in two other versions of this compound, in which the ligands have been modified, show that slight variations of the relative distance between the Mn ions determine whether the molecule behaves as a rigid magnetic unit of spin S = 7 or as two exchange-coupled halves of spin S = 7/2. We analyze the effect of the Dzyaloshinskii-Moriya antisymmetric exchange interaction in a molecule with a centre of inversion symmetry and propose a formal model to account for the observed broken degeneracy that preserves the molecular inversion symmetry.

  2. Groups of automorphisms of the canonical commutation and anticommutation relations

    International Nuclear Information System (INIS)

    Grosse, H.; Pittner, L.

    1987-01-01

    Observables of supersymmetric quantum mechanics are coded by taking the antisymmetric tensor product with anticommuting parameters. Next we define superunitary transformations, which mix bosonic and fermionic degrees of freedom, in order to construct automorphisms of the canonical (anti-) commutation relations. Conversely, every automorphism of the C(A)CR is implemented by an essentially unique superunitary transformation. 12 refs. (Author)

  3. Tensor squeezed limits and the Higuchi bound

    Energy Technology Data Exchange (ETDEWEB)

    Bordin, Lorenzo [SISSA, via Bonomea 265, 34136, Trieste (Italy); Creminelli, Paolo [Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11, 34151, Trieste (Italy); Mirbabayi, Mehrdad [Institute for Advanced Study, Princeton, NJ 08540 (United States); Noreña, Jorge, E-mail: lbordin@sissa.it, E-mail: creminel@ictp.it, E-mail: mehrdadm@ias.edu, E-mail: jorge.norena@pucv.cl [Instituto de Física, Pontificia Universidad Católica de Valparaíso, Avenida Universidad 330, Curauma, Valparaíso (Chile)

    2016-09-01

    We point out that tensor consistency relations—i.e. the behavior of primordial correlation functions in the limit a tensor mode has a small momentum—are more universal than scalar consistency relations. They hold in the presence of multiple scalar fields and as long as anisotropies are diluted exponentially fast. When de Sitter isometries are approximately respected during inflation this is guaranteed by the Higuchi bound, which forbids the existence of light particles with spin: de Sitter space can support scalar hair but no curly hair. We discuss two indirect ways to look for the violation of tensor consistency relations in observations, as a signature of models in which inflation is not a strong isotropic attractor, such as solid inflation: (a) graviton exchange contribution to the scalar four-point function; (b) quadrupolar anisotropy of the scalar power spectrum due to super-horizon tensor modes. This anisotropy has a well-defined statistics which can be distinguished from cases in which the background has a privileged direction.

  4. Relativistic interpretation of the nature of the nuclear tensor force

    Science.gov (United States)

    Zong, Yao-Yao; Sun, Bao-Yuan

    2018-02-01

    The spin-dependent nature of the nuclear tensor force is studied in detail within the relativistic Hartree-Fock approach. The relativistic formalism for the tensor force is supplemented with an additional Lorentz-invariant tensor formalism in the σ-scalar channel, so as to take into account almost fully the nature of the tensor force brought about by the Fock diagrams in realistic nuclei. Specifically, the tensor sum rules are tested for the spin and pseudo-spin partners with and without nodes, to further understand the nature of the tensor force within the relativistic model. It is shown that the interference between the two components of nucleon spinors causes distinct violations of the tensor sum rules in realistic nuclei, mainly due to the opposite signs on the κ quantities of the upper and lower components, as well as the nodal difference. However, the sum rules can be precisely reproduced if the same radial wave functions are taken for the spin/pseudo-spin partners in addition to neglecting the lower/upper components, revealing clearly the nature of the tensor force. Supported by National Natural Science Foundation of China (11375076, 11675065) and the Fundamental Research Funds for the Central Universities (lzujbky-2016-30)

  5. Massless and massive quanta resulting from a mediumlike metric tensor

    International Nuclear Information System (INIS)

    Soln, J.

    1985-01-01

    A simple model of the ''primordial'' scalar field theory is presented in which the metric tensor is a generalization of the metric tensor from electrodynamics in a medium. The radiation signal corresponding to the scalar field propagates with a velocity that is generally less than c. This signal can be associated simultaneously with imaginary and real effective (momentum-dependent) masses. The requirement that the imaginary effective mass vanishes, which we take to be the prerequisite for the vacuumlike signal propagation, leads to the ''spontaneous'' splitting of the metric tensor into two distinct metric tensors: one metric tensor gives rise to masslesslike radiation and the other to a massive particle. (author)

  6. Interplay between tensor force and deformation in even–even nuclei

    Energy Technology Data Exchange (ETDEWEB)

    Bernard, Rémi N., E-mail: rbernard@ugr.es; Anguiano, Marta

    2016-09-15

    In this work we study the effect of the nuclear tensor force on properties related with deformation. We focus on isotopes in the Mg, Si, S, Ar, Sr and Zr chains within the Hartree–Fock–Bogoliubov theory using the D1ST2a Gogny interaction. Contributions to the tensor energy in terms of saturated and unsaturated subshells are analyzed. Like–particle and proton–neutron parts of the tensor term are independently examinated. We found that the tensor term may considerably modify the potential energy landscapes and change the ground state shape. We analyze too how the pairing characteristics of the ground state change when the tensor force is included.

  7. Superconformal tensor calculus and matter couplings in six dimensions

    International Nuclear Information System (INIS)

    Bergshoeff, E.; Sezgin, E.; van Proeyen, A.

    1989-01-01

    Using superconformal tensor calculus the authors construct general interactions of N = 2, d = 6 supergravity with a tensor multiplet and a number of scalar, vector and linear multiplets. They start from the superconformal algebra which they realize on a 40 + 40 Weyl multiplet and on several matter multiplets. A special role is played by the tensor multiplet, which cannot be treated as an ordinary matter multiplet, but leads to a second 40 + 40 version of the Weyl multiplet. The authors also obtain a 48 + 48 off-shell formulation of Poincare supergravity coupled to a tensor multiplet

  8. Tensor product varieties and crystals. GL case

    OpenAIRE

    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.

  9. 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 ...

  10. Study of the tensor correlation in a neutron-rich sd-shell region with the charge- and parity-projected Hartree-Fock method

    International Nuclear Information System (INIS)

    Sugimoto, Satoru; Toki, Hiroshi; Ikeda, Kiyomi

    2008-01-01

    We study the effect of the tensor force on nuclear structure with mean-field and beyond-mean-field methods. An important correlation induced by the tensor force is two-particle-two-hole (2p2h) correlation, which cannot be treated with a usual mean-filed method. To treat the 2p2h tensor correlation, we develop a new framework (charge- and parity-projected Hartree-Fock (CPPHF) method), which is a beyond-mean-field method. In the CPPHF method, we introduce single-particle states with parity and charge mixing. The parity and charge projections are performed on a total wave function before variation. We apply the CPPHF method to oxygen isotopes including neutron-rich ones. The potential energy from the tensor force has the same order of magnitude with that from the LS force and becomes smaller with neutron number, which indicates that excess neutrons do not contribute to the 2p2h tensor correlation significantly. We also study the effect of the tensor force on spin-orbit-splitting (ls-splitting) in a neutron-rich fluorine isotope 23 F. The tensor force reduces the ls-splitting for the proton d-orbits by about 3 MeV. This effect is important to reproduce the experimental value. We also find that the 2p2h tensor correlation does not affect the ls-splitting in 23 F

  11. Atomic-batched tensor decomposed two-electron repulsion integrals

    Science.gov (United States)

    Schmitz, Gunnar; Madsen, Niels Kristian; Christiansen, Ove

    2017-04-01

    We present a new integral format for 4-index electron repulsion integrals, in which several strategies like the Resolution-of-the-Identity (RI) approximation and other more general tensor-decomposition techniques are combined with an atomic batching scheme. The 3-index RI integral tensor is divided into sub-tensors defined by atom pairs on which we perform an accelerated decomposition to the canonical product (CP) format. In a first step, the RI integrals are decomposed to a high-rank CP-like format by repeated singular value decompositions followed by a rank reduction, which uses a Tucker decomposition as an intermediate step to lower the prefactor of the algorithm. After decomposing the RI sub-tensors (within the Coulomb metric), they can be reassembled to the full decomposed tensor (RC approach) or the atomic batched format can be maintained (ABC approach). In the first case, the integrals are very similar to the well-known tensor hypercontraction integral format, which gained some attraction in recent years since it allows for quartic scaling implementations of MP2 and some coupled cluster methods. On the MP2 level, the RC and ABC approaches are compared concerning efficiency and storage requirements. Furthermore, the overall accuracy of this approach is assessed. Initial test calculations show a good accuracy and that it is not limited to small systems.

  12. Janus field theories from non-linear BF theories for multiple M2-branes

    International Nuclear Information System (INIS)

    Ryang, Shijong

    2009-01-01

    We integrate the nonpropagating B μ gauge field for the non-linear BF Lagrangian describing N M2-branes which includes terms with even number of the totally antisymmetric tensor M IJK in arXiv:0808.2473 and for the two-types of non-linear BF Lagrangians which include terms with odd number of M IJK as well in arXiv:0809:0985. For the former Lagrangian we derive directly the DBI-type Lagrangian expressed by the SU(N) dynamical A μ gauge field with a spacetime dependent coupling constant, while for the low-energy expansions of the latter Lagrangians the B μ integration is iteratively performed. The derived Janus field theory Lagrangians are compared.

  13. Inflationary tensor fossils in large-scale structure

    Energy Technology Data Exchange (ETDEWEB)

    Dimastrogiovanni, Emanuela [School of Physics and Astronomy, University of Minnesota, Minneapolis, MN 55455 (United States); Fasiello, Matteo [Department of Physics, Case Western Reserve University, Cleveland, OH 44106 (United States); Jeong, Donghui [Department of Astronomy and Astrophysics, The Pennsylvania State University, University Park, PA 16802 (United States); Kamionkowski, Marc, E-mail: ema@physics.umn.edu, E-mail: mrf65@case.edu, E-mail: duj13@psu.edu, E-mail: kamion@jhu.edu [Department of Physics and Astronomy, 3400 N. Charles St., Johns Hopkins University, Baltimore, MD 21218 (United States)

    2014-12-01

    Inflation models make specific predictions for a tensor-scalar-scalar three-point correlation, or bispectrum, between one gravitational-wave (tensor) mode and two density-perturbation (scalar) modes. This tensor-scalar-scalar correlation leads to a local power quadrupole, an apparent departure from statistical isotropy in our Universe, as well as characteristic four-point correlations in the current mass distribution in the Universe. So far, the predictions for these observables have been worked out only for single-clock models in which certain consistency conditions between the tensor-scalar-scalar correlation and tensor and scalar power spectra are satisfied. Here we review the requirements on inflation models for these consistency conditions to be satisfied. We then consider several examples of inflation models, such as non-attractor and solid-inflation models, in which these conditions are put to the test. In solid inflation the simplest consistency conditions are already violated whilst in the non-attractor model we find that, contrary to the standard scenario, the tensor-scalar-scalar correlator probes directly relevant model-dependent information. We work out the predictions for observables in these models. For non-attractor inflation we find an apparent local quadrupolar departure from statistical isotropy in large-scale structure but that this power quadrupole decreases very rapidly at smaller scales. The consistency of the CMB quadrupole with statistical isotropy then constrains the distance scale that corresponds to the transition from the non-attractor to attractor phase of inflation to be larger than the currently observable horizon. Solid inflation predicts clustering fossils signatures in the current galaxy distribution that may be large enough to be detectable with forthcoming, and possibly even current, galaxy surveys.

  14. Low-dose 4D cone-beam CT via joint spatiotemporal regularization of tensor framelet and nonlocal total variation

    Science.gov (United States)

    Han, Hao; Gao, Hao; Xing, Lei

    2017-08-01

    Excessive radiation exposure is still a major concern in 4D cone-beam computed tomography (4D-CBCT) due to its prolonged scanning duration. Radiation dose can be effectively reduced by either under-sampling the x-ray projections or reducing the x-ray flux. However, 4D-CBCT reconstruction under such low-dose protocols is prone to image artifacts and noise. In this work, we propose a novel joint regularization-based iterative reconstruction method for low-dose 4D-CBCT. To tackle the under-sampling problem, we employ spatiotemporal tensor framelet (STF) regularization to take advantage of the spatiotemporal coherence of the patient anatomy in 4D images. To simultaneously suppress the image noise caused by photon starvation, we also incorporate spatiotemporal nonlocal total variation (SNTV) regularization to make use of the nonlocal self-recursiveness of anatomical structures in the spatial and temporal domains. Under the joint STF-SNTV regularization, the proposed iterative reconstruction approach is evaluated first using two digital phantoms and then using physical experiment data in the low-dose context of both under-sampled and noisy projections. Compared with existing approaches via either STF or SNTV regularization alone, the presented hybrid approach achieves improved image quality, and is particularly effective for the reconstruction of low-dose 4D-CBCT data that are not only sparse but noisy.

  15. Properties of the tensor correlation in He isotopes

    International Nuclear Information System (INIS)

    Myo, Takayuki; Sugimoto, Satoru; Kato, Kiyoshi; Toki, Hiroshi; Ikeda, Kiyomi

    2006-01-01

    We investigate the roles of the tensor correlation on the structures of 4,5 He. For 4 He, we take the high angular momentum states as much as possible with the 2p2h excitations of the shell model type method to describe the tensor correlation. Three specific configurations are found to be favored for the tensor correlation. This correlation is also important to describe the scattering phenomena of the 4 He+nsystem including the higher partial waves consistently

  16. Energy-momentum tensor in the quantum field theory

    International Nuclear Information System (INIS)

    Azakov, S.I.

    1977-01-01

    An energy-momentum tensor in the scalar field theory is built. The tensor must satisfy the finiteness requirement of the Green function. The Green functions can always be made finite by renormalizations in the S-matrix by introducing counter terms into the Hamiltonian (or Lagrangian) of the interaction. Such a renormalization leads to divergencies in the Green functions. Elimination of these divergencies requires the introduction of new counter terms, which must be taken into account in the energy-momentum tensor

  17. Tensor product of quantum logics

    Science.gov (United States)

    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.

  18. A Closed-Form Solution to Tensor Voting: Theory and Applications

    OpenAIRE

    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...

  19. 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)

  20. The tensor distribution function.

    Science.gov (United States)

    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.

  1. Inductive Framework for Multi-Aspect Streaming Tensor Completion with Side Information

    OpenAIRE

    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...

  2. The classification of the Ricci tensor in the general theory of relativity

    International Nuclear Information System (INIS)

    Cormack, W.J.

    1979-10-01

    A comprehensive classification of the Ricci tensor in General Relativity using several techniques is given and their connection with existing classification studied under the headings; canonical forms for the Ricci tensor, invariant 2-spaces in the classification of the Ricci tensor, Riemannian curvature and the classification of the Riemann and Ricci tensors, and spinor classifications of the Ricci tensor. (U.K.)

  3. Susceptibility Tensor Imaging (STI) of the Brain

    Science.gov (United States)

    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

  4. Singular Poisson tensors

    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

  5. Structure of the Einstein tensor for class-1 embedded space time

    Energy Technology Data Exchange (ETDEWEB)

    Krause, J [Universidad Central de Venezuela, Caracas

    1976-04-11

    Continuing previous work, some features of the flat embedding theory of class-1 curved space-time are further discussed. In the two-metric formalism provided by the embedding approach the Gauss tensor obtains as the flat-covariant gradient of a fundamental vector potential. The Einstein tensor is then examined in terms of the Gauss tensor. It is proved that the Einstein tensor is divergence free in flat space-time, i.e. a true Lorentz-covariant conservation law for the Einstein tensor is shown to hold. The form of the Einstein tensor in flat space-time also appears as a canonical energy-momentum tensor of the vector potential. The corresponding Lagrangian density, however, does not provide us with a set of field equations for the fundamental vector potential; indeed, the Euler-Lagrange ''equations'' collapse to a useless identity, while the Lagrangian density has the form of a flat divergence.

  6. TENSOR MODELING BASED FOR AIRBORNE LiDAR DATA CLASSIFICATION

    Directory of Open Access Journals (Sweden)

    N. Li

    2016-06-01

    Full Text Available Feature selection and description is a key factor in classification of Earth observation data. In this paper a classification method based on tensor decomposition is proposed. First, multiple features are extracted from raw LiDAR point cloud, and raster LiDAR images are derived by accumulating features or the “raw” data attributes. Then, the feature rasters of LiDAR data are stored as a tensor, and tensor decomposition is used to select component features. This tensor representation could keep the initial spatial structure and insure the consideration of the neighborhood. Based on a small number of component features a k nearest neighborhood classification is applied.

  7. Validation of diffusion tensor MRI measurements of cardiac microstructure with structure tensor synchrotron radiation imaging.

    Science.gov (United States)

    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

  8. Tensor Completion for Estimating Missing Values in Visual Data

    KAUST Repository

    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

  9. Tensor Completion for Estimating Missing Values in Visual Data

    KAUST Repository

    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

  10. Tensor completion for estimating missing values in visual data.

    Science.gov (United States)

    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

  11. Inference of segmented color and texture description by tensor voting.

    Science.gov (United States)

    Jia, Jiaya; Tang, Chi-Keung

    2004-06-01

    A robust synthesis method is proposed to automatically infer missing color and texture information from a damaged 2D image by (N)D tensor voting (N > 3). The same approach is generalized to range and 3D data in the presence of occlusion, missing data and noise. Our method translates texture information into an adaptive (N)D tensor, followed by a voting process that infers noniteratively the optimal color values in the (N)D texture space. A two-step method is proposed. First, we perform segmentation based on insufficient geometry, color, and texture information in the input, and extrapolate partitioning boundaries by either 2D or 3D tensor voting to generate a complete segmentation for the input. Missing colors are synthesized using (N)D tensor voting in each segment. Different feature scales in the input are automatically adapted by our tensor scale analysis. Results on a variety of difficult inputs demonstrate the effectiveness of our tensor voting approach.

  12. Diffusion tensor smoothing through weighted Karcher means

    Science.gov (United States)

    Carmichael, Owen; Chen, Jun; Paul, Debashis; Peng, Jie

    2014-01-01

    Diffusion tensor magnetic resonance imaging (MRI) quantifies the spatial distribution of water Diffusion at each voxel on a regular grid of locations in a biological specimen by Diffusion tensors– 3 × 3 positive definite matrices. Removal of noise from DTI is an important problem due to the high scientific relevance of DTI and relatively low signal to noise ratio it provides. Leading approaches to this problem amount to estimation of weighted Karcher means of Diffusion tensors within spatial neighborhoods, under various metrics imposed on the space of tensors. However, it is unclear how the behavior of these estimators varies with the magnitude of DTI sensor noise (the noise resulting from the thermal e!ects of MRI scanning) as well as the geometric structure of the underlying Diffusion tensor neighborhoods. In this paper, we combine theoretical analysis, empirical analysis of simulated DTI data, and empirical analysis of real DTI scans to compare the noise removal performance of three kernel-based DTI smoothers that are based on Euclidean, log-Euclidean, and affine-invariant metrics. The results suggest, contrary to conventional wisdom, that imposing a simplistic Euclidean metric may in fact provide comparable or superior noise removal, especially in relatively unstructured regions and/or in the presence of moderate to high levels of sensor noise. On the contrary, log-Euclidean and affine-invariant metrics may lead to better noise removal in highly structured anatomical regions, especially when the sensor noise is of low magnitude. These findings emphasize the importance of considering the interplay of sensor noise magnitude and tensor field geometric structure when assessing Diffusion tensor smoothing options. They also point to the necessity for continued development of smoothing methods that perform well across a large range of scenarios. PMID:25419264

  13. Diffusion tensor imaging in spinal cord compression

    International Nuclear Information System (INIS)

    Wang, Wei; Qin, Wen; Hao, Nanxin; Wang, Yibin; Zong, Genlin

    2012-01-01

    Background Although diffusion tensor imaging has been successfully applied in brain research for decades, several main difficulties have hindered its extended utilization in spinal cord imaging. Purpose To assess the feasibility and clinical value of diffusion tensor imaging and tractography for evaluating chronic spinal cord compression. Material and Methods Single-shot spin-echo echo-planar DT sequences were scanned in 42 spinal cord compression patients and 49 healthy volunteers. The mean values of the apparent diffusion coefficient and fractional anisotropy were measured in region of interest at the cervical and lower thoracic spinal cord. The patients were divided into two groups according to the high signal on T2WI (the SCC-HI group and the SCC-nHI group for with or without high signal). A one-way ANOVA was used. Diffusion tensor tractography was used to visualize the morphological features of normal and impaired white matter. Results There were no statistically significant differences in the apparent diffusion coefficient and fractional anisotropy values between the different spinal cord segments of the normal subjects. All of the patients in the SCC-HI group had increased apparent diffusion coefficient values and decreased fractional anisotropy values at the lesion level compared to the normal controls. However, there were no statistically significant diffusion index differences between the SCC-nHI group and the normal controls. In the diffusion tensor imaging maps, the normal spinal cord sections were depicted as fiber tracts that were color-encoded to a cephalocaudal orientation. The diffusion tensor images were compressed to different degrees in all of the patients. Conclusion Diffusion tensor imaging and tractography are promising methods for visualizing spinal cord tracts and can provide additional information in clinical studies in spinal cord compression

  14. 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.

  15. Fermionic topological quantum states as tensor networks

    Science.gov (United States)

    Wille, C.; Buerschaper, O.; Eisert, J.

    2017-06-01

    Tensor network states, and in particular projected entangled pair states, play an important role in the description of strongly correlated quantum lattice systems. They do not only serve as variational states in numerical simulation methods, but also provide a framework for classifying phases of quantum matter and capture notions of topological order in a stringent and rigorous language. The rapid development in this field for spin models and bosonic systems has not yet been mirrored by an analogous development for fermionic models. In this work, we introduce a tensor network formalism capable of capturing notions of topological order for quantum systems with fermionic components. At the heart of the formalism are axioms of fermionic matrix-product operator injectivity, stable under concatenation. Building upon that, we formulate a Grassmann number tensor network ansatz for the ground state of fermionic twisted quantum double models. A specific focus is put on the paradigmatic example of the fermionic toric code. This work shows that the program of describing topologically ordered systems using tensor networks carries over to fermionic models.

  16. 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

  17. Tensor B mode and stochastic Faraday mixing

    CERN Document Server

    Giovannini, Massimo

    2014-01-01

    This paper investigates the Faraday effect as a different source of B mode polarization. The E mode polarization is Faraday rotated provided a stochastic large-scale magnetic field is present prior to photon decoupling. In the first part of the paper we discuss the case where the tensor modes of the geometry are absent and we argue that the B mode recently detected by the Bicep2 collaboration cannot be explained by a large-scale magnetic field rotating, through the Faraday effect, the well established E mode polarization. In this case, the observed temperature autocorrelations would be excessively distorted by the magnetic field. In the second part of the paper the formation of Faraday rotation is treated as a stationary, random and Markovian process with the aim of generalizing a set of scaling laws originally derived in the absence of the tensor modes of the geometry. We show that the scalar, vector and tensor modes of the brightness perturbations can all be Faraday rotated even if the vector and tensor par...

  18. On t-quark decay

    International Nuclear Information System (INIS)

    Chizhov, M.V.

    1995-07-01

    An extended electroweak model with second rank antisymmetric tensor field is proposed. The effective interactions resulting from the exchange of these fields have specific dependence on the transfer momentum. This leads to the introduction of new model-independent muon decay parameters (Mod. Phys. Lett. A9 (1994) 2979), which can be measured experimentally in SLAC and TRIUMF. The new tensor interactions can effect the three-particles semileptonic meson decays (Mod. Phys. Lett. A8 (1993) 2753). In this connection it will be interesting to propose new experiments on K + → l + νγ, K + → π 0 l + ν decays in DAΦNE. The K L -K s mass difference sets constraints on the tensor particles masses. The mass of the lightest tensor particle could be less than the t-quark mass. Therefore the lightest tensor particle may give an additional to the W-boson contribution into the t- quark decay with the same signature. (author). 10 refs, 2 figs

  19. Some spacetimes with higher rank Killing-Staeckel tensors

    International Nuclear Information System (INIS)

    Gibbons, G.W.; Houri, T.; Kubiznak, D.; Warnick, C.M.

    2011-01-01

    By applying the lightlike Eisenhart lift to several known examples of low-dimensional integrable systems admitting integrals of motion of higher-order in momenta, we obtain four- and higher-dimensional Lorentzian spacetimes with irreducible higher-rank Killing tensors. Such metrics, we believe, are first examples of spacetimes admitting higher-rank Killing tensors. Included in our examples is a four-dimensional supersymmetric pp-wave spacetime, whose geodesic flow is superintegrable. The Killing tensors satisfy a non-trivial Poisson-Schouten-Nijenhuis algebra. We discuss the extension to the quantum regime.

  20. Symmetric tensor spherical harmonics on the N-sphere and their application to the de Sitter group SO(N,1)

    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

  1. Tensor perturbations during inflation in a spatially closed Universe

    Energy Technology Data Exchange (ETDEWEB)

    Bonga, Béatrice; Gupt, Brajesh; Yokomizo, Nelson, E-mail: bpb165@psu.edu, E-mail: bgupt@gravity.psu.edu, E-mail: yokomizo@gravity.psu.edu [Institute for Gravitation and the Cosmos and Physics Department, The Pennsylvania State University, 104 Lavey Lab, University Park, PA 16802 (United States)

    2017-05-01

    In a recent paper [1], we studied the evolution of the background geometry and scalar perturbations in an inflationary, spatially closed Friedmann-Lemaȋtre-Robertson-Walker (FLRW) model having constant positive spatial curvature and spatial topology S{sup 3}. Due to the spatial curvature, the early phase of slow-roll inflation is modified, leading to suppression of power in the scalar power spectrum at large angular scales. In this paper, we extend the analysis to include tensor perturbations. We find that, similarly to the scalar perturbations, the tensor power spectrum also shows suppression for long wavelength modes. The correction to the tensor spectrum is limited to the very long wavelength modes, therefore the resulting observable CMB B-mode polarization spectrum remains practically the same as in the standard scenario with flat spatial sections. However, since both the tensor and scalar power spectra are modified, there are scale dependent corrections to the tensor-to-scalar ratio that leads to violation of the standard slow-roll consistency relation.

  2. Papapetrou energy-momentum tensor for Chern-Simons modified gravity

    International Nuclear Information System (INIS)

    Guarrera, David; Hariton, A. J.

    2007-01-01

    We construct a conserved, symmetric energy-momentum (pseudo-)tensor for Chern-Simons modified gravity, thus demonstrating that the theory is Lorentz invariant. The tensor is discussed in relation to other gravitational energy-momentum tensors and analyzed for the Schwarzschild, Reissner-Nordstrom, and Friedmann-Robertson-Walker solutions. To our knowledge this is the first confirmation that the Reissner-Nordstrom and Friedmann-Robertson-Walker metrics are solutions of the modified theory

  3. Supergravity tensor calculus in 5D from 6D

    International Nuclear Information System (INIS)

    Kugo, Taichiro; Ohashi, Keisuke

    2000-01-01

    Supergravity tensor calculus in five spacetime dimensions is derived by dimensional reduction from the d=6 superconformal tensor calculus. In particular, we obtain an off-shell hypermultiplet in 5D from the on-shell hypermultiplet in 6D. Our tensor calculus retains the dilatation gauge symmetry, so that it is a trivial gauge fixing to make the Einstein term canonical in a general matter-Yang-Mills-supergravity coupled system. (author)

  4. Applied tensor stereology

    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...

  5. 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

  6. Generalized Møller-Plesset Multiconfiguration Perturbation Theory Applied to an Open-Shell Antisymmetric Product of Strongly Orthogonal Geminals Reference Wave Function.

    Science.gov (United States)

    Tarumi, Moto; Kobayashi, Masato; Nakai, Hiromi

    2012-11-13

    The antisymmetric product of strongly orthogonal geminals (APSG) method is a wave function theory that can effectively treat the static electron correlation. Recently, we proposed the open-shell APSG method using one-electron orbitals for open-shell parts. In this paper, we have extended the perturbation correction to the open-shell APSG calculations through Møller-Plesset-type multiconfiguration perturbation theory (MP-MCPT). Numerical applications demonstrate that the present open-shell MP-MCPT can reasonably reproduce the dissociation energies or equilibrium distances for open-shell systems.

  7. Erratum to Surface‐wave green’s tensors in the near field

    Science.gov (United States)

    Haney, Matthew M.; Hisashi Nakahara,

    2016-01-01

    Haney and Nakahara (2014) derived expressions for surface‐wave Green’s tensors that included near‐field behavior. Building on the result for a force source, Haney and Nakahara (2014) further derived expressions for a general point moment tensor source using the exact Green’s tensors. However, it has come to our attention that, although the Green’s tensors were correct, the resulting expressions for a general point moment tensor source were missing some terms. In this erratum, we provide updated expressions with these missing terms. The inclusion of the missing terms changes the example given in Haney and Nakahara (2014).

  8. Susceptibility tensor imaging (STI) of the brain.

    Science.gov (United States)

    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.

  9. Energy-momentum tensor in quantum field theory

    International Nuclear Information System (INIS)

    Fujikawa, Kazuo.

    1980-12-01

    The definition of the energy-momentum tensor as a source current coupled to the background gravitational field receives an important modification in quantum theory. In the path integral approach, the manifest covariance of the integral measure under general coordinate transformations dictates that field variables with weight 1/2 should be used as independent integration variables. An improved energy-momentum tensor is then generated by the variational derivative, and it gives rise to well-defined gravitational conformal (Weyl) anomalies. In the flat space-time limit, all the Ward-Takahashi identities associate with space-time transformations including the global dilatation become free from anomalies, reflecting the general covariance of the integral measure; the trace of this energy-momentum tensor is thus finite at the zero momentum transfer. The Jacobian for the local conformal transformation however becomes non-trivial, and it gives rise to an anomaly for the conformal identity. All the familiar anomalies are thus reduced to either chiral or conformal anomalies. The consistency of the dilatation and conformal identities at the vanishing momentum transfer determines the trace anomaly of this energy-momentum tensor in terms of the renormalization group β-function and other parameters. In contrast, the trace of the conventional energy-momentum tensor generally diverges even at the vanishing momentum transfer depending on the regularization scheme, and it is subtractively renormalized. We also explain how the apparently different renormalization properties of the chiral and trace anomalies arise. (author)

  10. Tri-Clustered Tensor Completion for Social-Aware Image Tag Refinement.

    Science.gov (United States)

    Tang, Jinhui; Shu, Xiangbo; Qi, Guo-Jun; Li, Zechao; Wang, Meng; Yan, Shuicheng; Jain, Ramesh

    2017-08-01

    Social image tag refinement, which aims to improve tag quality by automatically completing the missing tags and rectifying the noise-corrupted ones, is an essential component for social image search. Conventional approaches mainly focus on exploring the visual and tag information, without considering the user information, which often reveals important hints on the (in)correct tags of social images. Towards this end, we propose a novel tri-clustered tensor completion framework to collaboratively explore these three kinds of information to improve the performance of social image tag refinement. Specifically, the inter-relations among users, images and tags are modeled by a tensor, and the intra-relations between users, images and tags are explored by three regularizations respectively. To address the challenges of the super-sparse and large-scale tensor factorization that demands expensive computing and memory cost, we propose a novel tri-clustering method to divide the tensor into a certain number of sub-tensors by simultaneously clustering users, images and tags into a bunch of tri-clusters. And then we investigate two strategies to complete these sub-tensors by considering (in)dependence between the sub-tensors. Experimental results on a real-world social image database demonstrate the superiority of the proposed method compared with the state-of-the-art methods.

  11. A defect in holographic interpretations of tensor networks

    Energy Technology Data Exchange (ETDEWEB)

    Czech, Bartłomiej [Institute for Advanced Study,Princeton, NJ 08540 (United States); Nguyen, Phuc H.; Swaminathan, Sivaramakrishnan [Theory Group, Department of Physics and Texas Cosmology Center,The University of Texas at Austin,Austin, TX 78712 (United States)

    2017-03-16

    We initiate the study of how tensor networks reproduce properties of static holographic space-times, which are not locally pure anti-de Sitter. We consider geometries that are holographically dual to ground states of defect, interface and boundary CFTs and compare them to the structure of the requisite MERA networks predicted by the theory of minimal updates. When the CFT is deformed, certain tensors require updating. On the other hand, even identical tensors can contribute differently to estimates of entanglement entropies. We interpret these facts holographically by associating tensor updates to turning on non-normalizable modes in the bulk. In passing, we also clarify and complement existing arguments in support of the theory of minimal updates, propose a novel ansatz called rayed MERA that applies to a class of generalized interface CFTs, and analyze the kinematic spaces of the thin wall and AdS{sub 3}-Janus geometries.

  12. TensorFlow: A system for large-scale machine learning

    OpenAIRE

    Abadi, Martín; Barham, Paul; Chen, Jianmin; Chen, Zhifeng; Davis, Andy; Dean, Jeffrey; Devin, Matthieu; Ghemawat, Sanjay; Irving, Geoffrey; Isard, Michael; Kudlur, Manjunath; Levenberg, Josh; Monga, Rajat; Moore, Sherry; Murray, Derek G.

    2016-01-01

    TensorFlow is a machine learning system that operates at large scale and in heterogeneous environments. TensorFlow uses dataflow graphs to represent computation, shared state, and the operations that mutate that state. It maps the nodes of a dataflow graph across many machines in a cluster, and within a machine across multiple computational devices, including multicore CPUs, general-purpose GPUs, and custom designed ASICs known as Tensor Processing Units (TPUs). This architecture gives flexib...

  13. Incompatibility of torsion with the Gauss-Bonnet combination in the bosonic string

    International Nuclear Information System (INIS)

    Bern, Z.; Shimada, T.; Hochberg, D.

    1987-01-01

    In general, either manifest unitarity or the inclusion of the antisymmetric tensor field strength as torsion can be trivially implemented via field redefinitions in string theory low energy effective actions. However, requiring both simultaneously is explicitly shown to be incompatible in the bosonic string effective action. We also discuss the usefulness of the redefinition theorem as a technical tool. (orig.)

  14. Spectral Analysis and Computation of Effective Diffusivities in Space-time Periodic Incompressible Flows

    Science.gov (United States)

    2015-11-01

    diffusive tracer fluxes, directed normal to the tracer gradient [64], are generally equivalent to antisymmetric components in the effective diffusivity...tensor D∗, while the symmetric part of D∗ represents irreversible diffusive effects [83, 87, 39] directed down the tracer gradient . The mixing of eddy...provides an operational calculus in Hilbert space which yields powerful integral representations involving the Stieltjes measures displayed in equation

  15. Worldline path integrals for fermions with general couplings

    International Nuclear Information System (INIS)

    D'Hoker, E.; Gagne, D.G.

    1996-01-01

    We derive a worldline path integral representation for the effective action of a multiplet of Dirac fermions coupled to the most general set of matrix-valued scalar, pseudoscalar, vector, axial vector and antisymmetric tensor background fields. By representing internal degrees of freedom in terms of worldline fermions as well, we obtain a formulation which manifestly exhibits chiral gauge invariance. (orig.)

  16. Prediction and measurement of the reflection of the fundamental anti-symmetric Lamb wave from cracks and notches

    International Nuclear Information System (INIS)

    Lowe, M.J.S.; Cawley, P.; Kao, J-Y; Diligent, O.

    2000-01-01

    The interaction of the fundamental antisymmetric Lamb wave (a o ) with cracks and with notches of different depth and width has been investigated both experimentally and by finite element analysis. Excellent agreement between the predictions and the measurements has been obtained. It has been shown that the reflection coefficient is a function of both the notch width to wavelength and notch depth to wavelength ratios. Both the relationship between the reflection coefficient and notch, depth, and the frequency dependence of the reflection coefficient, are very different for the a o mode compared to the s o mode which was studied earlier. Physical insight into the reasons for the different behavior is given by examination of the stress fields and opening displacements at the crack or notch

  17. 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.

  18. Tucker Tensor analysis of Matern functions in spatial statistics

    KAUST Repository

    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||.

  19. A closed-form solution to tensor voting: theory and applications.

    Science.gov (United States)

    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.

  20. Mean-intercept anisotropy analysis of porous media. II. Conceptual shortcomings of the MIL tensor definition and Minkowski tensors as an alternative.

    Science.gov (United States)

    Klatt, Michael A; Schröder-Turk, Gerd E; Mecke, Klaus

    2017-07-01

    Structure-property relations, which relate the shape of the microstructure to physical properties such as transport or mechanical properties, need sensitive measures of structure. What are suitable fabric tensors to quantify the shape of anisotropic heterogeneous materials? The mean intercept length is among the most commonly used characteristics of anisotropy in porous media, e.g., of trabecular bone in medical physics. Yet, in this series of two papers we demonstrate that it has conceptual shortcomings that limit the validity of its results. We test the validity of general assumptions regarding the properties of the mean-intercept length tensor using analytical formulas for the mean-intercept lengths in anisotropic Boolean models (derived in part I of this series), augmented by numerical simulations. We discuss in detail the functional form of the mean intercept length as a function of the test line orientations. As the most prominent result, we find that, at least for the example of overlapping grains modeling porous media, the polar plot of the mean intercept length is in general not an ellipse and hence not represented by a second-rank tensor. This is in stark contrast to the common understanding that for a large collection of grains the mean intercept length figure averages to an ellipse. The standard mean intercept length tensor defined by a least-square fit of an ellipse is based on a model mismatch, which causes an intrinsic lack of accuracy. Our analysis reveals several shortcomings of the mean intercept length tensor analysis that pose conceptual problems and limitations on the information content of this commonly used analysis method. We suggest the Minkowski tensors from integral geometry as alternative sensitive measures of anisotropy. The Minkowski tensors allow for a robust, comprehensive, and systematic approach to quantify various aspects of structural anisotropy. We show the Minkowski tensors to be more sensitive, in the sense, that they can

  1. A forgotten argument by Gordon uniquely selects Abraham's tensor as the energy-momentum tensor for the electromagnetic field in homogeneous, isotropic matter

    International Nuclear Information System (INIS)

    Antoci, S.; Mihich, L.

    1997-01-01

    Given the present status of the problem of the electromagnetic energy tensor in matter, there is perhaps use in recalling a forgotten argument given in 1923 by W. Gordon. Let us consider a material medium which is homogeneous and isotropic when observed in its rest frame. For such a medium, Gordon's argument allows to reduce the above-mentioned problem to an analogous one, defined in a general relativistic vacuum. For the latter problem the form of the Lagrangian is known already, hence the determination of the energy tensor is a straightforward matter. One just performs the Hamiltonian derivative of the Lagrangian chosen in this way with respect to the true metric g ik . Abraham's tensor is thus selected as the electromagnetic energy tensor for a medium which is homogeneous and isotropic in its rest frame

  2. Classification of the Ricci and Plebanski tensors in general relativity using Newman--Penrose formalism

    International Nuclear Information System (INIS)

    McIntosh, C.B.G.; Foyster, J.M.; Lun, A.W.h.

    1981-01-01

    A list is given of a canonical set of the Newman--Penrose quantities Phi/sub A/B, the tetrad components of the trace-free Ricci tensor, for each Plebanski class according to Plebanski's classification of this tensor. This comparative list can easily be extended to cover the classification in tetrad language of any second-order, trace-free, symmetric tensor in a space-time. A fourth-order tensor which is the product of two such tensors was defined by Plebanski and used in his classification. This has the same symmetries as the Weyl tensor. The Petrov classification of this tensor, here called the Plebanski tensor, is discussed along with the classification of the Ricci tensor. The use of the Plebanski tensor in a couple of areas of general relativity is also briefly discussed

  3. Multiple M2-branes and the embedding tensor

    NARCIS (Netherlands)

    Bergshoeff, Eric A.; de Roo, Mees; Hohm, Olaf

    2008-01-01

    We show that the Bagger-Lambert theory of multiple M2-branes fits into the general construction of maximally supersymmetric gauge theories using the embedding tensor technique. We apply the embedding tensor technique in order to systematically obtain the consistent gaugings of N = 8 superconformal

  4. Two-perfect fluid interpretation of an energy tensor

    International Nuclear Information System (INIS)

    Ferrando, J.J.; Morales, J.A.; Portilla, M.

    1990-01-01

    There are many topics in General Relativity where matter is represented by a mixture of two fluids. In fact, some astrophysical and cosmological situations need to be described by an energy tensor made up of the sum of two or more perfect fluids rather than that with only one. The paper contains the necessary and sufficient conditions for a given energy tensor to be interpreted as a sum of two perfect fluids. Given a tensor of this class, the decomposition in two perfect fluids (which is determined up to a couple of real functions) is obtained

  5. Outcome assessment of hemiparesis due to intracerebral hemorrhage using diffusion tensor fractional anisotropy.

    Science.gov (United States)

    Koyama, Tetsuo; Marumoto, Kohei; Uchiyama, Yuki; Miyake, Hiroji; Domen, Kazuhisa

    2015-04-01

    This study aimed to evaluate the prognostic efficacy of magnetic resonance diffusion tensor fractional anisotropy (FA) for patients with hemiparesis due to intracerebral hemorrhage. Diffusion tensor FA brain images were acquired 14-21 days after putaminal and/or thalamic hemorrhage. The ratio of FA values within the cerebral peduncles of the affected and unaffected hemispheres (rFA) was calculated for each patient (n = 40) and assessed for correlation with Brunnstrom stage (BRS, 1-6), motor component of the functional independence measure (FIM-motor, 13-91), and the total length of stay (LOS) until discharge from rehabilitation (P hemiparesis due to putaminal and/or thalamic hemorrhage, particularly hand function recovery. Copyright © 2015 National Stroke Association. Published by Elsevier Inc. All rights reserved.

  6. QCD vacuum tensor susceptibility and properties of transversely polarized mesons

    International Nuclear Information System (INIS)

    Bakulev, A.P.; Mikhajlov, S.V.

    1999-01-01

    We re-estimate the tensor susceptibility of QCD vacuum, χ, and to this end, we re-estimate the leptonic decay constants for transversely polarized ρ-, ρ'- and b 1 -mesons. The origin of the susceptibility is analyzed using duality between ρ- and b 1 -channels in a 2-point correlator of tensor currents and disagree with [2] on both OPE expansion and the value of QCD vacuum tensor susceptibility. Using our value for the latter we determine new estimations of nucleon tensor charges related to the first moment of the transverse structure functions h 1 of a nucleon

  7. Identification of θ(f2(1720)) as a tensor glueball

    International Nuclear Information System (INIS)

    Liu, K.F.

    1988-01-01

    The energy-momentum tensor matrix element for the tensor glueball is obtained from the tensor dominance model. Branching ratio of θ(f 2 (1720)) in J/ψ radiative decay is thus calculated which is in accord with the observed experimental branching ratio. The decay modes of θ(f 2 (1720)) and results from J/ψ→ γK bar K,ωK bar K, and φK bar K are taken as good indicators for flavor independence of the tensor meson Θ. Suppression of θ(f 2 (1720)) in γγ reaction and K - p → ΛK o s K o s are considered as evidence for the fact that there are no quarks in θ. From the combined theoretical and experimental studies, the authors conclude that θ is by far the best tensor glueball candidate

  8. All-at-once Optimization for Coupled Matrix and Tensor Factorizations

    DEFF Research Database (Denmark)

    Evrim, Acar Ataman; Kolda, Tamara G.; Dunlavy, Daniel M.

    2011-01-01

    .g., the person by person social network matrix or the restaurant by category matrix, and higher-order tensors, e.g., the "ratings" tensor of the form restaurant by meal by person. In this paper, we are particularly interested in fusing data sets with the goal of capturing their underlying latent structures. We...... formulate this problem as a coupled matrix and tensor factorization (CMTF) problem where heterogeneous data sets are modeled by fitting outer-product models to higher-order tensors and matrices in a coupled manner. Unlike traditional approaches solving this problem using alternating algorithms, we propose...... an all-at-once optimization approach called CMTF-OPT (CMTF-OPTimization), which is a gradient-based optimization approach for joint analysis of matrices and higher-order tensors. We also extend the algorithm to handle coupled incomplete data sets. Using numerical experiments, we demonstrate...

  9. A General Expression for the Quintic Lovelock Tensor

    OpenAIRE

    Briggs, C. C.

    1996-01-01

    A general expression is given for the quintic Lovelock tensor as well as for the coefficient of the quintic Lovelock Lagrangian in terms of the Riemann-Christoffel and Ricci curvature tensors and the Riemann curvature scalar for n-dimensional differentiable manifolds having a general linear connection.

  10. Nonperturbative loop quantization of scalar-tensor theories of gravity

    International Nuclear Information System (INIS)

    Zhang Xiangdong; Ma Yongge

    2011-01-01

    The Hamiltonian formulation of scalar-tensor theories of gravity is derived from their Lagrangian formulation by Hamiltonian analysis. The Hamiltonian formalism marks off two sectors of the theories by the coupling parameter ω(φ). In the sector of ω(φ)=-(3/2), the feasible theories are restricted and a new primary constraint generating conformal transformations of spacetime is obtained, while in the other sector of ω(φ)≠-(3/2), the canonical structure and constraint algebra of the theories are similar to those of general relativity coupled with a scalar field. By canonical transformations, we further obtain the connection-dynamical formalism of the scalar-tensor theories with real su(2) connections as configuration variables in both sectors. This formalism enables us to extend the scheme of nonperturbative loop quantum gravity to the scalar-tensor theories. The quantum kinematical framework for the scalar-tensor theories is rigorously constructed. Both the Hamiltonian constraint operator and master constraint operator are well defined and proposed to represent quantum dynamics. Thus the loop quantum gravity method is also valid for general scalar-tensor theories.

  11. Federated Tensor Factorization for Computational Phenotyping

    Science.gov (United States)

    Kim, Yejin; Sun, Jimeng; Yu, Hwanjo; Jiang, Xiaoqian

    2017-01-01

    Tensor factorization models offer an effective approach to convert massive electronic health records into meaningful clinical concepts (phenotypes) for data analysis. These models need a large amount of diverse samples to avoid population bias. An open challenge is how to derive phenotypes jointly across multiple hospitals, in which direct patient-level data sharing is not possible (e.g., due to institutional policies). In this paper, we developed a novel solution to enable federated tensor factorization for computational phenotyping without sharing patient-level data. We developed secure data harmonization and federated computation procedures based on alternating direction method of multipliers (ADMM). Using this method, the multiple hospitals iteratively update tensors and transfer secure summarized information to a central server, and the server aggregates the information to generate phenotypes. We demonstrated with real medical datasets that our method resembles the centralized training model (based on combined datasets) in terms of accuracy and phenotypes discovery while respecting privacy. PMID:29071165

  12. Tensor calculus for engineers and physicists

    CERN Document Server

    de Souza Sánchez Filho, Emil

    2016-01-01

    This textbook provides a rigorous approach to tensor manifolds in several aspects relevant for Engineers and Physicists working in industry or academia. With a thorough, comprehensive, and unified presentation, this book offers insights into several topics of tensor analysis, which covers all aspects of N dimensional spaces. The main purpose of this book is to give a self-contained yet simple, correct and comprehensive mathematical explanation of tensor calculus for undergraduate and graduate students and for professionals. In addition to many worked problems, this book features a selection of examples, solved step by step. Although no emphasis is placed on special and particular problems of Engineering or Physics, the text covers the fundamentals of these fields of science. The book makes a brief introduction into the basic concept of the tensorial formalism so as to allow the reader to make a quick and easy review of the essential topics that enable having the grounds for the subsequent themes, without need...

  13. Stress-energy tensors for vector fields outside a static black hole

    International Nuclear Information System (INIS)

    Barrios, F.A.; Vaz, C.

    1989-01-01

    We obtain new, approximate stress-energy tensors to describe gauge fields in the neighborhood of a Schwarzschild black hole. We assume that the coefficient of ∇ 2 R in the trace anomaly is correctly given by ζ-function regularization. Our approximation differs from that of Page and of Brown and Ottewill and relies upon a new, improved ansatz for the form of the stress-energy tensor in the ultrastatic optical metric of the black hole. The Israel-Hartle-Hawking thermal tensor is constructed to be regular on the horizon and possess the correct asymptotic behavior. Our approximation of Unruh's tensor is likewise constructed to be regular on the future horizon and exhibit a luminosity which agrees with Page's numerically obtained value. Geometric expressions for the approximate tensors are given, and the approximate energy density of the thermal tensor on the horizon is compared with recent numerical estimates

  14. Improving Tensor Based Recommenders with Clustering

    DEFF Research Database (Denmark)

    Leginus, Martin; Dolog, Peter; Zemaitis, Valdas

    2012-01-01

    Social tagging systems (STS) model three types of entities (i.e. tag-user-item) and relationships between them are encoded into a 3-order tensor. Latent relationships and patterns can be discovered by applying tensor factorization techniques like Higher Order Singular Value Decomposition (HOSVD),...... of the recommendations and execution time are improved and memory requirements are decreased. The clustering is motivated by the fact that many tags in a tag space are semantically similar thus the tags can be grouped. Finally, promising experimental results are presented...

  15. Tensor modes in pure natural inflation

    Science.gov (United States)

    Nomura, Yasunori; Yamazaki, Masahito

    2018-05-01

    We study tensor modes in pure natural inflation [1], a recently-proposed inflationary model in which an axionic inflaton couples to pure Yang-Mills gauge fields. We find that the tensor-to-scalar ratio r is naturally bounded from below. This bound originates from the finiteness of the number of metastable branches of vacua in pure Yang-Mills theories. Details of the model can be probed by future cosmic microwave background experiments and improved lattice gauge theory calculations of the θ-angle dependence of the vacuum energy.

  16. The Chevreton tensor and Einstein-Maxwell spacetimes conformal to Einstein spaces

    International Nuclear Information System (INIS)

    Bergqvist, Goeran; Eriksson, Ingemar

    2007-01-01

    In this paper, we characterize the source-free Einstein-Maxwell spacetimes which have a trace-free Chevreton tensor. We show that this is equivalent to the Chevreton tensor being of pure radiation type and that it restricts the spacetimes to Petrov type N or O. We prove that the trace of the Chevreton tensor is related to the Bach tensor and use this to find all Einstein-Maxwell spacetimes with a zero cosmological constant that have a vanishing Bach tensor. Among these spacetimes we then look for those which are conformal to Einstein spaces. We find that the electromagnetic field and the Weyl tensor must be aligned, and in the case that the electromagnetic field is null, the spacetime must be conformally Ricci-flat and all such solutions are known. In the non-null case, since the general solution is not known on a closed form, we settle by giving the integrability conditions in the general case, but we do give new explicit examples of Einstein-Maxwell spacetimes that are conformal to Einstein spaces, and we also find examples where the vanishing of the Bach tensor does not imply that the spacetime is conformal to a C-space. The non-aligned Einstein-Maxwell spacetimes with vanishing Bach tensor are conformally C-spaces, but none of them are conformal to Einstein spaces

  17. A General Sparse Tensor Framework for Electronic Structure Theory.

    Science.gov (United States)

    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.

  18. An eigenvalue localization set for tensors and its applications.

    Science.gov (United States)

    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.

  19. Traffic speed data imputation method based on tensor completion.

    Science.gov (United States)

    Ran, Bin; Tan, Huachun; Feng, Jianshuai; Liu, Ying; Wang, Wuhong

    2015-01-01

    Traffic speed data plays a key role in Intelligent Transportation Systems (ITS); however, missing traffic data would affect the performance of ITS as well as Advanced Traveler Information Systems (ATIS). In this paper, we handle this issue by a novel tensor-based imputation approach. Specifically, tensor pattern is adopted for modeling traffic speed data and then High accurate Low Rank Tensor Completion (HaLRTC), an efficient tensor completion method, is employed to estimate the missing traffic speed data. This proposed method is able to recover missing entries from given entries, which may be noisy, considering severe fluctuation of traffic speed data compared with traffic volume. The proposed method is evaluated on Performance Measurement System (PeMS) database, and the experimental results show the superiority of the proposed approach over state-of-the-art baseline approaches.

  20. TENSOR DECOMPOSITIONS AND SPARSE LOG-LINEAR MODELS

    Science.gov (United States)

    Johndrow, James E.; Bhattacharya, Anirban; Dunson, David B.

    2017-01-01

    Contingency table analysis routinely relies on log-linear models, with latent structure analysis providing a common alternative. Latent structure models lead to a reduced rank tensor factorization of the probability mass function for multivariate categorical data, while log-linear models achieve dimensionality reduction through sparsity. Little is known about the relationship between these notions of dimensionality reduction in the two paradigms. We derive several results relating the support of a log-linear model to nonnegative ranks of the associated probability tensor. Motivated by these findings, we propose a new collapsed Tucker class of tensor decompositions, which bridge existing PARAFAC and Tucker decompositions, providing a more flexible framework for parsimoniously characterizing multivariate categorical data. Taking a Bayesian approach to inference, we illustrate empirical advantages of the new decompositions. PMID:29332971

  1. Heterotic string in an arbitrary background field

    International Nuclear Information System (INIS)

    Sen, A.

    1985-01-01

    An expression for the light-cone gauge action for the first-quantized heterotic string in the presence of arbitrary background gauge, gravitational, and antisymmetric tensor fields is derived. The result is a two-dimensional local field theory with N = 1/2 supersymmetry. The constraints imposed on the background fields in order to make this theory one-loop finite are derived. These constraints are identical to the equations of motion for the massless fields at the linearized level. Finally, it is shown that if there is no background antisymmetric tensor field, and if the gauge connection is set equal to the spin connection, the effective action is that of an N = 1 supersymmetric nonlinear and N = 2 supersymmetric Georgi-Glashow models the occurrence of the fermion fractionization is the necessity; the ignorance of it results in the inconsistency in the perturbative calculation of the mass splittings among the members of the supermultiplets. The notable feature of our result is that the degeneracy due to the Jackiw-Rebbi zero mode is not independent of the one required by the supersymmetry, suggesting a nontrivial structure in embedding the topology of Higgs fields into supersymmetric gauge theories

  2. Energy momentum tensor in local causal perturbation theory

    International Nuclear Information System (INIS)

    Prange, D.

    2001-01-01

    We study the energy momentum tensor in the Bogolyubov-Epstein-Glaser approach to perturbation theory. It is found to be locally conserved for a class of theories containing to derivated fields in the interaction. For the massless φ 4 -theory we derive the trace anomaly of the improved tensor. (orig.)

  3. Tucker Tensor analysis of Matern functions in spatial statistics

    KAUST Repository

    Litvinenko, Alexander; Keyes, David E.; Khoromskaia, Venera; Khoromskij, Boris N.; Matthies, Hermann G.

    2018-01-01

    in a low-rank tensor format. We apply the Tucker and canonical tensor decompositions to a family of Matern- and Slater-type functions with varying parameters and demonstrate numerically that their approximations exhibit exponentially fast convergence

  4. Tensor polarized deuteron targets for intermediate energy physics experiments

    International Nuclear Information System (INIS)

    Meyer, W.; Schilling, E.

    1985-03-01

    At intermediate energies measurements from a tensor polarized deuteron target are being prepared for the following reactions: the photodisintegration of the deuteron, the elastic pion-deuteron scattering and the elastic electron-deuteron scattering. The experimental situation of the polarization experiments for these reactions is briefly discussed in section 2. In section 3 the definitions of the deuteron polarization and the possibilities to determine the vector and tensor polarization are given. Present tensor polarization values and further improvements in this field are reported in section 4. (orig.)

  5. A Nonlinear GMRES Optimization Algorithm for Canonical Tensor Decomposition

    OpenAIRE

    De Sterck, Hans

    2011-01-01

    A new algorithm is presented for computing a canonical rank-R tensor approximation that has minimal distance to a given tensor in the Frobenius norm, where the canonical rank-R tensor consists of the sum of R rank-one components. Each iteration of the method consists of three steps. In the first step, a tentative new iterate is generated by a stand-alone one-step process, for which we use alternating least squares (ALS). In the second step, an accelerated iterate is generated by a nonlinear g...

  6. 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.

  7. 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)

  8. Analyzing vortex breakdown flow structures by assignment of colors to tensor invariants.

    Science.gov (United States)

    Rütten, Markus; Chong, Min S

    2006-01-01

    Topological methods are often used to describe flow structures in fluid dynamics and topological flow field analysis usually relies on the invariants of the associated tensor fields. A visual impression of the local properties of tensor fields is often complex and the search of a suitable technique for achieving this is an ongoing topic in visualization. This paper introduces and assesses a method of representing the topological properties of tensor fields and their respective flow patterns with the use of colors. First, a tensor norm is introduced, which preserves the properties of the tensor and assigns the tensor invariants to values of the RGB color space. Secondly, the RGB colors of the tensor invariants are transferred to corresponding hue values as an alternative color representation. The vectorial tensor invariants field is reduced to a scalar hue field and visualization of iso-surfaces of this hue value field allows us to identify locations with equivalent flow topology. Additionally highlighting by the maximum of the eigenvalue difference field reflects the magnitude of the structural change of the flow. The method is applied on a vortex breakdown flow structure inside a cylinder with a rotating lid.

  9. Introduction to the nuclear structure studies of exotic nuclei by using antisymmetrized molecular dynamics method

    International Nuclear Information System (INIS)

    Kimura, Masaaki; Dote, Akinobu; Ohnishi, Akira; Matsumiya, Hiroshi

    2009-01-01

    This article is originally prepared as the course text for the practice of the AMD course of 'studies of the strangeness nuclei by using the antisymmetrized molecular dynamics (AMD) method' in the Summer School held at KEK and IPCR in 2006-8 for postgraduate as well as undergraduate students and to foster young physicists in the titled area. The fundamental principle and the formalism of the AMD method which have been commonly used in the nuclear physics are explained at first, and it is described how to extend the AMD method to the studies of exotic nuclei especially to hypernuclei. Then calculation procedure is explained in detail so that the readers can understand the structure of exotic nuclei as they follow the process by themselves. It is intended here that they will be able not only to become familiar with the research by using the AMD method but also to visually enjoy the structure of exotic nuclei and will have further interest in this field. (S. Funahashi)

  10. X-ray strain tensor imaging: FEM simulation and experiments with a micro-CT.

    Science.gov (United States)

    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.

  11. Core Polarization and Tensor Coupling Effects on Magnetic Moments of Hypernuclei

    International Nuclear Information System (INIS)

    Jiang-Ming, Yao; Jie, Meng; Hong-Feng, Lü; Greg, Hillhouse

    2008-01-01

    Effects of core polarization and tensor coupling on the magnetic moments in Λ 13 C, Λ 17 O, and Λ 41 Ca Λ-hypernuclei are studied by employing the Dirac equation with scalar, vector and tensor potentials. It is found that the effect of core polarization on the magnetic moments is suppressed by Λ tensor coupling. The Λ tensor potential reduces the spin-orbit splitting of p Λ states considerably. However, almost the same magnetic moments are obtained using the hyperon wavefunction obtained via the Dirac equation either with or without the A tensor potential in the electromagnetic current vertex. The deviations of magnetic moments for p Λ states from the Schmidt values are found to increase with nuclear mass number. (nuclear physics)

  12. Gauge theories, duality relations and the tensor hierarchy

    NARCIS (Netherlands)

    Bergshoeff, Eric A.; Hartong, Jelle; Hohm, Olaf; Huebscher, Mechthild; Ortin, Tomas; Hübscher, Mechthild

    We compute the complete 3- and 4-dimensional tensor hierarchies, i.e. sets of p-form fields, with 1 We construct gauge-invariant actions that include all the fields in the tensor hierarchies. We elucidate the relation between the gauge transformations of the p-form fields in the action and those of

  13. a tensor theory of gravitation in a curved metric on a flat background

    International Nuclear Information System (INIS)

    Drummond, J.E.

    1979-01-01

    A theory of gravity is proposed using a tensor potential for the field on a flat metric. This potential cannot be isolated by local observations, but some details can be deduced from measurements at a distance. The requirement that the field equations for the tensor potential shall be deducible from an action integral, that the action and field equations are gauge invariant, and, conversely, that the Lagrangian in the action integral can be integrated from the field equations leads to Einstein's field equations. The requirement that the field energy-momentum tensor exists leads to a constraint on the tensor potential. If the constraint is a differential gauge condition, then it can only be the Hilbert condition giving a unique background tensor, metric tensor and tensor potential. For a continuous field inside a solid sphere the metric must be homogeneous in the spatial coordinates, and the associated field energy-momentum tensor has properties consistent with Newtonian dynamics. (author)

  14. Degenerate Perturbation Theory for Electronic g Tensors: Leading-Order Relativistic Effects.

    Science.gov (United States)

    Rinkevicius, Zilvinas; de Almeida, Katia Julia; Oprea, Cornel I; Vahtras, Olav; Ågren, Hans; Ruud, Kenneth

    2008-11-11

    A new approach for the evaluation of the leading-order relativistic corrections to the electronic g tensors of molecules with a doublet ground state is presented. The methodology is based on degenerate perturbation theory and includes all relevant contributions to the g tensor shift up to order O(α(4)) originating from the one-electron part of the Breit-Pauli Hamiltonian-that is, it allows for the treatment of scalar relativistic, spin-orbit, and mixed corrections to the spin and orbital Zeeman effects. This approach has been implemented in the framework of spin-restricted density functional theory and is in the present paper, as a first illustration of the theory, applied to study relativistic effects on electronic g tensors of dihalogen anion radicals X2(-) (X = F, Cl, Br, I). The results indicate that the spin-orbit interaction is responsible for the large parallel component of the g tensor shift of Br2(-) and I2(-), and furthermore that both the leading-order scalar relativistic and spin-orbit corrections are of minor importance for the perpendicular component of the g tensor in these molecules since they effectively cancel each other. In addition to investigating the g tensors of dihalogen anion radicals, we also critically examine the importance of various relativistic corrections to the electronic g tensor of linear molecules with Σ-type ground states and present a two-state model suitable for an approximate estimation of the g tensor in such molecules.

  15. 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)

  16. Decorated tensor network renormalization for lattice gauge theories and spin foam models

    Science.gov (United States)

    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.

  17. Tensor products of process matrices with indefinite causal structure

    Science.gov (United States)

    Jia, Ding; Sakharwade, Nitica

    2018-03-01

    Theories with indefinite causal structure have been studied from both the fundamental perspective of quantum gravity and the practical perspective of information processing. In this paper we point out a restriction in forming tensor products of objects with indefinite causal structure in certain models: there exist both classical and quantum objects the tensor products of which violate the normalization condition of probabilities, if all local operations are allowed. We obtain a necessary and sufficient condition for when such unrestricted tensor products of multipartite objects are (in)valid. This poses a challenge to extending communication theory to indefinite causal structures, as the tensor product is the fundamental ingredient in the asymptotic setting of communication theory. We discuss a few options to evade this issue. In particular, we show that the sequential asymptotic setting does not suffer the violation of normalization.

  18. 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.

  19. Traffic Speed Data Imputation Method Based on Tensor Completion

    Directory of Open Access Journals (Sweden)

    Bin Ran

    2015-01-01

    Full Text Available Traffic speed data plays a key role in Intelligent Transportation Systems (ITS; however, missing traffic data would affect the performance of ITS as well as Advanced Traveler Information Systems (ATIS. In this paper, we handle this issue by a novel tensor-based imputation approach. Specifically, tensor pattern is adopted for modeling traffic speed data and then High accurate Low Rank Tensor Completion (HaLRTC, an efficient tensor completion method, is employed to estimate the missing traffic speed data. This proposed method is able to recover missing entries from given entries, which may be noisy, considering severe fluctuation of traffic speed data compared with traffic volume. The proposed method is evaluated on Performance Measurement System (PeMS database, and the experimental results show the superiority of the proposed approach over state-of-the-art baseline approaches.

  20. One-loop tensor Feynman integral reduction with signed minors

    DEFF Research Database (Denmark)

    Fleischer, Jochem; Riemann, Tord; Yundin, Valery

    2012-01-01

    of the formalism is the immediate evaluation of complete contractions of the tensor integrals with external momenta. This leads to the problem of evaluating sums over products of signed minors with scalar products of chords. Chords are differences of external momenta. These sums may be evaluated analytically......We present an algebraic approach to one-loop tensor integral reduction. The integrals are presented in terms of scalar one- to four-point functions. The reduction is worked out explicitly until five-point functions of rank five. The numerical C++ package PJFry evaluates tensor coefficients in terms...

  1. Exploring extra dimensions through inflationary tensor modes

    Science.gov (United States)

    Im, Sang Hui; Nilles, Hans Peter; Trautner, Andreas

    2018-03-01

    Predictions of inflationary schemes can be influenced by the presence of extra dimensions. This could be of particular relevance for the spectrum of gravitational waves in models where the extra dimensions provide a brane-world solution to the hierarchy problem. Apart from models of large as well as exponentially warped extra dimensions, we analyze the size of tensor modes in the Linear Dilaton scheme recently revived in the discussion of the "clockwork mechanism". The results are model dependent, significantly enhanced tensor modes on one side and a suppression on the other. In some cases we are led to a scheme of "remote inflation", where the expansion is driven by energies at a hidden brane. In all cases where tensor modes are enhanced, the requirement of perturbativity of gravity leads to a stringent upper limit on the allowed Hubble rate during inflation.

  2. Diffusion tensor optical coherence tomography

    Science.gov (United States)

    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.

  3. Supersymmetry breaking through confining and dual theory gauge dynamics

    International Nuclear Information System (INIS)

    Csaki, C.; Massachusetts Inst. of Tech., Cambridge, MA; Randall, L.; Massachusetts Inst. of Tech., Cambridge, MA; Skiba, W.; Massachusetts Inst. of Tech., Cambridge, MA; Leigh, R.G.

    1997-01-01

    We show that theories in the confining, free magnetic, and conformal phases can break supersymmetry through dynamical effects. To illustrate this, we present theories based on the gauge groups SU(n) x SU(4) x U(1) and SU(n) x SU(5) x U(1) with the field content obtained by decomposing an SU(m) theory with an antisymmetric tensor and m - 4 antifundamentals. (orig.)

  4. A large class of new gravitational and axionic backgrounds for four-dimensional superstrings

    CERN Document Server

    Kiritsis, Elias B; Lüst, Dieter

    1994-01-01

    A large class of new 4-D superstring vacua with non-trivial/singular geometries, spacetime supersymmetry and other background fields (axion, dilaton) are found. Killing symmetries are generic and are associated with non-trivial dilaton and antisymmetric tensor fields. Duality symmetries preserving N=2 superconformal invariance are employed to generate a large class of explicit metrics for non-compact 4-D Calabi-Yau manifolds with Killing symmetries.

  5. Flat-space holography and stress tensor of Kerr black hole

    Energy Technology Data Exchange (ETDEWEB)

    Baghchesaraei, Omid, E-mail: omidbaghchesaraei@gmail.com [Department of Physics, Shahid Beheshti University, G.C., Evin, Tehran 19839 (Iran, Islamic Republic of); Fareghbal, Reza, E-mail: r_fareghbal@sbu.ac.ir [Department of Physics, Shahid Beheshti University, G.C., Evin, Tehran 19839 (Iran, Islamic Republic of); Izadi, Yousef, E-mail: yizadi2015@fau.edu [Department of Physics, Florida Atlantic University, Boca Raton, FL 33431 (United States)

    2016-09-10

    We propose a stress tensor for the Kerr black hole written in the Boyer–Lindquist coordinate. To achieve this, we use the dictionary of the Flat/CCFT correspondence and take the flat-space limit from the quasi-local stress tensor of the four-dimensional Kerr–AdS black hole. The proposed stress tensor yields the correct values for the mass and angular momentum of the Kerr black hole at spatial infinity. We also calculate some components of the energy momentum tensor of the three dimensional CCFT and show that they are consistent with the holographic calculation of the Kerr black hole. The calculation we present in this paper is another confirmation for the Flat/CCFT proposal.

  6. Partition-based Collaborative Tensor Factorization for POI Recommendation

    Institute of Scientific and Technical Information of China (English)

    Wenjing Luan; Guanjun Liu; Changjun Jiang; Liang Qi

    2017-01-01

    The rapid development of location-based social networks (LBSNs) provides people with an opportunity of better understanding their mobility behavior which enables them to decide their next location.For example,it can help travelers to choose where to go next,or recommend salesmen the most potential places to deliver advertisements or sell products.In this paper,a method for recommending points of interest (POIs) is proposed based on a collaborative tensor factorization (CTF) technique.Firstly,a generalized objective function is constructed for collaboratively factorizing a tensor with several feature matrices.Secondly,a 3-mode tensor is used to model all users' check-in behaviors,and three feature matrices are extracted to characterize the time distribution,category distribution and POI correlation,respectively.Thirdly,each user's preference to a POI at a specific time can be estimated by using CTF.In order to further improve the recommendation accuracy,PCTF (Partitionbased CTF) is proposed to fill the missing entries of a tensor after clustering its every mode.Experiments on a real checkin database show that the proposed method can provide more accurate location recommendation.

  7. 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.

  8. A higher-order tensor vessel tractography for segmentation of vascular structures.

    Science.gov (United States)

    Cetin, Suheyla; Unal, Gozde

    2015-10-01

    A new vascular structure segmentation method, which is based on a cylindrical flux-based higher order tensor (HOT), is presented. On a vessel structure, the HOT naturally models branching points, which create challenges for vessel segmentation algorithms. In a general linear HOT model embedded in 3D, one has to work with an even order tensor due to an enforced antipodal-symmetry on the unit sphere. However, in scenarios such as in a bifurcation, the antipodally-symmetric tensor embedded in 3D will not be useful. In order to overcome that limitation, we embed the tensor in 4D and obtain a structure that can model asymmetric junction scenarios. During construction of a higher order tensor (e.g. third or fourth order) in 4D, the orientation vectors lie on the unit 3-sphere, in contrast to the unit 2-sphere in 3D tensor modeling. This 4D tensor is exploited in a seed-based vessel segmentation algorithm, where the principal directions of the 4D HOT is obtained by decomposition, and used in a HOT tractography approach. We demonstrate quantitative validation of the proposed algorithm on both synthetic complex tubular structures as well as real cerebral vasculature in Magnetic Resonance Angiography (MRA) datasets and coronary arteries from Computed Tomography Angiography (CTA) volumes.

  9. Tensor Based Representation and Analysis of Diffusion-Weighted Magnetic Resonance Images

    Science.gov (United States)

    Barmpoutis, Angelos

    2009-01-01

    Cartesian tensor bases have been widely used to model spherical functions. In medical imaging, tensors of various orders can approximate the diffusivity function at each voxel of a diffusion-weighted MRI data set. This approximation produces tensor-valued datasets that contain information about the underlying local structure of the scanned tissue.…

  10. The average number of critical rank-one approximations to a tensor

    NARCIS (Netherlands)

    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

  11. On the axial anomalies in external tensor fields

    International Nuclear Information System (INIS)

    Khudaverdyan, O.M.; Mkrtchyan, R.L.; Zurabyan, L.A.

    1985-01-01

    Computation of the axial anomaly for Dirac fermions in external tensor fields is studied. The sequence of the supersymmetric one-dimensional models is presented. Their supercharges are equal, after quantization, to Dirac operators in external tensor fields, and the density of Witten's partition function gives the anomaly. It is shown that action in the corresponding path integral differs from the classical one. Gaussian approximation gives the anomaly only in the case of third-rank tensor with zero exterior derivative and in that case anomaly is calculated in all dimensions. The interpretation of that field as the torsion of gravitational field and also connection with the results of Witten and Alvarez-Gaume and Atiyah-Singer index theorem are discussed

  12. Structural connectivity via the tensor-based morphometry

    OpenAIRE

    Kim, S.; Chung, M.; Hanson, J.; Avants, B.; Gee, J.; Davidson, R.; Pollak, S.

    2011-01-01

    The tensor-based morphometry (TBM) has been widely used in characterizing tissue volume difference between populations at voxel level. We present a novel computational framework for investigating the white matter connectivity using TBM. Unlike other diffusion tensor imaging (DTI) based white matter connectivity studies, we do not use DTI but only T1-weighted magnetic resonance imaging (MRI). To construct brain network graphs, we have developed a new data-driven approach called the ε-neighbor ...

  13. Geometrical foundations of tensor calculus and relativity

    OpenAIRE

    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...

  14. The Simon and Simon-Mars tensors for stationary Einstein-Maxwell fields

    International Nuclear Information System (INIS)

    Bini, Donato; Cherubini, Christian; Jantzen, Robert T; Miniutti, Giovanni

    2004-01-01

    Modulo conventional scale factors, the Simon and Simon-Mars tensors are defined for stationary vacuum spacetimes so that their equality follows from the Bianchi identities of the second kind. In the nonvacuum case one can absorb additional source terms into a redefinition of the Simon tensor so that this equality is maintained. Among the electrovacuum class of solutions of the Einstein-Maxwell equations, the expression for the Simon tensor in the Kerr-Newman-Taub-NUT spacetime in terms of the Ernst potential is formally the same as in the vacuum case (modulo a scale factor), and its vanishing guarantees the simultaneous alignment of the principal null directions of the Weyl tensor, the Papapetrou field associated with the timelike Killing vector field, the electromagnetic field of the spacetime and even the Killing-Yano tensor

  15. Anisotropic conductivity tensor imaging in MREIT using directional diffusion rate of water molecules

    International Nuclear Information System (INIS)

    Kwon, Oh In; Jeong, Woo Chul; Sajib, Saurav Z K; Kim, Hyung Joong; Woo, Eung Je

    2014-01-01

    Magnetic resonance electrical impedance tomography (MREIT) is an emerging method to visualize electrical conductivity and/or current density images at low frequencies (below 1 KHz). Injecting currents into an imaging object, one component of the induced magnetic flux density is acquired using an MRI scanner for isotropic conductivity image reconstructions. Diffusion tensor MRI (DT-MRI) measures the intrinsic three-dimensional diffusion property of water molecules within a tissue. It characterizes the anisotropic water transport by the effective diffusion tensor. Combining the DT-MRI and MREIT techniques, we propose a novel direct method for absolute conductivity tensor image reconstructions based on a linear relationship between the water diffusion tensor and the electrical conductivity tensor. We first recover the projected current density, which is the best approximation of the internal current density one can obtain from the measured single component of the induced magnetic flux density. This enables us to estimate a scale factor between the diffusion tensor and the conductivity tensor. Combining these values at all pixels with the acquired diffusion tensor map, we can quantitatively recover the anisotropic conductivity tensor map. From numerical simulations and experimental verifications using a biological tissue phantom, we found that the new method overcomes the limitations of each method and successfully reconstructs both the direction and magnitude of the conductivity tensor for both the anisotropic and isotropic regions. (paper)

  16. Doubly Self-Dual Actions in Various Dimensions

    CERN Document Server

    Ferrara, S.; Yeranyan, A.

    2015-05-11

    The self-duality of the N=1 supersymmetric Born--Infeld action implies a double self-duality of the tensor multiplet square-root action when the scalar and the antisymmetric tensor are interchanged via Poincare' duality. We show how this phenomenon extends to D space-time dimensions for non-linear actions involving pairs of forms of rank p and D-p-2. As a byproduct, we construct a new two-field generalization of the Born-Infeld action whose equations of motion are invariant under a U(1) duality. In these systems, the introduction of Green-Schwarz terms results in explicit non-linear mass-like terms for dual massive pairs.

  17. New curvature-torsion relations through decomposition of the Bianchi identities

    International Nuclear Information System (INIS)

    Davies, J.B.

    1988-01-01

    The Bianchi Identities relating asymmetric curvature to torsion are obtained as a new set of equations governing second-order curvature tensors. The usual contribution of symmetric curvature to the gravitational field is found to be a subset of these identities though with an added contribution due to torsion gradients. The antisymmetric curvature two-tensor is shown to be related to the divergence of the torsion. Using a model of particle-antiparticle pair production, identification of certain torsion components with electroweak fields is proposed. These components obey equations, similar to Maxwell's that are subsets of these linear Bianchi identities. These results are shown to be consistent with gauge and other previous analyses

  18. Non-Abelian tensor gauge fields and higher-spin extension of standard model

    International Nuclear Information System (INIS)

    Savvidy, G.

    2006-01-01

    We suggest an extension of the gauge principle which includes non-Abelian tensor gauge fields. The invariant Lagrangian is quadratic in the field strength tensors and describes interaction of charged tensor gauge bosons of arbitrary large integer spin 1,2,l. Non-Abelian tensor gauge fields can be viewed as a unique gauge field with values in the infinite-dimensional current algebra associated with compact Lie group. The full Lagrangian exhibits also enhanced local gauge invariance with double number of gauge parameters which allows to eliminate all negative norm states of the nonsymmetric second-rank tensor gauge field, which describes therefore two polarizations of helicity-two massless charged tensor gauge boson and the helicity-zero ''axion'' The geometrical interpretation of the enhanced gauge symmetry with double number of gauge parameters is not yet known. (Abstract Copyright [2006], Wiley Periodicals, Inc.)

  19. Mesh Denoising based on Normal Voting Tensor and Binary Optimization

    OpenAIRE

    Yadav, S. K.; Reitebuch, U.; Polthier, K.

    2016-01-01

    This paper presents a tensor multiplication based smoothing algorithm that follows a two step denoising method. Unlike other traditional averaging approaches, our approach uses an element based normal voting tensor to compute smooth surfaces. By introducing a binary optimization on the proposed tensor together with a local binary neighborhood concept, our algorithm better retains sharp features and produces smoother umbilical regions than previous approaches. On top of that, we provide a stoc...

  20. Tensor Fukunaga-Koontz transform for small target detection in infrared images

    Science.gov (United States)

    Liu, Ruiming; Wang, Jingzhuo; Yang, Huizhen; Gong, Chenglong; Zhou, Yuanshen; Liu, Lipeng; Zhang, Zhen; Shen, Shuli

    2016-09-01

    Infrared small targets detection plays a crucial role in warning and tracking systems. Some novel methods based on pattern recognition technology catch much attention from researchers. However, those classic methods must reshape images into vectors with the high dimensionality. Moreover, vectorizing breaks the natural structure and correlations in the image data. Image representation based on tensor treats images as matrices and can hold the natural structure and correlation information. So tensor algorithms have better classification performance than vector algorithms. Fukunaga-Koontz transform is one of classification algorithms and it is a vector version method with the disadvantage of all vector algorithms. In this paper, we first extended the Fukunaga-Koontz transform into its tensor version, tensor Fukunaga-Koontz transform. Then we designed a method based on tensor Fukunaga-Koontz transform for detecting targets and used it to detect small targets in infrared images. The experimental results, comparison through signal-to-clutter, signal-to-clutter gain and background suppression factor, have validated the advantage of the target detection based on the tensor Fukunaga-Koontz transform over that based on the Fukunaga-Koontz transform.

  1. Retinal Vessel Segmentation via Structure Tensor Coloring and Anisotropy Enhancement

    Directory of Open Access Journals (Sweden)

    Mehmet Nergiz

    2017-11-01

    Full Text Available Retinal vessel segmentation is one of the preliminary tasks for developing diagnosis software systems related to various retinal diseases. In this study, a fully automated vessel segmentation system is proposed. Firstly, the vessels are enhanced using a Frangi Filter. Afterwards, Structure Tensor is applied to the response of the Frangi Filter and a 4-D tensor field is obtained. After decomposing the Eigenvalues of the tensor field, the anisotropy between the principal Eigenvalues are enhanced exponentially. Furthermore, this 4-D tensor field is converted to the 3-D space which is composed of energy, anisotropy and orientation and then a Contrast Limited Adaptive Histogram Equalization algorithm is applied to the energy space. Later, the obtained energy space is multiplied by the enhanced mean surface curvature of itself and the modified 3-D space is converted back to the 4-D tensor field. Lastly, the vessel segmentation is performed by using Otsu algorithm and tensor coloring method which is inspired by the ellipsoid tensor visualization technique. Finally, some post-processing techniques are applied to the segmentation result. In this study, the proposed method achieved mean sensitivity of 0.8123, 0.8126, 0.7246 and mean specificity of 0.9342, 0.9442, 0.9453 as well as mean accuracy of 0.9183, 0.9442, 0.9236 for DRIVE, STARE and CHASE_DB1 datasets, respectively. The mean execution time of this study is 6.104, 6.4525 and 18.8370 s for the aforementioned three datasets respectively.

  2. Thermal entanglement and teleportation in a two-qubit Heisenberg chain with Dzyaloshinski-Moriya anisotropic antisymmetric interaction

    International Nuclear Information System (INIS)

    Zhang, Guo-Feng

    2007-01-01

    Thermal entanglement of a two-qubit Heisenberg chain in the presence of the Dzyaloshinski-Moriya (DM) anisotropic antisymmetric interaction and entanglement teleportation when using two independent Heisenberg chains as the quantum channel are investigated. It is found that the DM interaction can excite entanglement and teleportation fidelity. The output entanglement increases linearly with increasing value of the input; its dependences on the temperature, DM interaction, and spin coupling constant are given in detail. Entanglement teleportation will be better realized via an antiferromagnetic spin chain when the DM interaction is turned off and the temperature is low. However, the introduction of the DM interaction can cause the ferromagnetic spin chain to be a better quantum channel for teleportation. A minimal entanglement of the thermal state in the model is needed to realize the entanglement teleportation regardless of whether the spin chains are antiferromagnetic or ferromagnetic

  3. Simultaneous tensor decomposition and completion using factor priors.

    Science.gov (United States)

    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.

  4. DuSK: A Dual Structure-preserving Kernel for Supervised Tensor Learning with Applications to Neuroimages.

    Science.gov (United States)

    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.

  5. Retrospective Correction of Physiological Noise in DTI Using an Extended Tensor Model and Peripheral Measurements

    Science.gov (United States)

    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

  6. An introduction to tensors and group theory for physicists

    CERN Document Server

    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...

  7. Motion Detection in Ultrasound Image-Sequences Using Tensor Voting

    Science.gov (United States)

    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.

  8. Total diffusing power of perturbed lattices and dissymmetry of reflections. Case of groups of defects

    International Nuclear Information System (INIS)

    Tournarie, Max

    1959-01-01

    The total diffusing power for a crystallite of any form containing a centrosymmetric defect has been established. The antisymmetrical part of the deformation potential only contributes very slightly to the primary dissymmetry. We then go on to study the case of a group of defects of the same type. The calculation converges sufficiently to describe the thermal agitation of an infinite crystal. Reprint of a paper published in 'Comptes Rendus des Seances de l'Academie des Sciences', t. 248, p. 2103-2105, sitting of April 6, 1959 [fr

  9. Adaptive distance learning scheme for diffusion tensor imaging using kernel target alignment

    NARCIS (Netherlands)

    Rodrigues, P.R.; Vilanova, A.; Twellmann, T.; Haar Romenij, ter B.M.; Alexander, D.; Gee, J.; Whitaker, R.

    2008-01-01

    In segmentation techniques for Diffusion Tensor Imaging (DTI) data, the similarity of diffusion tensors must be assessed for partitioning data into regions which are homogeneous in terms of tensor characteristics. Various distance measures have been proposed in literature for analysing the

  10. MR-NTD: Manifold Regularization Nonnegative Tucker Decomposition for Tensor Data Dimension Reduction and Representation.

    Science.gov (United States)

    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.

  11. The tensor part of the Skyrme energy density functional. I. Spherical nuclei

    Energy Technology Data Exchange (ETDEWEB)

    Lesinski, T.; Meyer, J. [Universite de Lyon, F-69003 Lyon (France)]|[Institut de Physique Nucleaire de Lyon, CNRS/IN2P3, Universite Lyon 1, F-69622 Villeurbanne (France); Bender, M. [DSM/DAPNIA/SPhN, CEA Saclay, F-91191 Gif-sur-Yvette Cedex (France)]|[Universite Bordeaux, CNRS/IN2P3, Centre d' Etudes Nucleaires de Bordeaux Gradignan, UMR5797, Chemin du Solarium, BP120, F-33175 Gradignan (France); Bennaceur, K. [Universite de Lyon, F-69003 Lyon (France)]|[Institut de Physique Nucleaire de Lyon, CNRS/IN2P3, Universite Lyon 1, F-69622 Villeurbanne (France)]|[DSM/DAPNIA/SPhN, CEA Saclay, F-91191 Gif-sur-Yvette Cedex (France); Duguet, T. [National Superconducting Cyclotron Laboratory and Department of Physics and Astronomy, Michigan State University, East Lansing, MI 48824 (United States)

    2007-04-15

    We perform a systematic study of the impact of the J-vector{sup 2} tensor term in the Skyrme energy functional on properties of spherical nuclei. In the Skyrme energy functional, the tensor terms originate both from zero-range central and tensor forces. We build a set of 36 parameterizations which cover a wide range of the parameter space of the isoscalar and isovector tensor term coupling constants with a fit protocol very similar to that of the successful SLy parameterizations. We analyze the impact of the tensor terms on a large variety of observables in spherical mean-field calculations, such as the spin-orbit splittings and single-particle spectra of doubly-magic nuclei, the evolution of spin-orbit splittings along chains of semi-magic nuclei, mass residuals of spherical nuclei, and known anomalies of radii. The major findings of our study are (i) tensor terms should not be added perturbatively to existing parameterizations, a complete refit of the entire parameter set is imperative. (ii) The free variation of the tensor terms does not lower the {chi}{sup 2} within a standard Skyrme energy functional. (iii) For certain regions of the parameter space of their coupling constants, the tensor terms lead to instabilities of the spherical shell structure, or even the coexistence of two configurations with different spherical shell structure. (iv) The standard spin-orbit interaction does not scale properly with the principal quantum number, such that single-particle states with one or several nodes have too large spin-orbit splittings, while those of node-less intruder levels are tentatively too small. Tensor terms with realistic coupling constants cannot cure this problem. (v) Positive values of the coupling constants of proton-neutron and like-particle tensor terms allow for a qualitative description of the evolution of spin-orbit splittings in chains of Ca, Ni and Sn isotopes. (vi) For the same values of the tensor term coupling constants, however, the overall

  12. Estimation of Uncertainties of Full Moment Tensors

    Science.gov (United States)

    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

  13. 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.

  14. A model for soft high-energy scattering: Tensor pomeron and vector odderon

    Energy Technology Data Exchange (ETDEWEB)

    Ewerz, Carlo, E-mail: C.Ewerz@thphys.uni-heidelberg.de [Institut für Theoretische Physik, Universität Heidelberg, Philosophenweg 16, D-69120 Heidelberg (Germany); ExtreMe Matter Institute EMMI, GSI Helmholtzzentrum für Schwerionenforschung, Planckstraße 1, D-64291 Darmstadt (Germany); Maniatis, Markos, E-mail: mmaniatis@ubiobio.cl [Departamento de Ciencias Básicas, Universidad del Bío-Bío, Avda. Andrés Bello s/n, Casilla 447, Chillán 3780000 (Chile); Nachtmann, Otto, E-mail: O.Nachtmann@thphys.uni-heidelberg.de [Institut für Theoretische Physik, Universität Heidelberg, Philosophenweg 16, D-69120 Heidelberg (Germany)

    2014-03-15

    A model for soft high-energy scattering is developed. The model is formulated in terms of effective propagators and vertices for the exchange objects: the pomeron, the odderon, and the reggeons. The vertices are required to respect standard rules of QFT. The propagators are constructed taking into account the crossing properties of amplitudes in QFT and the power-law ansätze from the Regge model. We propose to describe the pomeron as an effective spin 2 exchange. This tensor pomeron gives, at high energies, the same results for the pp and pp{sup -bar} elastic amplitudes as the standard Donnachie–Landshoff pomeron. But with our tensor pomeron it is much more natural to write down effective vertices of all kinds which respect the rules of QFT. This is particularly clear for the coupling of the pomeron to particles carrying spin, for instance vector mesons. We describe the odderon as an effective vector exchange. We emphasise that with a tensor pomeron and a vector odderon the corresponding charge-conjugation relations are automatically fulfilled. We compare the model to some experimental data, in particular to data for the total cross sections, in order to determine the model parameters. The model should provide a starting point for a general framework for describing soft high-energy reactions. It should give to experimentalists an easily manageable tool for calculating amplitudes for such reactions and for obtaining predictions which can be compared in detail with data. -- Highlights: •A general model for soft high-energy hadron scattering is developed. •The pomeron is described as effective tensor exchange. •Explicit expressions for effective reggeon–particle vertices are given. •Reggeon–particle and particle–particle vertices are related. •All vertices respect the standard C parity and crossing rules of QFT.

  15. Tensor meson dominance and e/sup +/e/sup -/-physics

    Energy Technology Data Exchange (ETDEWEB)

    Genz, H [Miami Univ., Coral Gables, FL (USA). Center for Theoretical Studies; Karlsruhe Univ. (T.H.) (Germany, F.R.). Inst. fuer Theoretische Kernphysik); Mallik, S [Karlsruhe Univ. (T.H.) (Germany, F.R.). Inst. fuer Theoretische Kernphysik

    1983-01-01

    The phenomenological status of tensor meson dominance is reported. Some new results concerning hadronic decays of the 2/sup + +/-meson chi/sub 2/(3.55) and the heavy lepton tau are also included. Considering experimental errors, tensor meson dominance is in agreement with experiment.

  16. A dielectric tensor for magnetoplasmas comprising components with generalized Lorentzian distributions

    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.)

  17. Scalar-Tensor Black Holes Embedded in an Expanding Universe

    Science.gov (United States)

    Tretyakova, Daria; Latosh, Boris

    2018-02-01

    In this review we focus our attention on scalar-tensor gravity models and their empirical verification in terms of black hole and wormhole physics. We focus on a black hole, embedded in an expanding universe, describing both cosmological and astrophysical scales. We show that in scalar-tensor gravity it is quite common that the local geometry is isolated from the cosmological expansion, so that it does not backreact on the black hole metric. We try to extract common features of scalar-tensor black holes in an expanding universe and point out the gaps that must be filled.

  18. Scalar-Tensor Black Holes Embedded in an Expanding Universe

    Directory of Open Access Journals (Sweden)

    Daria Tretyakova

    2018-02-01

    Full Text Available In this review, we focus our attention on scalar-tensor gravity models and their empirical verification in terms of black hole and wormhole physics. We focus on black holes, embedded in an expanding universe, describing both cosmological and astrophysical scales. We show that in scalar-tensor gravity it is quite common that the local geometry is isolated from the cosmological expansion, so that it does not backreact on the black hole metric. We try to extract common features of scalar-tensor black holes in an expanding universe and point out the issues that are not fully investigated.

  19. 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)

  20. 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.

  1. Micromechanics based framework with second-order damage tensors

    Science.gov (United States)

    Desmorat, R.; Desmorat, B.; Olive, M.; Kolev, B.

    2018-05-01

    The harmonic product of tensors---leading to the concept of harmonic factorization---has been defined in a previous work (Olive et al, 2017). In the practical case of 3D crack density measurements on thin or thick walled structures, this mathematical tool allows us to factorize the harmonic (irreducible) part of the fourth-order damage tensor as an harmonic square: an exact harmonic square in 2D, an harmonic square over the set of so-called mechanically accessible directions for measurements in the 3D case. The corresponding micro-mechanics framework based on second---instead of fourth---order damage tensors is derived. An illustrating example is provided showing how the proposed framework allows for the modeling of the so-called hydrostatic sensitivity up to high damage levels.

  2. DuSK: A Dual Structure-preserving Kernel for Supervised Tensor Learning with Applications to Neuroimages

    Science.gov (United States)

    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

  3. Bayesian CP Factorization of Incomplete Tensors with Automatic Rank Determination.

    Science.gov (United States)

    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.

  4. New results for algebraic tensor reduction of Feynman integrals

    Energy Technology Data Exchange (ETDEWEB)

    Fleischer, Jochem [Bielefeld Univ. (Germany). Fakultaet fuer Physik; Riemann, Tord [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Yundin, Valery [Copenhagen Univ. (Denmark). Niels Bohr International Academy and Discovery Center

    2012-02-15

    We report on some recent developments in algebraic tensor reduction of one-loop Feynman integrals. For 5-point functions, an efficient tensor reduction was worked out recently and is now available as numerical C++ package, PJFry, covering tensor ranks until five. It is free of inverse 5- point Gram determinants and inverse small 4-point Gram determinants are treated by expansions in higher-dimensional 3-point functions. By exploiting sums over signed minors, weighted with scalar products of chords (or, equivalently, external momenta), extremely efficient expressions for tensor integrals contracted with external momenta were derived. The evaluation of 7-point functions is discussed. In the present approach one needs for the reductions a (d +2)-dimensional scalar 5-point function in addition to the usual scalar basis of 1- to 4-point functions in the generic dimension d=4-2{epsilon}. When exploiting the four-dimensionality of the kinematics, this basis is sufficient. We indicate how the (d+2)-dimensional 5-point function can be evaluated. (orig.)

  5. New results for algebraic tensor reduction of Feynman integrals

    International Nuclear Information System (INIS)

    Fleischer, Jochem; Yundin, Valery

    2012-02-01

    We report on some recent developments in algebraic tensor reduction of one-loop Feynman integrals. For 5-point functions, an efficient tensor reduction was worked out recently and is now available as numerical C++ package, PJFry, covering tensor ranks until five. It is free of inverse 5- point Gram determinants and inverse small 4-point Gram determinants are treated by expansions in higher-dimensional 3-point functions. By exploiting sums over signed minors, weighted with scalar products of chords (or, equivalently, external momenta), extremely efficient expressions for tensor integrals contracted with external momenta were derived. The evaluation of 7-point functions is discussed. In the present approach one needs for the reductions a (d +2)-dimensional scalar 5-point function in addition to the usual scalar basis of 1- to 4-point functions in the generic dimension d=4-2ε. When exploiting the four-dimensionality of the kinematics, this basis is sufficient. We indicate how the (d+2)-dimensional 5-point function can be evaluated. (orig.)

  6. 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

  7. Examining the consistency relations describing the three-point functions involving tensors

    International Nuclear Information System (INIS)

    Sreenath, V.; Sriramkumar, L.

    2014-01-01

    It is well known that the non-Gaussianity parameter f NL characterizing the scalar bi-spectrum can be expressed in terms of the scalar spectral index in the squeezed limit, a property that is referred to as the consistency relation. In contrast to the scalar bi-spectrum, the three-point cross-correlations involving scalars and tensors and the tensor bi-spectrum have not received adequate attention, which can be largely attributed to the fact that the tensors had remained undetected at the level of the power spectrum until very recently. The detection of the imprints of the primordial tensor perturbations by BICEP2 and its indication of a rather high tensor-to-scalar ratio, if confirmed, can open up a new window for understanding the tensor perturbations, not only at the level of the power spectrum, but also in the realm of non-Gaussianities. In this work, we consider the consistency relations associated with the three-point cross-correlations involving scalars and tensors as well as the tensor bi-spectrum in inflationary models driven by a single, canonical, scalar field. Characterizing the cross-correlations in terms of the dimensionless non-Gaussianity parameters C NL R and C NL γ that we had introduced earlier, we express the consistency relations governing the cross-correlations as relations between these non-Gaussianity parameters and the scalar or tensor spectral indices, in a fashion similar to that of the purely scalar case. We also discuss the corresponding relation for the non-Gaussianity parameter h NL used to describe the tensor bi-spectrum. We analytically establish these consistency relations explicitly in the following two situations: a simple example involving a specific case of power law inflation and a non-trivial scenario in the so-called Starobinsky model that is governed by a linear potential with a sharp change in its slope. We also numerically verify the consistency relations in three types of inflationary models that permit deviations from

  8. Comparison of two global digital algorithms for Minkowski tensor estimation

    DEFF Research Database (Denmark)

    The geometry of real world objects can be described by Minkowski tensors. Algorithms have been suggested to approximate Minkowski tensors if only a binary image of the object is available. This paper presents implementations of two such algorithms. The theoretical convergence properties...... are confirmed by simulations on test sets, and recommendations for input arguments of the algorithms are given. For increasing resolutions, we obtain more accurate estimators for the Minkowski tensors. Digitisations of more complicated objects are shown to require higher resolutions....

  9. X-linked adrenoleukodystrophy: correlation between Loes score and diffusion tensor imaging parameters.

    Science.gov (United States)

    Ono, Sergio Eiji; de Carvalho Neto, Arnolfo; Gasparetto, Emerson Leandro; Coelho, Luiz Otávio de Mattos; Escuissato, Dante Luiz; Bonfim, Carmem Maria Sales; Ribeiro, Lisandro Lima

    2014-01-01

    The present study was aimed at evaluating the correlation between diffusion tensor imaging parameters and Loes score as well as whether those parameters could indicate early structural alterations. Diffusion tensor imaging measurements were obtained in 30 studies of 14 patients with X-linked adrenoleukodystrophy and were correlated with Loes scores. A control group including 28 male patients was created to establish agematched diffusion tensor imaging measurements. Inter- and intraobserver statistical analyses were undertaken. Diffusion tensor imaging measurements presented strong Pearson correlation coefficients (r) of -0.86, 0.89, 0.89 and 0.84 for fractional anisotropy and mean, radial and axial diffusivities (p tensor measurements at early stage of the disease indicates that mean and radial diffusivities might be useful to predict the disease progression. Measurements of diffusion tensor parameters can be used as an adjunct to the Loes score, aiding in the monitoring of the disease and alerting for possible Loes score progression in the range of interest for therapeutic decisions.

  10. Realizability of metamaterials with prescribed electric permittivity and magnetic permeability tensors

    International Nuclear Information System (INIS)

    Milton, Graeme W

    2010-01-01

    We show that any pair of real symmetric tensors ε and μ can be realized as the effective electric permittivity and effective magnetic permeability of a metamaterial at a given fixed frequency. The construction starts with two extremely low-loss metamaterials, with arbitrarily small microstructure, whose existence is ensured by the work of Bouchitte and Bourel and Bouchitte and Schweizer: one having, at the given frequency, a permittivity tensor with exactly one negative eigenvalue, and a positive permeability tensor; and the other having a positive permittivity tensor, and a permeability tensor having exactly one negative eigenvalue. To achieve the desired effective properties, these materials are laminated together in a hierarchical multiple rank laminate structure, with widely separated length scales, and varying directions of lamination, but with the largest length scale still much shorter than the wavelengths and attenuation lengths in the macroscopic effective medium.

  11. 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...

  12. Superconformal tensor calculus and matter couplings in six dimensions

    NARCIS (Netherlands)

    Bergshoeff, E.; Sezgin, E.; Proeyen, A. Van

    1986-01-01

    Using superconformal tensor calculus we construct general interactions of N = 2, d = 6 supergravity with a tensor multiplet and a number of scalar, vector and linear multiplets. We start from the superconformal algebra which we realize on a 40+40 Weyl multiplet and on several matter multiplets. A

  13. TensorFlow Distributions

    OpenAIRE

    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...

  14. The gauge-invariant canonical energy-momentum tensor

    Science.gov (United States)

    Lorcé, Cédric

    2016-03-01

    The canonical energy-momentum tensor is often considered as a purely academic object because of its gauge dependence. However, it has recently been realized that canonical quantities can in fact be defined in a gauge-invariant way provided that strict locality is abandoned, the non-local aspect being dictacted in high-energy physics by the factorization theorems. Using the general techniques for the parametrization of non-local parton correlators, we provide for the first time a complete parametrization of the energy-momentum tensor (generalizing the purely local parametrizations of Ji and Bakker-Leader-Trueman used for the kinetic energy-momentum tensor) and identify explicitly the parts accessible from measurable two-parton distribution functions (TMDs and GPDs). As by-products, we confirm the absence of model-independent relations between TMDs and parton orbital angular momentum, recover in a much simpler way the Burkardt sum rule and derive three similar new sum rules expressing the conservation of transverse momentum.

  15. The gauge-invariant canonical energy-momentum tensor

    International Nuclear Information System (INIS)

    Lorce, C.

    2016-01-01

    The canonical energy-momentum tensor is often considered as a purely academic object because of its gauge dependence. However, it has recently been realized that canonical quantities can in fact be defined in a gauge-invariant way provided that strict locality is abandoned, the non-local aspect being dictated in high-energy physics by the factorization theorems. Using the general techniques for the parametrization of non-local parton correlators, we provide for the first time a complete parametrization of the energy-momentum tensor (generalizing the purely local parametrizations of Ji and Bakker-Leader-Trueman used for the kinetic energy-momentum tensor) and identify explicitly the parts accessible from measurable two-parton distribution functions (TMD and GPD). As by-products, we confirm the absence of model-independent relations between TMDs and parton orbital angular momentum, recover in a much simpler way the Burkardt sum rule and derive 3 similar new sum rules expressing the conservation of transverse momentum. (author)

  16. On an uninterpretated tensor in Dirac's theory

    International Nuclear Information System (INIS)

    Costa de Beauregard, O.

    1989-01-01

    Franz, in 1935, deduced systematically from the Dirac equation 10 tensorial equations, 5 with a mechanical interpretation, 5 with an electromagnetic interpretation, which are also consequences of Kemmer's formalism for spins 1 and 0; Durand, in 1944, operating similarly with the second order Dirac equation, obtained, 10 equations, 5 of which expressing the divergences of the Gordon type tensors. Of these equations, together with the tensors they imply, some are easily interpreted by reference to the classical theories, some other remain uniterpreted. Recently (1988) we proposed a theory of the coupling between Einstein's gravity field and the 5 Franz mechanical equations, yielding as a bonus the complete interpretation of the 5 Franz mechanical equations. This is an incitation to reexamine the 5 electromagnetic equations. We show here that two of these, together with one of the Durand equations, implying the same tensor, remain uninterpreted. This is proposed as a challenge to the reader's sagacity [fr

  17. On deformed tensor potential for inelastic deuteron scattering

    International Nuclear Information System (INIS)

    Raynal, Jacques.

    1980-08-01

    Tensor analysing powers for inelastic deuteron scattering have been measured around 12 to 15 MeV. There is no problem to use such a tensor potential for the excited states in coupled channel calculations. However, for transition potentials, form factors are very different. A fit has been done with the first order vibrational model for 64 Ni(d,d') 64 Ni*, 2 + at 1,344 MeV

  18. Monte Carlo Volcano Seismic Moment Tensors

    Science.gov (United States)

    Waite, G. P.; Brill, K. A.; Lanza, F.

    2015-12-01

    Inverse modeling of volcano seismic sources can provide insight into the geometry and dynamics of volcanic conduits. But given the logistical challenges of working on an active volcano, seismic networks are typically deficient in spatial and temporal coverage; this potentially leads to large errors in source models. In addition, uncertainties in the centroid location and moment-tensor components, including volumetric components, are difficult to constrain from the linear inversion results, which leads to a poor understanding of the model space. In this study, we employ a nonlinear inversion using a Monte Carlo scheme with the objective of defining robustly resolved elements of model space. The model space is randomized by centroid location and moment tensor eigenvectors. Point sources densely sample the summit area and moment tensors are constrained to a randomly chosen geometry within the inversion; Green's functions for the random moment tensors are all calculated from modeled single forces, making the nonlinear inversion computationally reasonable. We apply this method to very-long-period (VLP) seismic events that accompany minor eruptions at Fuego volcano, Guatemala. The library of single force Green's functions is computed with a 3D finite-difference modeling algorithm through a homogeneous velocity-density model that includes topography, for a 3D grid of nodes, spaced 40 m apart, within the summit region. The homogenous velocity and density model is justified by long wavelength of VLP data. The nonlinear inversion reveals well resolved model features and informs the interpretation through a better understanding of the possible models. This approach can also be used to evaluate possible station geometries in order to optimize networks prior to deployment.

  19. 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.

  20. Tensor force and debye screening in quarkonium-type mesons

    International Nuclear Information System (INIS)

    Kovacs, L.B.; Kovacs, T.G.; Lovas, I.

    1990-01-01

    We use a non-relativistic quantum-mechanical model to investigate the effect of a screening plasma on two quarkonium-type mesons: the charmonium and bottonium. The stability of these mesons in the plasma is estimated in two cases: including the tensor and spin-orbit term in the potential and without these terms. It turns out that while the bottonium is somewhat stabilized by the tensor force, the charmonium becomes less stabil due to this modification of the potential. Thus the charmonium seems to be a more sensitive probe of the quark-gluon plasma formation than it was thought to be without including the tensor force. (Authors)