Gravitational waveforms in scalar-tensor gravity at 2PN relative order
Sennett, Noah; Buonanno, Alessandra
2016-01-01
We compute the gravitational waveform from a binary system in scalar-tensor gravity at 2PN relative order. We restrict our calculation to non-spinning binary systems on quasi-circular orbits and compute the spin-weighted spherical modes of the radiation. The evolution of the phase of the waveform is computed in the time and frequency domains. The emission of dipolar radiation is the lowest-order dissipative process in scalar-tensor gravity. However, stringent constraints set by current astrophysical observations indicate that this effect is subdominant to quadrupolar radiation for most prospective gravitational-wave sources. We compute the waveform for systems whose inspiral is driven by: (a) dipolar radiation (e.g., binary pulsars or spontaneously scalarized systems) and (b) quadrupolar radiation (e.g., typical sources for space-based and ground-based detectors).
Tensors, relativity, and cosmology
Dalarsson, Mirjana
2015-01-01
Tensors, Relativity, and Cosmology, Second Edition, combines relativity, astrophysics, and cosmology in a single volume, providing a simplified introduction to each subject that is followed by detailed mathematical derivations. The book includes a section on general relativity that gives the case for a curved space-time, presents the mathematical background (tensor calculus, Riemannian geometry), discusses the Einstein equation and its solutions (including black holes and Penrose processes), and considers the energy-momentum tensor for various solutions. In addition, a section on relativistic astrophysics discusses stellar contraction and collapse, neutron stars and their equations of state, black holes, and accretion onto collapsed objects, with a final section on cosmology discussing cosmological models, observational tests, and scenarios for the early universe. This fully revised and updated second edition includes new material on relativistic effects, such as the behavior of clocks and measuring rods in m...
Fang, L.; Zhang, Y. J.; Fang, J.; Zhu, Y.
2016-08-01
We show by direct numerical simulations (DNSs) that in different types of isotropic turbulence, the fourth-order statistical invariants have approximately a linear relation, which can be represented by a straight line in the phase plane, passing two extreme states: the Gaussian state and the restricted Euler state. Also, each DNS case corresponds to an equilibrium region that is roughly Reynolds-dependent. In addition, both the time reversal and the compressibility effect lead to nonequilibrium transition processes in this phase plane. This observation adds a new restriction on the mean-field theory.
Šprlák, Michal; Novák, Pavel
2017-02-01
New spherical integral formulas between components of the second- and third-order gravitational tensors are formulated in this article. First, we review the nomenclature and basic properties of the second- and third-order gravitational tensors. Initial points of mathematical derivations, i.e., the second- and third-order differential operators defined in the spherical local North-oriented reference frame and the analytical solutions of the gradiometric boundary-value problem, are also summarized. Secondly, we apply the third-order differential operators to the analytical solutions of the gradiometric boundary-value problem which gives 30 new integral formulas transforming (1) vertical-vertical, (2) vertical-horizontal and (3) horizontal-horizontal second-order gravitational tensor components onto their third-order counterparts. Using spherical polar coordinates related sub-integral kernels can efficiently be decomposed into azimuthal and isotropic parts. Both spectral and closed forms of the isotropic kernels are provided and their limits are investigated. Thirdly, numerical experiments are performed to test the consistency of the new integral transforms and to investigate properties of the sub-integral kernels. The new mathematical apparatus is valid for any harmonic potential field and may be exploited, e.g., when gravitational/magnetic second- and third-order tensor components become available in the future. The new integral formulas also extend the well-known Meissl diagram and enrich the theoretical apparatus of geodesy.
Šprlák, Michal; Novák, Pavel
2016-10-01
New spherical integral formulas between components of the second- and third-order gravitational tensors are formulated in this article. First, we review the nomenclature and basic properties of the second- and third-order gravitational tensors. Initial points of mathematical derivations, i.e., the second- and third-order differential operators defined in the spherical local North-oriented reference frame and the analytical solutions of the gradiometric boundary-value problem, are also summarized. Secondly, we apply the third-order differential operators to the analytical solutions of the gradiometric boundary-value problem which gives 30 new integral formulas transforming (1) vertical-vertical, (2) vertical-horizontal and (3) horizontal-horizontal second-order gravitational tensor components onto their third-order counterparts. Using spherical polar coordinates related sub-integral kernels can efficiently be decomposed into azimuthal and isotropic parts. Both spectral and closed forms of the isotropic kernels are provided and their limits are investigated. Thirdly, numerical experiments are performed to test the consistency of the new integral transforms and to investigate properties of the sub-integral kernels. The new mathematical apparatus is valid for any harmonic potential field and may be exploited, e.g., when gravitational/magnetic second- and third-order tensor components become available in the future. The new integral formulas also extend the well-known Meissl diagram and enrich the theoretical apparatus of geodesy.
A Simplified Algorithm for Inverting Higher Order Diffusion Tensors
Laura Astola
2014-11-01
Full Text Available In Riemannian geometry, a distance function is determined by an inner product on the tangent space. In Riemann–Finsler geometry, this distance function can be determined by a norm. This gives more freedom on the form of the so-called indicatrix or the set of unit vectors. This has some interesting applications, e.g., in medical image analysis, especially in diffusion weighted imaging (DWI. An important application of DWI is in the inference of the local architecture of the tissue, typically consisting of thin elongated structures, such as axons or muscle fibers, by measuring the constrained diffusion of water within the tissue. From high angular resolution diffusion imaging (HARDI data, one can estimate the diffusion orientation distribution function (dODF, which indicates the relative diffusivity in all directions and can be represented by a spherical polynomial. We express this dODF as an equivalent spherical monomial (higher order tensor to directly generalize the (second order diffusion tensor approach. To enable efficient computation of Riemann–Finslerian quantities on diffusion weighted (DW-images, such as the metric/norm tensor, we present a simple and efficient algorithm to invert even order spherical monomials, which extends the familiar inversion of diffusion tensors, i.e., symmetric matrices.
Lagrange Multipliers and Third Order Scalar-Tensor Field Theories
Horndeski, Gregory W
2016-01-01
In a space of 4-dimensions, I will examine constrained variational problems in which the Lagrangian, and constraint scalar density, are concomitants of a (pseudo-Riemannian) metric tensor and its first two derivatives. The Lagrange multiplier for these constrained extremal problems will be a scalar field. For suitable choices of the Lagrangian, and constraint, we can obtain Euler-Lagrange equations which are second order in the scalar field and third order in the metric tensor. The effect of disformal transformations on the constraint Lagrangians, and their generalizations, is examined. This will yield other second order scalar-tensor Lagrangians which yield field equations which are at most of third order. No attempt is made to construct all possible third order scalar-tensor Euler-Lagrange equations in a 4-space, although nine classes of such field equations are presented. Two of these classes admit subclasses which yield conformally invariant field equations. A few remarks on scalar-tensor-connection theor...
Irreducible Cartesian tensors of highest weight, for arbitrary order
Mane, S. R.
2016-03-01
A closed form expression is presented for the irreducible Cartesian tensor of highest weight, for arbitrary order. Two proofs are offered, one employing bookkeeping of indices and, after establishing the connection with the so-called natural tensors and their projection operators, the other one employing purely coordinate-free tensor manipulations. Some theorems and formulas in the published literature are generalized from SO(3) to SO(n), for dimensions n ≥ 3.
Transversely isotropic higher-order averaged structure tensors
Hashlamoun, Kotaybah; Federico, Salvatore
2017-08-01
For composites or biological tissues reinforced by statistically oriented fibres, a probability distribution function is often used to describe the orientation of the fibres. The overall effect of the fibres on the material response is accounted for by evaluating averaging integrals over all possible directions in space. The directional average of the structure tensor (tensor product of the unit vector describing the fibre direction by itself) is of high significance. Higher-order averaged structure tensors feature in several models and carry similarly important information. However, their evaluation has a quite high computational cost. This work proposes to introduce mathematical techniques to minimise the computational cost associated with the evaluation of higher-order averaged structure tensors, for the case of a transversely isotropic probability distribution of orientation. A component expression is first introduced, using which a general tensor expression is obtained, in terms of an orthonormal basis in which one of the vectors coincides with the axis of symmetry of transverse isotropy. Then, a higher-order transversely isotropic averaged structure tensor is written in an appropriate basis, constructed starting from the basis of the space of second-order transversely isotropic tensors, which is constituted by the structure tensor and its complement to the identity.
Lagrange Multipliers and Third Order Scalar-Tensor Field Theories
Horndeski, Gregory W.
2016-01-01
In a space of 4-dimensions, I will examine constrained variational problems in which the Lagrangian, and constraint scalar density, are concomitants of a (pseudo-Riemannian) metric tensor and its first two derivatives. The Lagrange multiplier for these constrained extremal problems will be a scalar field. For suitable choices of the Lagrangian, and constraint, we can obtain Euler-Lagrange equations which are second order in the scalar field and third order in the metric tensor. The effect of ...
Effective description of higher-order scalar-tensor theories
Langlois, David; Mancarella, Michele; Noui, Karim; Vernizzi, Filippo
2017-05-01
Most existing theories of dark energy and/or modified gravity, involving a scalar degree of freedom, can be conveniently described within the framework of the Effective Theory of Dark Energy, based on the unitary gauge where the scalar field is uniform. We extend this effective approach by allowing the Lagrangian in unitary gauge to depend on the time derivative of the lapse function. Although this dependence generically signals the presence of an extra scalar degree of freedom, theories that contain only one propagating scalar degree of freedom, in addition to the usual tensor modes, can be constructed by requiring the initial Lagrangian to be degenerate. Starting from a general quadratic action, we derive the dispersion relations for the linear perturbations around Minkowski and a cosmological background. Our analysis directly applies to the recently introduced Degenerate Higher-Order Scalar-Tensor (DHOST) theories. For these theories, we find that one cannot recover a Poisson-like equation in the static linear regime except for the subclass that includes the Horndeski and so-called "beyond Horndeski" theories. We also discuss Lorentz-breaking models inspired by Horava gravity.
Murg, V; Verstraete, F; Schneider, R; Nagy, P R; Legeza, Ö
2015-03-10
We study the tree-tensor-network-state (TTNS) method with variable tensor orders for quantum chemistry. TTNS is a variational method to efficiently approximate complete active space (CAS) configuration interaction (CI) wave functions in a tensor product form. TTNS can be considered as a higher order generalization of the matrix product state (MPS) method. The MPS wave function is formulated as products of matrices in a multiparticle basis spanning a truncated Hilbert space of the original CAS-CI problem. These matrices belong to active orbitals organized in a one-dimensional array, while tensors in TTNS are defined upon a tree-like arrangement of the same orbitals. The tree-structure is advantageous since the distance between two arbitrary orbitals in the tree scales only logarithmically with the number of orbitals N, whereas the scaling is linear in the MPS array. It is found to be beneficial from the computational costs point of view to keep strongly correlated orbitals in close vicinity in both arrangements; therefore, the TTNS ansatz is better suited for multireference problems with numerous highly correlated orbitals. To exploit the advantages of TTNS a novel algorithm is designed to optimize the tree tensor network topology based on quantum information theory and entanglement. The superior performance of the TTNS method is illustrated on the ionic-neutral avoided crossing of LiF. It is also shown that the avoided crossing of LiF can be localized using only ground state properties, namely one-orbital entanglement.
Geometric second order field equations for general tensor gauge fields
de Medeiros, Paul; Hull, Christopher M.
2003-05-01
Higher spin tensor gauge fields have natural gauge-invariant field equations written in terms of generalised curvatures, but these are typically of higher than second order in derivatives. We construct geometric second order field equations and actions for general higher spin boson fields, and first order ones for fermions, which are non-local but which become local on gauge-fixing, or on introducing auxiliary fields. This generalises the results of Francia and Sagnotti to all representations of the Lorentz group.
Geometric Second Order Field Equations for General Tensor Gauge Fields
De Medeiros, P
2003-01-01
Higher spin tensor gauge fields have natural gauge-invariant field equations written in terms of generalised curvatures, but these are typically of higher than second order in derivatives. We construct geometric second order field equations and actions for general higher spin boson fields, and first order ones for fermions, which are non-local but which become local on gauge-fixing, or on introducing auxiliary fields. This generalises the results of Francia and Sagnotti to all representations of the Lorentz group.
On higher order relations in Fedosov supermanifolds
Lavrov, P M; Radchenko, O V [Tomsk State Pedagogical University, 634041 Tomsk (Russian Federation)
2006-05-26
Higher order relations existing in normal coordinates between affine extensions of the symplectic curvature tensor and basic objects for any Fedosov supermanifolds are derived. Representation of these relations in general coordinates is discussed.
Higher order relations in Fedosov supermanifolds
Lavrov, P M
2005-01-01
Higher order relations existing in normal coordinates between affine extensions of the curvature tensor and basic objects for any Fedosov supermanifolds are derived. Representation of these relations in general coordinates is discussed.
Tensors the mathematics of relativity and continuum mechanics
Das, A J
2007-01-01
Tensors: The Mathematics of Relativity Theory and Continuum Mechanics, by Anadijiban Das, emerged from courses taught over the years at the University College of Dublin, Carnegie-Mellon University and Simon Fraser University. This book will serve readers well as a modern introduction to the theories of tensor algebra and tensor analysis. Throughout Tensors, examples and worked-out problems are furnished from the theory of relativity and continuum mechanics. Topics covered in this book include, but are not limited to: -tensor algebra -differential manifold -tensor analysis -differential forms -connection forms -curvature tensors -Riemannian and pseudo-Riemannian manifolds The extensive presentation of the mathematical tools, examples and problems make the book a unique text for the pursuit of both the mathematical relativity theory and continuum mechanics.
Practical definition of averages of tensors in general relativity
Boero, Ezequiel F
2016-01-01
We present a definition of tensor fields which are average of tensors over a manifold, with a straightforward and natural definition of derivative for the averaged fields; which in turn makes a suitable and practical construction for the study of averages of tensor fields that satisfy differential equations. Although we have in mind applications to general relativity, our presentation is applicable to a general n-dimensional manifold. The definition is based on the integration of scalars constructed from a physically motivated basis, making use of the least amount of geometrical structure. We also present definitions of covariant derivative of the averaged tensors and Lie derivative.
Regularized Positive-Definite Fourth Order Tensor Field Estimation from DW-MRI★
2008-01-01
In Diffusion Weighted Magnetic Resonance Image (DW-MRI) processing, a 2nd order tensor has been commonly used to approximate the diffusivity function at each lattice point of the DW-MRI data. From this tensor approximation, one can compute useful scalar quantities (e.g. anisotropy, mean diffusivity) which have been clinically used for monitoring encephalopathy, sclerosis, ischemia and other brain disorders. It is now well known that this 2nd-order tensor approximation fails to capture complex...
Scalar and tensor perturbations in loop quantum cosmology: High-order corrections
Zhu, Tao; Cleaver, Gerald; Kirsten, Klaus; Sheng, Qin; Wu, Qiang
2015-01-01
Loop quantum cosmology (LQC) provides promising resolutions to the trans-Planckian issue and initial singularity arising in the inflationary models of general relativity. In general, due to different quantization approaches, LQC involves two types of quantum corrections, the holonomy and inverse-volume, to both of the cosmological background evolution and perturbations. In this paper, using {\\em the third-order uniform asymptotic approximations}, we derive explicitly the observational quantities of the slow-roll inflation in the framework of LQC with these quantum corrections. We calculate the power spectra, spectral indices, and running of the spectral indices for both scalar and tensor perturbations, whereby the tensor-to-scalar ratio is obtained. We expand all the observables at the time when the inflationary mode crosses the Hubble horizon. As the upper error bounds for the uniform asymptotic approximation at the third-order are $\\lesssim 0.15\\%$, these results represent the most accurate results obtained...
Regularized Positive-Definite Fourth Order Tensor Field Estimation from DW-MRI★
Barmpoutis, Angelos; Vemuri, Baba C.; Howland, Dena; Forder, John R.
2009-01-01
In Diffusion Weighted Magnetic Resonance Image (DW-MRI) processing, a 2nd order tensor has been commonly used to approximate the diffusivity function at each lattice point of the DW-MRI data. From this tensor approximation, one can compute useful scalar quantities (e.g. anisotropy, mean diffusivity) which have been clinically used for monitoring encephalopathy, sclerosis, ischemia and other brain disorders. It is now well known that this 2nd-order tensor approximation fails to capture complex local tissue structures, e.g. crossing fibers, and as a result, the scalar quantities derived from these tensors are grossly inaccurate at such locations. In this paper we employ a 4th order symmetric positive-definite (SPD) tensor approximation to represent the diffusivity function and present a novel technique to estimate these tensors from the DW-MRI data guaranteeing the SPD property. Several articles have been reported in literature on higher order tensor approximations of the diffusivity function but none of them guarantee the positivity of the estimates, which is a fundamental constraint since negative values of the diffusivity are not meaningful. In this paper we represent the 4th-order tensors as ternary quartics and then apply Hilbert’s theorem on ternary quartics along with the Iwasawa parametrization to guarantee an SPD 4th-order tensor approximation from the DW-MRI data. The performance of this model is depicted on synthetic data as well as real DW-MRIs from a set of excised control and injured rat spinal cords, showing accurate estimation of scalar quantities such as generalized anisotropy and trace as well as fiber orientations. PMID:19063978
Regularized positive-definite fourth order tensor field estimation from DW-MRI.
Barmpoutis, Angelos; Hwang, Min Sig; Howland, Dena; Forder, John R; Vemuri, Baba C
2009-03-01
In Diffusion Weighted Magnetic Resonance Image (DW-MRI) processing, a 2nd order tensor has been commonly used to approximate the diffusivity function at each lattice point of the DW-MRI data. From this tensor approximation, one can compute useful scalar quantities (e.g. anisotropy, mean diffusivity) which have been clinically used for monitoring encephalopathy, sclerosis, ischemia and other brain disorders. It is now well known that this 2nd-order tensor approximation fails to capture complex local tissue structures, e.g. crossing fibers, and as a result, the scalar quantities derived from these tensors are grossly inaccurate at such locations. In this paper we employ a 4th order symmetric positive-definite (SPD) tensor approximation to represent the diffusivity function and present a novel technique to estimate these tensors from the DW-MRI data guaranteeing the SPD property. Several articles have been reported in literature on higher order tensor approximations of the diffusivity function but none of them guarantee the positivity of the estimates, which is a fundamental constraint since negative values of the diffusivity are not meaningful. In this paper we represent the 4th-order tensors as ternary quartics and then apply Hilbert's theorem on ternary quartics along with the Iwasawa parametrization to guarantee an SPD 4th-order tensor approximation from the DW-MRI data. The performance of this model is depicted on synthetic data as well as real DW-MRIs from a set of excised control and injured rat spinal cords, showing accurate estimation of scalar quantities such as generalized anisotropy and trace as well as fiber orientations.
Tensor calculus, relativity, and cosmology a first course
Dalarsson, M
2005-01-01
This book combines relativity, astrophysics, and cosmology in a single volume, providing an introduction to each subject that enables students to understand more detailed treatises as well as the current literature. The section on general relativity 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, Penrose processes, and similar topics), and considers the energy-momentum tensor for various solutions. The next section on relativistic astrophysics discusses
Tensor-entanglement-filtering renormalization approach and symmetry-protected topological order
Gu, Zheng-Cheng; Wen, Xiao-Gang
2009-10-01
We study the renormalization group flow of the Lagrangian for statistical and quantum systems by representing their path integral in terms of a tensor network. Using a tensor-entanglement-filtering renormalization approach that removes local entanglement and produces a coarse-grained lattice, we show that the resulting renormalization flow of the tensors in the tensor network has a nice fixed-point structure. The isolated fixed-point tensors Tinv plus the symmetry group Gsym of the tensors (i.e., the symmetry group of the Lagrangian) characterize various phases of the system. Such a characterization can describe both the symmetry breaking phases and topological phases, as illustrated by two-dimensional (2D) statistical Ising model, 2D statistical loop-gas model, and 1+1D quantum spin-1/2 and spin-1 models. In particular, using such a (Gsym,Tinv) characterization, we show that the Haldane phase for a spin-1 chain is a phase protected by the time-reversal, parity, and translation symmetries. Thus the Haldane phase is a symmetry-protected topological phase. The (Gsym,Tinv) characterization is more general than the characterizations based on the boundary spins and string order parameters. The tensor renormalization approach also allows us to study continuous phase transitions between symmetry breaking phases and/or topological phases. The scaling dimensions and the central charges for the critical points that describe those continuous phase transitions can be calculated from the fixed-point tensors at those critical points.
Zumalacárregui, Miguel
2013-01-01
We study the structure of scalar-tensor theories of gravity based on derivative couplings between the scalar and the matter degrees of freedom introduced through an effective metric. Such interactions are classified by their tensor structure into conformal (scalar), disformal (vector) and extended disformal (traceless tensor), as well as by the derivative order of the scalar field. Relations limited to first derivatives of the field ensure second order equations of motion in the Einstein frame and hence the absence of Ostrogradski ghosts. The existence of a mapping to the Jordan frame is not trivial in the general case, and can be addressed using the Jacobian of the frame transformation through its eigenvalues and eigentensors. These objects also appear in the study of different aspects of such theories, including the metric and field redefinition transformation of the path integral in the quantum mechanical description. Although sane in the Einstein frame, generic disformally coupled theories are described b...
PPN-limit of Fourth Order Gravity inspired by Scalar-Tensor Gravity
Capozziello, S.; Troisi, A
2005-01-01
Based on the {\\it dynamical} equivalence between higher order gravity and scalar-tensor gravity the PPN-limit of fourth order gravity is discussed. We exploit this analogy developing a fourth order gravity version of the Eddington PPN-parameters. As a result, Solar System experiments can be reconciled with higher order gravity, if physical constraints descending from experiments are fulfilled.
PPN-limit of Fourth Order Gravity inspired by Scalar-Tensor Gravity
Capozziello, S.; Troisi, A.
2005-01-01
Based on the {\\it dynamical} equivalence between higher order gravity and scalar-tensor gravity the PPN-limit of fourth order gravity is discussed. We exploit this analogy developing a fourth order gravity version of the Eddington PPN-parameters. As a result, Solar System experiments can be reconciled with higher order gravity, if physical constraints descending from experiments are fulfilled.
Towards a double-scaling limit for tensor models: probing sub-dominant orders
Kaminski, Wojciech; Ryan, James P
2013-01-01
The definition of a double-scaling limit represents an important goal in the development of tensor models. We take the first steps towards this goal by extracting and analysing the next-to-leading order contributions, in the 1/N expansion, for the IID tensor models. We show that the radius of convergence of the NLO series coincides with that of the leading order melonic sector. Meanwhile, the value of the susceptibility exponent at NLO is 3/2, signaling a departure from the leading order behaviour. Both pieces of information provide clues for a non-trivial double-scaling limit, for which we put forward some precise conjecture.
Chetyrkin, K. G.; Maier, A
2010-01-01
We present analytical results both in momentum and position space for the massless correlators of the vector and scalar currents to order alpha_s^4 as well as for the tensor currents to order alpha_s^3. The evolution equations for the correlators together with all relevant anomalous dimensions are discussed in detail. As an application we present explicit conversion formulas relating the MSbar-renormalized vector, scalar and tensor currents to their counterparts renormalized in the X-space re...
Vilanova, Anna; Burgeth, Bernhard; Visualization and Processing of Tensors and Higher Order Descriptors for Multi-Valued Data
2014-01-01
Arising from the fourth Dagstuhl conference entitled Visualization and Processing of Tensors and Higher Order Descriptors for Multi-Valued Data (2011), this book offers a broad and vivid view of current work in this emerging field. Topics covered range from applications of the analysis of tensor fields to research on their mathematical and analytical properties. Part I, Tensor Data Visualization, surveys techniques for visualization of tensors and tensor fields in engineering, discusses the current state of the art and challenges, and examines tensor invariants and glyph design, including an overview of common glyphs. The second Part, Representation and Processing of Higher-order Descriptors, describes a matrix representation of local phase, outlines mathematical morphological operations techniques, extended for use in vector images, and generalizes erosion to the space of diffusion weighted MRI. Part III, Higher Order Tensors and Riemannian-Finsler Geometry, offers powerful mathematical language to model and...
Riesz Isomorphisms of Tensor Products of Order Unit Banach Spaces
T S S R K Rao
2009-06-01
In this paper we formulate and prove an order unit Banach space version of a Banach–Stone theorem type theorem for Riesz isomorphisms of the space of vector-valued continuous functions. Similar results were obtained recently for the case of lattice-valued continuous functions in [5] and [6].
Invariant tensors related with natural connections for a class Riemannian product manifolds
Gribacheva, Dobrinka
2012-01-01
Some invariant tensors in two Naveira classes of Riemannian product manifolds are considered. These tensors are related with natural connections, i.e. linear connections preserving the Riemannian metric and the product structure.
Domanov, Ignat; De Lathauwer, Lieven
2013-01-01
Canonical Polyadic Decomposition (CPD) of a third-order tensor is decomposition in a minimal number of rank-$1$ tensors. We call an algorithm algebraic if it is guaranteed to find the decomposition when it is exact and if it only relies on standard linear algebra (essentially sets of linear equations and matrix factorizations). The known algebraic algorithms for the computation of the CPD are limited to cases where at least one of the factor matrices has full column rank. In the paper we pres...
General second order scalar-tensor theory, self tuning, and the Fab Four
Charmousis, Christos; Padilla, Antonio; Saffin, Paul M
2011-01-01
Starting from the most general scalar-tensor theory with second order field equations in four dimensions, we establish the unique action that will allow for the existence of a consistent self-tuning mechanism on FLRW backgrounds, and show how it can be understood as a combination of just four base Lagrangians with an intriguing geometric structure dependent on the Ricci scalar, the Einstein tensor, the double dual of the Riemann tensor and the Gauss-Bonnet combination. Spacetime curvature can be screened from the net cosmological constant at any given moment because we allow the scalar field to break Poincar\\'e invariance on the self-tuning vacua, thereby evading the Weinberg no-go theorem. We show how the four arbitrary functions of the scalar field combine in an elegant way opening up the possibility of obtaining non-trivial cosmological solutions.
Fast and Analytical EAP Approximation from a 4th-Order Tensor
Aurobrata Ghosh
2012-01-01
Full Text Available Generalized diffusion tensor imaging (GDTI was developed to model complex apparent diffusivity coefficient (ADC using higher-order tensors (HOTs and to overcome the inherent single-peak shortcoming of DTI. However, the geometry of a complex ADC profile does not correspond to the underlying structure of fibers. This tissue geometry can be inferred from the shape of the ensemble average propagator (EAP. Though interesting methods for estimating a positive ADC using 4th-order diffusion tensors were developed, GDTI in general was overtaken by other approaches, for example, the orientation distribution function (ODF, since it is considerably difficult to recuperate the EAP from a HOT model of the ADC in GDTI. In this paper, we present a novel closed-form approximation of the EAP using Hermite polynomials from a modified HOT model of the original GDTI-ADC. Since the solution is analytical, it is fast, differentiable, and the approximation converges well to the true EAP. This method also makes the effort of computing a positive ADC worthwhile, since now both the ADC and the EAP can be used and have closed forms. We demonstrate our approach with 4th-order tensors on synthetic data and in vivo human data.
Higher-order principal component pursuit via tensor approximation and convex optimization
Sijia Cai; Ping Wang; Linhao Li; Chuhan Zhang
2014-01-01
Recovering the low-rank structure of data matrix from sparse errors arises in the principal component pursuit (PCP). This paper exploits the higher-order generalization of matrix recovery, named higher-order principal component pursuit (HOPCP), since it is critical in multi-way data analysis. Unlike the convexification (nuclear norm) for matrix rank function, the tensorial nuclear norm is stil an open problem. While existing preliminary works on the tensor completion field provide a viable way to indicate the low complexity estimate of tensor, therefore, the paper focuses on the low multi-linear rank tensor and adopt its convex relaxation to formulate the convex optimization model of HOPCP. The paper further propose two algorithms for HOPCP based on alternative minimization scheme: the augmented Lagrangian alternating di-rection method (ALADM) and its truncated higher-order singular value decomposition (ALADM-THOSVD) version. The former can obtain a high accuracy solution while the latter is more efficient to handle the computational y intractable problems. Experimental re-sults on both synthetic data and real magnetic resonance imaging data show the applicability of our algorithms in high-dimensional tensor data processing.
Filtering Overpopulated Isoscalar Tensor States with Mass Relations
Burakovsky, L; Burakovsky, Leonid; Page, Philip R.
2000-01-01
The overpopulated isoscalar tensor states are sifted using Schwinger-type mass relations. Two solutions are found: one where the glueball is the fJ(2220), and one where the glueball is more distributed, with f2(1820) having the largest component. The f2(1565) and fJ(1710) cannot be accommodated as glueball-(hybrid) meson mixtures in the absense of significant coupling to decay channels. f2'(1525) -> pi pi is in agreement with experiment. The fJ(2220) decays neither flavour democratically nor is narrow.
Tensor-product preconditioners for higher-order space-time discontinuous Galerkin methods
Diosady, Laslo T.; Murman, Scott M.
2017-02-01
A space-time discontinuous-Galerkin spectral-element discretization is presented for direct numerical simulation of the compressible Navier-Stokes equations. An efficient solution technique based on a matrix-free Newton-Krylov method is developed in order to overcome the stiffness associated with high solution order. The use of tensor-product basis functions is key to maintaining efficiency at high-order. Efficient preconditioning methods are presented which can take advantage of the tensor-product formulation. A diagonalized Alternating-Direction-Implicit (ADI) scheme is extended to the space-time discontinuous Galerkin discretization. A new preconditioner for the compressible Euler/Navier-Stokes equations based on the fast-diagonalization method is also presented. Numerical results demonstrate the effectiveness of these preconditioners for the direct numerical simulation of subsonic turbulent flows.
Delgado Acosta, E.G.; Banda Guzman, V.M.; Kirchbach, M. [UASLP, Instituto de Fisica, San Luis Potosi (Mexico)
2015-03-01
We propose a general method for the description of arbitrary single spin-j states transforming according to (j, 0) + (0, j) carrier spaces of the Lorentz algebra in terms of Lorentz tensors for bosons, and tensor-spinors for fermions, and by means of second-order Lagrangians. The method allows to avoid the cumbersome matrix calculus and higher ∂{sup 2j} order wave equations inherent to the Weinberg-Joos approach. We start with reducible Lorentz tensor (tensor-spinor) representation spaces hosting one sole (j, 0) + (0, j) irreducible sector and design there a representation reduction algorithm based on one of the Casimir invariants of the Lorentz algebra. This algorithm allows us to separate neatly the pure spin-j sector of interest from the rest, while preserving the separate Lorentz and Dirac indexes. However, the Lorentz invariants are momentum independent and do not provide wave equations. Genuine wave equations are obtained by conditioning the Lorentz tensors under consideration to satisfy the Klein-Gordon equation. In so doing, one always ends up with wave equations and associated Lagrangians that are of second order in the momenta. Specifically, a spin-3/2 particle transforming as (3/2, 0) + (0, 3/2) is comfortably described by a second-order Lagrangian in the basis of the totally anti-symmetric Lorentz tensor-spinor of second rank, Ψ {sub [μν]}. Moreover, the particle is shown to propagate causally within an electromagnetic background. In our study of (3/2, 0) + (0, 3/2) as part of Ψ {sub [μν]} we reproduce the electromagnetic multipole moments known from the Weinberg-Joos theory. We also find a Compton differential cross-section that satisfies unitarity in forward direction. The suggested tensor calculus presents itself very computer friendly with respect to the symbolic software FeynCalc. (orig.)
Delgado Acosta, E. G.; Banda Guzmán, V. M.; Kirchbach, M.
2015-03-01
We propose a general method for the description of arbitrary single spin- j states transforming according to ( j, 0) ⊕ (0, j) carrier spaces of the Lorentz algebra in terms of Lorentz tensors for bosons, and tensor-spinors for fermions, and by means of second-order Lagrangians. The method allows to avoid the cumbersome matrix calculus and higher ∂2 j order wave equations inherent to the Weinberg-Joos approach. We start with reducible Lorentz tensor (tensor-spinor) representation spaces hosting one sole ( j, 0) ⊕ (0, j) irreducible sector and design there a representation reduction algorithm based on one of the Casimir invariants of the Lorentz algebra. This algorithm allows us to separate neatly the pure spin- j sector of interest from the rest, while preserving the separate Lorentz and Dirac indexes. However, the Lorentz invariants are momentum independent and do not provide wave equations. Genuine wave equations are obtained by conditioning the Lorentz tensors under consideration to satisfy the Klein-Gordon equation. In so doing, one always ends up with wave equations and associated Lagrangians that are of second order in the momenta. Specifically, a spin-3/2 particle transforming as (3/2, 0) ⊕ (0, 3/2) is comfortably described by a second-order Lagrangian in the basis of the totally anti-symmetric Lorentz tensor-spinor of second rank, Ψ [ μν]. Moreover, the particle is shown to propagate causally within an electromagnetic background. In our study of (3/2, 0) ⊕ (0, 3/2) as part of Ψ [ μν] we reproduce the electromagnetic multipole moments known from the Weinberg-Joos theory. We also find a Compton differential cross-section that satisfies unitarity in forward direction. The suggested tensor calculus presents itself very computer friendly with respect to the symbolic software FeynCalc.
The Schwinger Dyson equations and the algebra of constraints of random tensor models at all orders
Gurau, Razvan, E-mail: rgurau@perimeterinstitute.ca [Perimeter Institute for Theoretical Physics, 31 Caroline St. N, ON N2L 2Y5, Waterloo (Canada)
2012-12-01
Random tensor models for a generic complex tensor generalize matrix models in arbitrary dimensions and yield a theory of random geometries. They support a 1/N expansion dominated by graphs of spherical topology. Their Schwinger Dyson equations, generalizing the loop equations of matrix models, translate into constraints satisfied by the partition function. The constraints have been shown, in the large N limit, to close a Lie algebra indexed by colored rooted D-ary trees yielding a first generalization of the Virasoro algebra in arbitrary dimensions. In this paper we complete the Schwinger Dyson equations and the associated algebra at all orders in 1/N. The full algebra of constraints is indexed by D-colored graphs, and the leading order D-ary tree algebra is a Lie subalgebra of the full constraints algebra.
二阶张量场可视化研究%The Research on Visualization of Second Order Tensor Fields
李海生; 杨钦; 陈其明
2003-01-01
Second-order tensors are widely existed in engineering,physical science and biomechanics. Examples arestresses and strains in solids and velocity gradients in fluid flows. This paper takes the Boussinesq' s problem as an ex-ample which is typical in Elasticity Mechanics ,and visualizes the second-order real symmetric tensor fields by ellipsoidicons and hyperStreamlines. The results are reasonable. The visualization methods adopted in this paper are also suit-able for other second-order symmetric tensor fields such as electromagnetic field.
A Review of Tensors and Tensor Signal Processing
Cammoun, L.; Castaño-Moraga, C. A.; Muñoz-Moreno, E.; Sosa-Cabrera, D.; Acar, B.; Rodriguez-Florido, M. A.; Brun, A.; Knutsson, H.; Thiran, J. P.
Tensors have been broadly used in mathematics and physics, since they are a generalization of scalars or vectors and allow to represent more complex properties. In this chapter we present an overview of some tensor applications, especially those focused on the image processing field. From a mathematical point of view, a lot of work has been developed about tensor calculus, which obviously is more complex than scalar or vectorial calculus. Moreover, tensors can represent the metric of a vector space, which is very useful in the field of differential geometry. In physics, tensors have been used to describe several magnitudes, such as the strain or stress of materials. In solid mechanics, tensors are used to define the generalized Hooke’s law, where a fourth order tensor relates the strain and stress tensors. In fluid dynamics, the velocity gradient tensor provides information about the vorticity and the strain of the fluids. Also an electromagnetic tensor is defined, that simplifies the notation of the Maxwell equations. But tensors are not constrained to physics and mathematics. They have been used, for instance, in medical imaging, where we can highlight two applications: the diffusion tensor image, which represents how molecules diffuse inside the tissues and is broadly used for brain imaging; and the tensorial elastography, which computes the strain and vorticity tensor to analyze the tissues properties. Tensors have also been used in computer vision to provide information about the local structure or to define anisotropic image filters.
Third-order energy derivative corrections to the Kohn-Sham orbital hardness tensor
Tzonka Mineva
2005-09-01
The third term in the Taylor expansion of the total energy functional around the number of electrons is evaluated as the second-order derivative of orbital Kohn-Sham energies with respect to orbital occupancy. Present approach is an extension of an efficient algorithm to compute densityfunctional based orbital reactivity indices. Various energy derivatives used to approximate orbital reactivity indices are defined within the space spanned by the orbital occupation numbers and the Kohn-Sham one-electron energies. The third-order energy functional derivative has to be considered for singular hardness tensor ([]). On the contrary, this term has negligible influence on the reactivity index values for atomic or molecular systems with positively defined hardness tensors. In this context, stability of a system in equilibrium state estimated through the eigenvalues of [h] is discussed. Numerical illustration of the Kohn-Sham energy functional derivatives in orbital resolution up to the third order is shown for benchmark molecules such as H2O, H2S, and OH-.
Equation of motion of canonical tensor model and Hamilton-Jacobi equation of general relativity
Chen, Hua; Sato, Yuki
2016-01-01
The canonical tensor model (CTM) is a rank-three tensor model formulated as a totally constrained system in the canonical formalism. The constraint algebra of CTM has a similar structure as that of the ADM formalism of general relativity, and is studied as a discretized model for quantum gravity. In this paper, we analyze the classical equation of motion (EOM) of CTM in a formal continuum limit through a derivative expansion of the tensor up to the forth order, and show that it is the same as the EOM of a coupled system of gravity and a scalar field derived from the Hamilton-Jacobi equation with an appropriate choice of an action. The action contains a scalar field potential of an exponential form, and the system classically respects a dilatational symmetry. We find that the system has a critical dimension, given by six, over which it becomes unstable due to the wrong sign of the scalar kinetic term. In six dimensions, de Sitter spacetime becomes a solution to the EOM, signaling the emergence of a conformal s...
Solving type-2 fuzzy relation equations via semi-tensor product of matrices
Yongyi YAN; Zengqiang CHEN; Zhongxin LIU
2014-01-01
The problem of solving type-2 fuzzy relation equations is investigated. In order to apply semi-tensor product of matrices, a new matrix analysis method and tool, to solve type-2 fuzzy relation equations, a type-2 fuzzy relation is decomposed into two parts as principal sub-matrices and secondary sub-matrices;an r-ary symmetrical-valued type-2 fuzzy relation model and its corresponding symmetrical-valued type-2 fuzzy relation equation model are established. Then, two algorithms are developed for solving type-2 fuzzy relation equations, one of which gives a theoretical description for general type-2 fuzzy relation equations;the other one can find all the solutions to the symmetrical-valued ones. The results can improve designing type-2 fuzzy controllers, because it provides knowledge to search the optimal solutions or to find the reason if there is no solution. Finally some numerical examples verify the correctness of the results/algorithms.
Domanov, Ignat; De Lathauwer, Lieven
2013-01-01
Canonical Polyadic (also known as Candecomp/Parafac) Decomposition (CPD) of a higher-order tensor is decomposition in a minimal number of rank-1 tensors. In Part I, we gave an overview of existing results concerning uniqueness and presented new, relaxed, conditions that guarantee uniqueness of one factor matrix. In Part II we use these results for establishing overall CPD uniqueness in cases where none of the factor matrices has full column rank. We obtain uniqueness conditions involving Khat...
Deffayet, C; Esposito-Farèse, G
2009-01-01
We extend to curved backgrounds all flat-space scalar field models that obey purely second-order equations, while maintaining their second-order dependence on both field and metric. This extension simultaneously restores to second order the, originally higher derivative, stress-tensors as well. The process is transparent and uniform for all dimensions.
Collineations of the curvature tensor in general relativity
Rishi Kumar Tiwari
2005-07-01
Curvature collineations for the curvature tensor, constructed from a fundamental Bianchi Type-V metric, are studied. We are concerned with a symmetry property of space-time which is called curvature collineation, and we briefly discuss the physical and kinematical properties of the models.
Analytical calculation of permittivity tensors for invisibility devices using general relativity
Ahn, Doyeol
2010-01-01
Analytical expressions for the permittivity tensors of invisibility devices for the cases of elliptic cylinder, prolate spheroid, and the confocal paraboloid are obtained using general relativistic relations between the electromagnetic tensor and its dual tensor and their application to the transformation between the electromagnetic spacetime and the physical spacetime. This approach has a merit of being intuitive. In the case of elliptic cylinder, we found that the point of infinite light speed in the electromagnetic space becomes two points in the physical space for the zz component of the permittivity tensor. This result is different from the case of perfect cylinder in which there is a line of cloak at which the speed of light becomes infinite. In the cases of prolate spheroid and confocal paraboloid, the point of infinite light speed in the electromagnetic space becomes line in the physical space in all tensor components.
Limits of the energy-momentum tensor in general relativity
Paiva, F M; Hall, G S; MacCallum, M A H; Paiva, Filipe M.; Reboucas, Marcelo J.; Hall, Graham S.; Callum, Malcolm A.H. Mac
1998-01-01
A limiting diagram for the Segre classification of the energy-momentum tensor is obtained and discussed in connection with a Penrose specialization diagram for the Segre types. A generalization of the coordinate-free approach to limits of Paiva et al. to include non-vacuum space-times is made. Geroch's work on limits of space-times is also extended. The same argument also justifies part of the procedure for classification of a given spacetime using Cartan scalars.
The most general second-order field equations of bi-scalar-tensor theory in four dimensions
Ohashi, Seiju; Tanahashi, Norihiro; Kobayashi, Tsutomu; Yamaguchi, Masahide
2015-07-01
The Horndeski theory is known as the most general scalar-tensor theory with second-order field equations. In this paper, we explore the bi-scalar extension of the Horndeski theory. Following Horndeski's approach, we determine all the possible terms appearing in the second-order field equations of the bi-scalar-tensor theory. We compare the field equations with those of the generalized multi-Galileons, and confirm that our theory contains new terms that are not included in the latter theory. We also discuss the construction of the Lagrangian leading to our most general field equations.
The most general second-order field equations of bi-scalar-tensor theory in four dimensions
Ohashi, Seiju; Kobayashi, Tsutomu; Yamaguchi, Masahide
2015-01-01
The Horndeski theory is known as the most general scalar-tensor theory with second-order field equations. In this paper, we explore the bi-scalar extension of the Horndeski theory. Following Horndeski's approach, we determine all the possible terms appearing in the second-order field equations of the bi-scalar-tensor theory. We compare the field equations with those of the generalized multi-Galileons, and confirm that our theory contains new terms that are not included in the latter theory. We also discuss the construction of the Lagrangian leading to our most general field equations.
Low-energy theory for strained graphene: an approach up to second-order in the strain tensor
Oliva-Leyva, Maurice; Wang, Chumin
2017-04-01
An analytical study of low-energy electronic excited states in uniformly strained graphene is carried out up to second-order in the strain tensor. We report a new effective Dirac Hamiltonian with an anisotropic Fermi velocity tensor, which reveals the graphene trigonal symmetry being absent in first-order low-energy theories. In particular, we demonstrate the dependence of the Dirac-cone elliptical deformation on the stretching direction with respect to graphene lattice orientation. We further analytically calculate the optical conductivity tensor of strained graphene and its transmittance for a linearly polarized light with normal incidence. Finally, the obtained analytical expression of the Dirac point shift allows a better determination and understanding of pseudomagnetic fields induced by nonuniform strains.
Constraint algebra of general relativity from a formal continuum limit of canonical tensor model
Sasakura, Naoki [Yukawa Institute for Theoretical Physics, Kyoto University,Oiwake-cho, Kitashirakawa, Sakyo-ku, Kyoto 606-8502 (Japan); Sato, Yuki [National Institute for Theoretical Physics, School of Physics andMandelstam Institute for Theoretical Physics, University of the Witwatersrand,Wits 2050 (South Africa)
2015-10-16
Canonical tensor model (CTM for short below) is a rank-three tensor model formulated as a totally constrained system in the canonical formalism. In the classical case, the constraints form a first-class constraint Poisson algebra with structures similar to that of the ADM formalism of general relativity, qualifying CTM as a possible discrete formalism for quantum gravity. In this paper, we show that, in a formal continuum limit, the constraint Poisson algebra of CTM with no cosmological constant exactly reproduces that of the ADM formalism. To this end, we obtain the expression of the metric tensor field in general relativity in terms of one of the dynamical rank-three tensors in CTM, and determine the correspondence between the constraints of CTM and those of the ADM formalism. On the other hand, the cosmological constant term of CTM seems to induce non-local dynamics, and is inconsistent with an assumption about locality of the continuum limit.
Examining the consistency relations describing the three-point functions involving tensors
Sreenath, V.; Sriramkumar, L.
2014-10-01
It is well known that the non-Gaussianity parameter fNL 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 CNLScript R and CNLγ 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 hNL 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
Triangular Alignment (TAME). A Tensor-based Approach for Higher-order Network Alignment
Mohammadi, Shahin [Purdue Univ., West Lafayette, IN (United States); Gleich, David F. [Purdue Univ., West Lafayette, IN (United States); Kolda, Tamara G. [Sandia National Laboratories (SNL-CA), Livermore, CA (United States); Grama, Ananth [Purdue Univ., West Lafayette, IN (United States)
2015-11-01
Network alignment is an important tool with extensive applications in comparative interactomics. Traditional approaches aim to simultaneously maximize the number of conserved edges and the underlying similarity of aligned entities. We propose a novel formulation of the network alignment problem that extends topological similarity to higher-order structures and provide a new objective function that maximizes the number of aligned substructures. This objective function corresponds to an integer programming problem, which is NP-hard. Consequently, we approximate this objective function as a surrogate function whose maximization results in a tensor eigenvalue problem. Based on this formulation, we present an algorithm called Triangular AlignMEnt (TAME), which attempts to maximize the number of aligned triangles across networks. We focus on alignment of triangles because of their enrichment in complex networks; however, our formulation and resulting algorithms can be applied to general motifs. Using a case study on the NAPABench dataset, we show that TAME is capable of producing alignments with up to 99% accuracy in terms of aligned nodes. We further evaluate our method by aligning yeast and human interactomes. Our results indicate that TAME outperforms the state-of-art alignment methods both in terms of biological and topological quality of the alignments.
Dirac-Kahler equation in curved space-time, relation between spinor and tensor formulations
Red'kov, V M
2011-01-01
A common view is that generalization of a wave equation on Riemannian space-time is substantially determined by what a particle is - boson or fermion. As a rule, they say that tensor equations for bosons are extended in a simpler way then spinor equations for fermions. In that context, a very interesting problem is of extension a wave equation for Dirac--K\\"{a}hler field (Ivanenko--Landau field was historically first term, also the term a vector field of general type was used). The article relates a generally covariant tensor formalism to a spinor one when these both are applied to description of the Dirac-K\\"ahler field in a Rimannian space-time. Both methods are taken to be equivalent and the tensor equations are derived from spinor ones. It is shown that, for characterization of Dirac-K\\"ahler's tensor components, two alternative approaches are suitable: these are whether a tetrad-based pseudo tensor classification or a generally coordinate pseudo tensor one. By imposing definite restrictions on the the Di...
Hollman, David S; Schaefer, Henry F
2012-10-28
In recent years, internal coordinates have become the preferred means of expressing potential energy surfaces. The ability to transform quantities from chemically significant internal coordinates to primitive Cartesian coordinates and spectroscopically relevant normal coordinates is thus critical to the further development of computational chemistry. In the present work, general nth order formulas are presented for the Cartesian derivatives of the five most commonly used internal coordinates--bond stretching, bond angle, torsion, out-of-plane angle, and linear bending. To compose such formulas in a reasonably understandable fashion, a new notation is developed that is a generalization of that which has been used previously for similar purposes. The notation developed leads to easily programmable and reasonably understandable arbitrary order formulas, yet it is powerful enough to express the arbitrary order B tensor of a general, N-point internal coordinate, as is done herein. The techniques employed in the derivation of such formulas are relatively straightforward, and could presumably be applied to a number of other internal coordinates as needed.
Fen Wei
2016-01-01
Full Text Available In order to sufficiently capture the useful fault-related information available in the multiple vibration sensors used in rotation machinery, while concurrently avoiding the introduction of the limitation of dimensionality, a new fault diagnosis method for rotation machinery based on supervised second-order tensor locality preserving projection (SSTLPP and weighted k-nearest neighbor classifier (WKNNC with an assembled matrix distance metric (AMDM is presented. Second-order tensor representation of multisensor fused conditional features is employed to replace the prevailing vector description of features from a single sensor. Then, an SSTLPP algorithm under AMDM (SSTLPP-AMDM is presented to realize dimensional reduction of original high-dimensional feature tensor. Compared with classical second-order tensor locality preserving projection (STLPP, the SSTLPP-AMDM algorithm not only considers both local neighbor information and class label information but also replaces the existing Frobenius distance measure with AMDM for construction of the similarity weighting matrix. Finally, the obtained low-dimensional feature tensor is input into WKNNC with AMDM to implement the fault diagnosis of the rotation machinery. A fault diagnosis experiment is performed for a gearbox which demonstrates that the second-order tensor formed multisensor fused fault data has good results for multisensor fusion fault diagnosis and the formulated fault diagnosis method can effectively improve diagnostic accuracy.
Afra, Sardar; Gildin, Eduardo
2016-09-01
Parameter estimation through robust parameterization techniques has been addressed in many works associated with history matching and inverse problems. Reservoir models are in general complex, nonlinear, and large-scale with respect to the large number of states and unknown parameters. Thus, having a practical approach to replace the original set of highly correlated unknown parameters with non-correlated set of lower dimensionality, that captures the most significant features comparing to the original set, is of high importance. Furthermore, de-correlating system's parameters while keeping the geological description intact is critical to control the ill-posedness nature of such problems. We introduce the advantages of a new low dimensional parameterization approach for reservoir characterization applications utilizing multilinear algebra based techniques like higher order singular value decomposition (HOSVD). In tensor based approaches like HOSVD, 2D permeability images are treated as they are, i.e., the data structure is kept as it is, whereas in conventional dimensionality reduction algorithms like SVD data has to be vectorized. Hence, compared to classical methods, higher redundancy reduction with less information loss can be achieved through decreasing present redundancies in all dimensions. In other words, HOSVD approximation results in a better compact data representation with respect to least square sense and geological consistency in comparison with classical algorithms. We examined the performance of the proposed parameterization technique against SVD approach on the SPE10 benchmark reservoir model as well as synthetic channelized permeability maps to demonstrate the capability of the proposed method. Moreover, to acquire statistical consistency, we repeat all experiments for a set of 1000 unknown geological samples and provide comparison using RMSE analysis. Results prove that, for a fixed compression ratio, the performance of the proposed approach
Hsu, Jung-Lung; Van Hecke, Wim; Bai, Chyi-Huey; Lee, Cheng-Hui; Tsai, Yuh-Feng; Chiu, Hou-Chang; Jaw, Fu-Shan; Hsu, Chien-Yeh; Leu, Jyu-Gang; Chen, Wei-Hung; Leemans, Alexander
2010-01-01
Diffusion tensor imaging (DTI) has already proven to be a valuable tool when investigating both global and regional microstructural white matter (WM) brain changes in the human aging process. Although subject to many criticisms, voxel-based analysis is currently one of the most common and preferred approaches in such DTI aging studies. In this context, voxel-based DTI analyses have assumed a 'linear' correlation when finding the significant brain regions that relate age with a particular diffusion measure of interest. Recent literature, however, has clearly demonstrated 'non-linear' relationships between age and diffusion metrics by using region-of-interest and tractography-based approaches. In this work, we incorporated polynomial regression models in the voxel-based DTI analysis framework to assess age-related changes in WM diffusion properties (fractional anisotropy and axial, transverse, and mean diffusivity) in a large cohort of 346 subjects (25 to 81 years old). Our novel approach clearly demonstrates that voxel-based DTI analyses can greatly benefit from incorporating higher-order regression models when investigating potential relationships between aging and diffusion properties.
Implementation of an anisotropic damage material model using general second order damage tensor
Niazi, Muhammad; Wisselink, Harm; Meinders, Timo; Horn, ten Carel; Mori, K.; Pietrzyk, M.; Kusiak, J.; Majta, J.; Hartley, P.; Lin, J.
2010-01-01
Damage in metals is mainly the process of the initiation and growth of voids. With the growing complexity in materials and forming proc-esses, it becomes inevitable to include anisotropy in damage (tensorial damage variable). Most of the anisotropic damage models define the damage tensor in the prin
Irreducible tensor basis and general Fierz relations for Bhabha scattering like amplitudes
Liu, Tao
2016-01-01
We construct an irreducible s- and t-channel tensor basis for Bhabha scattering like amplitudes based on the properties of the underlying Lorentz symmetry in four space-time dimensions. In the given basis the calculation of amplitude contractions like the amplitude square reduces to the contraction of their corresponding coefficient tensors. Further the basis retains the full amplitude information and thus can be applied in off-shell cases. The general Fierz transformations which relate the s- and t-channel basis with each other are obtained. As an example for application we use the basis to calculate the tree-level Bhabha scattering amplitude.
Examining the consistency relations describing the three-point functions involving tensors
Sreenath, V
2014-01-01
It is well known that the non-Gaussianity parameter $f_{_{\\rm NL}}$ 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 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 $C_{_{\\rm NL}}^{\\mathcal R}$ and $C_{_{\\rm NL}}^{\\mathcal \\gamma}$ 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 $h_{_{\\rm NL}}$ used to describe the tensor bi-spec...
TensorLy: Tensor Learning in Python
Kossaifi, Jean; Panagakis, Yannis; Pantic, Maja
2016-01-01
Tensor methods are gaining increasing traction in machine learning. However, there are scant to no resources available to perform tensor learning and decomposition in Python. To answer this need we developed TensorLy. TensorLy is a state of the art general purpose library for tensor learning. Writte
TensorLy: Tensor learning in Python
Kossaifi, Jean; Panagakis, Yannis; Pantic, Maja
2016-01-01
Tensor methods are gaining increasing traction in machine learning. However, there are scant to no resources available to perform tensor learning and decomposition in Python. To answer this need we developed TensorLy. TensorLy is a state of the art general purpose library for tensor learning. Writt
TensorLy: Tensor Learning in Python
Kossaifi, Jean; Panagakis, Yannis; Pantic, Maja
2016-01-01
Tensor methods are gaining increasing traction in machine learning. However, there are scant to no resources available to perform tensor learning and decomposition in Python. To answer this need we developed TensorLy. TensorLy is a state of the art general purpose library for tensor learning.
Convergence of scalar-tensor theories towards general relativity and primordial nucleosynthesis
Serna, A [Dept. Fisica y Computacion, Universidad Miguel Hernandez, E03202-Elche (Spain); Alimi, J-M [LAEC, CNRS-UMR 8631, Observatoire de Paris-Meudon, F92195-Meudon (France); Navarro, A [Dept. Fisica, Universidad de Murcia, E30071-Murcia (Spain)
2002-03-07
In this paper, we analyse the conditions for convergence towards general relativity of scalar-tensor gravity theories defined by an arbitrary coupling function {alpha} (in the Einstein frame). We show that, in general, the evolution of the scalar field ({phi}) is governed by two opposite mechanisms: an attraction mechanism which tends to drive scalar-tensor models towards Einstein's theory, and a repulsion mechanism which has the contrary effect. The attraction mechanism dominates the recent epochs of the universe evolution if, and only if, the scalar field and its derivative satisfy certain boundary conditions. Since these conditions for convergence towards general relativity depend on the particular scalar-tensor theory used to describe the universe evolution, the nucleosynthesis bounds on the present value of the coupling function, {alpha}{sub 0}, strongly differ from some theories to others. For example, in theories defined by {alpha} {proportional_to} |{phi}| analytical estimates lead to very stringent nucleosynthesis bounds on {alpha}{sub 0}({approx}<10{sup -19}). By contrast, in scalar-tensor theories defined by {alpha} {proportional_to} {phi} much larger limits on {alpha}{sub 0}({approx}<10{sup -7}) are found.
The Energy-Momentum Tensor for a Dissipative Fluid in General Relativity
Pimentel, Oscar M; Lora-Clavijo, F D
2016-01-01
Considering the growing interest of the astrophysicist community in the study of dissipative fluids with the aim of getting a more realistic description of the universe, we present in this paper a physical analysis of the energy-momentum tensor of a viscous fluid with heat flux. We introduce the general form of this tensor and, using the approximation of small velocity gradients, we relate the stresses of the fluid with the viscosity coefficients, the shear tensor and the expansion factor. Exploiting these relations, we can write the stresses in terms of the extrinsic curvature of the normal surface to the 4-velocity vector of the fluid, and we can also establish a connection between the perfect fluid and the symmetries of the spacetime. On the other hand, we calculate the energy conditions for a dissipative fluid through contractions of the energy-momentum tensor with the 4-velocity vector of an arbitrary observer. This method is interesting because it allows us to compute the conditions in a reasonable easy...
TensorLy: Tensor Learning in Python
Kossaifi, Jean; Panagakis, Yannis; Pantic, Maja
2016-01-01
Tensor methods are gaining increasing traction in machine learning. However, there are scant to no resources available to perform tensor learning and decomposition in Python. To answer this need we developed TensorLy. TensorLy is a state of the art general purpose library for tensor learning. Written in Python, it aims at following the same standard adopted by the main projects of the Python scientific community and fully integrating with these. It allows for fast and straightforward tensor d...
Detection of Crossing White Matter Fibers with High-Order Tensors and Rank-k Decompositions
Jiao, Fangxiang
2011-01-01
Fundamental to high angular resolution diffusion imaging (HARDI), is the estimation of a positive-semidefinite orientation distribution function (ODF) and extracting the diffusion properties (e.g., fiber directions). In this work we show that these two goals can be achieved efficiently by using homogeneous polynomials to represent the ODF in the spherical deconvolution approach, as was proposed in the Cartesian Tensor-ODF (CT-ODF) formulation. Based on this formulation we first suggest an estimation method for positive-semidefinite ODF by solving a linear programming problem that does not require special parameterization of the ODF. We also propose a rank-k tensor decomposition, known as CP decomposition, to extract the fibers information from the estimated ODF. We show that this decomposition is superior to the fiber direction estimation via ODF maxima detection as it enables one to reach the full fiber separation resolution of the estimation technique. We assess the accuracy of this new framework by applying it to synthetic and experimentally obtained HARDI data. © 2011 Springer-Verlag.
Loibl, Stefan; Schütz, Martin
2014-07-14
In this paper, we present theory and implementation of an efficient program for calculating magnetizabilities and rotational g tensors of closed-shell molecules at the level of local second-order Møller-Plesset perturbation theory (MP2) using London orbitals. Density fitting is employed to factorize the electron repulsion integrals with ordinary Gaussians as fitting functions. The presented program for the calculation of magnetizabilities and rotational g tensors is based on a previous implementation of NMR shielding tensors reported by S. Loibl and M. Schütz [J. Chem. Phys. 137, 084107 (2012)]. Extensive test calculations show (i) that the errors introduced by density fitting are negligible, and (ii) that the errors of the local approximation are still rather small, although larger than for nuclear magnetic resonance (NMR) shielding tensors. Electron correlation effects for magnetizabilities are tiny for most of the molecules considered here. MP2 appears to overestimate the correlation contribution of magnetizabilities such that it does not constitute an improvement over Hartree-Fock (when comparing to higher-order methods like CCSD(T)). For rotational g tensors the situation is different and MP2 provides a significant improvement in accuracy over Hartree-Fock. The computational performance of the new program was tested for two extended systems, the larger comprising about 2200 basis functions. It turns out that a magnetizability (or rotational g tensor) calculation takes about 1.5 times longer than a corresponding NMR shielding tensor calculation.
Estimations of Pareto-eigenvalues for Higher-order Tensors%高阶张量Pareto-特征值的估计
徐凤; 凌晨
2015-01-01
Eigenvalue complementarity problems of tensors have many practical applications, and have closely connection with high order homogeneous polynomial optimization which is NP-hard.In this paper,some estimation proprieties of Pareto-eigenvalues of high order tensors are studied.We also prove that all the Pareto-eigenvalues of symmetric strong M-tensor and monotone tensor are positive.%张量特征值互补问题有许多实际应用,它与一类高次齐次多项式优化关系密切,而后者是NP-难问题. 给出了高阶张量Pareto-特征值的若干估计性质,并证明了对称的强-M-张量及单调张量的Pareto-特征值均为正.
Domanov, Ignat; De Lathauwer, Lieven
2013-01-01
Canonical Polyadic Decomposition (CPD) of a higher-order tensor is decomposition in a minimal number of rank-1 tensors. We give an overview of existing results concerning uniqueness. We present new, relaxed, conditions that guarantee uniqueness of one factor matrix. These conditions involve Khatri-Rao products of compound matrices. We make links with existing results involving ranks and k-ranks of factor matrices. We give a shorter proof, based on properties of second compound matrices, of ex...
Fast Second-Order Orthogonal Tensor Subspace Analysis for Face Recognition
Yujian Zhou
2014-01-01
Full Text Available Tensor subspace analysis (TSA and discriminant TSA (DTSA are two effective two-sided projection methods for dimensionality reduction and feature extraction of face image matrices. However, they have two serious drawbacks. Firstly, TSA and DTSA iteratively compute the left and right projection matrices. At each iteration, two generalized eigenvalue problems are required to solve, which makes them inapplicable for high dimensional image data. Secondly, the metric structure of the facial image space cannot be preserved since the left and right projection matrices are not usually orthonormal. In this paper, we propose the orthogonal TSA (OTSA and orthogonal DTSA (ODTSA. In contrast to TSA and DTSA, two trace ratio optimization problems are required to be solved at each iteration. Thus, OTSA and ODTSA have much less computational cost than their nonorthogonal counterparts since the trace ratio optimization problem can be solved by the inexpensive Newton-Lanczos method. Experimental results show that the proposed methods achieve much higher recognition accuracy and have much lower training cost.
Fourth order deformed general relativity
Cuttell, Peter D
2014-01-01
Whenever the condition of anomaly freedom is imposed within the framework of effective approaches to loop quantum cosmology, one seems to conclude that a deformation of general covariance is required. Here, starting from a general deformation we regain an effective gravitational Lagrangian including terms up to fourth order in extrinsic curvature. We subsequently constrain the form of the corrections, and then investigate the conditions for the occurrence of a big bounce and the realisation of an inflationary era, in the presence of a perfect fluid or scalar field.
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.
Deriving Laws from Ordering Relations
Knuth, Kevin H.
2004-01-01
The effect of Richard T. Cox's contribution to probability theory was to generalize Boolean implication among logical statements to degrees of implication, which are manipulated using rules derived from consistency with Boolean algebra. These rules are known as the sum rule, the product rule and Bayes Theorem, and the measure resulting from this generalization is probability. In this paper, I will describe how Cox s technique can be further generalized to include other algebras and hence other problems in science and mathematics. The result is a methodology that can be used to generalize an algebra to a calculus by relying on consistency with order theory to derive the laws of the calculus. My goals are to clear up the mysteries as to why the same basic structure found in probability theory appears in other contexts, to better understand the foundations of probability theory, and to extend these ideas to other areas by developing new mathematics and new physics. The relevance of this methodology will be demonstrated using examples from probability theory, number theory, geometry, information theory, and quantum mechanics.
Antonov, N. V.; Kompaniets, M. V.; Lebedev, N. M.
2017-02-01
We consider the critical behavior of the O( n)-symmetric model of the ϕ 4 type with an antisymmetric tensor order parameter. According to a previous study of the one-loop approximation in the quantum field theory renormalization group, there is an IR-attractive fixed point in the model, and IR scaling with universal indices hence applies. Using a more specific analysis based on three-loop calculations of the renormalization-group functions and Borel conformal summation, we show that the IR behavior is in fact governed by another fixed point of the renormalization-group equations and the model therefore belongs to a different universality class than the one suggested by the simplest one-loop approximation. Nevertheless, the validity of the obtained results remains a subject for discussion.
Etingof, Pavel; Nikshych, Dmitri; Ostrik, Victor
2015-01-01
Is there a vector space whose dimension is the golden ratio? Of course not-the golden ratio is not an integer! But this can happen for generalizations of vector spaces-objects of a tensor category. The theory of tensor categories is a relatively new field of mathematics that generalizes the theory of group representations. It has deep connections with many other fields, including representation theory, Hopf algebras, operator algebras, low-dimensional topology (in particular, knot theory), homotopy theory, quantum mechanics and field theory, quantum computation, theory of motives, etc. This bo
Amore, Paolo; Fernandez, Francisco M; Rösler, Boris
2015-01-01
We apply second order finite difference to calculate the lowest eigenvalues of the Helmholtz equation, for complicated non-tensor domains in the plane, using different grids which sample exactly the border of the domain. We show that the results obtained applying Richardson and Pad\\'e-Richardson extrapolation to a set of finite difference eigenvalues corresponding to different grids allows to obtain extremely precise values. When possible we have assessed the precision of our extrapolations comparing them with the highly precise results obtained using the method of particular solutions. Our empirical findings suggest an asymptotic nature of the FD series. In all the cases studied, we are able to report numerical results which are more precise than those available in the literature.
Renormalization of an Abelian Tensor Group Field Theory: Solution at Leading Order
Lahoche, Vincent; Rivasseau, Vincent
2015-01-01
We study a just renormalizable tensorial group field theory of rank six with quartic melonic interactions and Abelian group U(1). We introduce the formalism of the intermediate field, which allows a precise characterization of the leading order Feynman graphs. We define the renormalization of the model, compute its (perturbative) renormalization group flow and write its expansion in terms of effective couplings. We then establish closed equations for the two point and four point functions at leading (melonic) order. Using the effective expansion and its uniform exponential bounds we prove that these equations admit a unique solution at small renormalized coupling.
Kobayashi, Tsutomu; Suyama, Teruaki
2012-01-01
We perform a fully relativistic analysis of odd-type linear perturbations around a static and spherically symmetric solution in the most general scalar-tensor theory with second-order field equations. It is shown that, as in the case of general relativity, the quadratic action for the perturbations reduces to the one having only a single dynamical variable, from which concise formulas for no-ghost and no-gradient instability conditions are derived. Our result is applicable to all the theories of gravity with an extra scalar degree of freedom. We demonstrate how the generic formulas can be applied to some particular examples such as the Brans-Dicke theory, $f(R)$ models, and Galileon gravity.
Banda Guzmán, V. M.; Kirchbach, M.
2016-09-01
A boson of spin j≥ 1 can be described in one of the possibilities within the Bargmann-Wigner framework by means of one sole differential equation of order twice the spin, which however is known to be inconsistent as it allows for non-local, ghost and acausally propagating solutions, all problems which are difficult to tackle. The other possibility is provided by the Fierz-Pauli framework which is based on the more comfortable to deal with second-order Klein-Gordon equation, but it needs to be supplemented by an auxiliary condition. Although the latter formalism avoids some of the pathologies of the high-order equations, it still remains plagued by some inconsistencies such as the acausal propagation of the wave fronts of the (classical) solutions within an electromagnetic environment. We here suggest a method alternative to the above two that combines their advantages while avoiding the related difficulties. Namely, we suggest one sole strictly D^{(j,0)oplus (0,j)} representation specific second-order differential equation, which is derivable from a Lagrangian and whose solutions do not violate causality. The equation under discussion presents itself as the product of the Klein-Gordon operator with a momentum-independent projector on Lorentz irreducible representation spaces constructed from one of the Casimir invariants of the spin-Lorentz group. The basis used is that of general tensor-spinors of rank 2 j.
Higher order terms in the inflaton potential and the lower bound on the tensor to scalar ratio r
Destri, C; Sánchez, N G
2009-01-01
The MCMC analysis of the CMB+LSS data in the context of the Ginsburg-Landau approach to inflation indicated that the fourth degree double--well inflaton potential best fits the present CMB and LSS data. This provided a lower bound for the ratio r of the tensor to scalar fluctuations and as most probable value r = 0.05, within reach of the forthcoming CMB observations. We systematically analyze here the effects of arbitrary higher order terms in the inflaton potential on the CMB observables: spectral index ns and ratio r. Furthermore, we compute in close form the inflaton potential dynamically generated when the inflaton field is a fermion condensate in the inflationary universe. This inflaton potential turns to belong to the Ginsburg-Landau class too. The theoretical values in the (ns,r) plane for all double well inflaton potentials in the Ginsburg-Landau approach (including the potential generated by fermions) turn to be inside a universal banana-shaped region B. The upper border of the banana-shaped region ...
Age-related changes of normal adult brain structure: analysed with diffusion tensor imaging
ZHANG Yun-ting; ZHANG Chun-yan; ZHANG Jing; LI Wei
2005-01-01
Background It is known that the brain structure changes with normal aging. The objective of this study was to quantify the anisotropy and average diffusion coefficient (DCavg) of the brain in normal adults to demonstrate the microstructure changes of brain with aging.Methods One hundred and six normal adults were examined with diffusion tensor imaging (DTI). The fractional anisotropy (FA), 1-volume ratio (1-VR), relative anisotropy (RA) and average diffusion coefficient (DCavg) of different anatomic sites of brain were measured, correlated with age and compared among three broad age groups.Results Except in lentiform nucleus, the anisotropy increased and DCavg decreased with aging. Both anisotropy and DCavg of lentiform nucleus increased with aging. The normal reference values of DTI parameters of normal Chinese adult in major anatomic sites were acquired. Conclusions DTI data obtained noninvasively can reflect the microstructural changes with aging. The normal reference values acquired can serve as reference standards in differentiation of brain white matter diseases.
Compressive sensing of sparse tensors.
Friedland, Shmuel; Li, Qun; Schonfeld, Dan
2014-10-01
Compressive sensing (CS) has triggered an enormous research activity since its first appearance. CS exploits the signal's sparsity or compressibility in a particular domain and integrates data compression and acquisition, thus allowing exact reconstruction through relatively few nonadaptive linear measurements. While conventional CS theory relies on data representation in the form of vectors, many data types in various applications, such as color imaging, video sequences, and multisensor networks, are intrinsically represented by higher order tensors. Application of CS to higher order data representation is typically performed by conversion of the data to very long vectors that must be measured using very large sampling matrices, thus imposing a huge computational and memory burden. In this paper, we propose generalized tensor compressive sensing (GTCS)-a unified framework for CS of higher order tensors, which preserves the intrinsic structure of tensor data with reduced computational complexity at reconstruction. GTCS offers an efficient means for representation of multidimensional data by providing simultaneous acquisition and compression from all tensor modes. In addition, we propound two reconstruction procedures, a serial method and a parallelizable method. We then compare the performance of the proposed method with Kronecker compressive sensing (KCS) and multiway compressive sensing (MWCS). We demonstrate experimentally that GTCS outperforms KCS and MWCS in terms of both reconstruction accuracy (within a range of compression ratios) and processing speed. The major disadvantage of our methods (and of MWCS as well) is that the compression ratios may be worse than that offered by KCS.
Wu, Xiongwu; Pickard, Frank C.; Brooks, Bernard R.
2016-10-01
Isotropic periodic sum (IPS) is a method to calculate long-range interactions based on the homogeneity of simulation systems. By using the isotropic periodic images of a local region to represent remote structures, long-range interactions become a function of the local conformation. This function is called the IPS potential; it folds long-ranged interactions into a short-ranged potential and can be calculated as efficiently as a cutoff method. It has been demonstrated that the IPS method produces consistent simulation results, including free energies, as the particle mesh Ewald (PME) method. By introducing the multipole homogeneous background approximation, this work derives multipole IPS potentials, abbreviated as IPSMm, with m being the maximum order of multipole interactions. To efficiently calculate the multipole interactions in Cartesian space, we propose a vector relation that calculates a multipole tensor as a dot product of a radial potential vector and a directional vector. Using model systems with charges, dipoles, and/or quadrupoles, with and without polarizability, we demonstrate that multipole interactions of order m can be described accurately with the multipole IPS potential of order 2 or m - 1, whichever is higher. Through simulations with the multipole IPS potentials, we examined energetic, structural, and dynamic properties of the model systems and demonstrated that the multipole IPS potentials produce very similar results as PME with a local region radius (cutoff distance) as small as 6 Å.
A systematic review of diffusion tensor imaging findings in sports-related concussion.
Gardner, Andrew; Kay-Lambkin, Frances; Stanwell, Peter; Donnelly, James; Williams, W Huw; Hiles, Alexandra; Schofield, Peter; Levi, Christopher; Jones, Derek K
2012-11-01
Sports-related concussion (SRC) is typically associated with functional, as opposed to structural, injury. The results of traditional structural neuroimaging techniques used to assess SRC tend to be normal in many athletes, and are only clinically helpful in ruling out a more serious injury. Diffusion tensor imaging (DTI) has increasingly been touted as a method offering greater clinical potential in mild traumatic brain injury (mTBI). Despite this, the utility of DTI as a clinical tool for diagnosing and managing SRC has received considerably less attention than it has in the general TBI research literature. The aim of this article is to conduct a systematic review of DTI in SRC, and to provide a focus and overview of research findings using this MRI technique in SRC. A systematic review of articles published in the English language, up to February 2012, was retrieved via PsycINFO(®), MEDLINE(®), EMBASE, SPORTDiscus(™), Scopus, Web of Science, and Informit; using the key search terms: diffusion tensor imaging, diffusion magnetic resonance imaging, diffusion weighted MRI, diffusion MRI, fractional anisotropy, tractography, apparent diffusion coefficient, magnetic resonance imaging, mild traumatic brain injury, mTBI, traumatic brain injury, concussion, sport, athletic and athlete. Observational, cohort, correlation, cross-sectional and longitudinal studies were all included in the current review. Results of the review found eight articles that met inclusion criteria, which included data on 214 athletes and 96 controls. Seven of eight studies reported some type of DTI abnormality, although the neuroanatomical sites involved varied. Although considerable methodological variations exist across studies, the current review suggests that DTI may possess adequate diagnostic sensitivity to detect SRC in affected athletes. Further longitudinal studies are required to demonstrate its discriminate validity and prognostic capacity within this field.
Kolecki, Joseph C.
2005-01-01
Tensor analysis is one of the more abstruse, even if one of the more useful, higher math subjects enjoined by students of physics and engineering. It is abstruse because of the intellectual gap that exists between where most physics and engineering mathematics leave off and where tensor analysis traditionally begins. It is useful because of its great generality, computational power, and compact, easy to use, notation. This paper bridges the intellectual gap. It is divided into three parts: algebra, calculus, and relativity. Algebra: In tensor analysis, coordinate independent quantities are sought for applications in physics and engineering. Coordinate independence means that the quantities have such coordinate transformations as to leave them invariant relative to a particular observer s coordinate system. Calculus: Non-zero base vector derivatives contribute terms to dynamical equations that correspond to pseudoaccelerations in accelerated coordinate systems and to curvature or gravity in relativity. These derivatives have a specific general form in tensor analysis. Relativity: Spacetime has an intrinsic geometry. Light is the tool for investigating that geometry. Since the observed geometry of spacetime cannot be made to match the classical geometry of Euclid, Einstein applied another more general geometry differential geometry. The merger of differential geometry and cosmology was accomplished in the theory of relativity. In relativity, gravity is equivalent to curvature.
Algebraically contractible topological tensor network states
Denny, S J; Jaksch, D; Clark, S R
2011-01-01
We adapt the bialgebra and Hopf relations to expose internal structure in the ground state of a Hamiltonian with $Z_2$ topological order. Its tensor network description allows for exact contraction through simple diagrammatic rewrite rules. The contraction property does not depend on specifics such as geometry, but rather originates from the non-trivial algebraic properties of the constituent tensors. We then generalise the resulting tensor network from a spin-half lattice to a class of exactly contractible states on spin-S degrees of freedom, yielding the most efficient tensor network description of finite Abelian lattice gauge theories. We gain a new perspective on these states as examples of two-dimensional quantum states with algebraically contractible tensor network representations. The introduction of local perturbations to the network is shown to reduce the von Neumann entropy of string-like regions, creating an unentangled sub-system within the bulk in a certain limit. We also show how perturbations l...
XU Dian-Yah
2000-01-01
Absorbing charged rotating (ACR) metric in de Sitter space and related energy-momentum tensor are derived.The ACR metric is very simple in advanced time coordinates. The ACR metric involves 8 independent parameters which are divided into two classes: (1) the mass M, charge Q, angular momentum per unit mass a, and cosmological constant A; (2) M/ v, 2M/ v2, Q/ v, and 2Q/ v2. The non-stationary part of the energy-momentum tensor is positive definite everywhere.
Bidimensional Relations for Reading Order Detection
Aiello, Marco; Smeulders, Arnold M.W.
2003-01-01
We use a propositional language of qualitative rectangle relations to detect the reading order from document images. Document encoding rules are introduced and, expressed in the propositional language of rectangles, are used to build a reading order detector for document images. Results of testing t
Bennett, Ilana J; Stark, Craig E L
2016-03-01
Pattern separation describes the orthogonalization of similar inputs into unique, non-overlapping representations. This computational process is thought to serve memory by reducing interference and to be mediated by the dentate gyrus of the hippocampus. Using ultra-high in-plane resolution diffusion tensor imaging (hrDTI) in older adults, we previously demonstrated that integrity of the perforant path, which provides input to the dentate gyrus from entorhinal cortex, was associated with mnemonic discrimination, a behavioral outcome designed to load on pattern separation. The current hrDTI study assessed the specificity of this perforant path integrity-mnemonic discrimination relationship relative to other cognitive constructs (identified using a factor analysis) and white matter tracts (hippocampal cingulum, fornix, corpus callosum) in 112 healthy adults (20-87 years). Results revealed age-related declines in integrity of the perforant path and other medial temporal lobe (MTL) tracts (hippocampal cingulum, fornix). Controlling for global effects of brain aging, perforant path integrity related only to the factor that captured mnemonic discrimination performance. Comparable integrity-mnemonic discrimination relationships were also observed for the hippocampal cingulum and fornix. Thus, whereas perforant path integrity specifically relates to mnemonic discrimination, mnemonic discrimination may be mediated by a broader MTL network.
Shifted power method for computing tensor eigenpairs.
Mayo, Jackson R.; Kolda, Tamara Gibson
2010-10-01
Recent work on eigenvalues and eigenvectors for tensors of order m {>=} 3 has been motivated by applications in blind source separation, magnetic resonance imaging, molecular conformation, and more. In this paper, we consider methods for computing real symmetric-tensor eigenpairs of the form Ax{sup m-1} = {lambda}x subject to {parallel}x{parallel} = 1, which is closely related to optimal rank-1 approximation of a symmetric tensor. Our contribution is a novel shifted symmetric higher-order power method (SS-HOPM), which we showis guaranteed to converge to a tensor eigenpair. SS-HOPM can be viewed as a generalization of the power iteration method for matrices or of the symmetric higher-order power method. Additionally, using fixed point analysis, we can characterize exactly which eigenpairs can and cannot be found by the method. Numerical examples are presented, including examples from an extension of the method to fnding complex eigenpairs.
Tourism versus spatial order: mutual relations
Meyer, Beata
2012-01-01
The relation between tourism and the spatial environment is characterized by mutual interaction. The proliferation of tourism and massive tourism development intensifies its impact on the spatial environment, yet the focus is usually placed on environmental degradation and the resulting distortion of spatial order. Concurrently, the significance of the spatial environment, and spatial order in particular, as one of the determinants of tourism development is understated. On a theoretical plane...
Beyond Special Relativity at second order
Carmona, J M; Relancio, J J
2016-01-01
The study of generic, non-linear, deformations of Special Relativity parametrized by a high-energy scale $M$, which was carried out at first order in $M$ in Phys.Rev. D86, 084032 (2012), is extended to second order. This can be done systematically through a ('generalized') change of variables from momentum variables that transform linearly. We discuss the different perspectives on the meaning of the change of variables, obtain the coefficients of modified composition laws and Lorentz transformations at second order, and work out how $\\kappa$-Poincar\\'e, the most commonly used example in the literature, is reproduced as a particular case of the generic framework exposed here.
Gravitational wave extraction in higher dimensional numerical relativity using the Weyl tensor
Cook, William G
2016-01-01
Gravitational waves are one of the most important diagnostic tools in the analysis of strong-gravity dynamics and have been turned into an observational channel with LIGO's detection of GW150914. Aside from their importance in astrophysics, black holes and compact matter distributions have also assumed a central role in many other branches of physics. These applications often involve spacetimes with $D>4$ dimensions where the calculation of gravitational waves is more involved than in the four dimensional case, but has now become possible thanks to substantial progress in the theoretical study of general relativity in $D>4$. Here, we develop a numerical implementation of the formalism by Godazgar and Reall (Ref.[1]) -- based on projections of the Weyl tensor analogous to the Newman-Penrose scalars -- that allows for the calculation of gravitational waves in higher dimensional spacetimes with rotational symmetry. We apply and test this method in black-hole head-on collisions from rest in $D=6$ spacetime dimens...
Diffusion tensor imaging differences relate to memory deficits in diffuse traumatic brain injury
Roig Teresa
2011-02-01
Full Text Available Abstract Background Memory is one of the most impaired functions after traumatic brain injury (TBI. We used diffusion tensor imaging (DTI to determine the structural basis of memory deficit. We correlated fractional anisotropy (FA of the fasciculi connecting the main cerebral regions that are involved in declarative and working memory functions. Methods Fifteen patients with severe and diffuse TBI and sixteen healthy controls matched by age and years of education were scanned. The neuropsychological assessment included: Letter-number sequencing test (LNS, 2-back task, digit span (forwards and backwards and the Rivermead profilet. DTI was analyzed by a tract-based spatial statics (TBSS approach. Results Whole brain DTI analysis showed a global decrease in FA values that correlated with the 2-back d-prime index, but not with the Rivermead profile. ROI analysis revealed positive correlations between working memory performance assessed by 2-back d-prime and superior longitudinal fasciculi, corpus callosum, arcuate fasciculi and fornix. Declarative memory assessed by the Rivermead profile scores correlated with the fornix and the corpus callosum. Conclusions Diffuse TBI is associated with a general decrease of white matter integrity. Nevertheless deficits in specific memory domains are related to different patterns of white matter damage.
Expansion Formulation of General Relativity: the Gauge Functions for Energy-Momentum Tensor
Beloushko, Konstantin; Karbanovski, Valeri
At present the one of the GR (General Relativity) basic problem remains a definition of the gravitation field (GF) energy. We shall analyze this content. As well known, the energy-momentum ``tensor'' (EMT) of GF was introduced by Einstein [1] with purpose of the SRT (Special Relativity Theory) generalization. It supposed also, that EMT of matter satisfy to the condition begin{equation} ⪉bel{GrindEQ__1_1_} T^{ik} _{;i} =0 (a semicolon denotes a covariant differentiation with respect to coordinates). In absence of GF the equation (ref{GrindEQ__1_1_}) reduces to a corresponding SRT expression begin{equation} ⪉bel{GrindEQ__1_2_} T^{ik} _{,i} =0 (a comma denotes a differentiation with respect to coordinates of space-time). Obviously, the ``conservation law'' (ref{GrindEQ__1_2_}) is not broken by transformation begin{equation} ⪉bel{GrindEQ__1_3_} T^{ik} to tilde{T}^{ik} =T^{ik} +h^{ikl} _{,l} , where for h(ikl) takes place a constrain begin{equation} ⪉bel{GrindEQ__1_4_} h^{ikl} =-h^{ilk} Later the given property has been used for a construction ``pseudo-tensor'' tau (ik) of ``pure'' GF [2, S 96] begin{equation} ⪉bel{GrindEQ__1_5_} -gleft(frac{c^{4} }{8pi G} left(R^{ik} -frac{1}{2} g^{ik} Rright)+tau ^{ik} right)=h^{ikl} _{,l} However such definition was a consequence of non-covariant transition from a reference system with condition g(ik) _{,l} =0 to an arbitrary frame. Therefore the Landau-Lifshitz pseudo-tensor has no physical contents and considered problem remains actual. ``The non-covariant character'' of GF energy was the reason for criticism of GR as Einstein's contemporaries [3, 4], as and during the subsequent period (see, for example, [5]). In [6] were analyzed the grounds of given problem, which are connected with a formulation indefiniteness of ``the conservation law'' in curved space-time. In [7] contends, that the gravitational energy in EMT can be separated only ``artificially'' by a choice of the certain coordinate system. In [8] is concluded
Cook, William G.; Sperhake, Ulrich
2017-02-01
Gravitational waves are one of the most important diagnostic tools in the analysis of strong-gravity dynamics and have been turned into an observational channel with LIGO’s detection of GW150914. Aside from their importance in astrophysics, black holes and compact matter distributions have also assumed a central role in many other branches of physics. These applications often involve spacetimes with D > 4 dimensions where the calculation of gravitational waves is more involved than in the four dimensional case, but has now become possible thanks to substantial progress in the theoretical study of general relativity in D > 4. Here, we develop a numerical implementation of the formalism by Godazgar and Reall [1]—based on projections of the Weyl tensor analogous to the Newman–Penrose scalars—that allows for the calculation of gravitational waves in higher dimensional spacetimes with rotational symmetry. We apply and test this method in black-hole head-on collisions from rest in D = 6 spacetime dimensions and find that a fraction (8.19+/- 0.05)× {{10}-4} of the Arnowitt–Deser–Misner mass is radiated away from the system, in excellent agreement with literature results based on the Kodama–Ishibashi perturbation technique. The method presented here complements the perturbative approach by automatically including contributions from all multipoles rather than computing the energy content of individual multipoles.
Introduction: interregional relations in the world order
Jordi Bacaria
2015-09-01
Full Text Available This article will analyse factors which, since the end of last century, have made interregional relations very important to understand the world geopolitical and economic order. Interregional relations are defined as those which pertain to relations between regions or between a given state and a given region, or within a megaregion. This evolution results from: the growing demand in the emerging economies and the interaction among them, a new framework of interregional economic relations, and the development of new commercial channels. Finally, this paper will introduce the different articled included in this issue.
REGULAR RELATIONS AND MONOTONE NORMAL ORDERED SPACES
XU XIAOQUAN; LIU YINGMING
2004-01-01
In this paper the classical theorem of Zareckii about regular relations is generalized and an intrinsic characterization of regularity is obtained. Based on the generalized Zareckii theorem and the intrinsic characterization of regularity, the authors give a characterization of monotone normality of ordered spaces. A new proof of the UrysohnNachbin lemma is presented which is quite different from the classical one.
Baker, Ben; Stachnik, Joshua; Rozhkov, Mikhail
2017-04-01
International Data Center is required to conduct expert technical analysis and special studies to improve event parameters and assist State Parties in identifying the source of specific event according to the protocol to the Protocol to the Comprehensive Nuclear Test Ban Treaty. Determination of seismic event source mechanism and its depth is closely related to these tasks. It is typically done through a strategic linearized inversion of the waveforms for a complete or subset of source parameters, or similarly defined grid search through precomputed Greens Functions created for particular source models. In this presentation we demonstrate preliminary results obtained with the latter approach from an improved software design. In this development we tried to be compliant with different modes of CTBT monitoring regime and cover wide range of source-receiver distances (regional to teleseismic), resolve shallow source depths, provide full moment tensor solution based on body and surface waves recordings, be fast to satisfy both on-demand studies and automatic processing and properly incorporate observed waveforms and any uncertainties a priori as well as accurately estimate posteriori uncertainties. Posterior distributions of moment tensor parameters show narrow peaks where a significant number of reliable surface wave observations are available. For earthquake examples, fault orientation (strike, dip, and rake) posterior distributions also provide results consistent with published catalogues. Inclusion of observations on horizontal components will provide further constraints. In addition, the calculation of teleseismic P wave Green's Functions are improved through prior analysis to determine an appropriate attenuation parameter for each source-receiver path. Implemented HDF5 based Green's Functions pre-packaging allows much greater flexibility in utilizing different software packages and methods for computation. Further additions will have the rapid use of Instaseis
De Felice, Antonio, E-mail: antoniod@nu.ac.th [Department of Physics, Faculty of Science, Tokyo University of Science, 1-3, Kagurazaka, Shinjuku-ku, Tokyo 162-8601 (Japan); TPTP and NEP, The Institute for Fundamental Study, Naresuan University, Phitsanulok, 65000 (Thailand); Thailand Center of Excellence in Physics, Ministry of Education, Bangkok 10400 (Thailand); Kobayashi, Tsutomu [Hakubi Center, Kyoto University, Kyoto 606-8302 (Japan); Department of Physics, Kyoto University, Kyoto 606-8502 (Japan); Tsujikawa, Shinji [Department of Physics, Faculty of Science, Tokyo University of Science, 1-3, Kagurazaka, Shinjuku-ku, Tokyo 162-8601 (Japan)
2011-12-06
In the Horndeski's most general scalar-tensor theories the equations of scalar density perturbations are derived in the presence of non-relativistic matter minimally coupled to gravity. Under a quasi-static approximation on sub-horizon scales we obtain the effective gravitational coupling G{sub eff} associated with the growth rate of matter perturbations as well as the effective gravitational potential {Phi}{sub eff} relevant to the deviation of light rays. We then apply our formulas to a number of modified gravitational models of dark energy - such as those based on f(R) theories, Brans-Dicke theories, kinetic gravity braidings, covariant Galileons, and field derivative couplings with the Einstein tensor. Our results are useful to test the large-distance modification of gravity from the future high-precision observations of large-scale structure, weak lensing, and cosmic microwave background.
De Felice, Antonio; Tsujikawa, Shinji
2011-01-01
In the Horndeski's most general scalar-tensor theories the equations of scalar density perturbations are derived in the presence of non-relativistic matter minimally coupled to gravity. Under a quasi-static approximation on sub-horizon scales we obtain the effective gravitational coupling $G_{eff}$ associated with the growth rate of matter perturbations as well as the effective gravitational potential $\\Phi_{eff}$ relevant to the deviation of light rays. We then apply our formulas to a number of modified gravitational models of dark energy--such as those based on f(R) theories, Brans-Dicke theories, kinetic gravity braidings, covariant Galileons, and field derivative couplings with the Einstein tensor. Our results are useful to test the large-distance modification of gravity from the future high-precision observations of large-scale structure, weak lensing, and cosmic microwave background.
Boundary-bulk relation in topological orders
Liang Kong
2017-09-01
Full Text Available In this paper, we study the relation between an anomaly-free n+1D topological order, which are often called n+1D topological order in physics literature, and its nD gapped boundary phases. We argue that the n+1D bulk anomaly-free topological order for a given nD gapped boundary phase is unique. This uniqueness defines the notion of the “bulk” for a given gapped boundary phase. In this paper, we show that the n+1D “bulk” phase is given by the “center” of the nD boundary phase. In other words, the geometric notion of the “bulk” corresponds precisely to the algebraic notion of the “center”. We achieve this by first introducing the notion of a morphism between two (potentially anomalous topological orders of the same dimension, then proving that the notion of the “bulk” satisfies the same universal property as that of the “center” of an algebra in mathematics, i.e. “bulk = center”. The entire argument does not require us to know the precise mathematical description of a (potentially anomalous topological order. This result leads to concrete physical predictions.
Linzer, LM
2005-04-01
Full Text Available The primary objective of this study was to develop a robust MTI method to estimate the moment tensors of clusters of seismic events recorded in the underground environment. To achieve this, three 'hybrid' MTI methods were developed by the author...
An Improved Method for Seismic Event Depth and Moment Tensor Determination: CTBT Related Application
Stachnik, J.; Rozhkov, M.; Baker, B.
2016-12-01
According to the Protocol to CTBT, International Data Center is required to conduct expert technical analysis and special studies to improve event parameters and assist State Parties in identifying the source of specific event. Determination of seismic event source mechanism and its depth is a part of these tasks. It is typically done through a strategic linearized inversion of the waveforms for a complete or subset of source parameters, or similarly defined grid search through precomputed Greens Functions created for particular source models. We show preliminary results using the latter approach from an improved software design and applied on a moderately powered computer. In this development we tried to be compliant with different modes of CTBT monitoring regime and cover wide range of source-receiver distances (regional to teleseismic), resolve shallow source depths, provide full moment tensor solution based on body and surface waves recordings, be fast to satisfy both on-demand studies and automatic processing and properly incorporate observed waveforms and any uncertainties a priori as well as accurately estimate posteriori uncertainties. Implemented HDF5 based Green's Functions pre-packaging allows much greater flexibility in utilizing different software packages and methods for computation. Further additions will have the rapid use of Instaseis/AXISEM full waveform synthetics added to a pre-computed GF archive. Along with traditional post processing analysis of waveform misfits through several objective functions and variance reduction, we follow a probabilistic approach to assess the robustness of moment tensor solution. In a course of this project full moment tensor and depth estimates are determined for DPRK 2009, 2013 and 2016 events and shallow earthquakes using a new implementation of waveform fitting of teleseismic P waves. A full grid search over the entire moment tensor space is used to appropriately sample all possible solutions. A recent method by
Age-related changes of the corticospinal tract in the human brain A diffusion tensor imaging study
Sung Ho Jang; Sang-Hyun Cho; Mi Young Lee; Yong Hyun Kwon; Min Cheul Chang
2011-01-01
The corticospinal tract (CST) is one of the most important neural tracts for motor function in the human brain. Little is known about age-related changes of the CST. In this study, we tried to evaluate age-related changes of the CST using diffusion tensor imaging in 60 healthy subjects. The diffusion tensor imaging result revealed that the tract number and fractional anisotropy value were decreased, and the apparent diffusion coefficient (ADC) value was increased with aging. The distribution showed a semilog pattern for tract number, fractional anisotropy and ADC of the CST, and the pattern of each graph was near-linear. When compared with the diffusion tensor imaging parameters of subjects in the 20 s age group, tract number and fractional anisotropy values were significantly decreased in the 50 s–70 s age groups. Likewise, the ADC value was significantly higher in the 50 s–70 s age groups. The CST in the brain of normal subjects degenerated continuously from the 20 s to the 70 s, with a near-linear pattern, and degeneration of the CST began to manifest significantly in the subjects in their 50 s, compared with the subjects in their 20 s.
Age-related changes of the diffusion tensor imaging parameters of the normal cervical spinal cord
Wang, Kun, E-mail: medsciwangkun@126.com [Orthopedics Department, Changhai Hospital Affiliated to Second Military Medical University, Shanghai (China); Song, Qingxin; Zhang, Fan; Chen, Zhi; Hou, Canglong; Tang, Yixing [Orthopedics Department, Changhai Hospital Affiliated to Second Military Medical University, Shanghai (China); Chen, Shiyue [Radiology Department, Changhai Hospital Affiliated to Second Military Medical University, Shanghai (China); Hao, Qiang, E-mail: haoqiang@189.cn [Radiology Department, Changhai Hospital Affiliated to Second Military Medical University, Shanghai (China); Shen, Hongxing, E-mail: shenhxgk@126.com [Orthopedics Department, Changhai Hospital Affiliated to Second Military Medical University, Shanghai (China)
2014-12-15
Highlights: • It is essential to determine the DTI parameters in the whole CSC. • To analyze DTI parameters in all intervertebral space levels of the CSC. • To study the impact of age on these parameters in healthy Chinese subjects. • Provide better insights in factors that could bias the diagnosis of CSC pathologies. - Abstract: Background: The diffusion tensor imaging (DTI) parameters of the cervical spinal cord (CSC) changes with age. However, previous studies only examined specific CSC areas. Objectives: To analyze the DTI parameters in all intervertebral space levels of the whole normal CSC and to study the impact of age on these parameters in a Chinese population. Methods: Thirty-six healthy subjects aged 20–77 years were recruited. DTI parameters were calculated for gray matter (GM) and white matter (WM) funiculi in all the CSC intervertebral spaces (C1/2-C6/7). Age-related changes of DTI parameters were analyzed for the GM and WM funiculi. Results: Fractional anisotropy (FA) and mean diffusivity (MD) were lower in GM than in WM. MD and FA values were lower in the WM in the lower CSC compared with the upper CSC (all P < 0.05), but no difference was observed in GM. In ventral funiculi, MD increased with age, while FA decreased (all P < 0.001). In lateral and dorsal funiculi, MD and FA decreased with age (all P < 0.001). In GM, MD and FA decreased with age (all P < 0.001). Significant age-related changes were observed in FA and MD from GM and WM funiculi. FA was correlated with age in all funiculi (ventral: r = −0.733; lateral: r = −0.468; dorsal: r = −0.607; GM: r = −0.724; all P < 0.01). Conclusion: Important changes in MD and FA were observed with advancing age at all levels of CSC in Chinese patients. DTI parameters may be useful to assess CSC pathology, but the influence of age and segments need to be taken into account in diagnosis.
Nakamura, Kouji
2008-01-01
Some formulae for the perturbations of the matter fields are summarized within the framework of the second-order gauge-invariant cosmological perturbation theory in a four dimensional homogeneous isotropic universe, which is developed in the papers [K. Nakamura, Prog. Theor. Phys. {\\bf 117} (2005), 17.]. We derive the formulae for the perturbations of the energy momentum tensors and equations of motion in the cases of a perfect fluid, an imperfect fluid, and a signle scalar field, and show that all equations are derived in terms of gauge-invariant variables without any gauge fixing.
Mantica, Carlo A
2012-01-01
The algebraic condition of Riemann compatibility for symmetric tensors generalizes the differential Codazzi condition, but preserves much of the geometric content. The compatibility condition can be extended to other curvature tensors. This paper is about Weyl compatible tensors and vectors. In particular it is shown that the existence of a Weyl compatible vector implies the Weyl tensor to be algebraically special, and it is a necessary and sufficient condition for the magnetic part to vanish. Some theorems (Derdzinski and Shen, Hall) are extended to the broader hypothesis of Weyl or Riemann compatibility. Weyl compatibility includes conditions that were investigated in the literature of general relativity (as McIntosh et al.). Hypersurfaces of pseudo Euclidean spaces provide a simple example of Weyl compatible Ricci tensor.
Bosnjak, Gary
2016-01-01
In this paper we construct a new factorized representation of the $R$-matrix related to the affine algebra $U_{q}(\\widehat{sl_{n}})$ for symmetric tensor representations with arbitrary weights. Using the 3D approach we obtain explicit formulas for the matrix elements of the $R$-matrix and give a simple proof that a "twisted" $R$-matrix is stochastic. We also discuss symmetries of the $R$-matrix, its degenerations and compare our formulas with other results available in the literature.
Staykov, Kalin V; Yazadjiev, Stoytcho S
2016-01-01
We are investigating universal relations between different normalisations of the moment of inertia and the compactness of neutron and strange stars. Slowly rotating as well as rapidly rotating models are studied in General Relativity, $\\mathcal{R}^2$ gravity and scalar--tensor theories of gravity. Moment of inertia -- compactness relations are examined for different normalisations of the moment of inertia. It is shown that for all studied cases the deviations from EOS universality are small for the examined equations of state. It turns out that in some of the cases the examined relations are also theory independent to a good extend. Universality in relations between the mass and the moment of inertia for some quasi-stable models is also investigated.
Algebraically contractible topological tensor network states
Denny, S J; Jaksch, D; Clark, S R [Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU (United Kingdom); Biamonte, J D, E-mail: s.denny1@physics.ox.ac.uk [Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543 (Singapore)
2012-01-13
We adapt the bialgebra and Hopf relations to expose internal structure in the ground state of a Hamiltonian with Z{sub 2} topological order. Its tensor network description allows for exact contraction through simple diagrammatic rewrite rules. The contraction property does not depend on specifics such as geometry, but rather originates from the non-trivial algebraic properties of the constituent tensors. We then generalise the resulting tensor network from a spin-1/2 lattice to a class of exactly contractible states on spin-S degrees of freedom, yielding the most efficient tensor network description of finite Abelian lattice gauge theories. We gain a new perspective on these states as examples of two-dimensional quantum states with algebraically contractible tensor network representations. The introduction of local perturbations to the network is shown to reduce the von Neumann entropy of string-like regions, creating an unentangled sub-system within the bulk in a certain limit. We also show how local perturbations induce finite-range correlations in this system. This class of tensor networks is readily translated onto any lattice, and we differentiate between the physical consequences of bipartite and non-bipartite lattices on the properties of the corresponding quantum states. We explicitly show this on the hexagonal, square, kagome and triangular lattices. (paper)
Tensors and their applications
Islam, Nazrul
2006-01-01
About the Book: The book is written is in easy-to-read style with corresponding examples. The main aim of this book is to precisely explain the fundamentals of Tensors and their applications to Mechanics, Elasticity, Theory of Relativity, Electromagnetic, Riemannian Geometry and many other disciplines of science and engineering, in a lucid manner. The text has been explained section wise, every concept has been narrated in the form of definition, examples and questions related to the concept taught. The overall package of the book is highly useful and interesting for the people associated with the field. Contents: Preliminaries Tensor Algebra Metric Tensor and Riemannian Metric Christoffel`s Symbols and Covariant Differentiation Riemann-Christoffel Tensor The e-Systems and the Generalized Krönecker Deltas Geometry Analytical Mechanics Curvature of a Curve, Geodesic Parallelism of Vectors Ricci`s Coefficients of Rotation and Congruence Hyper Surfaces
OPERATOR NORM INEQUALITIES BETWEEN TENSOR UNFOLDINGS ON THE PARTITION LATTICE.
Wang, Miaoyan; Duc, Khanh Dao; Fischer, Jonathan; Song, Yun S
2017-05-01
Interest in higher-order tensors has recently surged in data-intensive fields, with a wide range of applications including image processing, blind source separation, community detection, and feature extraction. A common paradigm in tensor-related algorithms advocates unfolding (or flattening) the tensor into a matrix and applying classical methods developed for matrices. Despite the popularity of such techniques, how the functional properties of a tensor changes upon unfolding is currently not well understood. In contrast to the body of existing work which has focused almost exclusively on matricizations, we here consider all possible unfoldings of an order-k tensor, which are in one-to-one correspondence with the set of partitions of {1, …, k}. We derive general inequalities between the l(p) -norms of arbitrary unfoldings defined on the partition lattice. In particular, we demonstrate how the spectral norm (p = 2) of a tensor is bounded by that of its unfoldings, and obtain an improved upper bound on the ratio of the Frobenius norm to the spectral norm of an arbitrary tensor. For specially-structured tensors satisfying a generalized definition of orthogonal decomposability, we prove that the spectral norm remains invariant under specific subsets of unfolding operations.
Link prediction via generalized coupled tensor factorisation
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....
Chung, Daniel J H
2016-01-01
We reformulate gauge theories in analogy with the vierbein formalism of general relativity. More specifically, we reformulate gauge theories such that their gauge dynamical degrees of freedom are local fields that transform linearly under the dual representation of the charged matter field. These local fields, which naively have the interpretation of non-local operators similar to Wilson lines, satisfy constraint equations. A set of basis tensor fields are used to solve these constraint equations, and their field theory is constructed. A new local symmetry in terms of the basis tensor fields is used to make this field theory local and maintain a Hamiltonian that is bounded from below. The field theory of the basis tensor fields is what we call the basis tensor gauge theory.
Busche, M J
2000-08-11
This document describes the software developed for use in calculating K, the 4th order parameter tensor used in ALE3D's anisotropic plasticity model. The multi-scale modeling method developed for this calculation begins with orientation imaging microscopy (OIM) data. The program OIMA3D characterizes the sizes and crystal orientation of the grains found in this data and then determines element orientations for a representative 3D mesh. A shell script, MAKEJOBS, then creates the necessary files to run six ALE3D simulations using this mesh. The results of these simulations are then read by SVD{_}K, a Matlab script, and K is calculated from this information.
Gurau, Razvan
2017-01-01
Written by the creator of the modern theory of random tensors, this book is the first self-contained introductory text to this rapidly developing theory. Starting from notions familiar to the average researcher or PhD student in mathematical or theoretical physics, the book presents in detail the theory and its applications to physics. The recent detections of the Higgs boson at the LHC and gravitational waves at LIGO mark new milestones in Physics confirming long standing predictions of Quantum Field Theory and General Relativity. These two experimental results only reinforce today the need to find an underlying common framework of the two: the elusive theory of Quantum Gravity. Over the past thirty years, several alternatives have been proposed as theories of Quantum Gravity, chief among them String Theory. While these theories are yet to be tested experimentally, key lessons have already been learned. Whatever the theory of Quantum Gravity may be, it must incorporate random geometry in one form or another....
48 CFR 2413.505 - Purchase order and related forms.
2010-10-01
... 48 Federal Acquisition Regulations System 6 2010-10-01 2010-10-01 true Purchase order and related... DEVELOPMENT CONTRACTING METHODS AND CONTRACTING TYPES SIMPLIFIED ACQUISITION PROCEDURES Purchase Orders 2413.505 Purchase order and related forms....
Testing gravity theories using tensor perturbations
Lin, Weikang; Ishak-Boushaki, Mustapha B.
2017-01-01
Primordial gravitational waves constitute a promising probe of the very early universe physics and the laws of gravity. We study the changes to tensor-mode perturbations that can arise in various modified gravity theories. These include a modified friction and a nonstandard dispersion relation. We introduce a physically motivated parametrization of these effects and use current data to obtain excluded parameter spaces. Taking into account the foreground subtraction, we then perform a forecast analysis focusing on the tensor-mode modified-gravity parameters as constrained by future experiments COrE, Stage-IV and PIXIE. For the tensor-to-scalar ratio r=0.01, we find the minimum detectible modified-gravity effects. In particular, the minimum detectable graviton mass is about 7.8˜9.7×10-33 eV, which is of the same order of magnitude as the graviton mass that allows massive gravity to produce late-time cosmic acceleration. Finally, we study the tensor-mode perturbations in modified gravity during inflation. We find that, the tensor spectral index would be additionally related to the friction parameter ν0 by nT=-3ν0-r/8. In some cases, the future experiments will be able to distinguish this relation from the standard one. In sum, primordial gravitational waves provide a complementary avenue to test gravity theories.
Hu, Yonggang; Wu, Yi; 10.3150/10-BEJ317
2012-01-01
The conventional definition of a depth function is vector-based. In this paper, a novel projection depth (PD) technique directly based on tensors, such as matrices, is instead proposed. Tensor projection depth (TPD) is still an ideal depth function and its computation can be achieved through the iteration of PD. Furthermore, we also discuss the cases for sparse samples and higher order tensors. Experimental results in data classification with the two projection depths show that TPD performs much better than PD for data with a natural tensor form, and even when the data have a natural vector form, TPD appears to perform no worse than PD.
Natalia K. Prykarpatska
2005-01-01
Full Text Available The geometric structure of characteristic surfaces related with partial differential equations of first and higher orders is studied making use the vector field technique on hypersurfaces. It is shown, that corresponding characteristics are defined uniquely up to some smooth tensor fields, thereby supplying additional information about the suitable set of their solutions. In particular, it may be very useful for studying asymptotic properties of solutions to our partial differential equations under some boundary conditions.
Matsueda, Hiroaki; Hashizume, Yoichiro
2012-01-01
A tensor network formalism of thermofield dynamics is introduced. The formalism relates the original Hilbert space with its tilde space by a product of two copies of a tensor network. Then, their interface becomes an event horizon, and the logarithm of the tensor rank corresponds to the black hole entropy. Eventually, multiscale entanglement renormalization anzats (MERA) reproduces an AdS black hole at finite temperature. Our finding shows rich functionalities of MERA as efficient graphical representation of AdS/CFT correspondence.
Primary Blast Traumatic Brain Injury in the Rat: Relating Diffusion Tensor Imaging and Behavior
Matthew D Budde
2013-10-01
Full Text Available The incidence of traumatic brain injury (TBI among military personnel is at its highest point in U.S. history. Experimental animal models of blast have provided a wealth of insight into blast injury. The mechanisms of neurotrauma caused by blast, however, are still under debate. Specifically, it is unclear whether the blast shockwave in the absence of head motion is sufficient to induce brain trauma. In this study, the consequences of blast injury were investigated in a rat model of primary blast TBI. Animals were exposed to blast shockwaves with peak overpressures of either 100 or 450 kPa and subsequently underwent a battery of behavioral tests. Diffusion tensor imaging (DTI, a promising method to detect blast injury in humans, was performed on fixed brains to detect and visualize the spatial dependence of blast injury. Blast TBI caused significant deficits in memory function as evidenced by the Morris Water Maze, but limited emotional deficits as evidenced by the Open Field Test and Elevated Plus Maze. Fractional anisotropy (FA, a metric derived from DTI, revealed significant brain abnormalities in blast-exposed animals. A significant relationship between memory deficits and brain microstructure was evident in the hippocampus, consistent with its role in memory function. The results provide fundamental insight into the neurological consequences of blast TBI, including the evolution of injury during the sub-acute phase and the spatially dependent pattern of injury. The relationship between memory dysfunction and microstructural brain abnormalities may provide insight into the persistent cognitive difficulties experienced by soldiers exposed to blast neurotrauma and may be important to guide therapeutic and rehabilitative efforts.
The atomistic representation of first strain-gradient elastic tensors
Admal, Nikhil Chandra; Marian, Jaime; Po, Giacomo
2017-02-01
We derive the atomistic representations of the elastic tensors appearing in the linearized theory of first strain-gradient elasticity for an arbitrary multi-lattice. In addition to the classical second-Piola) stress and elastic moduli tensors, these include the rank-three double-stress tensor, the rank-five tensor of mixed elastic moduli, and the rank-six tensor of strain-gradient elastic moduli. The atomistic representations are closed-form analytical expressions in terms of the first and second derivatives of the interatomic potential with respect to interatomic distances, and dyadic products of relative atomic positions. Moreover, all expressions are local, in the sense that they depend only on the atomic neighborhood of a lattice site. Our results emanate from the condition of energetic equivalence between continuum and atomistic representations of a crystal, when the kinematics of the latter is governed by the Cauchy-Born rule. Using the derived expressions, we prove that the odd-order tensors vanish if the lattice basis admits central-symmetry. The analytical expressions are implemented as a KIM compliant algorithm to compute the strain gradient elastic tensors for various materials. Numerical results are presented to compare representative interatomic potentials used in the literature for cubic crystals, including simple lattices (fcc Al and Cu and bcc Fe and W) and multi-lattices (diamond-cubic Si). We observe that central potentials exhibit generalized Cauchy relations for the rank-six tensor of strain-gradient elastic moduli. In addition, this tensor is found to be indefinite for many potentials. We discuss the relationship between indefiniteness and material stability. Finally, the atomistic representations are specialized to central potentials in simple lattices. These expressions are used with analytical potentials to study the sensitivity of the elastic tensors to the choice of the cutoff radius.
Tuer, Adam E; Akens, Margarete K; Krouglov, Serguei; Sandkuijl, Daaf; Wilson, Brian C; Whyne, Cari M; Barzda, Virginijus
2012-11-21
The second-order nonlinear polarization properties of fibrillar collagen in various rat tissues (vertebrae, tibia, tail tendon, dermis, and cornea) are investigated with polarization-dependent second-harmonic generation (P-SHG) microscopy. Three parameters are extracted: the second-order susceptibility ratio, R = [Formula: see text] ; a measure of the fibril distribution asymmetry, |A|; and the weighted-average fibril orientation, . A hierarchical organizational model of fibrillar collagen is developed to interpret the second-harmonic generation polarization properties. Highlights of the model include: collagen type (e.g., type-I, type-II), fibril internal structure (e.g., straight, constant-tilt), and fibril architecture (e.g., parallel fibers, intertwined, lamellae). Quantifiable differences in internal structure and architecture of the fibrils are observed. Occurrence histograms of R and |A| distinguished parallel from nonparallel fibril distributions. Parallel distributions possessed low parameter values and variability, whereas nonparallel distributions displayed an increase in values and variability. From the P-SHG parameters of vertebrae tissue, a three-dimensional reconstruction of lamellae of intervertebral disk is presented.
Tensor norms and operator ideals
Defant, A; Floret, K
1992-01-01
The three chapters of this book are entitled Basic Concepts, Tensor Norms, and Special Topics. The first may serve as part of an introductory course in Functional Analysis since it shows the powerful use of the projective and injective tensor norms, as well as the basics of the theory of operator ideals. The second chapter is the main part of the book: it presents the theory of tensor norms as designed by Grothendieck in the Resumé and deals with the relation between tensor norms and operator ideals. The last chapter deals with special questions. Each section is accompanied by a series of exer
Symmetric tensor decomposition
Brachat, Jerome; Mourrain, Bernard; Tsigaridas, Elias
2009-01-01
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 total degree d as a sum of powers of linear forms (Waring's problem), incidence properties on secant varieties of the Veronese Variety and the representation of linear forms as a linear combination of evaluations at distinct points. Then we reformulate Sylvester's approach from the dual point of view. Exploiting this duality, we propose necessary and sufficient conditions for the existence of such a decomposition of a given rank, using the properties of Hankel (and quasi-Hankel) matrices, derived from multivariate polynomials and normal form computations. This leads to the resolution of polynomial equations of small degree in non-generic cases. We propose a new algorithm for symmetric tensor decomposition, based on th...
Kobayashi, Tsutomu; Suyama, Teruaki
2014-01-01
We perform a fully relativistic analysis of even-parity linear perturbations around a static and spherically symmetric solution in the most general scalar-tensor theory with second-order field equations. This paper is a sequel to Kobayashi {\\em et al.} (2012), in which the linear perturbation analysis for the odd-parity modes is presented. Expanding the Horndeski action to second order in perturbations and eliminating auxiliary variables, we derive the quadratic action for even-parity perturbations written solely in terms of two dynamical variables. The two perturbations can be interpreted as the gravitational and scalar waves. Correspondingly, we obtain two conditions to evade ghosts and two conditions for the absence of gradient instabilities. Only one in each pair of conditions yields a new stability criterion, as the conditions derived from the stability of the gravitational-wave degree of freedom coincide with those in the odd-parity sector. Similarly, the propagation speed of one of the two modes is the...
Cho, C.; Shin, J. S.; Kim, G.
2016-12-01
The fourth nuclear explosion testing in North Korea was executed in January 6, 2006. This event was located near the previous. The master event method and double difference method(Waldhauser and Ellsworth, 2000) were used to improve the relative location of the events accurately. The master event method with searching for optimal grid was revised. Two results show the very similar locations. First arrival times were picked with cross-correlation method for data of stations surrounding the event location. The distance from the third event to the fourth is about 0.88 km with azimuth 352 356o. Depths from sea level of the events are similar. The fourth location was guessed under the higher elevation of the Mantap mountain. Comparison between cross-correlation of the waveforms of the events show that the value of cross-correlation with the second and the third is higher than that of cross-correlation with the third and the fourth. The results of moment tensor inversion for the events were acquired with the modified TDMT(Minson and Dreger, 2008; Cho, 2015) with frequency band of 0.04 0.08 Hz. The results show the typical characteristics of explosion in T-k plot. The moment magnitude of the second, the third, fourth in the same depth 0.7 km is about 4.4, 4.7, 4.5 respectively. The fourth event has higher amplitude of the vertical component than the others. The third showed the highest amplitude of tangential component among the events. But the real data showed the tangential component. It may be caused by the tectonic stress, topography effect, inhomogeneous structure near source or anomalous chemical effect. The fourth has lower tangential component. This may mean that the depth from the surface was deeper. Moment tensor inversion with 3D viscoelastic FDM was applied with 3D velocity structure derived from Bayesian hierarchical method(Rhie, et al, 2015).
48 CFR 1513.505 - Purchase order and related forms.
2010-10-01
... 48 Federal Acquisition Regulations System 6 2010-10-01 2010-10-01 true Purchase order and related... CONTRACTING METHODS AND CONTRACT TYPES SIMPLIFIED ACQUISITION PROCEDURES Purchase Orders 1513.505 Purchase order and related forms. Contracting Officers may use the EPA Form 1900-8, Procurement Request/Order,...
A preliminary report on the development of MATLAB tensor classes for fast algorithm prototyping.
Bader, Brett William; Kolda, Tamara Gibson (Sandia National Laboratories, Livermore, CA)
2004-07-01
We describe three MATLAB classes for manipulating tensors in order to allow fast algorithm prototyping. A tensor is a multidimensional or N-way array. We present a tensor class for manipulating tensors which allows for tensor multiplication and 'matricization.' We have further added two classes for representing tensors in decomposed format: cp{_}tensor and tucker{_}tensor. We demonstrate the use of these classes by implementing several algorithms that have appeared in the literature.
Loibl, Stefan; Schütz, Martin
2012-08-28
An efficient method for the calculation of nuclear magnetic resonance (NMR) shielding tensors is presented, which treats electron correlation at the level of second-order Mo̸ller-Plesset perturbation theory. It uses spatially localized functions to span occupied and virtual molecular orbital spaces, respectively, which are expanded in a basis of gauge including atomic orbitals (GIAOs or London atomic orbitals). Doubly excited determinants are restricted to local subsets of the virtual space and pair energies with an interorbital distance beyond a certain threshold are omitted. Furthermore, density fitting is employed to factorize the electron repulsion integrals. Ordinary Gaussians are employed as fitting functions. It is shown that the errors in the resulting NMR shielding constant, introduced (i) by the local approximation and (ii) by density fitting, are very small or even negligible. The capabilities of the new program are demonstrated by calculations on some extended molecular systems, such as the cyclobutane pyrimidine dimer photolesion with adjacent nucleobases in the native intrahelical DNA double strand (ATTA sequence). Systems of that size were not accessible to correlated ab initio calculations of NMR spectra before. The presented method thus opens the door to new and interesting applications in this area.
Tensor-based dynamic reconstruction method for electrical capacitance tomography
Lei, J.; Mu, H. P.; Liu, Q. B.; Li, Z. H.; Liu, S.; Wang, X. Y.
2017-03-01
Electrical capacitance tomography (ECT) is an attractive visualization measurement method, in which the acquisition of high-quality images is beneficial for the understanding of the underlying physical or chemical mechanisms of the dynamic behaviors of the measurement objects. In real-world measurement environments, imaging objects are often in a dynamic process, and the exploitation of the spatial-temporal correlations related to the dynamic nature will contribute to improving the imaging quality. Different from existing imaging methods that are often used in ECT measurements, in this paper a dynamic image sequence is stacked into a third-order tensor that consists of a low rank tensor and a sparse tensor within the framework of the multiple measurement vectors model and the multi-way data analysis method. The low rank tensor models the similar spatial distribution information among frames, which is slowly changing over time, and the sparse tensor captures the perturbations or differences introduced in each frame, which is rapidly changing over time. With the assistance of the Tikhonov regularization theory and the tensor-based multi-way data analysis method, a new cost function, with the considerations of the multi-frames measurement data, the dynamic evolution information of a time-varying imaging object and the characteristics of the low rank tensor and the sparse tensor, is proposed to convert the imaging task in the ECT measurement into a reconstruction problem of a third-order image tensor. An effective algorithm is developed to search for the optimal solution of the proposed cost function, and the images are reconstructed via a batching pattern. The feasibility and effectiveness of the developed reconstruction method are numerically validated.
48 CFR 1913.505 - Purchase order and related forms.
2010-10-01
... 48 Federal Acquisition Regulations System 6 2010-10-01 2010-10-01 true Purchase order and related... CONTRACTING METHODS AND CONTRACT TYPES SMALL PURCHASES AND OTHER SIMPLIFIED PURCHASE PROCEDURES Purchase Orders 1913.505 Purchase order and related forms....
Second order tensor finite element
Oden, J. Tinsley; Fly, J.; Berry, C.; Tworzydlo, W.; Vadaketh, S.; Bass, J.
1990-01-01
The results of a research and software development effort are presented for the finite element modeling of the static and dynamic behavior of anisotropic materials, with emphasis on single crystal alloys. Various versions of two dimensional and three dimensional hybrid finite elements were implemented and compared with displacement-based elements. Both static and dynamic cases are considered. The hybrid elements developed in the project were incorporated into the SPAR finite element code. In an extension of the first phase of the project, optimization of experimental tests for anisotropic materials was addressed. In particular, the problem of calculating material properties from tensile tests and of calculating stresses from strain measurements were considered. For both cases, numerical procedures and software for the optimization of strain gauge and material axes orientation were developed.
Quantum canonical tensor model and an exact wave function
Sasakura, Naoki
2013-01-01
Tensor models in various forms are being studied as models of quantum gravity. Among them the canonical tensor model has a canonical pair of rank-three tensors as dynamical variables, and is a pure constraint system with first-class constraints. The Poisson algebra of the first-class constraints has structure functions, and provides an algebraically consistent way of discretizing the Dirac first-class constraint algebra for general relativity. This paper successfully formulates the Wheeler-DeWitt scheme of quantization of the canonical tensor model; the ordering of operators in the constraints is determined without ambiguity by imposing Hermiticity and covariance on the constraints, and the commutation algebra of constraints takes essentially the same from as the classical Poisson algebra, i.e. is first-class. Thus one could consistently obtain, at least locally in the configuration space, wave functions of "universe" by solving the partial differential equations representing the constraints, i.e. the Wheeler...
Gravitational wave stress tensor from the linearised field equations
Balbus, Steven A
2016-01-01
A conserved stress energy tensor for weak field gravitational waves in standard general relativity is derived directly from the linearised wave equation alone, for an arbitrary gauge. The form of the tensor leads directly to the classical expression for the outgoing wave energy in any harmonic gauge. The method described here, however, is a much simpler, shorter, and more physically motivated approach than is the customary procedure, which involves a lengthy and cumbersome second-order (in wave-amplitude) calculation starting with the Einstein tensor. Our method has the added advantage of exhibiting the direct coupling between the outgoing energy flux in gravitational waves and the work done by the gravitational field on the sources. For nonharmonic gauges, the derived wave stress tensor has an index asymmetry. This coordinate artefact may be removed by techniques similar to those used in classical electrodynamics (where this issue also arises), but only by appeal to a more lengthy calculation. For any harmon...
Palmkvist, Jakob, E-mail: palmkvist@ihes.fr [Institut des Hautes Etudes Scientifiques, 35 Route de Chartres, FR-91440 Bures-sur-Yvette (France)
2014-01-15
We introduce an infinite-dimensional Lie superalgebra which is an extension of the U-duality Lie algebra of maximal supergravity in D dimensions, for 3 ⩽ D ⩽ 7. The level decomposition with respect to the U-duality Lie algebra gives exactly the tensor hierarchy of representations that arises in gauge deformations of the theory described by an embedding tensor, for all positive levels p. We prove that these representations are always contained in those coming from the associated Borcherds-Kac-Moody superalgebra, and we explain why some of the latter representations are not included in the tensor hierarchy. The most remarkable feature of our Lie superalgebra is that it does not admit a triangular decomposition like a (Borcherds-)Kac-Moody (super)algebra. Instead the Hodge duality relations between level p and D − 2 − p extend to negative p, relating the representations at the first two negative levels to the supersymmetry and closure constraints of the embedding tensor.
Strictly nonnegative tensors and nonnegative tensor partition
HU ShengLong; HUANG ZhengHai; QI LiQun
2014-01-01
We introduce a new class of nonnegative tensors—strictly nonnegative tensors.A weakly irreducible nonnegative tensor is a strictly nonnegative tensor but not vice versa.We show that the spectral radius of a strictly nonnegative tensor is always positive.We give some necessary and su？cient conditions for the six wellconditional classes of nonnegative tensors,introduced in the literature,and a full relationship picture about strictly nonnegative tensors with these six classes of nonnegative tensors.We then establish global R-linear convergence of a power method for finding the spectral radius of a nonnegative tensor under the condition of weak irreducibility.We show that for a nonnegative tensor T,there always exists a partition of the index set such that every tensor induced by the partition is weakly irreducible;and the spectral radius of T can be obtained from those spectral radii of the induced tensors.In this way,we develop a convergent algorithm for finding the spectral radius of a general nonnegative tensor without any additional assumption.Some preliminary numerical results show the feasibility and effectiveness of the algorithm.
Colored Tensor Models - a Review
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.
Invariant tensors for simple groups
De Azcarraga, J.A.; Macfarlane, A.J.; Mountain, A.J.; Perez Bueno, J.C. [Cambridge Univ. (United Kingdom). Dept. of Applied Mathematics and Theoretical Physics (DAMTP)
1998-01-26
The forms of the invariant primitive tensors for the simple Lie algebras A{sub l}, B{sub l}, C{sub l} and D{sub l} are investigated. A new family of symmetric invariant tensors is introduced using the non-trivial cocycles for the Lie algebra cohomology. For the A{sub l} algebra it is explicitly shown that the generic forms of these tensors become zero except for the l primitive ones and that they give rise to the l primitive Casimir operators. Some recurrence and duality relations are given for the Lie algebra cocycles. Tables for the 3- and 5-cocycles for su(3) and su(4) are also provided. Finally, new relations involving the d and f su(n) tensors are given. (orig.). 34 refs.
Elasticity tensor and ultrasonic velocities for anisotropic cubic polycrystal
2008-01-01
The orientation distribution of crystallites in a polycrystal can be described by the orientation distribution function(ODF) . The ODF can be expanded under the Wigner D-bases. The expanded coefficients in the ODF are called the texture coefficients. In this paper,we use the Clebsch-Gordan expression to derive an explicit expression of the elasticity tensor for an anisotropic cubic polycrystal. The elasticity tensor contains three material constants and nine texture coefficients. In order to measure the nine texture coefficients by ultrasonic wave,we give relations between the nine texture coefficients and ultrasonic propagation velocities. We also give a numerical example to check the relations.
Solution of Second Order Supersymmetrical Intertwining Relations in Minkowski Plane
Ioffe, M V; Nishnianidze, D N
2016-01-01
Supersymmetrical (SUSY) intertwining relations are generalized to the case of quantum Hamiltonians in Minkowski space. For intertwining operators (supercharges) of second order in derivatives the intertwined Hamiltonians correspond to completely integrable systems with the symmetry operators of fourth order in momenta. In terms of components, the itertwining relations correspond to the system of nonlinear differential equations which are solvable with the simplest - constant - ansatzes for the "metric" matrix in second order part of the supercharges. The corresponding potentials are built explicitly both for diagonalizable and nondiagonalizable form of "metric" matrices, and their properties are discussed.
Solution of second order supersymmetrical intertwining relations in Minkowski plane
Ioffe, M. V.; Kolevatova, E. V.; Nishnianidze, D. N.
2016-08-01
Supersymmetrical (SUSY) intertwining relations are generalized to the case of quantum Hamiltonians in Minkowski space. For intertwining operators (supercharges) of second order in derivatives, the intertwined Hamiltonians correspond to completely integrable systems with the symmetry operators of fourth order in momenta. In terms of components, the intertwining relations correspond to the system of nonlinear differential equations which are solvable with the simplest—constant—ansatzes for the "metric" matrix in second order part of the supercharges. The corresponding potentials are built explicitly both for diagonalizable and nondiagonalizable form of "metric" matrices, and their properties are discussed.
Tensors and Riemannian geometry with applications to differential equations
Ibragimov, Nail H
2015-01-01
This graduate textbook begins by introducing Tensors and Riemannian Spaces, and then elaborates their application in solving second-order differential equations, and ends with introducing theory of relativity and de Sitter space. Based on 40 years of teaching experience, the author compiles a well-developed collection of examples and exercises to facilitate the reader’s learning.
Hess, Siegfried
2015-01-01
This book presents the science of tensors in a didactic way. The various types and ranks of tensors and the physical basis is presented. Cartesian Tensors are needed for the description of directional phenomena in many branches of physics and for the characterization the anisotropy of material properties. The first sections of the book provide an introduction to the vector and tensor algebra and analysis, with applications to physics, at undergraduate level. Second rank tensors, in particular their symmetries, are discussed in detail. Differentiation and integration of fields, including generalizations of the Stokes law and the Gauss theorem, are treated. The physics relevant for the applications in mechanics, quantum mechanics, electrodynamics and hydrodynamics is presented. The second part of the book is devoted to tensors of any rank, at graduate level. Special topics are irreducible, i.e. symmetric traceless tensors, isotropic tensors, multipole potential tensors, spin tensors, integration and spin-...
Relative effects at work : Bayes factors for order hypotheses
Braeken, J.; Mulder, J.; Wood, S.
2015-01-01
Assessing the relative importance of predictors has been of historical importance in a variety of disciplines including management, medicine, economics, and psychology. When approaching hypotheses on the relative ordering of the magnitude of predicted effects (e.g., the effects of discrimination fro
Testing gravity theories using tensor perturbations
Lin, Weikang; Ishak, Mustapha
2016-12-01
Primordial gravitational waves constitute a promising probe of the very early Universe and the laws of gravity. We study in this work changes to tensor-mode perturbations that can arise in various proposed modified gravity theories. These include additional friction effects, nonstandard dispersion relations involving a massive graviton, a modified speed, and a small-scale modification. We introduce a physically motivated parametrization of these effects and use current available data to obtain exclusion regions in the parameter spaces. Taking into account the foreground subtraction, we then perform a forecast analysis focusing on the tensor-mode modified-gravity parameters as constrained by the future experiments COrE, Stage-IV and PIXIE. For a fiducial value of the tensor-to-scalar ratio r =0.01 , we find that an additional friction of 3.5-4.5% compared to GR will be detected at 3 -σ by these experiments, while a decrease in friction will be more difficult to detect. The speed of gravitational waves needs to be by 5-15% different from the speed of light for detection. We find that the minimum detectable graviton mass is about 7.8 - 9.7 ×10-33 eV , which is of the same order of magnitude as the graviton mass that allows massive gravity theories to produce late-time cosmic acceleration. Finally, we study the tensor-mode perturbations in modified gravity during inflation using our parametrization. We find that, in addition to being related to r , the tensor spectral index would be related to the friction parameter ν0 by nT=-3 ν0-r /8 . Assuming that the friction parameter is unchanged throughout the history of the Universe, and that ν0 is much larger than r , the future experiments considered here will be able to distinguish this modified-gravity consistency relation from the standard inflation consistency relation, and thus can be used as a further test of modified gravity. In summary, tensor-mode perturbations and cosmic-microwave-background B
TIAN Dongyan; JIN Ming; DUI Guansuo
2006-01-01
A new approach for the derivation of the principal invariants of the stretch tensor with respect to the right Cauchy Green tensor is presented in this paper. According to the definition of the derivation of tensor function, the three first-order derivatives for the principal invariants of the stretch tensor are obtained through derivation directly to the right Cauchy-Green tensor by incremental method. Then the three second-order derivatives are yielded by the derivation to the right Cauchy-Green strain tensor directly. Furthermore, an explicit expression of the tangent modulus of the general Varga material is given as an example.
Kuang-dai Leng
2012-01-01
Full Text Available Fabric tensor has proved to be an effective tool statistically characterizing directional data in a smooth and frame-indifferent form. Directional data arising from microscopic physics and mechanics can be summed up as tensor-valued orientation distribution functions (ODFs. Two characterizations of the tensor-valued ODFs are proposed, using the asymmetric and symmetric fabric tensors respectively. The later proves to be nonconvergent and less accurate but still an available solution for where fabric tensors are required in full symmetry. Analytic solutions of the two types of fabric tensors characterizing centrosymmetric and anticentrosymmetric tensor-valued ODFs are presented in terms of orthogonal irreducible decompositions in both two- and three-dimensional (2D and 3D spaces. Accuracy analysis is performed on normally distributed random ODFs to evaluate the approximation quality of the two characterizations, where fabric tensors of higher orders are employed. It is shown that the fitness is dominated by the dispersion degree of the original ODFs rather than the orders of fabric tensors. One application of tensor-valued ODF and fabric tensor in continuum damage mechanics is presented.
Toddlers infer higher-order relational principles in causal learning.
Walker, Caren M; Gopnik, Alison
2014-01-01
Children make inductive inferences about the causal properties of individual objects from a very young age. When can they infer higher-order relational properties? In three experiments, we examined 18- to 30-month-olds' relational inferences in a causal task. Results suggest that at this age, children are able to infer a higher-order relational causal principle from just a few observations and use this inference to guide their own subsequent actions and bring about a novel causal outcome. Moreover, the children passed a revised version of the relational match-to-sample task that has proven very difficult for nonhuman primates. The findings are considered in light of their implications for understanding the nature of relational and causal reasoning, and their evolutionary origins.
Killing tensors in pp-wave spacetimes
Keane, Aidan J [87 Carlton Place, Glasgow G5 9TD, Scotland (United Kingdom); Tupper, Brian O J, E-mail: aidan@countingthoughts.co, E-mail: bt32@rogers.co [Department of Mathematics and Statistics, University of New Brunswick, Fredericton, New Brunswick, E3B 5A3 (Canada)
2010-12-21
The formal solution of the second-order Killing tensor equations for the general pp-wave spacetime is given. The Killing tensor equations are integrated fully for some specific pp-wave spacetimes. In particular, the complete solution is given for the conformally flat plane wave spacetimes and we find that irreducible Killing tensors arise for specific classes. The maximum number of independent irreducible Killing tensors admitted by a conformally flat plane wave spacetime is shown to be six. It is shown that every pp-wave spacetime that admits an homothety will admit a Killing tensor of Koutras type and, with the exception of the singular scale-invariant plane wave spacetimes, this Killing tensor is irreducible.
Second-order relative exponent of isotropic turbulence
无
2011-01-01
Theoretical results on the scaling properties of turbulent velocity fields are reported in this letter.Based on the Kolmogorov equation and typical models of the second-order statistical moments (energy spectrum and the second-order structure function),we have studied the relative scaling using the ESS method.It is found that the relative EES scaling exponent S_2 is greater than the real or theoretical inertial range scaling exponentξ_2,which is attributed to an evident bump in the ESS range.
Carrozza, Sylvain; Tanasa, Adrian
2016-11-01
We define in this paper a class of three-index tensor models, endowed with {O(N)^{⊗ 3}} invariance ( N being the size of the tensor). This allows to generate, via the usual QFT perturbative expansion, a class of Feynman tensor graphs which is strictly larger than the class of Feynman graphs of both the multi-orientable model (and hence of the colored model) and the U( N) invariant models. We first exhibit the existence of a large N expansion for such a model with general interactions. We then focus on the quartic model and we identify the leading and next-to-leading order (NLO) graphs of the large N expansion. Finally, we prove the existence of a critical regime and we compute the critical exponents, both at leading order and at NLO. This is achieved through the use of various analytic combinatorics techniques.
Rodríguez-Vázquez, Jose Francisco; Honkura, Yohei; Katori, Yukio; Murakami, Gen; Abe, Hiroshi
2017-01-01
The existence of hard tissue pulleys that act to change the direction of a muscle insertion tendon is well known in the human body. These include (1) the trochlea for the extraocular obliquus superior muscle, (2) the pterygoid hamulus for the tensor veli palatini muscle, (3) the deep sulcus on the plantar aspect of the cuboid bone for the peroneus longus tendon, (4) the lesser sciatic notch for the obturator internus muscle, and (5) the bony trochleariformis process for the tensor tympani muscle tendon. In addition, (6) the stapedius muscle tendon shows a lesser or greater angulation at the pyramidal eminence of the temporal bone. Our recent studies have shown that the development of pulleys Nos. 1 and 2 can be explained by a change in the topographical relationship between the pulley and the tendon, that of pulley No. 3 by the rapidly growing calcaneus pushing the tendon, and that of pulley No. 4 by migration of the insertion along the sciatic nerve and gluteus medius tendon. Therefore, in Nos. 1-4, an initially direct tendon curves secondarily and obtains an attachment to the pulley. In case No. 6, the terminal part of the stapedius tendon originates secondarily from the interzone mesenchymal tissue of the incudostapedial joint. In the case of pulley No. 5, we newly demonstrated that its initial phase of development was similar to No. 6, but the tensor tympani tendon achieved a right-angled turn under guidance by a specific fibrous tissue and it migrated along the growing malleus manubrium. Copyright Â© 2016 Elsevier GmbH. All rights reserved.
The Topology of Symmetric Tensor Fields
Levin, Yingmei; Batra, Rajesh; Hesselink, Lambertus; Levy, Yuval
1997-01-01
Combinatorial topology, also known as "rubber sheet geometry", has extensive applications in geometry and analysis, many of which result from connections with the theory of differential equations. A link between topology and differential equations is vector fields. Recent developments in scientific visualization have shown that vector fields also play an important role in the analysis of second-order tensor fields. A second-order tensor field can be transformed into its eigensystem, namely, eigenvalues and their associated eigenvectors without loss of information content. Eigenvectors behave in a similar fashion to ordinary vectors with even simpler topological structures due to their sign indeterminacy. Incorporating information about eigenvectors and eigenvalues in a display technique known as hyperstreamlines reveals the structure of a tensor field. The simplify and often complex tensor field and to capture its important features, the tensor is decomposed into an isotopic tensor and a deviator. A tensor field and its deviator share the same set of eigenvectors, and therefore they have a similar topological structure. A a deviator determines the properties of a tensor field, while the isotopic part provides a uniform bias. Degenerate points are basic constituents of tensor fields. In 2-D tensor fields, there are only two types of degenerate points; while in 3-D, the degenerate points can be characterized in a Q'-R' plane. Compressible and incompressible flows share similar topological feature due to the similarity of their deviators. In the case of the deformation tensor, the singularities of its deviator represent the area of vortex core in the field. In turbulent flows, the similarities and differences of the topology of the deformation and the Reynolds stress tensors reveal that the basic addie-viscosity assuptions have their validity in turbulence modeling under certain conditions.
Quantification of Partially Ordered Sets with Application to Special Relativity
Bahreyni, Newshaw; Knuth, Kevin H.
2011-03-01
A partially ordered set is a set of elements ordered by a binary ordering relation. We have shown that a subset of a partially ordered set can be quantified by projecting elements onto a pair of chains where the elements of each chain are quantified by real numbers. This results in a quantification based on pairs of real numbers (pair). Intervals, defined by pairs of elements, can be quantified similarly. A pair can be decomposed into a sum of a symmetric pair and an antisymmetric pair and mapped to a unique scalar which results in the Minkowskian form. Changing the basis of quantification from one pair of chains to another, under special conditions, leads to the generalized Lorentz transformation for pairs. We apply these results to a causally-ordered set of events by identifying a chain of events with an observer equipped with a clock in an inertial frame. We obtain the Minkowski metric of flat space-time as well as Lorentz transformations, which results in there being a maximum invariant speed. We find that the mathematics of special relativity arises from quantifying causal relationships among events, and requires neither the principle of relativity nor the fact that the speed of light is constant.
Threshold singularities, dispersion relations and fixed-order perturbative calculations
Beneke, Martin
2016-01-01
We show how to correctly treat threshold singularities in fixed-order perturbative calculations of the electron anomalous magnetic moment and hadronic pair production processes such as top pair production. With respect to the former, we demonstrate the equivalence of the "non-perturbative", resummed treatment of the vacuum polarization contribution, whose spectral function exhibits bound state poles, with the fixed-order calculation by identifying a threshold localized term in the four-loop spectral function. In general, we find that a modification of the dispersion relation by threshold subtractions is required to make fixed-order calculations well-defined and provide the subtraction term. We then solve the apparent problem of a divergent convolution of the partonic cross section with the parton luminosity in the computation of the top pair production cross section starting from the fourth-order correction. We find that when the computation is performed in the usual way as an integral of real and virtual cor...
33 CFR 335.6 - Related laws and Executive Orders.
2010-07-01
... 33 Navigation and Navigable Waters 3 2010-07-01 2010-07-01 false Related laws and Executive Orders. 335.6 Section 335.6 Navigation and Navigable Waters CORPS OF ENGINEERS, DEPARTMENT OF THE ARMY, DEPARTMENT OF DEFENSE OPERATION AND MAINTENANCE OF ARMY CORPS OF ENGINEERS CIVIL WORKS PROJECTS INVOLVING THE...
Birth order and selected work-related personality variables.
Phillips, A S; Bedeian, A G; Mossholder, K W; Touliatos, J
1988-12-01
A possible link between birth order and various individual characteristics (e. g., intelligence, potential eminence, need for achievement, sociability) has been suggested by personality theorists such as Adler for over a century. The present study examines whether birth order is associated with selected personality variables that may be related to various work outcomes. 3 of 7 hypotheses were supported and the effect sizes for these were small. Firstborns scored significantly higher than later borns on measures of dominance, good impression, and achievement via conformity. No differences between firstborns and later borns were found in managerial potential, work orientation, achievement via independence, and sociability. The study's sample consisted of 835 public, government, and industrial accountants responding to a national US survey of accounting professionals. The nature of the sample may have been partially responsible for the results obtained. Its homogeneity may have caused any birth order effects to wash out. It can be argued that successful membership in the accountancy profession requires internalization of a set of prescribed rules and standards. It may be that accountants as a group are locked in to a behavioral framework. Any differentiation would result from spurious interpersonal differences, not from predictable birth-order related characteristics. A final interpretation is that birth order effects are nonexistent or statistical artifacts. Given the present data and particularistic sample, however, the authors have insufficient information from which to draw such a conclusion.
Guzman, V M Banda
2016-01-01
A boson of spin-j>1 can be described in one of the possibilities within the Bargmann-Wigner framework by means of one sole differential equation of order twice the spin, which however is known to be inconsistent as it allows for non-local, ghost and acausally propagating solutions, all problems which are difficult to tackle. The other possibility is provided by the Fierz-Pauli framework which is based on the more comfortable to deal with second order Klein-Gordon equation, but it needs to be supplemented by an auxiliary condition. Although the latter formalism avoids some of the pathologies of the high-order equations, it still remains plagued by some inconsistencies such as the acausal propagation of the wave fronts of the (classical) solutions within an electromagnetic environment. We here suggest a method alternative to the above two that combines their advantages while avoiding the related difficulties. Namely, we suggest one sole strictly (j,0)+ (0,j) representation specific second order differential equ...
Moment tensors of a dislocation in a porous medium
Wang, Zhi; Hu, Hengshan
2016-06-01
A dislocation can be represented by a moment tensor for calculating seismic waves. However, the moment tensor expression was derived in an elastic medium and cannot completely describe a dislocation in a porous medium. In this paper, effective moment tensors of a dislocation in a porous medium are derived. It is found that the dislocation is equivalent to two independent moment tensors, i.e., the bulk moment tensor acting on the bulk of the porous medium and the isotropic fluid moment tensor acting on the pore fluid. Both of them are caused by the solid dislocation as well as the fluid-solid relative motion corresponding to fluid injection towards the surrounding rocks (or fluid outflow) through the fault plane. For a shear dislocation, the fluid moment tensor is zero, and the dislocation is equivalent to a double couple acting on the bulk; for an opening dislocation or fluid injection, the two moment tensors are needed to describe the source. The fluid moment tensor only affects the radiated compressional waves. By calculating the ratio of the radiation fields generated by unit fluid moment tensor and bulk moment tensor, it is found that the fast compressional wave radiated by the bulk moment tensor is much stronger than that radiated by the fluid moment tensor, while the slow compressional wave radiated by the fluid moment tensor is several times stronger than that radiated by the bulk moment tensor.
Reduced-Order Kalman Filtering for Processing Relative Measurements
Bayard, David S.
2008-01-01
A study in Kalman-filter theory has led to a method of processing relative measurements to estimate the current state of a physical system, using less computation than has previously been thought necessary. As used here, relative measurements signifies measurements that yield information on the relationship between a later and an earlier state of the system. An important example of relative measurements arises in computer vision: Information on relative motion is extracted by comparing images taken at two different times. Relative measurements do not directly fit into standard Kalman filter theory, in which measurements are restricted to those indicative of only the current state of the system. One approach heretofore followed in utilizing relative measurements in Kalman filtering, denoted state augmentation, involves augmenting the state of the system at the earlier of two time instants and then propagating the state to the later time instant.While state augmentation is conceptually simple, it can also be computationally prohibitive because it doubles the number of states in the Kalman filter. When processing a relative measurement, if one were to follow the state-augmentation approach as practiced heretofore, one would find it necessary to propagate the full augmented state Kalman filter from the earlier time to the later time and then select out the reduced-order components. The main result of the study reported here is proof of a property called reduced-order equivalence (ROE). The main consequence of ROE is that it is not necessary to augment with the full state, but, rather, only the portion of the state that is explicitly used in the partial relative measurement. In other words, it suffices to select the reduced-order components first and then propagate the partial augmented state Kalman filter from the earlier time to the later time; the amount of computation needed to do this can be substantially less than that needed for propagating the full augmented
Group-theoretical method for physical property tensors of quasicrystals
Gong Ping; Hu Cheng-Zheng; Zhou Xiang; Wang Ai-Jun; Miao Ling
2006-01-01
In addition to the phonon variable there is the phason variable in hydrodynamics for quasicrystals. These two kinds of hydrodynamic variables have different transformation properties. The phonon variable transforms under the vector representation, whereas the phason variable transforms under another related representation. Thus, a basis (or a set of basis functions) in the representation space should include such two kinds of variables. This makes it more difficult to determine the physical property tensors of quasicrystals. In this paper the group-theoretical method is given to determine the physical property tensors of quasicrystals. As an illustration of this method we calculate the third-order elasticity tensors of quasicrystals with five-fold symmetry by means of basis functions. It follows that the linear phonon elasticity is isotropic, but the nonlinear phonon elasticity is anisotropic for pentagonal quasicrystals. Meanwhile, the basis functions are constructed for all noncrystallographic point groups of quasicrystals.
A DISCUSSION ABOUT SCALE INVARIANTS FOR TENSOR FUNCTIONS
Huang Yongnian; Luo Xiongping; Emily S.C.Ching
2000-01-01
It is found that in some cases the complete and irreducible scale invariants given by Ref.[1]are not independent.There are some implicit functional relations among them.The scale invariants for two different cases are calculated.The first case is an arbitrary second order tensor.The second case includes a symmetric tensor,an antisymmetric tensor and a vector.By using the eigentensor notation it is proved that in the first case there are only six independent scale invariants rather than seven as reported in Ref.[1]and in the second case there are only nine independent scale invariants which are leas than that obtained in Ref.[1].
A geometrical approach to degenerate scalar-tensor theories
Chagoya, Javier
2016-01-01
Degenerate scalar-tensor theories are recently proposed covariant theories of gravity coupled with a scalar field. Despite being characterised by higher order equations of motion, they do not propagate more than three degrees of freedom, thanks to the existence of constraints. We discuss a geometrical approach to degenerate scalar-tensor systems, and analyse its consequences. We show that some of these theories emerge as a certain limit of DBI Galileons. In absence of dynamical gravity, these systems correspond to scalar theories enjoying a symmetry which is different from Galileon invariance. The scalar theories have however problems concerning the propagation of fluctuations around a time dependent background. These issues can be tamed by breaking the symmetry by hand, or by minimally coupling the scalar with dynamical gravity in a way that leads to degenerate scalar-tensor systems. We show that distinct theories can be connected by a relation which generalizes Galileon duality, in certain cases also when g...
Tensor eigenvalues and entanglement of symmetric states
Bohnet-Waldraff, F.; Braun, D.; Giraud, O.
2016-10-01
Tensor eigenvalues and eigenvectors have been introduced in the recent mathematical literature as a generalization of the usual matrix eigenvalues and eigenvectors. We apply this formalism to a tensor that describes a multipartite symmetric state or a spin state, and we investigate to what extent the corresponding tensor eigenvalues contain information about the multipartite entanglement (or, equivalently, the quantumness) of the state. This extends previous results connecting entanglement to spectral properties related to the state. We show that if the smallest tensor eigenvalue is negative, the state is detected as entangled. While for spin-1 states the positivity of the smallest tensor eigenvalue is equivalent to separability, we show that for higher values of the angular momentum there is a correlation between entanglement and the value of the smallest tensor eigenvalue.
Gurau, Razvan
2016-09-01
This article is preface to the SIGMA special issue ''Tensor Models, Formalism and Applications'', http://www.emis.de/journals/SIGMA/Tensor_Models.html. The issue is a collection of eight excellent, up to date reviews on random tensor models. The reviews combine pedagogical introductions meant for a general audience with presentations of the most recent developments in the field. This preface aims to give a condensed panoramic overview of random tensors as the natural generalization of random matrices to higher dimensions.
Phase Transition in Tensor Models
Delepouve, Thibault
2015-01-01
Generalizing matrix models, tensor models generate dynamical triangulations in any dimension and support a $1/N$ expansion. Using the intermediate field representation we explicitly rewrite a quartic tensor model as a field theory for a fluctuation field around a vacuum state corresponding to the resummation of the entire leading order in $1/N$ (a resummation of the melonic family). We then prove that the critical regime in which the continuum limit in the sense of dynamical triangulations is reached is precisely a phase transition in the field theory sense for the fluctuation field.
The Physical Squeezed Limit: Consistency Relations at Order q^2
Creminelli, Paolo; Senatore, Leonardo; Simonović, Marko; Trevisan, Gabriele
2013-01-01
In single-field models of inflation the effect of a long mode with momentum q reduces to a diffeomorphism at zeroth and first order in q. This gives the well-known consistency relations for the n-point functions. At order q^2 the long mode has a physical effect on the short ones, since it induces curvature, and we expect that this effect is the same as being in a curved FRW universe. In this paper we verify this intuition in various examples of the three-point function, whose behaviour at order q^2 can be written in terms of the power spectrum in a curved universe. This gives a simple alternative understanding of the level of non-Gaussianity in single-field models. Non-Gaussianity is always parametrically enhanced when modes freeze at a physical scale k_{ph, f} shorter than H: f_{NL} \\sim (k_{ph, f}/H)^2.
The physical squeezed limit: consistency relations at order q2
Creminelli, Paolo; Perko, Ashley; Senatore, Leonardo; Simonović, Marko; Trevisan, Gabriele
2013-11-01
In single-field models of inflation the effect of a long mode with momentum q reduces to a diffeomorphism at zeroth and first order in q. This gives the well-known consistency relations for the n-point functions. At order q2 the long mode has a physical effect on the short ones, since it induces curvature, and we expect that this effect is the same as being in a curved FRW universe. In this paper we verify this intuition in various examples of the three-point function, whose behaviour at order q2 can be written in terms of the power spectrum in a curved universe. This gives a simple alternative understanding of the level of non-Gaussianity in single-field models. Non-Gaussianity is always parametrically enhanced when modes freeze at a physical scale kph, f shorter than H: fNL ~ (kph, f/H)2.
Tensor fields on orbits of quantum states and applications
Volkert, Georg Friedrich
2010-07-19
On classical Lie groups, which act by means of a unitary representation on finite dimensional Hilbert spaces H, we identify two classes of tensor field constructions. First, as pull-back tensor fields of order two from modified Hermitian tensor fields, constructed on Hilbert spaces by means of the property of having the vertical distributions of the C{sub 0}-principal bundle H{sub 0} {yields} P(H) over the projective Hilbert space P(H) in the kernel. And second, directly constructed on the Lie group, as left-invariant representation-dependent operator-valued tensor fields (LIROVTs) of arbitrary order being evaluated on a quantum state. Within the NP-hard problem of deciding whether a given state in a n-level bi-partite quantum system is entangled or separable (Gurvits, 2003), we show that both tensor field constructions admit a geometric approach to this problem, which evades the traditional ambiguity on defining metrical structures on the convex set of mixed states. In particular by considering manifolds associated to orbits passing through a selected state when acted upon by the local unitary group U(n) x U(n) of Schmidt coefficient decomposition inducing transformations, we find the following results: In the case of pure states we show that Schmidt-equivalence classes which are Lagrangian submanifolds define maximal entangled states. This implies a stronger statement as the one proposed by Bengtsson (2007). Moreover, Riemannian pull-back tensor fields split on orbits of separable states and provide a quantitative characterization of entanglement which recover the entanglement measure proposed by Schlienz and Mahler (1995). In the case of mixed states we highlight a relation between LIROVTs of order two and a class of computable separability criteria based on the Bloch-representation (de Vicente, 2007). (orig.)
Applications of tensor analysis
McConnell, A J
2011-01-01
Standard work applies tensorial methods to subjects within realm of advanced college mathematics. Text explains fundamental ideas and notation of tensor theory; covers geometrical treatment of tensor algebra; introduces theory of differentiation of tensors; and applies mathematics to dynamics, electricity, elasticity and hydrodynamics. 685 exercises, most with answers.
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.
Renormalizable Tensor Field Theories
Geloun, Joseph Ben
2016-01-01
Extending tensor models at the field theoretical level, tensor field theories are nonlocal quantum field theories with Feynman graphs identified with simplicial complexes. They become relevant for addressing quantum topology and geometry in any dimension and therefore form an interesting class of models for studying quantum gravity. We review the class of perturbatively renormalizable tensor field theories and some of their features.
The relative worst order ratio applied to paging
Boyar, Joan; Favrholdt, Lene Monrad; Larsen, Kim Skak
2007-01-01
The relative worst order ratio, a new measure for the quality of on-line algorithms, was recently defined and applied to two bin packing problems. Here, we apply it to the paging problem and obtain the following results: We devise a new deterministic paging algorithm, Retrospective-LRU, and show...... that it performs better than LRU. This is supported by experimental results, but contrasts with the competitive ratio. All deterministic marking algorithms have the same competitive ratio, but here we find that LRU is better than FWF. According to the relative worst order ratio, no deterministic marking algorithm...... can be significantly better than LRU, but the randomized algorithm MARK is better than LRU. Finally, look-ahead is shown to be a significant advantage, in contrast to the competitive ratio, which does not reflect that look-ahead can be helpful....
Threshold singularities, dispersion relations and fixed-order perturbative calculations
Beneke, M.; Ruiz-Femenía, P. [Physik Department T31, Technische Universität München,James-Franck-Straße, D-85748 Garching (Germany)
2016-08-24
We show how to correctly treat threshold singularities in fixed-order perturbative calculations of the electron anomalous magnetic moment and hadronic pair production processes such as top pair production. With respect to the former, we demonstrate the equivalence of the “non-perturbative”, resummed treatment of the vacuum polarization contribution, whose spectral function exhibits bound state poles, with the fixed-order calculation by identifying a threshold localized term in the four-loop spectral function. In general, we find that a modification of the dispersion relation by threshold subtractions is required to make fixed-order calculations well-defined and provide the subtraction term. We then solve the apparent problem of a divergent convolution of the partonic cross section with the parton luminosity in the computation of the top pair production cross section starting from the fourth-order correction. We find that when the computation is performed in the usual way as an integral of real and virtual corrections over phase space at a given order in the expansion in the strong coupling, an additional contribution has to be added at N3LO.
Sidaros, A.; Engberg, A.W.; Sidaros, K.
2008-01-01
Diffusion tensor imaging (DTI) has been proposed as a sensitive biomarker of traumatic white matter injury, which could potentially serve as a tool for prognostic assessment and for studying microstructural changes during recovery from traumatic brain injury (TBI). However, there is a lack...... peduncle and in corpus callosum, λ∥ and λ⊥ both increased during the scan interval and, particularly in patients with unfavourable outcome, fractional anisotropy remained depressed. No significant DTI parameter changes over time were found in controls, or in CSF of patients. These findings support that DTI...... is a clinically relevant biomarker in TBI, which may have prognostic value and also might serve as a tool for revealing changes in the neural tissue during recovery. © Published by Oxford University Press on behalf of the Guarantors of Brain. All rights reserved....
Sidaros, A.; Engberg, A.W.; Sidaros, K.
2008-01-01
Diffusion tensor imaging (DTI) has been proposed as a sensitive biomarker of traumatic white matter injury, which could potentially serve as a tool for prognostic assessment and for studying microstructural changes during recovery from traumatic brain injury (TBI). However, there is a lack...... of longitudinal studies on TBI that follow DTI changes over time and correlate findings with long-term clinical outcome. We performed a prospective longitudinal study of 30 adult patients admitted for subacute rehabilitation following severe traumatic brain injury. DTI and conventional MRI were acquired at mean 8...... weeks (5-11 weeks), and repeated in 23 of the patients at mean 12 months (9-15 months) post-trauma. Using a region-of-interest-based approach, DTI parameters were compared to those of healthy matched controls, scanned during the same time period and rescanned with a similar interval as that of patients...
Structure of the velocity gradient tensor in turbulent shear flows
Pumir, Alain
2017-07-01
The expected universality of small-scale properties of turbulent flows implies isotropic properties of the velocity gradient tensor in the very large Reynolds number limit. Using direct numerical simulations, we determine the tensors formed by n =2 and 3 velocity gradients at a single point in turbulent homogeneous shear flows and in the log-layer of a turbulent channel flow, and we characterize the departure of these tensors from the corresponding isotropic prediction. Specifically, we separate the even components of the tensors, invariant under reflexion with respect to all axes, from the odd ones, which identically vanish in the absence of shear. Our results indicate that the largest deviation from isotropy comes from the odd component of the third velocity gradient correlation function, especially from the third moment of the derivative along the normal direction of the streamwise velocity component. At the Reynolds numbers considered (Reλ≈140 ), we observe that these second- and third-order correlation functions are significantly larger in turbulent channel flows than in homogeneous shear flow. Overall, our work demonstrates that a mean shear leads to relatively simple structure of the velocity gradient tensor. How isotropy is restored in the very large Reynolds limit remains to be understood.
Zhang Xiang; Li Baoqing; Shan Baoci
2014-01-01
Background Diffusion tensor imaging can evaluate white matter function in human brain.Fractional anisotropy is the most important parameter.This study aimed to find regional reduction of fractional anisotropy (FA) with aging in the whole brain and the changing rules of anisotropy with aging.Methods Fifty volunteers from 20 to 75 years old were divided into five consecutive age groups; a young group and four senior groups.FA values were calculated with diffusion tensor imaging (DTI) studio software.The difference of FA between the young group and the four senior groups were analyzed by analysis of voxel-level height threshold in Statistic Parametric Mapping (SPM),and the regions with decreased FA were obtained.The FA values of these regions were then extracted using an in-house developed program,and a multiple linear regression model was built to assess the influence of age and sex on the FA values of these regions.Results Eight regions,including frontal lobe,postcentral gyrus,optic radiation,hippocampus,cerebella hemisphere,corona radiate,corpus callosum and internal capsule,were found to have decreased FA.There was a strong negative correlation between age and the FA in the frontal lobe,postcentral gyrus,optic radiation,hippocampus,and cerebella hemisphere,while a weaker negative correlation in the corona radiate,corpus callosum,and internal capsule was found.The FA reduction in the frontal lobe,postcentral gyrus,optic radiation,hippocampus and cerebella hemisphere were found earlier than in the corona radiate,corpus callosum and internal capsule.There was no correlation between sex and FA in these regions.Conclusions The FA in the subcortical white matter area reduces earlier than that in deep white matter.The areas with decreased FA continuously enlarge with aqing.The FAs in these regions have a strong negative correlation with age.
An $OSp$ extension of Canonical Tensor Model
Narain, Gaurav
2015-01-01
Tensor models are generalizations of matrix models, and are studied as discrete models of quantum gravity for arbitrary dimensions. Among them, the canonical tensor model (CTM for short) is a rank-three tensor model formulated as a totally constrained system with a number of first-class constraints, which have a similar algebraic structure as the constraints of the ADM formalism of general relativity. In this paper, we formulate a super-extension of CTM as an attempt to incorporate fermionic degrees of freedom. The kinematical symmetry group is extended from $O(N)$ to $OSp(N,\\tilde N)$, and the constraints are constructed so that they form a first-class constraint super-Poisson algebra. This is a straightforward super-extension, and the constraints and their algebraic structure are formally unchanged from the purely bosonic case, except for the additional signs associated to the order of the fermionic indices and dynamical variables. However, this extension of CTM leads to the existence of negative norm state...
Axiomatization of Special Relativity in First Order Logic
Luo, Yi-Chen; Chen, Lei; He, Wan-Ting; Ma, Yong-Ge; Zhang, Xin-Yu
2016-07-01
The axiomatization of physical theories is a fundamental issue of science. The first-order axiomatic system SpecRel for special relativity proposed recently by Andréka et al. is not enough to explain all the main results in the theory, including the twin paradox and energy-mass relation. In this paper, from a four-dimensional space-time perspective, we introduce the concepts of world-line, proper time and four-momentum to our axiomatic system SpecRel+. Then we introduce an axiom of mass (AxMass) and take four-momentum conservation as an axiom (AxCFM) in SpecRel+. It turns out that the twin paradox and energy-mass relation can be derived from SpecRel+ logically. Hence, as an extension of SpecRel, SpecRel+ is a suitable first-order axiomatic system to describe the kinematics and dynamics of special relativity. Supported by the National Science Foundation of China under Grant Nos. 11235003 and 11475023, National Social Sciences Foundation of China under Grant No. 14BZX078 and the Research Fund for the Doctoral Program of Higher Education of China, and the Undergraduate Training Program of Beijing
A Recurrence Relation Approach to Higher Order Quantum Superintegrability
Ernie G. Kalnins
2011-03-01
Full Text Available We develop our method to prove quantum superintegrability of an integrable 2D system, based on recurrence relations obeyed by the eigenfunctions of the system with respect to separable coordinates. We show that the method provides rigorous proofs of superintegrability and explicit constructions of higher order generators for the symmetry algebra. We apply the method to 5 families of systems, each depending on a parameter k, including most notably the caged anisotropic oscillator, the Tremblay, Turbiner and Winternitz system and a deformed Kepler-Coulomb system, and we give proofs of quantum superintegrability for all rational values of k, new for 4 of these systems. In addition, we show that the explicit information supplied by the special function recurrence relations allows us to prove, for the first time in 4 cases, that the symmetry algebra generated by our lowest order symmetries closes and to determine the associated structure equations of the algebras for each k. We have no proof that our generating symmetries are of lowest possible order, but we have no counterexamples, and we are confident we can can always find any missing generators from our raising and lowering operator recurrences. We also get for free, one variable models of the action of the symmetry algebra in terms of difference operators. We describe how the Stäckel transform acts and show that it preserves the structure equations.
The Invar tensor package: Differential invariants of Riemann
Martín-García, J. M.; Yllanes, D.; Portugal, R.
2008-10-01
The long standing problem of the relations among the scalar invariants of the Riemann tensor is computationally solved for all 6ṡ10 objects with up to 12 derivatives of the metric. This covers cases ranging from products of up to 6 undifferentiated Riemann tensors to cases with up to 10 covariant derivatives of a single Riemann. We extend our computer algebra system Invar to produce within seconds a canonical form for any of those objects in terms of a basis. The process is as follows: (1) an invariant is converted in real time into a canonical form with respect to the permutation symmetries of the Riemann tensor; (2) Invar reads a database of more than 6ṡ10 relations and applies those coming from the cyclic symmetry of the Riemann tensor; (3) then applies the relations coming from the Bianchi identity, (4) the relations coming from commutations of covariant derivatives, (5) the dimensionally-dependent identities for dimension 4, and finally (6) simplifies invariants that can be expressed as product of dual invariants. Invar runs on top of the tensor computer algebra systems xTensor (for Mathematica) and Canon (for Maple). Program summaryProgram title:Invar Tensor Package v2.0 Catalogue identifier:ADZK_v2_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADZK_v2_0.html Program obtainable from:CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions:Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.:3 243 249 No. of bytes in distributed program, including test data, etc.:939 Distribution format:tar.gz Programming language:Mathematica and Maple Computer:Any computer running Mathematica versions 5.0 to 6.0 or Maple versions 9 and 11 Operating system:Linux, Unix, Windows XP, MacOS RAM:100 Mb Word size:64 or 32 bits Supplementary material:The new database of relations is much larger than that for the previous version and therefore has not been included in
Gerganov, Venelin M; Giordano, Mario; Samii, Madjid; Samii, Amir
2011-12-01
The reliable preoperative visualization of facial nerve location in relation to vestibular schwannoma (VS) would allow surgeons to plan tumor removal accordingly and may increase the safety of surgery. In this prospective study, the authors attempted to validate the reliability of facial nerve diffusion tensor (DT) imaging-based fiber tracking in a series of patients with large VSs. Furthermore, the authors evaluated the potential of this visualization technique to predict the morphological shape of the facial nerve (tumor compression-related flattening of the nerve). Diffusion tensor imaging and anatomical images (constructive interference in steady state) were acquired in a series of 22 consecutive patients with large VSs and postprocessed with navigational software to obtain facial nerve fiber tracking. The location of the cerebellopontine angle (CPA) part of the nerve in relation to the tumor was recorded during surgery by the surgeon, who was blinded to the results of the fiber tracking. A correlative analysis was performed of the imaging-based location of the nerve compared with its in situ position in relation to the VS. Fibers corresponding to the anatomical location and course of the facial nerve from the brainstem to the internal auditory meatus were identified with the DT imaging-based fiber tracking technique in all 22 cases. The location of the CPA segment of the facial nerve in relation to the VS determined during surgery corresponded to the location of the fibers, predicted by the DT imaging-based fiber tracking, in 20 (90.9%) of the 22 patients. No DT imaging-based fiber tracking correlates were found with the 2 morphological types of the nerve (compact or flat). The current study of patients with large VSs has shown that the position of the facial nerve in relation to the tumor can be predicted reliably (in 91%) using DT imaging-based fiber tracking. These are preliminary results that need further verification in a larger series.
A uniform parameterization of moment tensors
Tape, C.; Tape, W.
2015-12-01
A moment tensor is a 3 x 3 symmetric matrix that expresses an earthquake source. We construct a parameterization of the five-dimensional space of all moment tensors of unit norm. The coordinates associated with the parameterization are closely related to moment tensor orientations and source types. The parameterization is uniform, in the sense that equal volumes in the coordinate domain of the parameterization correspond to equal volumes of moment tensors. Uniformly distributed points in the coordinate domain therefore give uniformly distributed moment tensors. A cartesian grid in the coordinate domain can be used to search efficiently over moment tensors. We find that uniformly distributed moment tensors have uniformly distributed orientations (eigenframes), but that their source types (eigenvalue triples) are distributed so as to favor double couples. An appropriate choice of a priori moment tensor probability is a prerequisite for parameter estimation. As a seemingly sensible choice, we consider the homogeneous probability, in which equal volumes of moment tensors are equally likely. We believe that it will lead to improved characterization of source processes.
Second-order relational manipulations affect both humans and monkeys.
Christoph D Dahl
Full Text Available Recognition and individuation of conspecifics by their face is essential for primate social cognition. This ability is driven by a mechanism that integrates the appearance of facial features with subtle variations in their configuration (i.e., second-order relational properties into a holistic representation. So far, there is little evidence of whether our evolutionary ancestors show sensitivity to featural spatial relations and hence holistic processing of faces as shown in humans. Here, we directly compared macaques with humans in their sensitivity to configurally altered faces in upright and inverted orientations using a habituation paradigm and eye tracking technologies. In addition, we tested for differences in processing of conspecific faces (human faces for humans, macaque faces for macaques and non-conspecific faces, addressing aspects of perceptual expertise. In both species, we found sensitivity to second-order relational properties for conspecific (expert faces, when presented in upright, not in inverted, orientation. This shows that macaques possess the requirements for holistic processing, and thus show similar face processing to that of humans.
Irreducible Killing Tensors from Third Rank Killing-Yano Tensors
Popa, Florian Catalin; Tintareanu-Mircea, Ovidiu
2006-01-01
We investigate higher rank Killing-Yano tensors showing that third rank Killing-Yano tensors are not always trivial objects being possible to construct irreducible Killing tensors from them. We give as an example the Kimura IIC metric were from two rank Killing-Yano tensors we obtain a reducible Killing tensor and from third rank Killing-Yano tensors we obtain three Killing tensors, one reducible and two irreducible.
Pellegrini, Yves-Patrick
2015-01-01
The two-dimensional elastodynamic Green tensor is the primary building block of solutions of linear elasticity problems dealing with nonuniformly moving rectilinear line sources, such as dislocations. Elastodynamic solutions for these problems involve derivatives of this Green tensor, which stand as hypersingular kernels. These objects, well defined as distributions, prove cumbersome to handle in practice. This paper, restricted to isotropic media, examines some of their representations in the framework of distribution theory. A particularly convenient regularization of the Green tensor is introduced, that amounts to considering line sources of finite width. Technically, it is implemented by an analytic continuation of the Green tensor to complex times. It is applied to the computation of regularized forms of certain integrals of tensor character that involve the gradient of the Green tensor. These integrals are fundamental to the computation of the elastodynamic fields in the problem of nonuniformly moving d...
On Lovelock analogs of the Riemann tensor
Camanho, Xian O. [Albert-Einstein-Institut, Max-Planck-Institut fuer Gravitationsphysik, Golm (Germany); Dadhich, Naresh [Jamia Millia Islamia, Centre for Theoretical Physics, New Delhi (India); Inter-University Centre for Astronomy and Astrophysics, Pune (India)
2016-03-15
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. (orig.)
Cross-Order Integral Relations from Maximal Cuts
Johansson, Henrik; Larsen, Kasper J.; Søgaard, Mads
2015-01-01
We study the ABDK relation using maximal cuts of one- and two-loop integrals with up to five external legs. We show how to find a special combination of integrals that allows the relation to exist, and how to reconstruct the terms with one-loop integrals squared. The reconstruction relies on the observation that integrals across different loop orders can have support on the same generalized unitarity cuts and can share global poles. We discuss the appearance of nonhomologous integration contours in multivariate residues. Their origin can be understood in simple terms, and their existence enables us to distinguish contributions from different integrals. Our analysis suggests that maximal and near-maximal cuts can be used to infer the existence of integral identities more generally.
On the order equivalence relation of binary association measures
Paradowski Mariusz
2015-09-01
Full Text Available Over a century of research has resulted in a set of more than a hundred binary association measures. Many of them share similar properties. An overview of binary association measures is presented, focused on their order equivalences. Association measures are grouped according to their relations. Transformations between these measures are shown, both formally and visually. A generalization coefficient is proposed, based on joint probability and marginal probabilities. Combining association measures is one of recent trends in computer science. Measures are combined in linear and nonlinear discrimination models, automated feature selection or construction. Knowledge about their relations is particularly important to avoid problems of meaningless results, zeroed generalized variances, the curse of dimensionality, or simply to save time
INTERNATIONAL SECURITY RELATIONS AND POST-IMPERIAL ORDERS
Radu-Sebastian UNGUREANU
2011-08-01
Full Text Available This paper intends to investigate the relations between former imperial powers and new sovereign states succeeding an empire in the field of international security, particularly when involving the use of force. Despite their stated attachment to the normative principles of what we usually call “Westphalian order”, former imperial powers continue to interfere in the domestic affairs of these new states, especially those unable to exercise their sovereignty efficiently and legitimately. One could say that, by military interventions, these powers deny the sovereignty of weak states in the regions once under their control; but the preparation of these missions makes the actions not to be interpreted as expressions of an imperialist attitude. I consider there are two major ideal-types that could better explain such interventions. In a power-oriented post-imperial order, the intervention of a former empire is the result of the projection of its national interests and identities. In a norm-oriented post-imperial order, the sense of moral responsibility of the former imperial power is the main reason for its interference. The intervention’s legitimacy and suitability require domestic and international support. This paper, grounded on a constructivist approach, intends to contribute to the understanding of international security issues in terms of a world shaped by actors’ interests and identities and the dynamics of their relations. The identified ideal-types of post-imperial orders consider both material and cultural factors. The analytical elements that may link extremely different situations are the socially variable interpretations of past and present.
Renormalization procedure for random tensor networks and the canonical tensor model
Sasakura, Naoki
2015-01-01
We discuss a renormalization procedure for random tensor networks, and show that the corresponding renormalization-group flow is given by the Hamiltonian vector flow of the canonical tensor model, which is a discretized model of quantum gravity. The result is the generalization of the previous one concerning the relation between the Ising model on random networks and the canonical tensor model with N=2. We also prove a general theorem which relates discontinuity of the renormalization-group flow and the phase transitions of random tensor networks.
3D reconstruction of tensors and vectors
Defrise, Michel; Gullberg, Grant T.
2005-02-17
Here we have developed formulations for the reconstruction of 3D tensor fields from planar (Radon) and line-integral (X-ray) projections of 3D vector and tensor fields. Much of the motivation for this work is the potential application of MRI to perform diffusion tensor tomography. The goal is to develop a theory for the reconstruction of both Radon planar and X-ray or line-integral projections because of the flexibility of MRI to obtain both of these type of projections in 3D. The development presented here for the linear tensor tomography problem provides insight into the structure of the nonlinear MRI diffusion tensor inverse problem. A particular application of tensor imaging in MRI is the potential application of cardiac diffusion tensor tomography for determining in vivo cardiac fiber structure. One difficulty in the cardiac application is the motion of the heart. This presents a need for developing future theory for tensor tomography in a motion field. This means developing a better understanding of the MRI signal for diffusion processes in a deforming media. The techniques developed may allow the application of MRI tensor tomography for the study of structure of fiber tracts in the brain, atherosclerotic plaque, and spine in addition to fiber structure in the heart. However, the relations presented are also applicable to other fields in medical imaging such as diffraction tomography using ultrasound. The mathematics presented can also be extended to exponential Radon transform of tensor fields and to other geometric acquisitions such as cone beam tomography of tensor fields.
Theoretical study of the relativistic molecular rotational g-tensor
Aucar, I. Agustín, E-mail: agustin.aucar@conicet.gov.ar; Gomez, Sergio S., E-mail: ssgomez@exa.unne.edu.ar [Institute for Modeling and Technological Innovation, IMIT (CONICET-UNNE) and Faculty of Exact and Natural Sciences, Northeastern University of Argentina, Avenida Libertad 5400, W3404AAS Corrientes (Argentina); Giribet, Claudia G.; Ruiz de Azúa, Martín C. [Physics Department, Faculty of Exact and Natural Sciences, University of Buenos Aires and IFIBA CONICET, Ciudad Universitaria, Pab. I, 1428 Buenos Aires (Argentina)
2014-11-21
An original formulation of the relativistic molecular rotational g-tensor valid for heavy atom containing compounds is presented. In such formulation, the relevant terms of a molecular Hamiltonian for non-relativistic nuclei and relativistic electrons in the laboratory system are considered. Terms linear and bilinear in the nuclear rotation angular momentum and an external uniform magnetic field are considered within first and second order (relativistic) perturbation theory to obtain the rotational g-tensor. Relativistic effects are further analyzed by carrying out the linear response within the elimination of the small component expansion. Quantitative results for model systems HX (X=F, Cl, Br, I), XF (X=Cl, Br, I), and YH{sup +} (Y=Ne, Ar, Kr, Xe, Rn) are obtained both at the RPA and density functional theory levels of approximation. Relativistic effects are shown to be small for this molecular property. The relation between the rotational g-tensor and susceptibility tensor which is valid in the non-relativistic theory does not hold within the relativistic framework, and differences between both molecular parameters are analyzed for the model systems under study. It is found that the non-relativistic relation remains valid within 2% even for the heavy HI, IF, and XeH{sup +} systems. Only for the sixth-row Rn atom a significant deviation of this relation is found.
Amandine ePelletier
2016-01-01
Full Text Available Microstructural changes of White Matter (WM associated with aging have been widely described through Diffusion Tensor Imaging (DTI parameters. In parallel, White Matter Hyperintensities (WMH as observed on a T2-MRI are extremely common in older individuals. However, few studies have investigated both phenomena conjointly. The present study investigates aging effects on DTI parameters in absence and in presence of WMH. Diffusion maps were constructed based on 21 directions DTI scans of young adults (n=19, mean age=33 SD=7.4 and two age-matched groups of older adults, one presenting low-level-WMH (n=20, mean age=78, SD= 3.2 and one presenting high-level-WMH (n=20, mean age=79, SD= 5.4. Older subjects with low-level-WMH presented modifications of DTI parameters in comparison to younger subjects, fitting with the DTI pattern classically described in aging, i.e. Fractional Anisotropy (FA decrease/Radial Diffusivity (RD increase. Furthermore, older subjects with high-level-WMH showed higher DTI modifications in Normal Appearing White Matter (NAWM in comparison to those with low-level-WMH. Finally, in older subjects with high-level-WMH, FA or RD values of NAWM were associated with to WMH burden. Therefore, our findings suggest that DTI modifications and the presence of WMH would be two inter-dependent processes but occurring within different temporal windows. DTI changes would reflect the early phase of white matter changes and WMH would appear as a consequence of those changes.
E.M. Meintjes
2014-01-01
Full Text Available Reductions in brain volumes represent a neurobiological signature of fetal alcohol spectrum disorders (FASD. Less clear is how regional brain tissue reductions differ after normalizing for brain size differences linked with FASD and whether these profiles can predict the degree of prenatal exposure to alcohol. To examine associations of regional brain tissue excesses/deficits with degree of prenatal alcohol exposure and diagnosis with and without correction for overall brain volume, tensor-based morphometry (TBM methods were applied to structural imaging data from a well-characterized, demographically homogeneous sample of children diagnosed with FASD (n = 39, 9.6–11.0 years and controls (n = 16, 9.5–11.0 years. Degree of prenatal alcohol exposure was significantly associated with regionally pervasive brain tissue reductions in: (1 the thalamus, midbrain, and ventromedial frontal lobe, (2 the superior cerebellum and inferior occipital lobe, (3 the dorsolateral frontal cortex, and (4 the precuneus and superior parietal lobule. When overall brain size was factored out of the analysis on a subject-by-subject basis, no regions showed significant associations with alcohol exposure. FASD diagnosis was associated with a similar deformation pattern, but few of the regions survived FDR correction. In data-driven independent component analyses (ICA regional brain tissue deformations successfully distinguished individuals based on extent of prenatal alcohol exposure and to a lesser degree, diagnosis. The greater sensitivity of the continuous measure of alcohol exposure compared with the categorical diagnosis across diverse brain regions underscores the dose dependence of these effects. The ICA results illustrate that profiles of brain tissue alterations may be a useful indicator of prenatal alcohol exposure when reliable historical data are not available and facial features are not apparent.
Categorical Tensor Network States
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.
The Order-Theoretic Origin of Special Relativity
Knuth, Kevin H.; Bahrenyi, Newshaw
2011-03-01
In this paper, we present a novel derivation of special relativity and the information physics of events. We postulate that events are fundamental, and that some events have the potential to be influenced by other events. However, this potential is not reciprocal, nor are all pairs of events related in such a way. This leads to the concept of a partially-ordered set of events, which is often called a causal set. Quantification proceeds by distinguishing two chains of coordinated events, each of which represents an observer, and assigning a numerical valuation to each chain. By projecting events onto each chain, each event can be quantified by a pair of numbers, referred to as a pair. We show that each pair can be decomposed into a sum of symmetric and antisymmetric pairs, which correspond to time-like and space-like coordinates. We show that one can map a pair to a scalar and that this gives rise to the Minkowski metric. The result is an observer-based theory of special relativity that quantifies events with pairs of numbers. Events are fundamental and space-time is an artificial construct designed to make events look simple.
Metzler, S; Miettinen, P
2015-01-01
Tensor factorizations are computationally hard problems, and in particular, are often significantly harder than their matrix counterparts. In case of Boolean tensor factorizations -- where the input tensor and all the factors are required to be binary and we use Boolean algebra -- much of that hardness comes from the possibility of overlapping components. Yet, in many applications we are perfectly happy to partition at least one of the modes. In this paper we investigate what consequences doe...
Black holes in vector-tensor theories
Heisenberg, Lavinia; Kase, Ryotaro; Minamitsuji, Masato; Tsujikawa, Shinji
2017-08-01
We study static and spherically symmetric black hole (BH) solutions in second-order generalized Proca theories with nonminimal vector field derivative couplings to the Ricci scalar, the Einstein tensor, and the double dual Riemann tensor. We find concrete Lagrangians which give rise to exact BH solutions by imposing two conditions of the two identical metric components and the constant norm of the vector field. These exact solutions are described by either Reissner-Nordström (RN), stealth Schwarzschild, or extremal RN solutions with a non-trivial longitudinal mode of the vector field. We then numerically construct BH solutions without imposing these conditions. For cubic and quartic Lagrangians with power-law couplings which encompass vector Galileons as the specific cases, we show the existence of BH solutions with the difference between two non-trivial metric components. The quintic-order power-law couplings do not give rise to non-trivial BH solutions regular throughout the horizon exterior. The sixth-order and intrinsic vector-mode couplings can lead to BH solutions with a secondary hair. For all the solutions, the vector field is regular at least at the future or past horizon. The deviation from General Relativity induced by the Proca hair can be potentially tested by future measurements of gravitational waves in the nonlinear regime of gravity.
Gurau, Razvan
2016-01-01
Preface to the SIGMA special issue "Tensor Models, Formalism and Applications." The SIGMA special issue "Tensor Models, Formalism and Applications" is a collection of eight excellent, up to date reviews \\cite{Ryan:2016sundry,Bonzom:2016dwy,Rivasseau:2016zco,Carrozza:2016vsq,Krajewski:2016svb,Rivasseau:2016rgt,Tanasa:2015uhr,Gielen:2016dss} on random tensor models. The reviews combine pedagogical introductions meant for a general audience with presentations of the most recent developments in the field. This preface aims to give a condensed panoramic overview of random tensors as the natural generalization of random matrices to higher dimensions.
Cartesian tensors an introduction
Temple, G
2004-01-01
This undergraduate text provides an introduction to the theory of Cartesian tensors, defining tensors as multilinear functions of direction, and simplifying many theorems in a manner that lends unity to the subject. The author notes the importance of the analysis of the structure of tensors in terms of spectral sets of projection operators as part of the very substance of quantum theory. He therefore provides an elementary discussion of the subject, in addition to a view of isotropic tensors and spinor analysis within the confines of Euclidean space. The text concludes with an examination of t
Tensor network algorithm by coarse-graining tensor renormalization on finite periodic lattices
Zhao, Hui-Hai; Xie, Zhi-Yuan; Xiang, Tao; Imada, Masatoshi
2016-03-01
We develop coarse-graining tensor renormalization group algorithms to compute physical properties of two-dimensional lattice models on finite periodic lattices. Two different coarse-graining strategies, one based on the tensor renormalization group and the other based on the higher-order tensor renormalization group, are introduced. In order to optimize the tensor network model globally, a sweeping scheme is proposed to account for the renormalization effect from the environment tensors under the framework of second renormalization group. We demonstrate the algorithms by the classical Ising model on the square lattice and the Kitaev model on the honeycomb lattice, and show that the finite-size algorithms achieve substantially more accurate results than the corresponding infinite-size ones.
Tensor supermultiplets and toric quaternion-Kaehler geometry
Wit, B. de; Saueressig, F. [Institute for Theoretical Physics and Spinoza Institute, Utrecht University, Utrecht (Netherlands)
2007-05-15
We review the relation between 4n-dimensional quaternion-Kaehler metrics with n+1 abelian isometries and superconformal theories of n+1 tensor supermultiplets. As an application we construct the class of eight-dimensional quaternion-Kaehler metrics with three abelian isometries in terms of a single function obeying a set of linear second-order partial differential equations. (Abstract Copyright [2007], Wiley Periodicals, Inc.)
On the tensor Permutation Matrices
Rakotonirina, Christian
2011-01-01
A property that tensor permutation matrices permutate tensor product of rectangle matrices is shown. Some examples, in the particular case of tensor commutation matrices, for studying some linear matricial equations are given.
On the structure of order domains
Geil, Olav; Pellikaan, Ruud
2002-01-01
The notion of an order domain is generalized. The behaviour of an order domain by taking a subalgebra, the extension of scalars, and the tensor product is studied. The relation of an order domain with valuation theory, Gröbner algebras, and graded structures is given. The theory of Gröbner bases ...
Data fusion in metabolomics using coupled matrix and tensor factorizations
Evrim, Acar Ataman; Bro, Rasmus; Smilde, Age Klaas
2015-01-01
With a goal of identifying biomarkers/patterns related to certain conditions or diseases, metabolomics focuses on the detection of chemical substances in biological samples such as urine and blood using a number of analytical techniques, including nuclear magnetic resonance (NMR) spectroscopy...... vast amounts of data using different analytical methods, data fusion remains a challenging task, in particular, when the goal is to capture the underlying factors and use them for interpretation, e.g., for biomarker identification. Furthermore, many data fusion applications require joint analysis...... of heterogeneous (i.e., in the form of higher order tensors and matrices) data sets with shared/unshared factors. In order to jointly analyze such heterogeneous data sets, we formulate data fusion as a coupled matrix and tensor factorization (CMTF) problem, which has already proved useful in many data mining...
Faber, J; Wilde, E A; Hanten, G; Ewing-Cobbs, L; Aitken, M E; Yallampalli, R; MacLeod, M C; Mullins, S H; Chu, Z D; Li, X; Hunter, J V; Noble-Haeusslein, L; Levin, H S
2016-01-01
The long-term effects of TBI on verbal fluency and related structures, as well as the relation between cognition and structural integrity, were evaluated. It was hypothesized that the group with TBI would evidence poorer performance on cognitive measures and a decrease in structural integrity. Between a paediatric group with TBI and a group of typically-developing children, the long-term effects of traumatic brain injury were investigated in relation to both structural integrity and cognition. Common metrics for diffusion tensor imaging (DTI) were used as indicators of white matter integrity. Using DTI, this study examined ventral striatum (VS) integrity in 21 patients aged 10-18 years sustaining moderate-to-severe traumatic brain injury (TBI) 5-15 years earlier and 16 demographically comparable subjects. All participants completed Delis-Kaplan Executive Functioning System (D-KEFS) sub-tests. The group with TBI exhibited lower fractional anisotropy (FA) and executive functioning performance and higher apparent diffusion coefficient (ADC). DTI metrics correlated with D-KEFS performance (right VS FA with Inhibition errors, right VS ADC with Letter Fluency, left VS FA and ADC with Category Switching). TBI affects VS integrity, even in a chronic phase, and may contribute to executive functioning deficits.
Koch, K; Wagner, G; Dahnke, R; Schachtzabel, C; Güllmar, D; Reichenbach, J R; Schlösser, R G M
2010-06-16
In the context of probabilistic learning, previous functional magnetic resonance imaging studies have shown decreasing uncertainty accompanying decreasing neuronal activation in task-relevant networks. Moreover, initial evidence points to a relationship between white matter structure and cognitive performance. Little is known, however, about the structural correlates underlying individual differences in activation and performance in the context of probabilistic learning. This combined functional magnetic resonance imaging-diffusion tensor imaging study aimed at investigating the individual ability to reduce processing resources with decreasing uncertainty in direct relation to individual characteristics in white matter brain structure. Results showed that more successful learners, as compared with less successful learners, exhibited stronger activation decreases with decreasing uncertainty. An increased mean and axial diffusivity in, among others, the inferior and superior longitudinal fasciculus, the posterior part of the cingulum bundle, and the corpus callosum were detectable in less successful learners compared with more successful learners. Most importantly, there was a negative correlation between uncertainty-related activation and diffusivity in a fronto-parieto-striatal network in less successful learners only, indicating a direct relation between diffusivity and the ability to reduce processing resources with decreasing uncertainty. These findings indicate that interindividual variations in white matter characteristics within the normal population might be linked to neuronal activation and critically influence individual learning performance.
Tensor network and a black hole
Matsueda, Hiroaki; Ishihara, Masafumi; Hashizume, Yoichiro
2013-03-01
A tensor-network variational formalism of thermofield dynamics is introduced. The formalism relates the original Hilbert space with its tilde space by a product of two copies of a tensor network. Then, their interface becomes an event horizon, and the logarithm of the tensor rank corresponds to the black hole entropy. Eventually, a multiscale entanglement renormalization ansatz reproduces an anti-de Sitter black hole at finite temperature. Our finding shows rich functionalities of multiscale entanglement renormalization ansatz as efficient graphical representation of AdS/CFT correspondence.
冯远静; 吴烨; 张贵军; 梁荣华
2015-01-01
高阶张量扩散磁共振成像技术是高分辨率显示活体脑白质微结构信息的重要方法，但其数据采集时间较长、纤维重构分辨率较低等缺点限制其在临床上的应用。文中在高阶张量模型的基础上提出一种稀疏加权的纤维方向分布估计方法。该方法首先建立高阶张量球面反卷积纤维方向估计模型，然后提出一种纤维方向的稀疏表示方法，最后建立稀疏约束反卷积的l1范数优化模型。针对优化模型的求，提出一种用低阶训练稀疏字典决高阶优化问题的计算方法。模拟数据和临床数据的实验表明，纤维方向分布估计方法有效提高高阶张量成像方法的角度分辨率，降低角度识别误差。%High Order Tensor ( HOT) diffusion magnetic resonance imaging is an important method to reveal the microstructural information of living brain white matter. However, its time﹣consuming data acquisition and low fiber reconstructing resolution limit its clinical application. In this paper, a fiber orientation estimation method with weighted sparse is presented based on HOT model. Firstly, the HOT spherical deconvolution model for fiber orientation estimation is established. Then, a sparse representation method of fiber orientation is put forward. Finally, a l1﹣norm optimization model is built for the sparse constraint deconvolution. A computing method of applying the training results of sparse dictionary with lower order into the high﹣order problem is proposed to achieve the solution of the optimization problem. The experimental results on simulated and vivo data show that the fiber orientation estimation method improves the angular resolution of HOT tensor imaging method and reduces the angle recognition error.
Agasian, N O
2016-01-01
A treatment is given of the nonperturbative QCD vacuum in a magnetic field. The low-energy equation for the trace of the energy-momentum tensor in a magnetic field is derived. It is shown that the derivatives with respect to a magnetic field of the quark and gluon contributions to the trace of the energy-momentum tensor are equal. The dependence of the gluon condensate on the magnetic field strength is derived both for strong and weak fields.
Disruption of Relational Processing Underlies Poor Memory for Order
Jonker, Tanya R.; MacLeod, Colin M.
2015-01-01
McDaniel and Bugg (2008) proposed that relatively uncommon stimuli and encoding tasks encourage elaborative encoding of individual items (item-specific processing), whereas relatively typical or common encoding tasks encourage encoding of associations among list items (relational processing). It is this relational processing that is thought to…
The Weyl tensor correlator in cosmological spacetimes
Fröb, Markus B
2014-01-01
We give a general expression for the Weyl tensor two-point function in a general Friedmann-Lema\\^itre-Robertson-Walker spacetime. We work in reduced phase space for the perturbations, i.e., quantize only the dynamical degrees of freedom without adding any gauge-fixing term. The general formula is illustrated by a calculation in slow-roll single-field inflation to first order in the slow-roll parameters $\\epsilon$ and $\\delta$, and the result is shown to have the correct de Sitter limit as $\\epsilon, \\delta \\to 0$. Furthermore, it is seen that the Weyl tensor correlation function does not suffer from infrared divergences, unlike the two-point functions of the metric and scalar field perturbations. Lastly, we show how to recover the usual tensor power spectrum from the Weyl tensor correlation function.
Primordial tensor modes of the early Universe
Martínez, Florencia Benítez
2016-01-01
We study cosmological tensor perturbations on a quantized background within the hybrid quantization approach. In particular, we consider a flat, homogeneous and isotropic spacetime and small tensor inhomogeneities on it. We truncate the action to second order in the perturbations. The dynamics is ruled by a homogeneous scalar constraint. We carry out a canonical transformation in the system where the Hamiltonian for the tensor perturbations takes a canonical form. The new tensor modes now admit a standard Fock quantization with a unitary dynamics. We then combine this representation with a generic quantum scheme for the homogeneous sector. We adopt a Born-Oppenheimer ansatz for the solutions to the constraint operator, previously employed to study the dynamics of scalar inhomogeneities. We analyze the approximations that allow us to recover, on the one hand, a Schr\\"odinger equation similar to the one emerging in the dressed metric approach, and, on the other hand, the ones necessary for the effective evoluti...
Educational Needs of Women in Relation to Postpartum Religious Orders
Beigi, Marjan; Nekuei, Nafisehsadat
2017-01-01
Introduction: Religious orders are one of the educational needs of the postpartum period. This study was conducted to determine the educational needs of postpartum religious orders. Materials and Methods: This cross-sectional study was conducted among 421 postpartum women and 15 specialists. Quota random sampling was conducted from January to March 2014 in Isfahan, Iran. Data analysis was performed using the Statistical Package for the Social Sciences software and statistical methods. Results...
Obtaining the Weyl tensor from the Bel-Robinson tensor
Ferrando, Joan J; 10.1007/s10714-009-0921-8
2010-01-01
The algebraic study of the Bel-Robinson tensor proposed and initiated in a previous work (Gen. Relativ. Gravit. {\\bf 41}, see ref [11]) is achieved. The canonical form of the different algebraic types is obtained in terms of Bel-Robinson eigen-tensors. An algorithmic determination of the Weyl tensor from the Bel-Robinson tensor is presented.
Tensor Network Skeletonization
Ying, Lexing
2016-01-01
We introduce a new coarse-graining algorithm, tensor network skeletonization, for the numerical computation of tensor networks. This approach utilizes a structure-preserving skeletonization procedure to remove short-range correlations effectively at every scale. This approach is first presented in the setting of 2D statistical Ising model and is then extended to higher dimensional tensor networks and disordered systems. When applied to the Euclidean path integral formulation, this approach also gives rise to new efficient representations of the ground states for 1D and 2D quantum Ising models.
Real-time framework for tensor-based image enhancement for object classification
Cyganek, Bogusław; Smołka, Bogdan
2016-04-01
In many practical situations visual pattern recognition is vastly burdened by low quality of input images due to noise, geometrical distortions, as well as low quality of the acquisition hardware. However, although there are techniques of image quality improvements, such as nonlinear filtering, there are only few attempts reported in the literature that try to build these enhancement methods into a complete chain for multi-dimensional object recognition such as color video or hyperspectral images. In this work we propose a joint multilinear signal filtering and classification system built upon the multi-dimensional (tensor) approach. Tensor filtering is performed by the multi-dimensional input signal projection into the tensor subspace spanned by the best-rank tensor decomposition method. On the other hand, object classification is done by construction of the tensor sub-space constructed based on the Higher-Order Singular Value Decomposition method applied to the prototype patters. In the experiments we show that the proposed chain allows high object recognition accuracy in the real-time even from the poor quality prototypes. Even more importantly, the proposed framework allows unified classification of signals of any dimensions, such as color images or video sequences which are exemplars of 3D and 4D tensors, respectively. The paper discussed also some practical issues related to implementation of the key components of the proposed system.
Birth Order, Sibling IQ Differences, and Family Relations.
Pfouts, Jane H.
The differential impact of birth order and IQ on sibling roles were examined with particular interest focused on achievement outcomes. Subjects were a stratified sample of 37 pairs of near-in-age siblings, all within the normal range in personality and IQ, but differing significantly in scores on the Slosson IQ Test. Results indicate that when the…
Exploring the Tensor Networks/AdS Correspondence
Bhattacharyya, Arpan; Hung, Ling-Yan; Liu, Si-Nong
2016-01-01
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. Study- ing 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, the leading contribution is given by structures related to geodesics connecting the operators inserted at the boundary physical dofs. Such considerations admits 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 ...
A gravito-electromagnetic analogy based on tidal tensors
Costa, L F; Herdeiro, Carlos A. R.
2006-01-01
We propose a new approach to a physical analogy between General Relativity and Electromagnetism, based on comparing tidal tensors of both theories. Using this approach we write a covariant form for the gravitational analogues of the Maxwell equations, from which the regime of validity of the analogy becomes manifest. Two explicit realisations of the analogy are given. The first one matches linearised gravitational tidal tensors to exact electromagnetic tidal tensors in Minkwoski spacetime. The second one matches exact magnetic gravitational tidal tensors for ultra-stationary metrics to exact magnetic tidal tensors of electromagnetism in curved spaces. We then establish a new proof for a class of tensor identities that define invariants of the type $\\vec{E}^2-\\vec{B}^2$ and $\\vec{E}\\cdot\\vec{B}$, and we exhibit the invariants built from tidal tensors in both gravity and electromagnetism. We contrast our approach with the two gravito-electromagnetic analogies commonly found in the literature, which are reviewed...
Westerhof, E.
1996-01-01
The hot plasma dielectric tensor is discussed in its various approximations. Collisionless cyclotron resonant damping and ion/electron Bernstein waves are discussed to exemplify the significance of a kinetic description of plasma waves.
Tensor Network Renormalization.
Evenbly, G; Vidal, G
2015-10-30
We introduce a coarse-graining transformation for tensor networks that can be applied to study both the partition function of a classical statistical system and the Euclidean path integral of a quantum many-body system. The scheme is based upon the insertion of optimized unitary and isometric tensors (disentanglers and isometries) into the tensor network and has, as its key feature, the ability to remove short-range entanglement or correlations at each coarse-graining step. Removal of short-range entanglement results in scale invariance being explicitly recovered at criticality. In this way we obtain a proper renormalization group flow (in the space of tensors), one that in particular (i) is computationally sustainable, even for critical systems, and (ii) has the correct structure of fixed points, both at criticality and away from it. We demonstrate the proposed approach in the context of the 2D classical Ising model.
Huisman, Thierry A G M; Loenneker, Thomas; Barta, Gerd; Bellemann, Matthias E; Hennig, Juergen; Fischer, Joachim E; Il'yasov, Kamil A
2006-08-01
The objectives were to study the "impact" of the magnetic field strength on diffusion tensor imaging (DTI) metrics and also to determine whether magnetic-field-related differences in T2-relaxation times of brain tissue influence DTI measurements. DTI was performed on 12 healthy volunteers at 1.5 and 3.0 Tesla (within 2 h) using identical DTI scan parameters. Apparent diffusion coefficient (ADC) and fractional anisotropy (FA) values were measured at multiple gray and white matter locations. ADC and FA values were compared and analyzed for statistically significant differences. In addition, DTI measurements were performed at different echo times (TE) for both field strengths. ADC values for gray and white matter were statistically significantly lower at 3.0 Tesla compared with 1.5 Tesla (% change between -1.94% and -9.79%). FA values were statistically significantly higher at 3.0 Tesla compared with 1.5 Tesla (% change between +4.04 and 11.15%). ADC and FA values are not significantly different for TE=91 ms and TE=125 ms. Thus, ADC and FA values vary with the used field strength. Comparative clinical studies using ADC or FA values should consequently compare ADC or FA results with normative ADC or FA values that have been determined for the field strength used.
Tensor-tensor theory of gravitation
Gogberashvili, Merab
1996-01-01
We consider the standard gauge theory of Poincar\\'{e} group, realizing as a subgroup of GL(5. R). The main problem of this theory was appearing of the fields connected with non-Lorentz symmetries, whose physical sense was unclear. In this paper we treat the gravitation as a Higgs-Goldstone field, and the translation gauge field as a new tensor field. The effective metric tensor in this case is hybrid of two tensor fields. In the linear approximation the massive translation gauge field can give the Yukava type correction to the Newtons potential. Also outer potentials of a sphere and ball of the same mass are different in this case. Corrections to the standard Einshtein post Newtonian formulas of the light deflection and radar echo delay is obtained. The string like solution of the nonlinear equations of the translation gauge fields is found. This objects can results a Aharonov-Bohm type effect even for the spinless particles. They can provide density fluctuations in the early universe, necessary for galaxy fo...
Positive representations of general commutation relations allowing Wick ordering
Jorgensen, P E T; Werner, R F
1993-01-01
where the $T_{ij}^{k\\ell}$ are essentially arbitrary scalar coefficients. Examples comprise the $q$-canonical commutation relations introduced by Greenberg, Bozejko, and Speicher, and the twisted canonical (anti-)commutation relations studied by Pusz and Woronowicz, as well as the quantum group S$_\
Sino-Russian Relations in a Changing World Order
2013-01-01
state sovereignty over internal affairs and a condominium of great powers, represented by the Security Council, to negotiate world trouble spots...addition, throughout the 1990s and early 2000s, the Russian defense industry was desperate for orders and cash. China wanted advanced weapons systems ...arenas. Today, however, apart from nuclear forces and the technological sophistication of some major weapons systems , China is ascendant in the
Sino-Russian Relations in a Changing World Order
2014-01-01
It also includes the development of multilateral organi- zations that exclude the West, such as the BRICS (Brazil, Russia, India, China, and South...on world order. In fact, Russia is overshadowed by more powerful states in most multilateral forums, including the G8 and BRICS gatherings...February 2014, http://blogs.ft.com/beyond- brics /2014/02/27/ukraine-a-setback-in -chinas-eastern-europe-strategy/?. 15. See, for example, “Backing
Causality and Primordial Tensor Modes
Baumann, Daniel
2009-01-01
We introduce the real space correlation function of $B$-mode polarization of the cosmic microwave background (CMB) as a probe of superhorizon tensor perturbations created by inflation. By causality, any non-inflationary mechanism for gravitational wave production after reheating, like global phase transitions or cosmic strings, must have vanishing correlations for angular separations greater than the angle subtended by the particle horizon at recombination, i.e. $\\theta \\gtrsim 2^\\circ$. Since ordinary $B$-modes are defined non-locally in terms of the Stokes parameters $Q$ and $U$ and therefore don't have to respect causality, special care is taken to define `causal $\\tilde B$-modes' for the analysis. We compute the real space $\\tilde B$-mode correlation function for inflation and discuss its detectability on superhorizon scales where it provides an unambiguous test of inflationary gravitational waves. The correct identification of inflationary tensor modes is crucial since it relates directly to the energy s...
Vijay eVenkatraman
2011-09-01
Full Text Available Background: Slowing information processing is common among community-dwelling elderly and it predicts greater mortality and disability risk. Slowing information processing is related to brain macro-structural abnormalities. Specifically, greater global atrophy and greater small vessel disease of the white matter have been associated to slower processing speed. However, community-dwelling elderly with such macro-structural abnormalities can maintain processing speed. The roles of brain micro-structure for slow processing in very old adults living in the community is uncertain, as epidemiological studies relating these brain markers to cognition and in the context of other health characteristics are sparse. Hypothesis: Information processing is cross-sectionally associated with white matter micro-structure independent of overt macro-structural abnormalities and also independent of health related characteristics. Methods: Imaging indices of micro-structure (diffusion tensor imaging, DTI, and magnetization transfer imaging, MTI, macro-structure (white matter hyperintensities, gray matter volume, Digit Symbol Substitution Test (DSST and health characteristics were measured in 272 elderly (mean age 83 years old, 43% men, 40% Black living in the community. Results: The DTI- and MTI-indices of micro-structure from the normal appearing white matter and not from the normal appearing gray matter were associated with DSST score independent of white matter hyperintensities and gray matter volumes. Associations were also independent of age, race, gender, mini-mental score, systolic blood pressure, prevalent myocardial infarction. Interpretation: DTI and MTI indices of normal appearing white matter are indicators of information processing speed in this cohort of very old adults living in the community. Since processing slowing is a potent index of mortality and disability, these indices may serve as biomarkers in prevention or treatment trials of disability.
Entangled scalar and tensor fluctuations during inflation
Collins, Hael; Vardanyan, Tereza [Department of Physics, Carnegie Mellon University,5000 Forbes Avenue, Pittsburgh, Pennsylvania (United States)
2016-11-29
We show how the choice of an inflationary state that entangles scalar and tensor fluctuations affects the angular two-point correlation functions of the T, E, and B modes of the cosmic microwave background. The propagators for a state starting with some general quadratic entanglement are solved exactly, leading to predictions for the primordial scalar-scalar, tensor-tensor, and scalar-tensor power spectra. These power spectra are expressed in terms of general functions that describe the entangling structure of the initial state relative to the standard Bunch-Davies vacuum. We illustrate how such a state would modify the angular correlations in the CMB with a simple example where the initial state is a small perturbation away from the Bunch-Davies state. Because the state breaks some of the rotational symmetries, the angular power spectra no longer need be strictly diagonal.
Barberi, G.; Cammarata, L.; Cocina, O.; Maiolino, V.; Musumeci, C.; Privitera, E.
2003-04-01
Late on the night of October 26, 2002, a bi-lateral eruption started on both the eastern and the southeastern flanks of Mt. Etna. The opening of the eruptive fracture system on the NE sector and the reactivation of the 2001 fracture system, on the S sector, were accompanied by a strong seismic swarm recorded between October 26 and 28 and by sharp increase of volcanic tremor amplitude. After this initial phase, on October 29 another seismogenetic zone became active in the SE sector of the volcano. At present (January 2003) the eruption is still in evolution. During the whole period a total of 862 earthquakes (Md≫1) was recorded by the local permanent seismic network run by INGV - Sezione di Catania. The maximum magnitude observed was Md=4.4. We focus our attention on 55 earthquakes with magnitude Md≫ 3.0. The dataset consists of accurate digital pickings of P- and S-phases including first-motion polarities. Firstly earthquakes were located using a 1D velocity model (Hirn et alii, 1991), then events were relocated by using two different 3D velocity models (Aloisi et alii, 2002; Patane et alii, 2002). Results indicate that most of earthquakes are located to the east of the Summit Craters and to northeast of them. Fault plane solutions (FPS) obtained show prevalent strike-slip rupture mechanisms. The suitable FPSs were considered for the application of Gephart and Forsyth`s algorithm in order to evaluate seismic stress field characteristics. Taking into account the preliminary results we propose a kinematic model of the eastern flank eastward movement in response of the intrusion processes in the central part of the volcano. References Aloisi M., Cocina O., Neri G., Orecchio B., Privitera E. (2002). Seismic tomography of the crust underneath the Etna volcano, Sicily. Physics of the Earth and Planetary Interiors 4154, pp. 1-17 Hirn A., Nercessian A., Sapin M., Ferrucci F., Wittlinger G. (1991). Seismic heterogeneity of Mt. Etna: structure and activity. Geophys. J
Ordinary Workers and Industrial Relations in a New World Order
Nielsen, Niels Jul
2014-01-01
—involving fieldwork at both workplaces and private homes—of Polish migrant laborers participating in the Danish labor market. Firstly, it is shown how the Polish laborers, due to the lower costs they represent, benefit from the new opportunities. Secondly, the paper illustrates how the trade union, though uneasy...... with the downward pressure on wage and working conditions that the Polish represent, prioritizes the organization of workers in order to maintain some degree of control over the labor market. Finally, the question is raised how the EU (European Union) is able to navigate two contrasting concerns: the urge both...
Novel Physics with Tensor Polarized Deuteron Targets
Slifer, Karl J. [UNH; Long, Elena A. [UNH
2013-09-01
Development of solid spin-1 polarized targets will open the study of tensor structure functions to precise measurement, and holds the promise to enable a new generation of polarized scattering experiments. In this talk we will discuss a measurement of the leading twist tensor structure function b1, along with prospects for future experiments with a solid tensor polarized target. The recently approved JLab experiment E12-13-011 will measure the lead- ing twist tensor structure function b1, which provides a unique tool to study partonic effects, while also being sensitive to coherent nuclear properties in the simplest nuclear system. At low x, shadowing effects are expected to dominate b1, while at larger values, b1 provides a clean probe of exotic QCD effects, such as hidden color due to 6-quark configuration. Since the deuteron wave function is relatively well known, any non-standard effects are expected to be readily observable. All available models predict a small or vanishing value of b1 at moderate x. However, the first pioneer measurement of b1 at HERMES revealed a crossover to an anomalously large negative value in the region 0.2 < x < 0.5, albeit with relatively large experimental uncertainty. E12-13-011 will perform an inclusive measurement of the deuteron tensor asymmetry in the region 0.16 < x < 0.49, for 0.8 < Q2 < 5.0 GeV2. The UVa solid polarized ND3 target will be used, along with the Hall C spectrometers, and an unpolarized 115 nA beam. This measurement will provide access to the tensor quark polarization, and allow a test of the Close-Kumano sum rule, which vanishes in the absence of tensor polarization in the quark sea. Until now, tensor structure has been largely unexplored, so the study of these quantities holds the potential of initiating a new field of spin physics at Jefferson Lab.
MULTISCALE TENSOR ANISOTROPIC FILTERING OF FLUORESCENCE MICROSCOPY FOR DENOISING MICROVASCULATURE.
Prasath, V B S; Pelapur, R; Glinskii, O V; Glinsky, V V; Huxley, V H; Palaniappan, K
2015-04-01
Fluorescence microscopy images are contaminated by noise and improving image quality without blurring vascular structures by filtering is an important step in automatic image analysis. The application of interest here is to automatically extract the structural components of the microvascular system with accuracy from images acquired by fluorescence microscopy. A robust denoising process is necessary in order to extract accurate vascular morphology information. For this purpose, we propose a multiscale tensor with anisotropic diffusion model which progressively and adaptively updates the amount of smoothing while preserving vessel boundaries accurately. Based on a coherency enhancing flow with planar confidence measure and fused 3D structure information, our method integrates multiple scales for microvasculature preservation and noise removal membrane structures. Experimental results on simulated synthetic images and epifluorescence images show the advantage of our improvement over other related diffusion filters. We further show that the proposed multiscale integration approach improves denoising accuracy of different tensor diffusion methods to obtain better microvasculature segmentation.
Invariant slow-roll parameters in scalar-tensor theories
Kuusk, Piret; Rünkla, Mihkel; Saal, Margus; Vilson, Ott
2016-10-01
A general scalar-tensor theory can be formulated in different parametrizations that are related by a conformal rescaling of the metric and a scalar field redefinition. We compare formulations of slow-roll regimes in the Einstein and Jordan frames using quantities that are invariant under the conformal rescaling of the metric and transform as scalar functions under the reparametrization of the scalar field. By comparing spectral indices, calculated up to second order, we find that the frames are equivalent up to this order, due to the underlying assumptions.
Invariant slow-roll parameters in scalar-tensor theories
Kuusk, Piret; Saal, Margus; Vilson, Ott
2016-01-01
A general scalar-tensor theory can be formulated in different parametrizations that are related by a conformal rescaling of the metric and a scalar field redefinition. We compare formulations of slow-roll regimes in the Einstein and Jordan frames using quantities that are invariant under the conformal rescaling of the metric and transform as scalar functions under the reparametrization of the scalar field. By comparing spectral indices, calculated up to second order, we find that the frames are equivalent up to this order, due to the underlying assumptions.
Improving Tensor Based Recommenders with Clustering
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...
Cross-Order Relations in N=4 Supersymmetric Gauge Theories
Anastasiou, C; Dixon, L J; Kosower, D A
2004-01-01
The anti-de Sitter/conformal field theory duality conjecture raises the question of how the perturbative expansion in the conformal field theory can resum to a simple function. We exhibit a relation between the one-loop and two-loop amplitudes whose generalization to higher-point and higher-loop amplitudes would answer this question. We also provide evidence for the first of these generalizations.
Electronic stress tensor analysis of molecules in gas phase of CVD process for GeSbTe alloy
Nozaki, Hiroo; Ichikawa, Kazuhide; Tachibana, Akitomo
2015-01-01
We analyze the electronic structure of molecules which may exist in gas phase of chemical vapor deposition process for GeSbTe alloy using the electronic stress tensor, with special focus on the chemical bonds between Ge, Sb and Te atoms. We find that, from the viewpoint of the electronic stress tensor, they have intermediate properties between alkali metals and hydrocarbon molecules. We also study the correlation between the bond order which is defined based on the electronic stress tensor, and energy-related quantities. We find that the correlation with the bond dissociation energy is not so strong while one with the force constant is very strong. We interpret these results in terms of the energy density on the "Lagrange surface", which is considered to define the boundary surface of atoms in a molecule in the framework of the electronic stress tensor analysis.
Electronic stress tensor analysis of molecules in gas phase of CVD process for GeSbTe alloy.
Nozaki, Hiroo; Ikeda, Yuji; Ichikawa, Kazuhide; Tachibana, Akitomo
2015-06-15
We analyze the electronic structure of molecules which may exist in gas phase of chemical vapor deposition process for GeSbTe alloy using the electronic stress tensor, with special focus on the chemical bonds between Ge, Sb, and Te atoms. We find that, from the viewpoint of the electronic stress tensor, they have intermediate properties between alkali metals and hydrocarbon molecules. We also study the correlation between the bond order which is defined based on the electronic stress tensor, and energy-related quantities. We find that the correlation with the bond dissociation energy is not so strong while one with the force constant is very strong. We interpret these results in terms of the energy density on the "Lagrange surface," which is considered to define the boundary surface of atoms in a molecule in the framework of the electronic stress tensor analysis.
Causality and primordial tensor modes
Baumann, Daniel; Zaldarriaga, Matias, E-mail: dbaumann@physics.harvard.edu, E-mail: mzaldarriaga@cfa.harvard.edu [Department of Physics, Harvard University, 17 Oxford Street, Cambridge, MA 02138, U.S.A. and Center for Astrophysics, Harvard University, 60 Garden Street, Cambridge, MA 02138 (United States)
2009-06-01
We introduce the real space correlation function of B-mode polarization of the cosmic microwave background (CMB) as a probe of superhorizon tensor perturbations created by inflation. By causality, any non-inflationary mechanism for gravitational wave production after reheating, like global phase transitions or cosmic strings, must have vanishing correlations for angular separations greater than the angle subtended by the particle horizon at recombination, i.e. θ ∼> 2°. Since ordinary B-modes are defined non-locally in terms of the Stokes parameters Q and U and therefore don't have to respect causality, special care is taken to define 'causal B-tilde -modes' for the analysis. We compute the real space B-tilde -mode correlation function for inflation and discuss its detectability on superhorizon scales where it provides an unambiguous test of inflationary gravitational waves. The correct identification of inflationary tensor modes is crucial since it relates directly to the energy scale of inflation. Wrongly associating tensor modes from causal seeds with inflation would imply an incorrect inference of the energy scale of inflation. We find that the superhorizon B-tilde -mode signal is above cosmic variance for the angular range 2° < θ < 4° and is therefore in principle detectable. In practice, the signal will be challenging to measure since it requires accurately resolving the recombination peak of the B-mode power spectrum. However, a future CMB satellite (CMBPol), with noise level Δ{sub P} ≅ 1μK-arcmin and sufficient resolution to efficiently correct for lensing-induced B-modes, should be able to detect the signal at more than 3σ if the tensor-to-scalar ratio isn't smaller than r ≅ 0.01.
Reformulation of the symmetries of first-order general relativity
Montesinos, Merced; González, Diego; Celada, Mariano; Díaz, Bogar
2017-10-01
We report a new internal gauge symmetry of the n-dimensional Palatini action with cosmological term (n>3 ) that is the generalization of three-dimensional local translations. This symmetry is obtained through the direct application of the converse of Noether’s second theorem on the theory under consideration. We show that diffeomorphisms can be expressed as linear combinations of it and local Lorentz transformations with field-dependent parameters up to terms involving the variational derivatives of the action. As a result, the new internal symmetry together with local Lorentz transformations can be adopted as the fundamental gauge symmetries of general relativity. Although their gauge algebra is open in general, it allows us to recover, without resorting to the equations of motion, the very well-known Lie algebra satisfied by translations and Lorentz transformations in three dimensions. We also report the analog of the new gauge symmetry for the Holst action with cosmological term, finding that it explicitly depends on the Immirzi parameter. The same result concerning its relation to diffeomorphisms and the open character of the gauge algebra also hold in this case. Finally, we consider the non-minimal coupling of a scalar field to gravity in n dimensions and establish that the new gauge symmetry is affected by this matter field. Our results indicate that general relativity in dimension greater than three can be thought of as a gauge theory.
Scalar perturbations in a Friedmann-like metric with non-null Weyl tensor
Santos, Grasiele B; Salim, José M
2013-01-01
In a previous work some of the authors have solved the Einstein equations of General Relativity for a class of metrics with constant spatial curvature, where it was found a non vanishing Weyl tensor in the presence of an energy-momentum tensor with an anisotropic pressure component. Here, we perform the perturbative analysis of this model in order to study the gravitational stability under linear scalar perturbations. For this purpose, we take the Quasi-Maxwellian formalism of General Relativity as our framework, which offers a naturally covariant and gauge-invariant approach to deal with perturbations that are directly linked to observational quantities. We also consider a generalization of the causal thermodynamics to include the effect of the non-null Weyl tensor, which introduces a "viscosity" due solely to the gravitational tidal forces.
Dirac tensor with heavy photon
Bytev, V.V.; Kuraev, E.A. [Joint Institute of Nuclear Research, Moscow (Russian Federation). Bogoliubov Lab. of Theoretical Physics; Scherbakova, E.S. [Hamburg Univ. (Germany). 1. Inst. fuer Theoretische Physik
2012-01-15
For the large-angles hard photon emission by initial leptons in process of high energy annihilation of e{sup +}e{sup -} {yields} to hadrons the Dirac tensor is obtained, taking into account the lowest order radiative corrections. The case of large-angles emission of two hard photons by initial leptons is considered. This result is being completed by the kinematics case of collinear hard photons emission as well as soft virtual and real photons and can be used for construction of Monte-Carlo generators. (orig.)
p-Norm SDD tensors and eigenvalue localization
Qilong Liu
2016-07-01
Full Text Available Abstract We present a new class of nonsingular tensors (p-norm strictly diagonally dominant tensors, which is a subclass of strong H $\\mathcal{H}$ -tensors. As applications of the results, we give a new eigenvalue inclusion set, which is tighter than those provided by Li et al. (Linear Multilinear Algebra 64:727-736, 2016 in some case. Based on this set, we give a checkable sufficient condition for the positive (semidefiniteness of an even-order symmetric tensor.
Tensor analysis for physicists
Schouten, J A
1989-01-01
This brilliant study by a famed mathematical scholar and former professor of mathematics at the University of Amsterdam integrates a concise exposition of the mathematical basis of tensor analysis with admirably chosen physical examples of the theory. The first five chapters incisively set out the mathematical theory underlying the use of tensors. The tensor algebra in EN and RN is developed in Chapters I and II. Chapter II introduces a sub-group of the affine group, then deals with the identification of quantities in EN. The tensor analysis in XN is developed in Chapter IV. In chapters VI through IX, Professor Schouten presents applications of the theory that are both intrinsically interesting and good examples of the use and advantages of the calculus. Chapter VI, intimately connected with Chapter III, shows that the dimensions of physical quantities depend upon the choice of the underlying group, and that tensor calculus is the best instrument for dealing with the properties of anisotropic media. In Chapte...
Carrozza, Sylvain
2015-01-01
We define in this paper a class of three indices tensor models, endowed with $O(N)^{\\otimes 3}$ invariance ($N$ being the size of the tensor). This allows to generate, via the usual QFT perturbative expansion, a class of Feynman tensor graphs which is strictly larger than the class of Feynman graphs of both the multi-orientable model (and hence of the colored model) and the $U(N)$ invariant models. We first exhibit the existence of a large $N$ expansion for such a model with general interactions. We then focus on the quartic model and we identify the leading and next-to-leading order (NLO) graphs of the large $N$ expansion. Finally, we prove the existence of a critical regime and we compute the critical exponents, both at leading order and at NLO. This is achieved through the use of various analytic combinatorics techniques.
Carrozza, Sylvain; Tanasa, Adrian
2016-08-01
We define in this paper a class of three-index tensor models, endowed with {O(N)^{⊗ 3}} invariance (N being the size of the tensor). This allows to generate, via the usual QFT perturbative expansion, a class of Feynman tensor graphs which is strictly larger than the class of Feynman graphs of both the multi-orientable model (and hence of the colored model) and the U(N) invariant models. We first exhibit the existence of a large N expansion for such a model with general interactions. We then focus on the quartic model and we identify the leading and next-to-leading order (NLO) graphs of the large N expansion. Finally, we prove the existence of a critical regime and we compute the critical exponents, both at leading order and at NLO. This is achieved through the use of various analytic combinatorics techniques.
LUO Bing; LU Nian-li; CHE Ren-wei
2009-01-01
Equivalent integrated finite element method is a canonical and efficient modeling method in dynamic analysis of complex mechanism. The key of establishing dynamic equations of spatial mechanism by the method is to confirm Jacobian matrix reflecting relations of all joints, nodes, and generalized coordinates, namely, relations of second-order and corresponding third-order conversion tensors. For complex motion relations of components in a parallel robot, it gives second-order and third-order conversion tensors of dynamic equations for the 6-HTRT parallel robot based on equivalent integrated f'mite element method. The method is suitable for the typical robots whose positions of work space and sizes of mechanism are different. The solving course of the method is simple and convenient, so the method lays the foundation of dynamic analysis for robots.
Liliani, N; Diningrum, J P; Sulaksono, A
2016-01-01
We have studied the effects of tensor coupling of $\\omega$ and $\\rho$ meson terms, Coulomb exchange term in local density approximation and various isoscalar-isovector coupling terms of relativistic mean field model on the properties of nuclear matter, finite nuclei, and super-heavy nuclei. We found that for the same fixed value of symmetry energy $J$ or its slope $L$ the presence of tensor coupling of $\\omega$ and $\\rho$ meson terms and Coulomb exchange term yields thicker neutron skin thickness of $^{208}$Pb. We also found that the roles of tensor coupling of $\\omega$ and $\\rho$ meson terms, Coulomb exchange term in local density approximation and various isoscalar-isovector coupling terms on the bulk properties of finite nuclei varies depending on the corresponding nucleus mass. However, on average, tensor coupling terms play a significant role in predicting the bulk properties of finite nuclei in a quite wide mass range especially in binding energies. We also observed that for some particular nuclei, the ...
Teguh Budi Prayitno
2011-04-01
Full Text Available This paper studies the effect of higher order derivative tensor in the Einstein field equations for vacuum condition on the planet perihelion precession. This tensor was initially proposed as the space-time curvature tensor by Deser and Tekin on discussions about the energy effects caused by this tensor. However, they include this tensor to Einstein field equations as a new model in general relativity theory. This is very interesting since there are some questions in cosmology and astrophysics that have no answers. Thus, they hoped this model could solve those problems by finding analytical or perturbative solution and interpreting it. In this case, the perturbative solution was used to find the Schwarzschild solution and it was also applied to consider the planetary motion in the solar gravitational field. Furthermore, it was proven that the tensor is divergence-free in order to keep the Einstein field equations remain valid.
Physical components of tensors
Altman, Wolf
2014-01-01
""This book provides a clear explanation of the mathematical properties of tensors, from a physical perspective. The book is rigorous and concise, yet easy to read and very accessible. The reader will enjoy the wide variety of examples and exercises with solution, which make the book very pedagogical. I believe this can be a very useful book for anyone interested in learning about the mathematics of tensors, no matter the field of study or research. I would definitely like to have this book on my shelf, and use it as a reference in my own lectures."" -Román Orús, Institut für Physik, Jo
Construction of energy-momentum tensor of gravitation
Bamba, Kazuharu; Shimizu, Katsutaro
2016-10-01
We construct the gravitational energy-momentum tensor in general relativity through the Noether theorem. In particular, we explicitly demonstrate that the constructed quantity can vary as a tensor under the general coordinate transformation. Furthermore, we verify that the energy-momentum conservation is satisfied because one of the two indices of the energy-momentum tensor should be in the local Lorentz frame. It is also shown that the gravitational energy and the matter one cancel out in certain space-times.
Williams, Owen A; Zeestraten, Eva A; Benjamin, Philip; Lambert, Christian; Lawrence, Andrew J; Mackinnon, Andrew D; Morris, Robin G; Markus, Hugh S; Charlton, Rebecca A; Barrick, Thomas R
2017-01-01
Cerebral small vessel disease (SVD) is the primary cause of vascular cognitive impairment and is associated with decline in executive function (EF) and information processing speed (IPS). Imaging biomarkers are needed that can monitor and identify individuals at risk of severe cognitive decline. Recently there has been interest in combining several magnetic resonance imaging (MRI) markers of SVD into a unitary score to describe disease severity. Here we apply a diffusion tensor image (DTI) segmentation technique (DSEG) to describe SVD related changes in a single unitary score across the whole cerebrum, to investigate its relationship with cognitive change over a three-year period. 98 patients (aged 43-89) with SVD underwent annual MRI scanning and cognitive testing for up to three years. DSEG provides a vector of 16 discrete segments describing brain microstructure of healthy and/or damaged tissue. By calculating the scalar product of each DSEG vector in reference to that of a healthy ageing control we generate an angular measure (DSEG θ) describing the patients' brain tissue microstructural similarity to a disease free model of a healthy ageing brain. Conventional MRI markers of SVD brain change were also assessed including white matter hyperintensities, cerebral atrophy, incident lacunes, cerebral-microbleeds, and white matter microstructural damage measured by DTI histogram parameters. The impact of brain change on cognition was explored using linear mixed-effects models. Post-hoc sample size analysis was used to assess the viability of DSEG θ as a tool for clinical trials. Changes in brain structure described by DSEG θ were related to change in EF and IPS (p cerebrum. Sample size estimates indicated that fewer patients would be required to detect treatment effects using DSEG θ compared to conventional MRI and DTI markers of SVD severity. DSEG θ is a powerful tool for characterising subtle brain change in SVD that has a negative impact on cognition and
U-dual branes and mixed symmetry tensor fields
Chatzistavrakidis, A. [Institut fuer Theoretische Physik, Appelstrasse 2, 30167 Hannover (Germany); Gautason, F.F. [Institut fuer Theoretische Physik, Appelstrasse 2, 30167 Hannover (Germany); Center for Quantum Engineering and Spacetime Research, Appelstrasse 2, 30167 Hannover (Germany)
2014-09-11
We review and explain the relation between U-dual branes in string theory and mixed symmetry tensors of various degrees. In certain cases these mixed symmetry tensors can be related to diverse types of fluxes that play an important role in compactifications of string theory. (Copyright copyright 2014 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
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...
Heil, Konstantin; Moroianu, Andrei; Semmelmann, Uwe
2017-07-01
We show that Killing tensors on conformally flat n-dimensional tori whose conformal factor only depends on one variable, are polynomials in the metric and in the Killing vector fields. In other words, every first integral of the geodesic flow polynomial in the momenta on the sphere bundle of such a torus is linear in the momenta.
Alam, Aftab; Johnson, D. D.
2012-04-01
We resolve issues that have plagued reliable prediction of relative phase stability for solid solutions and compounds. Due to its commercially important phase diagram, we showcase the Al-Li system because historically density-functional theory (DFT) results show large scatter and limited success in predicting the structural properties and stability of solid solutions relative to ordered compounds. Using recent advances in an optimal basis-set representation of the topology of electronic charge density (and, hence, atomic size), we present DFT results that agree reasonably well with all known experimental data for the structural properties and formation energies of ordered, off-stoichiometric partially ordered, and disordered alloys, opening the way for reliable study in complex alloys.
Estimates of the Nucleon Tensor Charge
Gamberg, L P; Gamberg, Leonard; Goldstein, Gary R.
2001-01-01
Like the axial vector charges, defined from the forward nucleon matrix element of the axial vector current on the light cone, the nucleon tensor charge, defined from the corresponding matrix element of the tensor current, is essential for characterizing the momentum and spin structure of the nucleon. Because there must be a helicity flip of the struck quark in order to probe the transverse spin polarization of the nucleon, the transversity distribution (and thus the tensor charge) decouples at leading twist in deep inelastic scattering, although no such suppression appears in Drell-Yan processes. This makes the tensor charge difficult to measure and its non-conservation makes its prediction model dependent. We present a different approach. Exploiting an approximate SU(6)xO(3) symmetric mass degeneracy of the light axial vector mesons (a1(1260), b1(1235) and h1(1170)) and using pole dominance, we calculate the tensor charge. The result is simple in form and depends on the decay constants of the axial vector me...
Physical properties of crystals their representation by tensors and matrices
Nye, J F
1985-01-01
First published in 1957, this classic study has been reissued in a paperback version that includes an additional chapter bringing the material up to date. The author formulates the physical properties of crystals systematically in tensor notation, presenting tensor properties in terms of their common mathematical basis and the thermodynamic relations between them. The mathematical groundwork is laid in a discussion of tensors of the first and second ranks. Tensors of higher ranks and matrix methods are then introduced as natural developments of the theory. A similar pattern is followed in discussing thermodynamic and optical aspects.
The pressure tensor in tangential equilibria
F. Mottez
2004-09-01
Full Text Available The tangential equilibria are characterized by a bulk plasma velocity and a magnetic field that are perpendicular to the gradient direction. Such equilibria can be spatially periodic (like waves, or they can separate two regions with asymptotic uniform conditions (like MHD tangential discontinuities. It is possible to compute the velocity moments of the particle distribution function. Even in very simple cases, the pressure tensor is not isotropic and not gyrotropic. The differences between a scalar pressure and the pressure tensor derived in the frame of the Maxwell-Vlasov theory are significant when the gradient scales are of the order of the Larmor radius; they concern mainly the ion pressure tensor.
Quantum Fluctuations Of The Stress Tensor
Wu, C
2002-01-01
Quantum fluctuations of the stress tensor are important in many branches of physics, including the study of the validity of semiclassical gravity and the backreaction problem in stochastic semiclassical gravity. The geometry fluctuations induced by stress tensor fluctuations are important to understand quantum gravity and the problem of lightcone fluctuations. Stress tensor fluctuations also hold the key to understand fundamental physical effects like quantum fluctuations of radiation pressure, and that is crucial to the sensitivity of interferometers and the limitations on the detection of gravitational waves. Even the wave-particle duality of light can be better understood by the study of quantum fluctuations of thermal radiation. It is well known in quantum field theory that the expectation value of the energy density, which contains quadratic field operators (e.g. E2 and B2 in the electromagnatic field case), is divergent and can be renormalized simply by normal ordering, which is subtracting out the vac...
Tensor Factorization for Precision Medicine in Heart Failure with Preserved Ejection Fraction.
Luo, Yuan; Ahmad, Faraz S; Shah, Sanjiv J
2017-01-23
Heart failure with preserved ejection fraction (HFpEF) is a heterogeneous clinical syndrome that may benefit from improved subtyping in order to better characterize its pathophysiology and to develop novel targeted therapies. The United States Precision Medicine Initiative comes amid the rapid growth in quantity and modality of clinical data for HFpEF patients ranging from deep phenotypic to trans-omic data. Tensor factorization, a form of machine learning, allows for the integration of multiple data modalities to derive clinically relevant HFpEF subtypes that may have significant differences in underlying pathophysiology and differential response to therapies. Tensor factorization also allows for better interpretability by supporting dimensionality reduction and identifying latent groups of data for meaningful summarization of both features and disease outcomes. In this narrative review, we analyze the modest literature on the application of tensor factorization to related biomedical fields including genotyping and phenotyping. Based on the cited work including work of our own, we suggest multiple tensor factorization formulations capable of integrating the deep phenotypic and trans-omic modalities of data for HFpEF, or accounting for interactions between genetic variants at different omic hierarchies. We encourage extensive experimental studies to tackle challenges in applying tensor factorization for precision medicine in HFpEF, including effectively incorporating existing medical knowledge, properly accounting for uncertainty, and efficiently enforcing sparsity for better interpretability.
Tensor Based Representation and Analysis of Diffusion-Weighted Magnetic Resonance Images
Barmpoutis, Angelos
2009-01-01
Cartesian tensor bases have been widely used to model spherical functions. In medical imaging, tensors of various orders can approximate the diffusivity function at each voxel of a diffusion-weighted MRI data set. This approximation produces tensor-valued datasets that contain information about the underlying local structure of the scanned tissue.…
Updated constraints and forecasts on primordial tensor modes
Cabass, Giovanni; Pagano, Luca; Salvati, Laura; Gerbino, Martina; Giusarma, Elena; Melchiorri, Alessandro
2016-03-01
We present new, tight, constraints on the cosmological background of gravitational waves (GWs) using the latest measurements of CMB temperature and polarization anisotropies provided by the Planck, BICEP2 and Keck Array experiments. These constraints are further improved when the GW contribution NeffGW to the effective number of relativistic degrees of freedom Neff is also considered. Parametrizing the tensor spectrum as a power law with tensor-to-scalar ratio r , tilt nt and pivot 0.01 Mpc-1, and assuming a minimum value of r =0.001 , we find r FIRAS). Finally, we show future constraints achievable from a COrE-like mission: if the tensor-to-scalar ratio is of order 1 0-2 and the inflationary consistency relation nt=-r /8 holds, COrE will be able to constrain nt with an error of 0.16 at 95% CL. In the case that lensing B -modes can be subtracted to 10% of their power, a feasible goal for COrE, these limits will be improved to 0.11 at (95% CL).
Liliani, N.; Nugraha, A. M.; Diningrum, J. P.; Sulaksono, A.
2016-05-01
We have studied the effects of tensor coupling of ω and ρ meson terms, the Coulomb exchange term in local density approximation, and various isoscalar-isovector coupling terms of relativistic mean-field model on the properties of nuclear matter, finite nuclei, and superheavy nuclei. We found that for the same fixed value of symmetry energy J or its slope L the presence of tensor coupling of ω and ρ meson terms and the Coulomb exchange term yields thicker neutron skin thickness of 208Pb. We also found that the roles of tensor coupling of ω and ρ meson terms, the Coulomb-exchange term in local density approximation, and various isoscalar-isovector coupling terms on the bulk properties of finite nuclei vary depending on the corresponding nucleus mass. However, on average, tensor coupling terms play a significant role in predicting the bulk properties of finite nuclei in a quite wide mass range, especially in binding energies. We also observed that for some particular nuclei, the corresponding experimental data of binding energies are rather less compatible with the presence of the Coulomb-exchange term in local density approximation and they tend to disfavor the presence of isoscalar-isovector coupling term with too-high Λ value. Furthermore, we have found that these terms influence the detail properties of 292120 superheavy nucleus such as binding energies, the magnitude of two-nucleon gaps, single-particle spectra, neutron densities, neutron skin thicknesses, and mean-square charge radii. However, the shell-closure predictions of 208Pb and 292120 nuclei are not affected by the presence of these terms.
Conductivity tensor mapping of the human brain using diffusion tensor MRI
Tuch, David S.; Wedeen, Van J.; Dale, Anders M.; George, John S.; Belliveau, John W.
2001-09-01
Knowledge of the electrical conductivity properties of excitable tissues is essential for relating the electromagnetic fields generated by the tissue to the underlying electrophysiological currents. Efforts to characterize these endogenous currents from measurements of the associated electromagnetic fields would significantly benefit from the ability to measure the electrical conductivity properties of the tissue noninvasively. Here, using an effective medium approach, we show how the electrical conductivity tensor of tissue can be quantitatively inferred from the water self-diffusion tensor as measured by diffusion tensor magnetic resonance imaging. The effective medium model indicates a strong linear relationship between the conductivity and diffusion tensor eigenvalues (respectively, σ and d) in agreement with theoretical bounds and experimental measurements presented here (σ/d ≈ 0.844 ± 0.0545 S·s/mm3, r2 = 0.945). The extension to other biological transport phenomena is also discussed.
Gogny interactions with tensor terms
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.)
Electromagnetic Energy Momentum Tensor in a Spatially Dispersive Medium
Fietz, Chris
2016-01-01
We derive a generalized Minkowski Energy Momentum Tensor for a monochromatic wave in a lossless medium exhibiting temporal and spatial dispersion. The Energy Momentum Tensor is then related to familiar expressions for energy density and energy flux, as well as new expressions for momentum density and momentum flux.
2010-11-30
ELECTROMAGNEETIC SURFACE IMPEDANCE PROPERTIES FA9550-09-C-0198 DR. ADOUR KABAKIAN HUGHES RESEARCH LABS AFOSR / RSE 875 North Randolph Street, Suit...325 Room 3112 Arlington, Virginia 22203-1768 AFOSR / RSE AFRL-OSR-VA-TR-2012-0770 Distribution A We have investigated and determined how the tensor...the case of a TM wave, which favors propagation along the shorter principal axis. Standard terms apply U U U UU Arje Nachman RSE (Program Manager
Inflatonic baryogenesis with large tensor mode
Naoyuki Takeda
2015-06-01
Full Text Available We consider a complex inflaton field with a CP asymmetric term for its potential. This CP asymmetric term produces the global charge of the inflaton after inflation. With the assignment of the baryon number to the inflaton, the baryon asymmetry of the universe is produced by inflaton's decay. In addition to this, the U(1 breaking term modulates the curvature of the inflaton radial direction depending on its phase, which affects the tensor-to-scalar ratio. In this paper, we have studied the relation between the baryon asymmetry and the tensor-to-scalar ratio, then verified that the future CMB observation could test this baryogenesis scenario with large tensor modes.
Friction tensor concept for textured surfaces
K R Y Simha; Anirudhan Pottirayil; Pradeep L Menezes; Satish V Kailas
2008-06-01
Directionality of grinding marks inﬂuences the coefﬁcient of friction during sliding. Depending on the sliding direction the coefﬁcient of friction varies between maximum and minimum for textured surfaces. For random surfaces without any texture the friction coefﬁcient becomes independent of the sliding direction. This paper proposes the concept of a friction tensor analogous to the heat conduction tensor in anisotropic media. This implies that there exists two principal friction coefﬁcients $\\mu_{1,2}$ analogous to the principal conductivities $k_{1,2}$. For symmetrically textured surfaces the principal directions are orthogonal with atleast one plane of symmetry. However, in the case of polished single crystalline solids in relative sliding motion, crystallographic texture controls the friction tensor.
Holographic duality from random tensor networks
Hayden, Patrick; Qi, Xiao-Liang; Thomas, Nathaniel; Walter, Michael; Yang, Zhao
2016-01-01
Tensor networks provide a natural framework for exploring holographic duality because they obey entanglement area laws. They have been used to construct explicit simple models realizing many of the interesting structural features of the AdS/CFT correspondence, including the non-uniqueness of bulk operator reconstruction in the boundary theory. In this article, we explore the holographic properties of networks of random tensors. We find that our models obey the Ryu-Takayanagi entropy formula for all boundary regions, whether connected or not, a fact closely related to known properties of the multipartite entanglement of assistance. Moreover, we find that all boundary regions faithfully encode the physics of their entire bulk entanglement wedges, not just their smaller causal wedges. Our method is to interpret the average over random tensors as the partition function of a classical ferromagnetic Ising model, so that the minimal surfaces of Ryu-Takayanagi appear as domain walls. Upon including the analog of a bu...
Tensor-optimized antisymmetrized molecular dynamics in nuclear physics
Myo, Takayuki; Ikeda, Kiyomi; Horiuchi, Hisashi; Suhara, Tadahiro
2015-01-01
We develop a new formalism to treat nuclear many-body systems using bare nucleon-nucleon interaction. It has become evident that the tensor interaction plays important role in nuclear many-body systems due to the role of the pion in strongly interacting system. We take the antisymmetrized molecular dynamics (AMD) as a basic framework and add a tensor correlation operator acting on the AMD wave function using the concept of the tensor-optimized shell model (TOSM). We demonstrate a systematical and straightforward formulation utilizing the Gaussian integration and differentiation method and the antisymmetrization technique to calculate all the matrix elements of the many-body Hamiltonian. We can include the three-body interaction naturally and calculate the matrix elements systematically in the progressive order of the tensor correlation operator. We call the new formalism "tensor-optimized antisymmetrized molecular dynamics".
Monotone Regression and Correction for Order Relation Deviations in Indicator Kriging
Han Yan; Yang Yiheng
2008-01-01
The indicator kriging (IK) is one of the most efficient nonparametric methods in geo-statistics. The order relation problem in the conditional cumulative distribution values obtained by IK is the most severe drawback of it. The correction of order relation deviations is an essential and important part of IK approach. A monotone regression was proposed as a new correction method which could minimize the deviation from original quintiles value, although, ensuring all order relations.
E6Tensors: A Mathematica Package for E6 Tensors
Deppisch, Thomas
2016-01-01
We present the Mathematica package E6Tensors, a tool for explicit tensor calculations in E6 gauge theories. In addition to matrix expressions for the group generators of E6, it provides structure constants, various higher rank tensors and expressions for the representations 27, 78, 351 and 351'. This paper comes along with a short manual including physically relevant examples. I further give a complete list of gauge invariant, renormalisable terms for superpotentials and Lagrangians.
Quantum tensor product structures are observable induced.
Zanardi, Paolo; Lidar, Daniel A; Lloyd, Seth
2004-02-13
It is argued that the partition of a quantum system into subsystems is dictated by the set of operationally accessible interactions and measurements. The emergence of a multipartite tensor product structure of the state space and the associated notion of quantum entanglement are then relative and observable induced. We develop a general algebraic framework aimed to formalize this concept.
Introduction to vector and tensor analysis
Wrede, Robert C
1972-01-01
A broad introductory treatment, this volume examines general Cartesian coordinates, the cross product, Einstein's special theory of relativity, bases in general coordinate systems, maxima and minima of functions of two variables, line integrals, integral theorems, fundamental notions in n-space, Riemannian geometry, algebraic properties of the curvature tensor, and more. 1963 edition.
Local Tensor Radiation Conditions For Elastic Waves
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...
The Kummer tensor density in electrodynamics and in gravity
Baekler, Peter [University of Appl. Sciences, 40474 Düsseldorf (Germany); Favaro, Alberto [Inst. Physics, Carl-von-Ossietzky-Univ., 26111 Oldenburg (Germany); Itin, Yakov [Inst. Mathematics, Hebrew University of Jerusalem (Israel); Jerusalem College of Technology (Israel); Hehl, Friedrich W., E-mail: hehl@thp.uni-koeln.de [Inst. Theor. Physics, University of Cologne, 50923 Köln (Germany); Department of Physics and Astron., University of Missouri, Columbia, MO 65211 (United States)
2014-10-15
Guided by results in the premetric electrodynamics of local and linear media, we introduce on 4-dimensional spacetime the new abstract notion of a Kummer tensor density of rank four, K{sup ijkl}. This tensor density is, by definition, a cubic algebraic functional of a tensor density of rank four T{sup ijkl}, which is antisymmetric in its first two and its last two indices: T{sup ijkl}=−T{sup jikl}=−T{sup ijlk}. Thus, K∼T{sup 3}, see Eq. (46). (i) If T is identified with the electromagnetic response tensor of local and linear media, the Kummer tensor density encompasses the generalized Fresnel wave surfaces for propagating light. In the reversible case, the wave surfaces turn out to be Kummer surfaces as defined in algebraic geometry (Bateman 1910). (ii) If T is identified with the curvature tensor R{sup ijkl} of a Riemann–Cartan spacetime, then K∼R{sup 3} and, in the special case of general relativity, K reduces to the Kummer tensor of Zund (1969). This K is related to the principal null directions of the curvature. We discuss the properties of the general Kummer tensor density. In particular, we decompose K irreducibly under the 4-dimensional linear group GL(4,R) and, subsequently, under the Lorentz group SO(1,3)
44 CFR 402.6 - Relation to Transportation Order T-2.
2010-10-01
... Order T-2. 402.6 Section 402.6 Emergency Management and Assistance DEPARTMENT OF COMMERCE AND DEPARTMENT OF TRANSPORTATION SHIPMENTS ON AMERICAN FLAG SHIPS AND AIRCRAFT (T-1, INT. 1) § 402.6 Relation to Transportation Order T-2. Transportation Order T-1 applies to the transportation of commodities to, or in transit...
Dubey, C. P.; Tiwari, V. M.; Rao, P. R.
2017-09-01
Comprehension of subsurface structures buried under thick sediments in the region of Bay of Bengal is vital as structural features are the key parameters that influence or are caused by the subsurface deformation and tectonic events like earthquakes. Here, we address this issue using the integrated analysis and interpretation of gravity and full gravity gradient tensor with few seismic profiles available in the poorly known region. A 2D model of the deep earth crust-mantle is constructed and interpreted with gravity gradients and seismic profiles, which made it possible to obtain a visual image of a deep seated fault below the basement associated with thick sediments strata. Gravity modelling along a NE-SW profile crossing the hypocentre of the earthquake of 21 May 2014 (M w 6.0) in the northern Bay of Bengal suggests that the location of intraplate normal dip fault earthquake in the upper mantle is at the boundary of density anomalies, which is probably connected to the crustal fault. We also report an enhanced structural trend of two major ridges, the 85°E and the 90°E ridges hidden under the sedimentary cover from the computed full gravity gradients tensor components.
Tensor Squeezed Limits and the Higuchi Bound
Bordin, Lorenzo; Mirbabayi, Mehrdad; Noreña, Jorge
2016-01-01
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 con- sistency 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...
The Symmetric Tensor Lichnerowicz Algebra and a Novel Associative Fourier-Jacobi Algebra
Hallowell, Karl; Waldron, Andrew
2007-09-01
Lichnerowicz's algebra of differential geometric operators acting on symmetric tensors can be obtained from generalized geodesic motion of an observer carrying a complex tangent vector. This relation is based upon quantizing the classical evolution equations, and identifying wavefunctions with sections of the symmetric tensor bundle and Noether charges with geometric operators. In general curved spaces these operators obey a deformation of the Fourier-Jacobi Lie algebra of sp(2,R). These results have already been generalized by the authors to arbitrary tensor and spinor bundles using supersymmetric quantum mechanical models and have also been applied to the theory of higher spin particles. These Proceedings review these results in their simplest, symmetric tensor setting. New results on a novel and extremely useful reformulation of the rank 2 deformation of the Fourier-Jacobi Lie algebra in terms of an associative algebra are also presented. This new algebra! was originally motivated by studies of operator orderings in enveloping algebras. It provides a new method that is superior in many respects to common techniques such as Weyl or normal ordering.
The Symmetric Tensor Lichnerowicz Algebra and a Novel Associative Fourier-Jacobi Algebra
Karl Hallowell
2007-09-01
Full Text Available Lichnerowicz's algebra of differential geometric operators acting on symmetric tensors can be obtained from generalized geodesic motion of an observer carrying a complex tangent vector. This relation is based upon quantizing the classical evolution equations, and identifying wavefunctions with sections of the symmetric tensor bundle and Noether charges with geometric operators. In general curved spaces these operators obey a deformation of the Fourier-Jacobi Lie algebra of sp(2,R. These results have already been generalized by the authors to arbitrary tensor and spinor bundles using supersymmetric quantum mechanical models and have also been applied to the theory of higher spin particles. These Proceedings review these results in their simplest, symmetric tensor setting. New results on a novel and extremely useful reformulation of the rank 2 deformation of the Fourier-Jacobi Lie algebra in terms of an associative algebra are also presented. This new algebra was originally motivated by studies of operator orderings in enveloping algebras. It provides a new method that is superior in many respects to common techniques such as Weyl or normal ordering.
Moral Judgment and Its Relation to Second-Order Theory of Mind
Fu, Genyue; Xiao, Wen S.; Killen, Melanie; Lee, Kang
2014-01-01
Recent research indicates that moral judgment and 1st-order theory of mind abilities are related. What is not known, however, is how 2nd-order theory of mind is related to moral judgment. In the present study, we extended previous findings by administering a morally relevant theory of mind task (an accidental transgressor) to 4- to 7-year-old…
Moral Judgment and Its Relation to Second-Order Theory of Mind
Fu, Genyue; Xiao, Wen S.; Killen, Melanie; Lee, Kang
2014-01-01
Recent research indicates that moral judgment and 1st-order theory of mind abilities are related. What is not known, however, is how 2nd-order theory of mind is related to moral judgment. In the present study, we extended previous findings by administering a morally relevant theory of mind task (an accidental transgressor) to 4- to 7-year-old…
Symmetric Tensor Decomposition
Brachat, Jerome; Comon, Pierre; Mourrain, Bernard
2010-01-01
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 total degree d as a sum of powers of linear forms (Waring’s problem), incidence properties on secant varieties of the Veronese variety and the representation of linear forms as a linear combination of evaluations at distinct points. Then we reformulate Sylvester’s approach from the dual point of view...
Coordinate independent expression for transverse trace-free tensors
Conboye, Rory
2015-01-01
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 3-space possess only two degrees of freedom, they cannot ordinarily be given solely by two differential functions. However, coordinate expressions depending on two scalar potentials alone have been derived for all TT tensors in flat space (Conboye and \\'O Murchadha 2014 Class. Quantum Grav. 31, 085019), with either a linear or axial symmetry. Since TT tensors are conformally covariant, these also give TT tensors in conformally-flat space. Here, this work has been extended to give a coordinate-independent expression for these TT tensors, also generalizing the symmetry conditions to invariance along any hypersurface orthogonal Killing vector.
A recursive approach to the reduction of tensor Feynman integrals
Diakonidis, Theodoros; Riemann, Tord; Tausk, Bas
2010-01-01
We describe a new, convenient, recursive tensor integral reduction scheme for one-loop $n$-point Feynman integrals. The reduction is based on the algebraic Davydychev-Tarasov formalism where the tensors are represented by scalars with shifted dimensions and indices, and then expressed by conventional scalars with generalized recurrence relations. The scheme is worked out explicitly for up to $n=6$ external legs and for tensor ranks $R\\leq n$. The tensors are represented by scalar one- to four-point functions in $d$ dimensions. For the evaluation of them, the Fortran code for the tensor reductions has to be linked with a package like QCDloop or LoopTools/FF. Typical numerical results are presented.
The Cauchy problem of scalar-tensor theories of gravity
Salgado, Marcelo [Instituto de Ciencias Nucleares, Universidad Nacional Autonoma de Mexico, Apdo. Postal 70-543 Mexico 04510 DF (Mexico)
2006-07-21
The 3 + 1 formulation of scalar-tensor theories of gravity (STT) is obtained in the physical (Jordan) frame departing from the 4 + 0 covariant field equations. Contrary to common belief (folklore), the new system of ADM-like equations shows that the Cauchy problem of STT is well formulated (in the sense that the whole system of evolution equations is of first order in the time derivative). This is the first step towards a full first-order (in time and space) formulation from which a subsequent hyperbolicity analysis (a well-posedness determination) can be performed. Several gauge (lapse and shift) conditions are considered and implemented for STT. In particular, a generalization of the harmonic gauge for STT allows us to prove the well posedness of the STT using a second-order analysis which is very similar to the one employed in general relativity. Several appendices complement the ideas of the main part of the paper.
Dynamic rotation and stretch tensors from a dynamic polar decomposition
Haller, George
2016-01-01
The local rigid-body component of continuum deformation is typically characterized by the rotation tensor, obtained from the polar decomposition of the deformation gradient. Beyond its well-known merits, the polar rotation tensor also has a lesser known dynamical inconsistency: it does not satisfy the fundamental superposition principle of rigid-body rotations over adjacent time intervals. As a consequence, the polar rotation diverts from the observed mean material rotation of fibers in fluids, and introduces a purely kinematic memory effect into computed material rotation. Here we derive a generalized polar decomposition for linear processes that yields a unique, dynamically consistent rotation component, the dynamic rotation tensor, for the deformation gradient. The left dynamic stretch tensor is objective, and shares the principal strain values and axes with its classic polar counterpart. Unlike its classic polar counterpart, however, the dynamic stretch tensor evolves in time without spin. The dynamic rotation tensor further decomposes into a spatially constant mean rotation tensor and a dynamically consistent relative rotation tensor that is objective for planar deformations. We also obtain simple expressions for dynamic analogues of Cauchy's mean rotation angle that characterize a deforming body objectively.
Exploring the tensor networks/AdS correspondence
Bhattacharyya, Arpan; Gao, Zhe-Shen; Hung, Ling-Yan; Liu, Si-Nong
2016-08-01
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.
First-order D-type Iterative Learning Control for Nonlinear Systems with Unknown Relative Degree
SONGZhao-Qing; MAOJian-Qin; DAIShao-Wu
2005-01-01
The classical D-type iterative learning control law depends crucially on the relative degree of the controlled system, high order differential iterative learning law must be taken for systems with high order relative degree. It is very difficult to ascertain the relative degree of the controlled system for uncertain nonlinear systems. A first-order D-type iterative learning control design method is presented for a class of nonlinear systems with unknown relative degree based on dummy model in this paper. A dummy model with relative degree 1 is constructed for a class of nonlinear systems with unknown relative degree. A first-order D-type iterative learning control law is designed based on the dummy model, so that the dummy model can track the desired trajectory perfectly, and the controlled system can track the desired trajectory within a certain error. The simulation example demonstrates the feasibility and effectiveness of the presented method.
Interpretation of the Weyl Tensor
Hofmann, Stefan; Schneider, Robert
2013-01-01
According to folklore in general relativity, the Weyl tensor can be decomposed into parts corresponding to Newton-like, incoming- and outgoing wave-like field components. It is shown here that this interpretation cannot be applied to space-time geometries with cylindrical isometries. This is done by investigating some well-known exact solutions of Einstein's field equations with whole-cylindrical symmetry, for which the physical interpretation is very clear, but for which the standard Weyl interpretation would give contradictory results. For planar or spherical geometries, however, the standard interpretation works for both, static and dynamical space-times. It is argued that one reason for the failure in the cylindrical case is that for waves spreading in two spatial dimensions there is no local criterion to distinguish incoming and outgoing waves already at the linear level. It turns out that Thorne's local energy notion, subject to certain qualifications, provides an efficient diagnostic tool to extract th...
Standard cosmological model with non vanishing Weyl tensor
Bittencourt, E
2013-01-01
We have solved Einstein's equations of general relativity for a homogeneous and isotropic metric with constant spatial curvature and found a non vanishing Weyl tensor in the presence of an anisotropic pressure component of the energy-momentum tensor. The time evolution of the space-time is guided by the usual Friedman equations and the properties of the spatial components comprise a separated system of equations that can be independently solved. The physical features of this solution are elucidated by using the Quasi-Maxwellian equations of general relativity which directly connect the anisotropic pressure to the electric part of the Weyl tensor for the cosmological fluid.
Multidimensional seismic data reconstruction using tensor analysis
Kreimer, Nadia
Exploration seismology utilizes the seismic wavefield for prospecting oil and gas. The seismic reflection experiment consists on deploying sources and receivers in the surface of an area of interest. When the sources are activated, the receivers measure the wavefield that is reflected from different subsurface interfaces and store the information as time-series called traces or seismograms. The seismic data depend on two source coordinates, two receiver coordinates and time (a 5D volume). Obstacles in the field, logistical and economical factors constrain seismic data acquisition. Therefore, the wavefield sampling is incomplete in the four spatial dimensions. Seismic data undergoes different processes. In particular, the reconstruction process is responsible for correcting sampling irregularities of the seismic wavefield. This thesis focuses on the development of new methodologies for the reconstruction of multidimensional seismic data. This thesis examines techniques based on tensor algebra and proposes three methods that exploit the tensor nature of the seismic data. The fully sampled volume is low-rank in the frequency-space domain. The rank increases when we have missing traces and/or noise. The methods proposed perform rank reduction on frequency slices of the 4D spatial volume. The first method employs the Higher-Order Singular Value Decomposition (HOSVD) immersed in an iterative algorithm that reinserts weighted observations. The second method uses a sequential truncated SVD on the unfoldings of the tensor slices (SEQ-SVD). The third method formulates the rank reduction problem as a convex optimization problem. The measure of the rank is replaced by the nuclear norm of the tensor and the alternating direction method of multipliers (ADMM) minimizes the cost function. All three methods have the interesting property that they are robust to curvature of the reflections, unlike many reconstruction methods. Finally, we present a comparison between the methods
The geomagnetic field gradient tensor
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 independe...... of the small-scale structure of the Earth’s lithospheric field....
Seismic moment tensors and estimated uncertainties in southern Alaska
Silwal, Vipul; Tape, Carl
2016-04-01
We present a moment tensor catalog of 106 earthquakes in southern Alaska, and we perform a conceptually based uncertainty analysis for 21 of them. For each earthquake, we use both body waves and surface waves to do a grid search over double couple moment tensors and source depths in order to find the minimum of the misfit function. Our uncertainty parameter or, rather, our confidence parameter is the average value of the curve 𝒫 (V), where 𝒫 (V) is the posterior probability as a function of the fractional volume V of moment tensor space surrounding the minimum misfit moment tensor. As a supplemental means for characterizing and visualizing uncertainties, we generate moment tensor samples of the posterior probability. We perform a series of inversion tests to quantify the impact of certain decisions made within moment tensor inversions and to make comparisons with existing catalogs. For example, using an L1 norm in the misfit function provides more reliable solutions than an L2 norm, especially in cases when all available waveforms are used. Using body waves in addition to surface waves, as well as using more stations, leads to the most accurate moment tensor solutions.
Generalized Einstein Tensor for a Weyl Manifold and Its Applications
Abdülkadir （O）ZDE（G）ER
2013-01-01
It is well known that the Einstein tensor G for a Piemannian manifold defined by Gβα =Rβα-1/2Rδα,Rβα =gβγRγα where Rγα and R are respectively the Ricci tensor and the scalar curvature of the manifold,plays an important part in Einstein's theory of gravitation as well as in proving some theorems in Riemannian geometry.In this work,we first obtain the generalized Einstein tensor for a Weyl manifold.Then,after studying some properties of generalized Einstein tensor,we prove that the conformed invariance of the generalized Einstein tensor implies the conformed invariance of the curvature tensor of the Weyl manifold and conversely.Moreover,we show that such Weyl manifolds admit a one-parameter family of hypersurfaces the orthogoned trajectories of which are geodesics.Finally,a necessary and sufficient condition in order that the generalized circles of a Weyl manifold be preserved by a conformal mapping is stated in terms of generalized Einstein tensors at corresponding points.
Relation between Feynman cycles and off-diagonal long-range order.
Ueltschi, Daniel
2006-10-27
The usual order parameter for Bose-Einstein condensation involves the off-diagonal correlation function of Penrose and Onsager, but an alternative is Feynman's notion of infinite cycles. We present a formula that relates both order parameters. We discuss its validity with the help of rigorous results and heuristic arguments. The conclusion is that infinite cycles do not always represent the Bose condensate.
Propagators of Generalized Schrödinger Equations Related by First-order Supersymmetry
A. Schulze-Halberg
2011-01-01
Full Text Available We construct an explicit relation between propagators of generalized Schrödinger equations that are linked by a first-order supersymmetric transformation. Our findings extend and complement recent results on the conventional case [1].
The tensor bi-spectrum in a matter bounce
Sreenath, V.; Chowdhury, Debika; Sriramkumar, L.
2016-03-01
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 hNL 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.
Estimation of dislocation density from precession electron diffraction data using the Nye tensor.
Leff, A C; Weinberger, C R; Taheri, M L
2015-06-01
The Nye tensor offers a means to estimate the geometrically necessary dislocation density of a crystalline sample based on measurements of the orientation changes within individual crystal grains. In this paper, the Nye tensor theory is applied to precession electron diffraction automated crystallographic orientation mapping (PED-ACOM) data acquired using a transmission electron microscope (TEM). The resulting dislocation density values are mapped in order to visualize the dislocation structures present in a quantitative manner. These density maps are compared with other related methods of approximating local strain dependencies in dislocation-based microstructural transitions from orientation data. The effect of acquisition parameters on density measurements is examined. By decreasing the step size and spot size during data acquisition, an increasing fraction of the dislocation content becomes accessible. Finally, the method described herein is applied to the measurement of dislocation emission during in situ annealing of Cu in TEM in order to demonstrate the utility of the technique for characterizing microstructural dynamics.
Quantum corrections to the stress-energy tensor in thermodynamic equilibrium with acceleration
Becattini, F
2015-01-01
We show that the stress-energy tensor has additional terms with respect to the ideal form in states of global thermodynamic equilibrium in flat spacetime with non-vanishing acceleration and vorticity. These corrections are of quantum origin and their leading terms are of second order in the gradients of the thermodynamic fields. The relevant coefficients can be expressed in terms of correlators of the stress-energy tensor operator and the generators of the Lorentz group. With respect to previous assessments, we find that there are more second order coefficients and that all thermodynamic functions including energy density receive acceleration and vorticity dependent corrections. Notably, also the relation between \\rho and p, that is the equation of state, is affected by acceleration and vorticity. We have calculated the corrections for a free real scalar field -- both massive and massless -- and we have found that they increase, particularly for a massive field, at very high acceleration and vorticity and ver...
Asken, Breton Michael; DeKosky, Steven T; Clugston, James R; Jaffee, Michael S; Bauer, Russell M
2017-03-24
This review seeks to summarize diffusion tensor imaging (DTI) studies that have evaluated structural changes attributed to the mechanisms of mild traumatic brain injury (mTBI) in adult civilian, military, and athlete populations. Articles from 2002 to 2016 were retrieved from PubMed/MEDLINE, EBSCOhost, and Google Scholar, using a Boolean search string containing the following terms: "diffusion tensor imaging", "diffusion imaging", "DTI", "white matter", "concussion", "mild traumatic brain injury", "mTBI", "traumatic brain injury", and "TBI". We added studies not identified by this method that were found via manually-searched reference lists. We identified 86 eligible studies from English-language journals using, adult, human samples. Studies were evaluated based on duration between injury and DTI assessment, categorized as acute, subacute/chronic, remote mTBI, and repetitive brain trauma considerations. Since changes in brain structure after mTBI can also be affected by other co-occurring medical and demographic factors, we also briefly review DTI studies that have addressed socioeconomic status factors (SES), major depressive disorder (MDD), and attention-deficit hyperactivity disorder (ADHD). The review describes population-specific risks and the complications of clinical versus pathophysiological outcomes of mTBI. We had anticipated that the distinct population groups (civilian, military, and athlete) would require separate consideration, and various aspects of the study characteristics supported this. In general, study results suggested widespread but inconsistent differences in white matter diffusion metrics (primarily fractional anisotropy [FA], mean diffusivity [MD], radial diffusivity [RD], and axial diffusivity [AD]) following mTBI/concussion. Inspection of study designs and results revealed potential explanations for discrepant DTI findings, such as control group variability, analytic techniques, the manner in which regional differences were reported, and
The magnetic part of the Weyl tensor, and the expansion of discrete universes
Clifton, Timothy; Gregoris, Daniele; Rosquist, Kjell
2017-02-01
We examine the effect that the magnetic part of the Weyl tensor has on the large-scale expansion of space. This is done within the context of a class of cosmological models that contain regularly arranged discrete masses, rather than a continuous perfect fluid. The natural set of geodesic curves that one should use to consider the cosmological expansion of these models requires the existence of a non-zero magnetic part of the Weyl tensor. We include this object in the evolution equations of these models by performing a Taylor series expansion about a hypersurface where it initially vanishes. At the same cosmological time, measured as a fraction of the age of the universe, we find that the influence of the magnetic part of the Weyl tensor increases as the number of masses in the universe is increased. We also find that the influence of the magnetic part of the Weyl tensor increases with time, relative to the leading-order electric part, so that its contribution to the scale of the universe can reach values of ˜ 1%, before the Taylor series approximation starts to break down.
Physical states in the canonical tensor model from the perspective of random tensor networks
Narain, Gaurav; Sato, Yuki
2014-01-01
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 physical wave-functions, which do not seem straightforward to solve 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 con...
Interplay between tensor force and deformation in even–even nuclei
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.
Interplay between tensor force and deformation in even-even nuclei
Bernard, Rémi N.; Anguiano, Marta
2016-09-01
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.
Toward a Consistent Framework for High Order Mesh Refinement Schemes in Numerical Relativity
Mongwane, Bishop
2015-01-01
It has now become customary in the field of numerical relativity to couple high order finite difference schemes to mesh refinement algorithms. To this end, different modifications to the standard Berger-Oliger adaptive mesh refinement algorithm have been proposed. In this work we present a fourth order stable mesh refinement scheme with sub-cycling in time for numerical relativity. We do not use buffer zones to deal with refinement boundaries but explicitly specify boundary data for refined grids. We argue that the incompatibility of the standard mesh refinement algorithm with higher order Runge Kutta methods is a manifestation of order reduction phenomena, caused by inconsistent application of boundary data in the refined grids. Our scheme also addresses the problem of spurious reflections that are generated when propagating waves cross mesh refinement boundaries. We introduce a transition zone on refined levels within which the phase velocity of propagating modes is allowed to decelerate in order to smoothl...
A Proposal of Proper Gravitational Energy Momentum Tensor
Shimizu, Katsutaro
2016-01-01
We propose a gravitational energy momentum tensor of the general relativity by using Noether theorem. It changes as an tensor under the general coordinate transformations. One of the two indices of the gravitational energy momentum tensor is a local Lorentz frame to satisfy an energy momentum conservation law. The energies of a gravitational wave, Schwarzschild black hole and Friedman-Lemertre-Robertoson-Walker universe are calculated as examples. The gravitational energy of Schwarzschild black hole exists only out of a horizon. Its amount is -M.
Construction of energy-momentum tensor of gravitation
Bamba, Kazuharu
2015-01-01
We argue the possibility that the gravitational energy-momentum tensor is constructed in general relativity through the Noether theorem. In particular, we explicitly demonstrate that the constructed quantity can vary as a tensor under the general coordinate transformation. Furthermore, we verify that the energy-momentum conservation is satisfied because one of the two indices of the energy-momentum tensor should be in the local Lorentz frame. It is also shown that the gravitational energy and the matter one cancel out in certain space-times.
Extended Scalar-Tensor Theories of Gravity
Crisostomi, Marco; Tasinato, Gianmassimo
2016-01-01
We determine new consistent scalar-tensor theories of gravity, with potentially interesting cosmological applications. We develop a general method to find the conditions for the existence of a primary constraint, which is necessary to prevent the propagation of an additional dangerous mode associated with higher order equations of motion. We then classify the most general, consistent scalar-tensor theories that are at most quadratic in the second derivatives of the scalar field. In addition, we investigate the possible connection between these theories and (beyond) Horndeski through conformal and disformal transformations. Finally, we point out that these theories can be associated with new operators in the effective field theory of dark energy, which might open up new possibilities to test dark energy models in future surveys.
Tensor Network Contractions for #SAT
Biamonte, Jacob D.; Morton, Jason; Turner, Jacob
2015-09-01
The computational cost of counting the number of solutions satisfying a Boolean formula, which is a problem instance of #SAT, has proven subtle to quantify. Even when finding individual satisfying solutions is computationally easy (e.g. 2-SAT, which is in ), determining the number of solutions can be #-hard. Recently, computational methods simulating quantum systems experienced advancements due to the development of tensor network algorithms and associated quantum physics-inspired techniques. By these methods, we give an algorithm using an axiomatic tensor contraction language for n-variable #SAT instances with complexity where c is the number of COPY-tensors, g is the number of gates, and d is the maximal degree of any COPY-tensor. Thus, n-variable counting problems can be solved efficiently when their tensor network expression has at most COPY-tensors and polynomial fan-out. This framework also admits an intuitive proof of a variant of the Tovey conjecture (the r,1-SAT instance of the Dubois-Tovey theorem). This study increases the theory, expressiveness and application of tensor based algorithmic tools and provides an alternative insight on these problems which have a long history in statistical physics and computer science.
MATLAB tensor classes for fast algorithm prototyping.
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.
Distance Adaptive Tensor Discriminative Geometry Preserving Projection for Face Recognition
Ziqiang Wang
2012-09-01
Full Text Available There is a growing interest in dimensionality reduction techniques for face recognition, however, the traditional dimensionality reduction algorithms often transform the input face image data into vectors before embedding. Such vectorization often ignores the underlying data structure and leads to higher computational complexity. To effectively cope with these problems, a novel dimensionality reduction algorithm termed distance adaptive tensor discriminative geometry preserving projection (DATDGPP is proposed in this paper. The key idea of DATDGPP is as follows: first, the face image data are directly encoded in high‐order tensor structure so that the relationships among the face image data can be preserved; second, the data‐adaptive tensor distance is adopted to model the correlation among different coordinates of tensor data; third, the transformation matrix which can preserve discrimination and local geometry information is obtained by an iteration algorithm. Experimental results on three face databases show that the proposed algorithm outperforms other representative dimensionality reduction algorithms.
Monodromy and Jacobi-like Relations for Color-Ordered Amplitudes
Bjerrum-Bohr, N E J; Sondergaard, Thomas; Vanhove, Pierre
2010-01-01
We discuss monodromy relations between different color-ordered amplitudes in gauge theories. We show that Jacobi-like relations of Bern, Carrasco and Johansson can be introduced in a manner that is compatible with these monodromy relations. The Jacobi-like relations are not the most general set of equations that satisfy this criterion. Applications to supergravity amplitudes follow straightforwardly through the KLT-relations. We explicitly show how the tree-level relations give rise to non-trivial identities at loop level.
Symmetric Topological Phases and Tensor Network States
Jiang, Shenghan
Classification and simulation of quantum phases are one of main themes in condensed matter physics. Quantum phases can be distinguished by their symmetrical and topological properties. The interplay between symmetry and topology in condensed matter physics often leads to exotic quantum phases and rich phase diagrams. Famous examples include quantum Hall phases, spin liquids and topological insulators. In this thesis, I present our works toward a more systematically understanding of symmetric topological quantum phases in bosonic systems. In the absence of global symmetries, gapped quantum phases are characterized by topological orders. Topological orders in 2+1D are well studied, while a systematically understanding of topological orders in 3+1D is still lacking. By studying a family of exact solvable models, we find at least some topological orders in 3+1D can be distinguished by braiding phases of loop excitations. In the presence of both global symmetries and topological orders, the interplay between them leads to new phases termed as symmetry enriched topological (SET) phases. We develop a framework to classify a large class of SET phases using tensor networks. For each tensor class, we can write down generic variational wavefunctions. We apply our method to study gapped spin liquids on the kagome lattice, which can be viewed as SET phases of on-site symmetries as well as lattice symmetries. In the absence of topological order, symmetry could protect different topological phases, which are often referred to as symmetry protected topological (SPT) phases. We present systematic constructions of tensor network wavefunctions for bosonic symmetry protected topological (SPT) phases respecting both onsite and spatial symmetries.
Solving Tensor Structured Problems with Computational Tensor Algebra
Morozov, Oleksii
2010-01-01
Since its introduction by Gauss, Matrix Algebra has facilitated understanding of scientific problems, hiding distracting details and finding more elegant and efficient ways of computational solving. Today's largest problems, which often originate from multidimensional data, might profit from even higher levels of abstraction. We developed a framework for solving tensor structured problems with tensor algebra that unifies concepts from tensor analysis, multilinear algebra and multidimensional signal processing. In contrast to the conventional matrix approach, it allows the formulation of multidimensional problems, in a multidimensional way, preserving structure and data coherence; and the implementation of automated optimizations of solving algorithms, based on the commutativity of all tensor operations. Its ability to handle large scientific tasks is showcased by a real-world, 4D medical imaging problem, with more than 30 million unknown parameters solved on a current, inexpensive hardware. This significantly...
Relative boundedness and compactness theory for second-order differential operators
Don B. Hinton
1997-01-01
Full Text Available The problem considered is to give necessary and sufficient conditions for perturbations of a second-order ordinary differential operator to be either relatively bounded or relatively compact. Such conditions are found for three classes of operators. The conditions are expressed in terms of integral averages of the coefficients of the perturbing operator.
Quark mass relations to four-loop order in perturbative QCD.
Marquard, Peter; Smirnov, Alexander V; Smirnov, Vladimir A; Steinhauser, Matthias
2015-04-10
We present results for the relation between a heavy quark mass defined in the on-shell and minimal subtraction (MS[over ¯]) scheme to four-loop order. The method to compute the four-loop on-shell integral is briefly described and the new results are used to establish relations between various short-distance masses and the MS[over ¯] quark mass to next-to-next-to-next-to-leading order accuracy. These relations play an important role in the accurate determination of the MS[over ¯] heavy quark masses.
Tensor perturbations in a general class of Palatini theories
Jiménez, Jose Beltrán; Olmo, Gonzalo J
2015-01-01
We study a general class of gravitational theories formulated in the Palatini approach and derive the equations governing the evolution of tensor perturbations. In the absence of torsion, the connection can be solved as the Christoffel symbols of an auxiliary metric which is non-trivially related to the space-time metric. We then consider background solutions corresponding to a perfect fluid and show that the tensor perturbations equations (including anisotropic stresses) for the auxiliary metric around such a background take an Einstein-like form. This facilitates the study in a homogeneous and isotropic cosmological scenario where we explicitly establish the relation between the auxiliary metric and the space-time metric tensor perturbations. As a general result, we show that both tensor perturbations coincide in the absence of anisotropic stresses.
Tensor perturbations in a general class of Palatini theories
Beltrán Jiménez, Jose; Heisenberg, Lavinia; Olmo, Gonzalo J.
2015-06-01
We study a general class of gravitational theories formulated in the Palatini approach and derive the equations governing the evolution of tensor perturbations. In the absence of torsion, the connection can be solved as the Christoffel symbols of an auxiliary metric which is non-trivially related to the space-time metric. We then consider background solutions corresponding to a perfect fluid and show that the tensor perturbations equations (including anisotropic stresses) for the auxiliary metric around such a background take an Einstein-like form. This facilitates the study in a homogeneous and isotropic cosmological scenario where we explicitly establish the relation between the auxiliary metric and the space-time metric tensor perturbations. As a general result, we show that both tensor perturbations coincide in the absence of anisotropic stresses.
Tensor analysis and elementary differential geometry for physicists and engineers
Nguyen-Schäfer, Hung
2017-01-01
This book comprehensively presents topics, such as Dirac notation, tensor analysis, elementary differential geometry of moving surfaces, and k-differential forms. Additionally, two new chapters of Cartan differential forms and Dirac and tensor notations in quantum mechanics are added to this second edition. The reader is provided with hands-on calculations and worked-out examples at which he will learn how to handle the bra-ket notation, tensors, differential geometry, and differential forms; and to apply them to the physical and engineering world. Many methods and applications are given in CFD, continuum mechanics, electrodynamics in special relativity, cosmology in the Minkowski four-dimensional spacetime, and relativistic and non-relativistic quantum mechanics. Tensors, differential geometry, differential forms, and Dirac notation are very useful advanced mathematical tools in many fields of modern physics and computational engineering. They are involved in special and general relativity physics, quantum m...
Imaging of first-order surface-related multiples by reverse-time migration
Liu, Xuejian; Liu, Yike; Hu, Hao; Li, Peng; Khan, Majid
2017-02-01
Surface-related multiples have been utilized in the reverse-time migration (RTM) procedures, and additional illumination for subsurface can be provided. Meanwhile, many cross-talks are generated from undesired interactions between forward- and backward-propagated seismic waves. In this paper, subsequent to analysing and categorizing these cross-talks, we propose RTM of first-order multiples to avoid most undesired interactions in RTM of all-order multiples, where only primaries are forward-propagated and crosscorrelated with the backward-propagated first-order multiples. With primaries and multiples separated during regular seismic data processing as the input data, first-order multiples can be obtained by a two-step scheme: (1) the dual-prediction of higher-order multiples; and (2) the adaptive subtraction of predicted higher-order multiples from all-order multiples within local offset-time windows. In numerical experiments, two synthetic and a marine field data sets are used, where different cross-talks generated by RTM of all-order multiples can be identified and the proposed RTM of first-order multiples can provide a very interpretable image with a few cross-talks.
MACH: Fast Randomized Tensor Decompositions
Tsourakakis, Charalampos E
2009-01-01
Tensors naturally model many real world processes which generate multi-aspect data. Such processes appear in many different research disciplines, e.g, chemometrics, computer vision, psychometrics and neuroimaging analysis. Tensor decompositions such as the Tucker decomposition are used to analyze multi-aspect data and extract latent factors, which capture the multilinear data structure. Such decompositions are powerful mining tools, for extracting patterns from large data volumes. However, most frequently used algorithms for such decompositions involve the computationally expensive Singular Value Decomposition. In this paper we propose MACH, a new sampling algorithm to compute such decompositions. Our method is of significant practical value for tensor streams, such as environmental monitoring systems, IP traffic matrices over time, where large amounts of data are accumulated and the analysis is computationally intensive but also in "post-mortem" data analysis cases where the tensor does not fit in the availa...
Cosmic no-hair conjecture in scalar–tensor theories
T Singh; R Chaubey
2006-12-01
We have shown that, within the context of scalar–tensor theories, the anisotropic Bianchi-type cosmological models evolve towards de Sitter Universe. A similar result holds in the case of cosmology in Lyra manifold. Thus the analogue of cosmic no-hair theorem of Wald [1] hold in both the cases. In fact, during inflation there is no difference between scalar–tensor theories, Lyra's manifold and general relativity (GR).
Tensor computations in computer algebra systems
Korolkova, A V; Sevastyanov, L A
2014-01-01
This paper considers three types of tensor computations. On their basis, we attempt to formulate criteria that must be satisfied by a computer algebra system dealing with tensors. We briefly overview the current state of tensor computations in different computer algebra systems. The tensor computations are illustrated with appropriate examples implemented in specific systems: Cadabra and Maxima.
A general theory of linear cosmological perturbations: scalar-tensor and vector-tensor theories
Lagos, Macarena; Ferreira, Pedro G; Noller, Johannes
2016-01-01
We present a method for parametrizing linear cosmological perturbations of theories of gravity, around homogeneous and isotropic backgrounds. The method is sufficiently general and systematic that it can be applied to theories with any degrees of freedom (DoFs) and arbitrary gauge symmetries. In this paper, we focus on scalar-tensor and vector-tensor theories, invariant under linear coordinate transformations. In the case of scalar-tensor theories, we use our framework to recover the simple parametrizations of linearized Horndeski and "Beyond Horndeski" theories, and also find higher-derivative corrections. In the case of vector-tensor theories, we first construct the most general quadratic action for perturbations that leads to second-order equations of motion, which propagates two scalar DoFs. Then we specialize to the case in which the vector field is time-like (\\`a la Einstein-Aether gravity), where the theory only propagates one scalar DoF. As a result, we identify the complete forms of the quadratic act...
Exploring Item Order in Anxiety-Related Constructs: Practical Impacts of Serial Position
R. Nicholas Carleton
2012-04-01
Full Text Available The present study was designed to test for item order effects by measuring four distinct constructs that contribute substantively to anxiety-related psychopathology (i.e., anxiety sensitivity, fear of negative evaluation, injury/illness sensitivity, and intolerance of uncertainty. Participants (n = 999; 71% women were randomly assigned to complete measures for each construct presented in one of two modalities: (a items presented cohesively as measures or (b items presented randomly interspersed with one another. The results suggested that item order had a relatively small impact on item endorsement, response patterns, and reliabilities. The small impact was such that item order appears unlikely to influence clinical decisions related to these measures. These findings not only have implications for these and other similar measures, but further inform a long-standing debate about whether item grouping is a substantial concern in measurement.
Tensor Product of Massey Products
Qi Bing ZHENG
2006-01-01
In this paper, we interpret Massey products in terms of realizations (twitsting cochains)of certain differential graded coalgebras with values in differential graded algebras. In the case where the target algebra is the cobar construction of a differential graded commutative Hopf algebra, we construct the tensor product of realizations and show that the tensor product is strictly associative,and commutative up to homotopy.
Tensor 2-sums and entanglement
Klavzar, Sandi
2009-01-01
To define a minimal mathematical framework for isolating some of the characteristic properties of quantum entanglement, we introduce a generalization of the tensor product of graphs. Inspired by the notion of a density matrix, the generalization is a simple one: every graph can be obtained by addiction modulo two, possibly with many summands, of tensor products of adjacency matrices. In this picture, we are still able to prove a combinatorial analogue of the Peres-Horodecki criterion for testing separability.
Scalable tensor factorizations with incomplete data.
Morup, Morten (Technical University of Denmark); Dunlavy, Daniel M. (Sandia National Laboratories, Albuquerque, NM); Acar, Evrim (Information Technologies Institute, Turkey); Kolda, Tamara Gibson
2010-07-01
The problem of incomplete data - i.e., data with missing or unknown values - in multi-way arrays is ubiquitous in biomedical signal processing, network traffic analysis, bibliometrics, social network analysis, chemometrics, computer vision, communication networks, etc. We consider the problem of how 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). In the presence of missing data, CP can be formulated as a weighted least squares problem that models only the known entries. We develop an algorithm called CP-WOPT (CP Weighted OPTimization) that uses a first-order optimization approach to solve the weighted least squares problem. Based on extensive numerical 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 x 1000 x 1000 with five million known entries (0.5% dense). We further demonstrate the usefulness of CP-WOPT on two real-world applications: a novel EEG (electroencephalogram) application where missing data is frequently encountered due to disconnections of electrodes and the problem of modeling computer network traffic where data may be absent due to the expense of the data collection process.
Positivity and conservation of superenergy tensors
Pozo, J M
2002-01-01
Two essential properties of energy-momentum tensors T submu subnu are their positivity and conservation. This is mathematically formalized by, respectively, an energy condition, as the dominant energy condition, and the vanishing of their divergence nabla supmu T submu subnu = 0. The classical Bel and Bel-Robinson superenergy tensors, generated from the Riemann and Weyl tensors, respectively, are rank-4 tensors. But they share these two properties with energy-momentum tensors: the dominant property (DP) and the divergence-free property in the absence of sources (vacuum). Senovilla defined a universal algebraic construction which generates a basic superenergy tensor T left brace A right brace from any arbitrary tensor A. In this construction, the seed tensor A is structured as an r-fold multivector, which can always be done. The most important feature of the basic superenergy tensors is that they satisfy automatically the DP, independently of the generating tensor A. We presented a more compact definition of T...
Lopuszynski, Michal; Majewski, Jacek A.
2007-01-01
We present theoretical studies for the third-order elastic constants $C_{ijk}$ in zinc-blende nitrides AlN, GaN, and InN. Our predictions for these compounds are based on detailed ab initio calculations of strain-energy and strain-stress relations in the framework of the density functional theory. To judge the computational accuracy, we compare the ab initio calculated results for $C_{ijk}$ with experimental data available for Si and GaAs. We also underline the relation of the third-order ela...
Monte Carlo Volcano Seismic Moment Tensors
Waite, G. P.; Brill, K. A.; Lanza, F.
2015-12-01
Inverse modeling of volcano seismic sources can provide insight into the geometry and dynamics of volcanic conduits. But given the logistical challenges of working on an active volcano, seismic networks are typically deficient in spatial and temporal coverage; this potentially leads to large errors in source models. In addition, uncertainties in the centroid location and moment-tensor components, including volumetric components, are difficult to constrain from the linear inversion results, which leads to a poor understanding of the model space. In this study, we employ a nonlinear inversion using a Monte Carlo scheme with the objective of defining robustly resolved elements of model space. The model space is randomized by centroid location and moment tensor eigenvectors. Point sources densely sample the summit area and moment tensors are constrained to a randomly chosen geometry within the inversion; Green's functions for the random moment tensors are all calculated from modeled single forces, making the nonlinear inversion computationally reasonable. We apply this method to very-long-period (VLP) seismic events that accompany minor eruptions at Fuego volcano, Guatemala. The library of single force Green's functions is computed with a 3D finite-difference modeling algorithm through a homogeneous velocity-density model that includes topography, for a 3D grid of nodes, spaced 40 m apart, within the summit region. The homogenous velocity and density model is justified by long wavelength of VLP data. The nonlinear inversion reveals well resolved model features and informs the interpretation through a better understanding of the possible models. This approach can also be used to evaluate possible station geometries in order to optimize networks prior to deployment.
A direct proof of uniqueness of square-root of a positive semi-definite tensor
Yue SHAO; Cun-jing L(U)
2009-01-01
Understanding of the basic properties of the positive semi-definite tensor is a prerequisite for its extensive applications in theoretical and practical fields,especially for its square-root.Uniqueness of the square-root of a positive semi-definite tensor is proven in this paper without resorting to the notion of eigenvalues,eigenvectors and the spectral decomposition of the second-order symmetric tensor.
2016-05-11
AFRL-AFOSR-JP-TR-2016-0046 Designing Feature and Data Parallel Stochastic Coordinate Descent Method for Matrix and Tensor Factorization U Kang Korea...Designing Feature and Data Parallel Stochastic Coordinate Descent Method for Matrix and Tensor Factorization 5a. CONTRACT NUMBER 5b. GRANT NUMBER FA2386...Release 13. SUPPLEMENTARY NOTES 14. ABSTRACT Given a high-order large-scale tensor , how can we decompose it into latent factors? Can we process it on
Physical states in the canonical tensor model from the perspective of random tensor networks
Narain, Gaurav; Sasakura, Naoki; Sato, Yuki
2015-01-01
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.
Tensor modes on the string theory landscape
Westphal, Alexander
2012-06-15
We attempt an estimate for the distribution of the tensor mode fraction r over the landscape of vacua in string theory. The dynamics of eternal inflation and quantum tunneling lead to a kind of democracy on the landscape, providing no bias towards large-field or small-field inflation regardless of the class of measure. The tensor mode fraction then follows the number frequency distributions of inflationary mechanisms of string theory over the landscape. We show that an estimate of the relative number frequencies for small-field vs large-field inflation, while unattainable on the whole landscape, may be within reach as a regional answer for warped Calabi-Yau flux compactifications of type IIB string theory.
Tensor modes on the string theory landscape
Westphal, Alexander
2012-01-01
We attempt an estimate for the distribution of the tensor mode fraction $r$ over the landscape of vacua in string theory. The dynamics of eternal inflation and quantum tunneling lead to a kind of democracy on the landscape, providing no bias towards large-field or small-field inflation regardless of the class of measure. The tensor mode fraction then follows the number frequency distributions of inflationary mechanisms of string theory over the landscape. We show that an estimate of the relative number frequencies for small-field vs large-field inflation, while unattainable on the whole landscape, may be within reach as a regional answer for warped Calabi-Yau flux compactifications of type IIB string theory.
Yoshino, Masanori; Kin, Taichi; Ito, Akihiro; Saito, Toki; Nakagawa, Daichi; Ino, Kenji; Kamada, Kyousuke; Mori, Harushi; Kunimatsu, Akira; Nakatomi, Hirofumi; Oyama, Hiroshi; Saito, Nobuhito
2015-12-01
The authors assessed whether the combined use of diffusion tensor tractography (DTT) and contrast-enhanced (CE) fast imaging employing steady-state acquisition (FIESTA) could improve the accuracy of predicting the courses of the facial and cochlear nerves before surgery. The population was composed of 22 patients with vestibular schwannoma in whom both the facial and cochlear nerves could be identified during surgery. According to DTT, depicted fibers running from the internal auditory canal to the brainstem were judged to represent the facial or vestibulocochlear nerve. With regard to imaging, the authors investigated multifused CE-FIESTA scans, in which all 3D vessel models were shown simultaneously, from various angles. The low-intensity areas running along the tumor from brainstem to the internal auditory canal were judged to represent the facial or vestibulocochlear nerve. For all 22 patients, the rate of fibers depicted by DTT coinciding with the facial nerve was 13.6% (3/22), and that of fibers depicted by DTT coinciding with the cochlear nerve was 63.6% (14/22). The rate of candidates for nerves predicted by multifused CE-FIESTA coinciding with the facial nerve was 59.1% (13/22), and that of candidates for nerves predicted by multifused CE-FIESTA coinciding with the cochlear nerve was 4.5% (1/22). The rate of candidates for nerves predicted by combined DTT and multifused CE-FIESTA coinciding with the facial nerve was 63.6% (14/22), and that of candidates for nerves predicted by combined DTT and multifused CE-FIESTA coinciding with the cochlear nerve was 63.6% (14/22). The rate of candidates predicted by DTT coinciding with both facial and cochlear nerves was 0.0% (0/22), that of candidates predicted by multifused CE-FIESTA coinciding with both facial and cochlear nerves was 4.5% (1/22), and that of candidates predicted by combined DTT and multifused CE-FIESTA coinciding with both the facial and cochlear nerves was 45.5% (10/22). By using a combination of
Chiral perturbation theory with tensor sources
Cata, Oscar; Cata, Oscar; Mateu, Vicent
2007-05-21
We construct the most general chirally-invariant Lagrangian for mesons in the presence of external sources coupled to the tensor current \\bar psi sigma_mu nu psi. In order to have only even terms in the chiral expansion, we consider the new source of O(p2). With this choice, we build the even-parity effective Lagrangian up to the p6-order (NLO). While there are only 4 new terms at the p4-order, at p6-order we find 78 terms for n_f=2 and 113 terms for n_f=3. We provide a detailed discussion on the different mechanisms that ensure that our final set of operators is complete and non-redundant. We also examine the odd-parity sector, to conclude that the first operators appear at the p8-order (NNLO).
Parity- and Time Reversal-Violating Pion Nucleon Couplings: Higher Order Chiral Matching Relations
Seng, Chien-Yeah
2016-01-01
Parity- and time reversal-violating (PVTV) pion-nucleon couplings govern the magnitude of long-range contributions to nucleon and atomic electric dipole moments. When these couplings arise from chiral symmetry-breaking CP-violating operators, such as the QCD $\\theta$-term or quark chromoelectric dipole moments, one may relate hadronic matrix elements entering the PVTV couplings to nucleon and pion mass shifts by exploiting the corresponding chiral transformation properties at leading order (LO) in the chiral expansion. We compute the higher-order contributions to the lowest order relations arising from chiral loops and next-to-next-to leading order (NNLO) operators. We find that for the QCD $\\theta$-term the higher order contributions are analytic in the quark masses, while for the quark chromoelectric dipole moments and chiral symmetry-breaking four-quark operators, the matching relations also receive non-analytic corrections. Numerical estimates suggest that for the isoscalar PVTV pion-nucleon coupling, the...
High-Order Numerical-Relativity Simulations of Binary Neutron Stars
Radice, David; Galeazzi, Filippo
2015-01-01
We report simulations of the inspiral and merger of binary neutron stars performed with \\texttt{WhiskyTHC}, the first of a new generation of numerical relativity codes employing higher than second-order methods for both the spacetime and the hydrodynamic evolution. We find that the use of higher-order schemes improves substantially the quality of the gravitational waveforms extracted from the simulations when compared to those computed using traditional second-order schemes. The reduced de-phasing and the faster convergence rate allow us to estimate the phase evolution of the gravitational waves emitted, as well as the magnitude of finite-resolution effects, without the need of phase- or time-alignments or rescalings of the waves, as sometimes done in other works. Furthermore, by using an additional unpublished simulation at very high resolution, we confirm the robustness of our high convergence order of $3.2$.
2012-12-18
... COMMISSION Order Granting Exemptions From Certain Rules of Regulation SHO Related to Hurricane Sandy December 12, 2012. I. Introduction Hurricane Sandy made landfall along the mid-Atlantic Coast on October 29... in the Vault at the time Hurricane Sandy made landfall, facilitating DTCC's ability to...
Do Children with Autism Perceive Second-Order Relational Features? The Case of the Thatcher Illusion
Rouse, Helen; Donnelly, Nick; Hadwin, Julie A.; Brown, Tony
2004-01-01
Background: This study presents two experiments that investigated whether children with autism were susceptible to the Thatcher illusion. Perception of the Thatcher illusion requires being able to compute second-order configural relations for facial stimuli. Method: In both experiments children with autism were matched for non-verbal and verbal…
Exploring Item Order in Anxiety-Related Constructs: Practical Impacts of Serial Position
Carleton, R. Nicholas; Thibodeau, Michel A.; Osborne, Jason W.; Asmundson, Gordon J. G.
2012-01-01
The present study was designed to test for item order effects by measuring four distinct constructs that contribute substantively to anxiety-related psychopathology (i.e., anxiety sensitivity, fear of negative evaluation, injury/illness sensitivity, and intolerance of uncertainty). Participants (n = 999; 71% women) were randomly assigned to…
无
2010-01-01
In this paper, we study an even order neutral differential equation with deviating arguments, and obtain new oscillation results without the assumptions which were required for related results given before. Our results extend and improve many known oscillation criteria, based on the standard integral averaging technique.
Nuclear response functions with finite range Gogny force: tensor terms and instabilities
De Pace, A
2016-01-01
A fully-antisymmetrized random phase approximation calculation employing the continued fraction technique is performed to study nuclear matter response functions with the finite range Gogny force. The most commonly used parameter sets of this force, as well as some recent generalizations that include the tensor terms are considered and the corresponding response functions are shown. The calculations are performed at the first and second order in the continued fraction expansion and the explicit expressions for the second order tensor contributions are given. Comparison between first and second order continued fraction expansion results are provided. The differences between the responses obtained at the two orders turn to be more pronounced for the forces including tensor terms than for the standard Gogny ones. In the vector channels the responses calculated with Gogny forces including tensor terms are characterized by a large heterogeneity, reflecting the different choices for the tensor part of the interacti...
Comments on the Stress-Energy Tensor Operator in Curved Spacetime
Moretti, V
2003-01-01
The technique based on the *-algebra of local Wick products of (formal) field operators in curved spacetime proposed by Hollands and Wald, is implemented and developed in order to define the stress-energy tensor operator in terms of local Wick products of (derived) field operators only. It shows that, within the proposed formalism, there may be room to accomplish all of physical requirements provided the known problems concerning the conservation property are assumed to be related to the interface between quantum and classical formalisms. Indeed, a stress-energy tensor operator is proposed which, written using local Wick products of fields only, is conserved and it reduces to the classical form when operators are replaced by classical fields satisfying the equation of the motion. The definition is based on the existence of convenient local Wick products of derived fields. These terms are independent from the arbitrary length scale and the quantum state and they classically vanish. Considering averaged stress-...
Diffusion Tensor Imaging of Pedophilia.
Cantor, James M; Lafaille, Sophie; Soh, Debra W; Moayedi, Massieh; Mikulis, David J; Girard, Todd A
2015-11-01
Pedophilia is a principal motivator of child molestation, incurring great emotional and financial burdens on victims and society. Even among pedophiles who never commit any offense,the condition requires lifelong suppression and control. Previous comparison using voxel-based morphometry (VBM)of MR images from a large sample of pedophiles and controls revealed group differences in white matter. The present study therefore sought to verify and characterize white matter involvement using diffusion tensor imaging (DTI), which better captures the microstructure of white matter than does VBM. Pedophilics ex offenders (n=24) were compared with healthy, age-matched controls with no criminal record and no indication of pedophilia (n=32). White matter microstructure was analyzed with Tract-Based Spatial Statistics, and the trajectories of implicated fiber bundles were identified by probabilistic tractography. Groups showed significant, highly focused differences in DTI parameters which related to participants’ genital responses to sexual depictions of children, but not to measures of psychopathy or to childhood histories of physical abuse, sexual abuse, or neglect. Some previously reported gray matter differences were suggested under highly liberal statistical conditions (p(uncorrected)<.005), but did not survive ordinary statistical correction (whole brain per voxel false discovery rate of 5%). These results confirm that pedophilia is characterized by neuroanatomical differences in white matter microstructure, over and above any neural characteristics attributable to psychopathy and childhood adversity, which show neuroanatomic footprints of their own. Although some gray matter structures were implicated previously, only few have emerged reliably.
Double Scaling in Tensor Models with a Quartic Interaction
Dartois, Stephane; Rivasseau, Vincent
2013-01-01
In this paper we identify and analyze in detail the subleading contributions in the 1/N expansion of random tensors, in the simple case of a quartically interacting model. The leading order for this 1/N expansion is made of graphs, called melons, which are dual to particular triangulations of the D-dimensional sphere, closely related to the "stacked" triangulations. For D<6 the subleading behavior is governed by a larger family of graphs, hereafter called cherry trees, which are also dual to the D-dimensional sphere. They can be resummed explicitly through a double scaling limit. In sharp contrast with random matrix models, this double scaling limit is stable. Apart from its unexpected upper critical dimension 6, it displays a singularity at fixed distance from the origin and is clearly the first step in a richer set of yet to be discovered multi-scaling limits.
Testing gravity theories using tensor perturbations
Lin, Weikang
2016-01-01
Primordial gravitational waves constitute a promising probe of the very-early universe and the laws of gravity. We study changes to tensor mode perturbations that can arise in various proposed modified gravity (MG) theories. These include additional friction effects, non-standard dispersion relations involving a massive graviton, a modified speed, and a small-scale modification. We introduce a physically-motivated parameterization of these effects and use current available data to obtain exclusion regions in the parameter spaces. Taking into account the foreground subtraction, we then perform a forecast analysis focusing on the tensor mode MG parameters as constrained by the future experiments COrE, Stage-IV and PIXIE. For a fiducial value of the tensor-to-scalar ratio r=0.01, we find that an additional friction of 3.5-4.5% compared to GR will be detected at $3\\sigma$ by these experiments while a decrease in friction will be more difficult to detect. The speed of gravitational waves needs to be 5-15% differen...
Effective elasticity tensor of a periodic composite
Nunan, Kevin C.; Keller, Joseph B.
THE EFFECTIVE elasticity tensor of a composite is defined to be the four-tensor C which relates the average stress to the average strain. We determine it for an array of rigid spheres centered on the points of a periodic lattice in a homogeneous isotropic elastic medium. We first express C in terms of the traction exerted on a single sphere by the medium, and then derive an integral equation for this traction. We solve this equation numerically for simple, body-centered and face-centered cubic lattices with inclusion concentrations up to 90% of the close-packing concentration. For lattices with cubic symmetry the effective elasticity tensor involves just three parameters, which we compute from the solution for the traction. We obtain approximate asymptotic formulas for low concentrations which agree well with the numerical results. We also derive asymptotic results for C at high inclusion concentrations for arbitrary lattice geometries. We find them to be in good agreement with the numerical results for cubic lattices. For low and moderate concentrations the approximate results of NEMAT- NASSERet al., also agree well with the numerical results for cubic lattices.
Ezquiaga, Jose María; Zumalacárregui, Miguel
2016-01-01
We use a description based on differential forms to systematically explore the space of scalar-tensor theories of gravity. Within this formalism, we propose a basis for the scalar sector at the lowest order in derivatives of the field and in any number of dimensions. This minimal basis is used to construct a finite and closed set of Lagrangians describing general scalar-tensor theories invariant under Local Lorentz Transformations in a pseudo-Riemannian manifold, which contains ten physically distinct elements in four spacetime dimensions. Subsequently, we compute their corresponding equations of motion and find which combinations are at most second order in derivatives in four as well as arbitrary number of dimensions. By studying the possible exact forms (total derivatives) and algebraic relations between the basis components, we discover that there are only four Lagrangian combinations producing second order equations, which can be associated with Horndeski's theory. In this process, we identify a new seco...
I-Love-Q, Spontaneously: Slowly Rotating Neutron Stars in Scalar-Tensor Theories
Pani, Paolo
2014-01-01
We construct models of slowly rotating, perfect-fluid neutron stars by extending the classical Hartle-Thorne formalism to generic scalar-tensor theories of gravity. Working at second order in the dimensionless angular momentum, we compute the mass $M$, radius $R$, scalar charge $q$, moment of inertia $I$ and spin-induced quadrupole moment $Q$, as well as the tidal and rotational Love numbers. Our formalism applies to generic scalar-tensor theories, but we focus in particular on theories that allow for spontaneous scalarization. It was recently discovered that the moment of inertia, quadrupole moment and Love numbers are connected by approximately universal (i.e., equation-of-state independent) "I-Love-Q" relations. We find that similar relations hold also for spontaneously scalarized stars. More interestingly, the I-Love-Q relations in scalar-tensor theories coincide with the general relativistic ones within less than a few percent, even for spontaneously scalarized stars with the largest couplings allowed by...
Tensor Decompositions for Learning Latent Variable Models
2012-12-08
Isotropic PCA and affine-invariant clustering. In FOCS, 2008. [Car91] J.-F. Cardoso . Super-symmetric decomposition of the fourth-order cumulant tensor...3109–3112. IEEE, 1991. [Car94] J.-F. Cardoso . Perturbation of joint diagonalizers. ref# 94d027. Technical report, Télécom Paris, 1994. [Cat44] R. B...CC96] J.-F. Cardoso and Pierre Comon. Independent component analysis, a survey of some algebraic methods. In IEEE International Symposium on Circuits
Hyperbolicity of Scalar Tensor Theories of Gravity
Salgado, Marcelo; Alcubierre, Miguel; Núñez, Dario
2008-01-01
Two first order strongly hyperbolic formulations of scalar tensor theories of gravity (STT) allowing non-minimal couplings (Jordan frame) are presented along the lines of the 3+1 decomposition of spacetime. One is based on the Bona-Masso formulation while the other one employs a conformal decomposition similar to that of Baumgarte-Shapiro-Shibata-Nakamura. A modified Bona-Masso slicing condition adapted to the STT is proposed for the analysis. This study confirms that STT posses a well posed Cauchy problem even when formulated in the Jordan frame.
Hypersurfaces with Isotropic Para-Blaschke Tensor
Jian Bo FANG; Kun ZHANG
2014-01-01
Let Mn be an n-dimensional submanifold without umbilical points in the (n+1)-dimen-sional unit sphere Sn+1. Four basic invariants of Mn under the Moebius transformation group of Sn+1 are a1-form Φ called moebius form, a symmetric (0, 2) tensor A called Blaschke tensor, a symmetric (0, 2) tensor B called Moebius second fundamental form and a positive definite (0, 2) tensor g called Moebius metric. A symmetric (0, 2) tensor D = A+μB called para-Blaschke tensor, where μ is constant, is also an Moebius invariant. We call the para-Blaschke tensor is isotropic if there exists a function λ such that D = λg. One of the basic questions in Moebius geometry is to classify the hypersurfaces with isotropic para-Blaschke tensor. When λ is not constant, all hypersurfaces with isotropic para-Blaschke tensor are explicitly expressed in this paper.
A tensor-based dictionary learning approach to tomographic image reconstruction
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...
On the relation between hydrogen bonds, tetrahedral order and molecular mobility in model water
Pereyra, R G; Malaspina, D C; Carignano, M A
2013-01-01
We studied by molecular dynamics simulations the relation existing between the lifetime of hydrogen bonds, the tetrahedral order and the diffusion coefficient of model water. We tested four different models: SPC/E, TIP4P-Ew, TIP5P-Ew and Six-site, these last two having sites explicitly resembling the water lone pairs. While all the models perform reasonably well at ambient conditions, their behavior is significantly different for temperatures below 270 K. The models with explicit lone-pairs have a longer hydrogen bond lifetime, a better tetrahedral order and a smaller diffusion coefficient than the models without them.
Understanding the Magnetic Polarizability Tensor
Ledger, P D
2015-01-01
The aim of this paper is provide new insights into the properties of the rank 2 polarizability tensor $\\check{\\check{\\mathcal M}}$ proposed in (P.D. Ledger and W.R.B. Lionheart Characterising the shape and material properties of hidden targets from magnetic induction data, IMA Journal of Applied Mathematics, doi: 10.1093/imamat/hxv015) for describing the perturbation in the magnetic field caused by the presence of a conducting object in the eddy current regime. In particular, we explore its connection with the magnetic polarizability tensor and the P\\'olya-Szeg\\"o tensor and how, by introducing new splittings of $\\check{\\check{\\mathcal M}}$, they form a family of rank 2 tensors for describing the response from different categories of conducting (permeable) objects. We include new bounds on the invariants of the P\\'olya-Szeg\\"o tensor and expressions for the low frequency and high conductivity limiting coefficients of $\\check{\\check{\\mathcal M}}$. We show, for the high conductivity case (and for frequencies at...
Classification of trivial spin-1 tensor network states on a square lattice
Lee, Hyunyong; Han, Jung Hoon
2016-09-01
Classification of possible quantum spin liquid (QSL) states of interacting spin-1/2's in two dimensions has been a fascinating topic of condensed matter for decades, resulting in enormous progress in our understanding of low-dimensional quantum matter. By contrast, relatively little work exists on the identification, let alone classification, of QSL phases for spin-1 systems in dimensions higher than one. Employing the powerful ideas of tensor network theory and its classification, we develop general methods for writing QSL wave functions of spin-1 respecting all the lattice symmetries, spin rotation, and time reversal with trivial gauge structure on the square lattice. We find 25 distinct classes characterized by five binary quantum numbers. Several explicit constructions of such wave functions are given for bond dimensions D ranging from two to four, along with thorough numerical analyses to identify their physical characters. Both gapless and gapped states are found. The topological entanglement entropy of the gapped states is close to zero, indicative of topologically trivial states. In D =4 , several different tensors can be linearly combined to produce a family of states within the same symmetry class. A rich "phase diagram" can be worked out among the phases of these tensors, as well as the phase transitions among them. Among the states we identified in this putative phase diagram is the plaquette-ordered phase, gapped resonating valence bond phase, and a critical phase. A continuous transition separates the plaquette-ordered phase from the resonating valence bond phase.
Solutions in the generalized Proca theory with the nonminimal coupling to the Einstein tensor
Minamitsuji, Masato
2016-10-01
We investigate the static and spherically symmetric solutions in a class of the generalized Proca theory with the nonminimal coupling to the Einstein tensor. First, we show that the solutions in the scalar-tensor theory with the nonminimal derivative coupling to the Einstein tensor can be those in the generalized Proca theory with the vanishing field strength. We then show that when the field strength takes the nonzero value, the static and spherically symmetric solutions can be found only for the specific value of the nonminimal coupling constant. Second, we investigate the first-order slow-rotation corrections to the static and spherically symmetric background. We find that for the background with the vanishing electric field strength the slowly rotating solution is identical to the Kerr-(anti-)de Sitter solutions in general relativity. On the other hand, for the background with the nonvanishing electric field strength the stealth property can be realized at the first order in the slow-rotation approximation.
Calculation of nonlinear magnetic susceptibility tensors for a uniaxial antiferromagnet
Lim, Siew-Choo; Osman, Junaidah; Tilley, D. R.
2000-11-01
In this paper, we present a derivation of the nonlinear susceptibility tensors for a two-sublattice uniaxial antiferromagnet up to the third-order effects within the standard definition by which the rf magnetization m is defined as a power series expansion in the rf fields h with the susceptibility tensors χ(q) as the coefficients. The starting point is the standard set of torque equations of motion for this problem. A complete set of tensor elements is derived for the case of a single-frequency input wave. Within a circular polarization frame (pnz) expressions are given for the first-order susceptibility, second-harmonic generation, optical rectification, third-harmonic generation and intensity-dependent susceptibility. Some of the coefficients with representative resonance features in the far infrared are illustrated graphically and we conclude with a brief discussion of the implications of the resonance features arising from the calculations and their potential applications.
The Kummer tensor density in electrodynamics and in gravity
Baekler, Peter; Itin, Yakov; Hehl, Friedrich W
2014-01-01
Guided by results in the premetric electrodynamics of local and linear media, we introduce on 4-dimensional spacetime the new abstract notion of a Kummer tensor density of rank four, ${\\cal K}^{ijkl}$. This tensor density is, by definition, a cubic algebraic functional of a tensor density of rank four ${\\cal T}^{ijkl}$, which is antisymmetric in its first two and its last two indices: ${\\cal T}^{ijkl} = - {\\cal T}^{jikl} = - {\\cal T}^{ijlk}$. Thus, ${\\cal K}\\sim {\\cal T}^3$, see Eq.(46). (i) If $\\cal T$ is identified with the electromagnetic response tensor of local and linear media, the Kummer tensor density encompasses the generalized {\\it Fresnel wave surfaces} for propagating light. In the reversible case, the wave surfaces turn out to be {\\it Kummer surfaces} as defined in algebraic geometry (Bateman 1910). (ii) If $\\cal T$ is identified with the {\\it curvature} tensor $R^{ijkl}$ of a Riemann-Cartan spacetime, then ${\\cal K}\\sim R^3$ and, in the special case of general relativity, ${\\cal K}$ reduces to t...
Renormalization Group Flows of Hamiltonians Using Tensor Networks
Bal, M.; Mariën, M.; Haegeman, J.; Verstraete, F.
2017-06-01
A renormalization group flow of Hamiltonians for two-dimensional classical partition functions is constructed using tensor networks. Similar to tensor network renormalization [G. Evenbly and G. Vidal, Phys. Rev. Lett. 115, 180405 (2015), 10.1103/PhysRevLett.115.180405; S. Yang, Z.-C. Gu, and X.-G. Wen, Phys. Rev. Lett. 118, 110504 (2017), 10.1103/PhysRevLett.118.110504], we obtain approximate fixed point tensor networks at criticality. Our formalism, however, preserves positivity of the tensors at every step and hence yields an interpretation in terms of Hamiltonian flows. We emphasize that the key difference between tensor network approaches and Kadanoff's spin blocking method can be understood in terms of a change of the local basis at every decimation step, a property which is crucial to overcome the area law of mutual information. We derive algebraic relations for fixed point tensors, calculate critical exponents, and benchmark our method on the Ising model and the six-vertex model.
Renormalization Group Flows of Hamiltonians Using Tensor Networks.
Bal, M; Mariën, M; Haegeman, J; Verstraete, F
2017-06-23
A renormalization group flow of Hamiltonians for two-dimensional classical partition functions is constructed using tensor networks. Similar to tensor network renormalization [G. Evenbly and G. Vidal, Phys. Rev. Lett. 115, 180405 (2015)PRLTAO0031-900710.1103/PhysRevLett.115.180405; S. Yang, Z.-C. Gu, and X.-G. Wen, Phys. Rev. Lett. 118, 110504 (2017)PRLTAO0031-900710.1103/PhysRevLett.118.110504], we obtain approximate fixed point tensor networks at criticality. Our formalism, however, preserves positivity of the tensors at every step and hence yields an interpretation in terms of Hamiltonian flows. We emphasize that the key difference between tensor network approaches and Kadanoff's spin blocking method can be understood in terms of a change of the local basis at every decimation step, a property which is crucial to overcome the area law of mutual information. We derive algebraic relations for fixed point tensors, calculate critical exponents, and benchmark our method on the Ising model and the six-vertex model.
Computer Tensor Codes to Design the War Drive
Maccone, C.
To address problems in Breakthrough Propulsion Physics (BPP) and design the Warp Drive one needs sheer computing capabilities. This is because General Relativity (GR) and Quantum Field Theory (QFT) are so mathematically sophisticated that the amount of analytical calculations is prohibitive and one can hardly do all of them by hand. In this paper we make a comparative review of the main tensor calculus capabilities of the three most advanced and commercially available “symbolic manipulator” codes. We also point out that currently one faces such a variety of different conventions in tensor calculus that it is difficult or impossible to compare results obtained by different scholars in GR and QFT. Mathematical physicists, experimental physicists and engineers have each their own way of customizing tensors, especially by using different metric signatures, different metric determinant signs, different definitions of the basic Riemann and Ricci tensors, and by adopting different systems of physical units. This chaos greatly hampers progress toward the design of the Warp Drive. It is thus suggested that NASA would be a suitable organization to establish standards in symbolic tensor calculus and anyone working in BPP should adopt these standards. Alternatively other institutions, like CERN in Europe, might consider the challenge of starting the preliminary implementation of a Universal Tensor Code to design the Warp Drive.
The tensor bi-spectrum in a matter bounce
Chowdhury, Debika; Sriramkumar, L
2015-01-01
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 $h_{_{\\rm NL}}$ 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 scenari...
Cebulak, Pola
2012-01-01
In the period since the end of the Cold War, the different layers of law in the international arena have become more interlinked and interwoven. This shift might suggest a development towards a legal “melting pot” involving an increased cross-application of judicial norms stemming from different.......” Hence, for instance, the Court of Justice of the EU has taken an active role in ensuring the effet utile of European law. This article discusses possible theoretical perspectives on the interactions between various legal orders in the international arena. The opposition between the dualist and monist...... not in fact lie exactly at the level of differentiating the relations between legal orders within or beyond the state. One could use both the monist and dualist theories to explain the hierarchy of transnational legal orders while applying constitutionalism and pluralism on the purely national level...
Tensor interactions and {tau} decays
Godina Nava, J.J.; Lopez Castro, G. [Departamento de Fisica, Cinvestav del IPN, Apartado Postal 14-740, 07000 Mexico, D.F. (Mexico)
1995-09-01
We study the effects of charged tensor weak currents on the strangeness-changing decays of the {tau} lepton. First, we use the available information on the {ital K}{sub {ital e}3}{sup +} form factors to obtain {ital B}({tau}{sup {minus}}{r_arrow}{ital K}{sup {minus}}{pi}{sup 0}{nu}{sub {tau}}){similar_to}10{sup {minus}4} when the {ital K}{pi} system is produced in an antisymmetric tensor configuration. Then we propose a mechanism for the direct production of the {ital K}{sub 2}{sup *}(1430) in {tau} decays. Using the current upper limit on this decay we set a bound on the symmetric tensor interactions.
Spectral Tensor-Train Decomposition
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.......e., the “cores”) comprising the functional TT decomposition. This result motivates an approximation scheme employing polynomial approximations of the cores. For functions with appropriate regularity, the resulting spectral tensor-train decomposition combines the favorable dimension-scaling of the TT...... decomposition with the spectral convergence rate of polynomial approximations, yielding efficient and accurate surrogates for high-dimensional functions. To construct these decompositions, we use the sampling algorithm \\tt TT-DMRG-cross to obtain the TT decomposition of tensors resulting from suitable...
van Wüllen, Christoph
2004-04-22
Wolf et al. have recently investigated a generalized Douglas-Kroll transformation. From a general class of unitary transformations that can be used in the Douglas-Kroll transformation, they pick one which is supposed to give, at a given order, an optimal transformed Dirac Hamiltonian. Results were presented through the fifth order. However, no data were given to demonstrate to which extent the so-called "optimal" Douglas-Kroll transformation is superior to other choices. In this work, the Douglas-Kroll transformation is extended to the sixth order for the first time, using computer algebra algorithms to obtain the working equations. It is shown how, at a given order, different variants of the Douglas-Kroll Hamiltonians are related. Various choices of the generalized transformation are examined numerically for the ground states of the one-electron atomic ions with nuclear charges Z=20, 40, 60, 80, 100, and 120. It is shown that compared to the improvement obtained by including the next order, the differences between various choices for the generalized Douglas-Kroll transformation are almost negligible. Results closest to the Dirac eigenvalues are not obtained with the optimal Douglas-Kroll transformation given by Wolf et al., but with the parametrization originally suggested by Douglas and Kroll.
Beyond second-order convergence in simulations of binary neutron stars in full general-relativity
Radice, David; Galeazzi, Filippo
2013-01-01
Despite the recent rapid progress in numerical relativity, a convergence order less than the second has so far plagued codes solving the Einstein-Euler system of equations. We report simulations of the inspiral of binary neutron stars in quasi-circular orbits computed with a new code employing high-order, high-resolution shock-capturing, finite-differencing schemes that, for the first time, go beyond the second-order barrier. In particular, without any tuning or alignment, we measure a convergence order above three both in the phase and in the amplitude of the gravitational waves. Because the new code is able to calculate waveforms with very small phase errors already at modest resolutions, we are able to obtain accurate estimates of tidal effects in the inspiral that are essentially free from the large numerical viscosity typical of lower-order methods, and even for the challenging large compactness and small-deformability binary considered here. We find a remarkable agreement between our Richardson-extrapol...
Access Graphs Results for LRU versus FIFO under Relative Worst Order Analysis
Boyar, Joan; Larsen, Kim S
2012-01-01
Access graphs, which have been used previously in connection with competitive analysis to model locality of reference in paging, are considered in connection with relative worst order analysis. In this model, FWF is shown to be strictly worse than both LRU and FIFO on any access graph. LRU is shown to be strictly better than FIFO on paths and cycles, but they are incomparable on some families of graphs which grow with the length of the sequences.
On Sequences of Numbers and Polynomials Defined by Linear Recurrence Relations of Order 2
Tian-Xiao He
2009-01-01
Full Text Available Here we present a new method to construct the explicit formula of a sequence of numbers and polynomials generated by a linear recurrence relation of order 2. The applications of the method to the Fibonacci and Lucas numbers, Chebyshev polynomials, the generalized Gegenbauer-Humbert polynomials are also discussed. The derived idea provides a general method to construct identities of number or polynomial sequences defined by linear recurrence relations. The applications using the method to solve some algebraic and ordinary differential equations are presented.
Tensor networks for dynamic spacetimes
May, Alex
2016-01-01
Existing tensor network models of holography are limited to representing the geometry of constant time slices of static spacetimes. We study the possibility of describing the geometry of a dynamic spacetime using tensor networks. We find it is necessary to give a new definition of length in the network, and propose a definition based on the mutual information. We show that by associating a set of networks with a single quantum state and making use of the mutual information based definition of length, a network analogue of the maximin formula can be used to calculate the entropy of boundary regions.
Unintended Transformations of Clinical Relations with a Computerized Physician Order Entry System
Wentzer, Helle; Böttger, Ulrich; Boye, Niels
2007-01-01
A socio-technical approach was used to study the qualitative effects of deploying a medication CPOE (Computerized Physician Order Entry System with no decision support) at two internal medical wards in a hospital in Denmark. Our results show spatial and temporal transformations of core acts...... and relations in medication work, i.e. of the intended use of the system inscribed in hardware and software, in the relations of care between doctors and patients, of collaboration between doctors and nurses, and prospectively of the patients’ trajectories when readmitted to hospital or another health care...... institution, reusing data from the system. This study throws light on problems of continuity of patient care paths, patient-related and IT-system-related error handling and time spent on core activities – when ubiquitous IT is used locally in a real physical setting with specific traditions of performing...
A BOUNDARY INTEGRAL METHOD FOR COMPUTING ELASTIC MOMENT TENSORS FOR ELLIPSES AND ELLIPSOIDS
Habib Ammari; Hyeonbae Kang; Hyundae Lee
2007-01-01
The concept of elastic moment tensor occurs in several interesting contexts, in particular in imaging small elastic inclusions and in asymptotic models of dilute elastic composites.In this paper, we compute the elastic moment tensors for ellipses and ellipsoids by using a systematic method based on layer potentials. Our computations reveal an underlying elegant relation between the elastic moment tensors and the single layer potential.
Spacetimes with Killing tensors. [for Einstein-Maxwell fields with certain spinor indices
Hughston, L. P.; Sommers, P.
1973-01-01
The characteristics of the Killing equation and the Killing tensor are discussed. A conformal Killing tensor is of interest inasmuch as it gives rise to a quadratic first integral for null geodesic orbits. The Einstein-Maxwell equations are considered together with the Bianchi identity and the conformal Killing tensor. Two examples for the application of the considered relations are presented, giving attention to the charged Kerr solution and the charged C-metric.
Lee, Jennifer E.; Watson, David; Frey Law, Laura A.
2010-01-01
Pain is a debilitating condition affecting millions each year, yet what predisposes certain individuals to be more sensitive to pain remains relatively unknown. Several psychological factors have been associated with pain perception, but the structural relations between multiple higher- and lower-order constructs and pain are not well understood. Thus, we aimed to examine the associations between pain perception using the cold pressor task (CPT), higher-order personality traits (neuroticism, ...
Tensor calculus for physics a concise guide
Neuenschwander, Dwight E
2015-01-01
Understanding tensors is essential for any physics student dealing with phenomena where causes and effects have different directions. A horizontal electric field producing vertical polarization in dielectrics; an unbalanced car wheel wobbling in the vertical plane while spinning about a horizontal axis; an electrostatic field on Earth observed to be a magnetic field by orbiting astronauts—these are some situations where physicists employ tensors. But the true beauty of tensors lies in this fact: When coordinates are transformed from one system to another, tensors change according to the same rules as the coordinates. Tensors, therefore, allow for the convenience of coordinates while also transcending them. This makes tensors the gold standard for expressing physical relationships in physics and geometry. Undergraduate physics majors are typically introduced to tensors in special-case applications. For example, in a classical mechanics course, they meet the "inertia tensor," and in electricity and magnetism...
Control design for the SISO system with the unknown order and the unknown relative degree.
Zhao, Chunzhe; Li, Donghai
2014-07-01
For the uncertain system whose order, relative degree and parameters are unknown in the control design, new research is still in need on the parameter tuning and close-loop stability. During the last 10 years, much progress is made in the application and theory research of the active disturbance rejection control (ADRC) for the uncertain system. In this study, the necessary and sufficient conditions are established for building the ADRC for the minimum-phase system and the open-loop stable system when the plant parameters, orders and relative degrees are unknown, the corresponding ideal dynamics are analyzed, and the theoretical results are verified by the simulations. Considering the wide application and the long history of the PID/PI controller, a method is given to design ADRC quickly based on the existing (generalized or conventional) PID/PI controller. A plenty of simulations are made to illustrate this PID/PI-based design method and the corresponding close-loop performances. The simulation examples include the minimum/nonminimum-phase plants, the stable/integrating plants, the high/low-order plant, and the plants with time delays. Such plants are from a wider scope than the theoretical result, and representative of many kinds of the industrial processes. That leads to a new way to simplify the ADRC design via absorbing the engineering experience in designing the PID/PI controller.
Decorated tensor network renormalization for lattice gauge theories and spin foam models
Dittrich, Bianca; Mizera, Sebastian; Steinhaus, Sebastian
2016-05-01
Tensor network techniques have proved to be powerful tools that can be employed to explore the large scale dynamics of lattice systems. Nonetheless, the redundancy of degrees of freedom in lattice gauge theories (and related models) poses a challenge for standard tensor network algorithms. We accommodate for such systems by introducing an additional structure decorating the tensor network. This allows to explicitly preserve the gauge symmetry of the system under coarse graining and straightforwardly interpret the fixed point tensors. We propose and test (for models with finite Abelian groups) a coarse graining algorithm for lattice gauge theories based on decorated tensor networks. We also point out that decorated tensor networks are applicable to other models as well, where they provide the advantage to give immediate access to certain expectation values and correlation functions.
Endomorphism Algebras of Tensor Powers of Modules for Quantum Groups
Andersen, Therese Søby
the group algebra of the braid group to the endomorphism algebra of any tensor power of the Weyl module with highest weight 2. We take a first step towards determining the kernel of this map by reformulating well-known results on the semisimplicity of the Birman-Murakami-Wenzl algebra in terms of the order...
Catino, Giovanni; Mazzieri, Lorenzo
2012-01-01
We discuss a gap in Besse's book, recently pointed out by Merton, which concerns the classification of Riemannian manifolds admitting a Codazzi tensors with exactly two distinct eigenvalues. For such manifolds, we prove a structure theorem, without adding extra hypotheses and then we conclude with some application of this theory to the classification of three-dimensional gradient Ricci solitons.
Intermediate Field Representation for Positive Matrix and Tensor Interactions
Lionni, Luca
2016-01-01
In this paper we introduce an intermediate field representation for random matrices and random tensors with positive (stable) interactions of degree higher than 4. This representation respects the symmetry axis responsible for positivity. It is non-perturbative and allows to prove that such models are Borel-Le Roy summable of the appropriate order in their coupling constant. However we have not been able yet to associate a convergent Loop Vertex Expansion to this representation, hence our Borel summability result is not of the optimal expected form when the size N of the matrix or of the tensor tends to infinity.
Symmetry-imposed shape of linear response tensors
Seemann, M.; Ködderitzsch, D.; Wimmer, S.; Ebert, H.
2015-10-01
A scheme suggested in the literature to determine the symmetry-imposed shape of linear response tensors is revised and extended to allow for the treatment of more complex situations. The extended scheme is applied to discuss the shape of the spin conductivity tensor for all magnetic space groups. This allows in particular investigating the character of longitudinal as well as transverse spin transport for arbitrary crystal structure and magnetic order that give rise, e.g., to the spin Hall, Nernst, and the spin-dependent Seebeck effects.
Tensor renormalization group analysis of CP(N-1) model
Kawauchi, Hikaru
2016-01-01
We apply the higher order tensor renormalization group to lattice CP($N-1$) model in two dimensions. A tensor network representation of the CP($N-1$) model in the presence of the $\\theta$-term is derived. We confirm that the numerical results of the CP(1) model without the $\\theta$-term using this method are consistent with that of the O(3) model which is analyzed by the same method in the region $\\beta \\gg 1$ and that obtained by Monte Carlo simulation in a wider range of $\\beta$. The numerical computation including the $\\theta$-term is left for future challenges.
Tensor renormalization group analysis of CP (N -1 ) model
Kawauchi, Hikaru; Takeda, Shinji
2016-06-01
We apply the higher-order tensor renormalization group to the lattice CP (N -1 ) model in two dimensions. A tensor network representation of the CP (N -1 ) model in the presence of the θ term is derived. We confirm that the numerical results of the CP(1) model without the θ term using this method are consistent with that of the O(3) model which is analyzed by the same method in the region β ≫1 and that obtained by the Monte Carlo simulation in a wider range of β . The numerical computation including the θ term is left for future challenges.
Anderson, David; Yunes, Nicolás
2017-09-01
Scalar-tensor theories of gravity modify general relativity by introducing a scalar field that couples nonminimally to the metric tensor, while satisfying the weak-equivalence principle. These theories are interesting because they have the potential to simultaneously suppress modifications to Einstein's theory on Solar System scales, while introducing large deviations in the strong field of neutron stars. Scalar-tensor theories can be classified through the choice of conformal factor, a scalar that regulates the coupling between matter and the metric in the Einstein frame. The class defined by a Gaussian conformal factor with a negative exponent has been studied the most because it leads to spontaneous scalarization (i.e. the sudden activation of the scalar field in neutron stars), which consequently leads to large deviations from general relativity in the strong field. This class, however, has recently been shown to be in conflict with Solar System observations when accounting for the cosmological evolution of the scalar field. We here study whether this remains the case when the exponent of the conformal factor is positive, as well as in another class of theories defined by a hyperbolic conformal factor. We find that in both of these scalar-tensor theories, Solar System tests are passed only in a very small subset of coupling parameter space, for a large set of initial conditions compatible with big bang nucleosynthesis. However, while we find that it is possible for neutron stars to scalarize, one must carefully select the coupling parameter to do so, and even then, the scalar charge is typically 2 orders of magnitude smaller than in the negative-exponent case. Our study suggests that future work on scalar-tensor gravity, for example in the context of tests of general relativity with gravitational waves from neutron star binaries, should be carried out within the positive coupling parameter class.
Link prediction via generalized coupled tensor factorisation
Ermiş, Beyza; Evrim, Acar Ataman; Taylan Cemgil, A.
2012-01-01
This study deals with the missing link prediction problem: the problem of predicting the existence of missing connections between entities of interest. We address link prediction using coupled analysis of relational datasets represented as heterogeneous data, i.e., datasets in the form of matrices...... 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....
Isotropic Super-symmetric Descartes Tensor%各向同性超对称Descartes张量
秦清锋; 吴伟; 尹红然
2011-01-01
Isotropic tensor plays an extremely role in constructing elastic solid constitutive equations. Based on the expression of isotropic Descartes tensor and the proposition of super-symmetric tensor, the scalars of isotropic Descartes tensor are discussed. Then it comes to the representations of isotropic super-symmetric Descartes tensor from two order to six order.%各向同性张量在构造各向同性弹性固体的本构方程时有着极其重要的作用.基于各向同性Descartes张量的表达式并结合超对称张量的性质,探讨了各向同性Descartes张量各标量之间的关系,进而得出了二到六阶各向同性超对称Descartes 张量的一般表达式.
Scalable tensor factorizations with missing data.
Morup, Morten (Technical University of Denmark); Dunlavy, Daniel M.; Acar, Evrim (Turkish National Research Institute of Electronics and Cryptology); Kolda, Tamara Gibson
2010-04-01
The problem of missing data is ubiquitous in domains such as biomedical signal processing, network traffic analysis, bibliometrics, social network analysis, chemometrics, computer vision, and communication networks|all domains in which data collection is subject to occasional errors. Moreover, these data sets can be quite large and have more than two axes of variation, e.g., sender, receiver, time. Many applications in those domains aim to capture the underlying latent structure of the data; in other words, they need to factorize data sets with missing entries. If we cannot address the problem 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), and formulate the CP model as a weighted least squares problem that models only the known entries. We develop an algorithm called CP-WOPT (CP Weighted OPTimization) using a first-order optimization approach to solve the weighted least squares problem. Based on extensive numerical experiments, our algorithm 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) application where missing data is frequently encountered due to disconnections of electrodes.
Irreducible decomposition of strain gradient tensor in isotropic strain gradient elasticity
Lazar, Markus
2016-01-01
In isotropic strain gradient elasticity, we decompose the strain gradient tensor into its irreducible pieces under the n-dimensional orthogonal group O(n). Using the Young tableau method for traceless tensors, four irreducible pieces (n>2), which are canonical, are obtained. In three dimensions, the strain gradient tensor can be decomposed into four irreducible pieces with 7+5+3+3 independent components whereas in two dimensions, the strain gradient tensor can be decomposed into three irreducible pieces with 2+2+2 independent components. The knowledge of these irreducible pieces is extremely useful when setting up constitutive relations and strain energy.
Decorated tensor network renormalization for lattice gauge theories and spin foam models
Dittrich, Bianca; Steinhaus, Sebastian
2014-01-01
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. Using this novel information encoded in the decoration might eventually lead to new methods incorporating both analytical and numerical techniques.
Vector and tensor analysis with applications
Borisenko, A I; Silverman, Richard A
1979-01-01
Concise and readable, this text ranges from definition of vectors and discussion of algebraic operations on vectors to the concept of tensor and algebraic operations on tensors. It also includes a systematic study of the differential and integral calculus of vector and tensor functions of space and time. Worked-out problems and solutions. 1968 edition.
GUT-scale inflation with sizeable tensor modes
Brummer, Felix; Sanz, Veronica
2014-01-01
A sizeable tensor-to-scalar ratio, such as recently claimed by BICEP2, would imply a scale of inflation at the typical scale of supersymmetric grand unification. This could be an accident, or strong support for supersymmetric theories. Models of F-term hybrid inflation naturally connect the GUT scale with the inflationary scale, but they also predict the tensor-to-scalar ratio to be unmeasurably small. In this work we analyze a general UV embedding of F-term hybrid inflation into a supergravity theory with a general Kahler potential. The CMB observables are generated during the early phase of inflation, at large inflaton values, where the potential is dominated by Planck-suppressed operators. Tuning the leading higher-order terms can give an inflaton potential with sizeable tensor fluctuations and a field excursion which is still sub-Planckian but close to the Planck scale, as expected from the Lyth bound.
Multi-Mode Tensor Representation of Motion Data
Meinard Müller
2008-08-01
Full Text Available In this paper, we investigate how a multilinear model can be used to represent human motion data. Based on technical modes (referring to degrees of freedom and number of frames and natural modes that typically appear in the context of a motion capture session (referring to actor, style, and repetition, the motion data is encoded in form of a high-order tensor. This tensor is then reduced by using N-mode singular value decomposition. Our experiments show that the reduced model approximates the original motion better then previously introduced PCA-based approaches. Furthermore, we discuss how the tensor representation may be used as a valuable tool for the synthesis of new motions.
2014-01-01
injuries caused by non-blast related trauma (e.g. falls, motor vehicle accidents, etc.), post - mortem pathological analyses have revealed that...issues: 1) Selection of control cases: we will select only young, otherwise healthy patients who died from non-head trauma and had a short post - mortem ...20 Oppenheimer, D. R. (1968). "Microscopic lesions in the brain following head injury." J Neurol Neurosurg Psychiatry 31(4): 299-306. http
Lefort, Ronan; Guégan, Régis; Guendouz, Mohammed; Zanotti, Jean-Marc; Frick, Bernhard; 10.1103/PhysRevE.78.040701
2009-01-01
We analyze the molecular dynamics heterogeneity of the liquid crystal 4-n-octyl-4'-cyanobiphenyl nanoconfined in porous silicon. We show that the temperature dependence of the dynamic correlation length ?wall, which measures the distance over which a memory of the interfacial slowing down of the molecular dynamics persists, is closely related to the growth of the short-range static order arising from quenched random fields. More generally, this result may also shed some light on the connection between static and dynamic heterogeneities in a wide class of condensed and soft matter systems.
Symmetric energy-momentum tensor: the Abraham form and the explicitly covariant formula
Nesterenko, V V
2015-01-01
We compare the explicitly covariant 4-dimensional formula, recently proposed by V.P.\\ Makarov and S.A.\\ Rukhadze [Phys. Usp. {\\bf 52} 937 (2011)] for symmetric energy-momentum tensor of electromagnetic field in a medium, and the energy-momentum tensor derived by Abraham in the 3-dimensional vector form. It is shown that these two objects coincide only on the physical configuration space $\\overline \\Gamma $, formed by the field vectors and the velocity of the medium, which satisfy the constitutive relations. It should be emphasized that the 3-dimensional vector formulae for the components of the energy-momentum tensor were obtained by Abraham only on $\\overline \\Gamma $, and the task of their extension to the whole unconditional configuration space $\\Gamma$ was not posed. In order to accomplish the comparison noted above we derive the Makarov-Rukhadze formula a new by another method, namely, by generalizing the Abraham reasoning. The comparison conducted enables one to treat the Makarov-Rukhadze formula as a u...
Seismic data filtering using non-local means algorithm based on structure tensor
Yang, Shuai; Chen, Anqing; Chen, Hongde
2017-05-01
Non-Local means algorithm is a new and effective filtering method. It calculates weights of all similar neighborhoods' center points relative to filtering point within searching range by Gaussian weighted Euclidean distance between neighborhoods, then gets filtering point's value by weighted average to complete the filtering operation. In this paper, geometric distance of neighborhood's center point is taken into account in the distance measure calculation, making the non-local means algorithm more reasonable. Furthermore, in order to better protect the geometry structure information of seismic data, we introduce structure tensor that can depict the local geometrical features of seismic data. The coherence measure, which reflects image local contrast, is extracted from the structure tensor, is integrated into the non-local means algorithm to participate in the weight calculation, the control factor of geometry structure similarity is added to form a non-local means filtering algorithm based on structure tensor. The experimental results prove that the algorithm can effectively restrain noise, with strong anti-noise and amplitude preservation effect, improving PSNR and protecting structure information of seismic image. The method has been successfully applied in seismic data processing, indicating that it is a new and effective technique to conduct the structure-preserved filtering of seismic data.
Higher-order factors of the big five and basic values: empirical and theoretical relations.
Vecchione, Michele; Alessandri, Guido; Barbaranelli, Claudio; Caprara, Gianvittorio
2011-08-01
The Big Five Model of personality and Schwartz's theory of basic values are two prominent taxonomies that offer a convenient way to organize the major individual differences in, respectively, personality traits and personal values. Both taxonomies provide a hierarchical framework, whose components can be traced back to a smaller number of broader dimensions. The current study investigated the relationship between the two superordinate factors of personality encompassing the Big Five dimensions (alpha and beta) and the four higher-level value types from Schwartz's theory (Self-transcendence, Self-enhancement, Conservation, and Openness to change). To examine the relations between higher-order traits and values, we relied on factor analysis and multidimensional scaling. Results indicated that alpha and beta were differently related to the Conservation versus Openness to change dimension. Alpha was positively related to values that emphasize protecting stability and respecting norms and traditions, and negatively related to values emphasizing receptiveness to change and independence of thought, feeling, and action. The opposite pattern of relations was found for beta.
Tables of Products of Tensor Operators and Stevens Operators
Lindgård, Per-Anker
1975-01-01
Numerical tables of products of tensor (Racah) operators, Rl,m(J), and Stevens operators Olm(J), working within a J-multiplet are given as a function of X=J(J+1). Examples of the use of the tables, such as the calculation of commutation relations and thermal averages are given.......Numerical tables of products of tensor (Racah) operators, Rl,m(J), and Stevens operators Olm(J), working within a J-multiplet are given as a function of X=J(J+1). Examples of the use of the tables, such as the calculation of commutation relations and thermal averages are given....
How can we strengthen students’ social relations in order to reduce school dropout?
Ingholt, Liselotte; Sørensen, Betina Bang; Andersen, Susan
2015-01-01
BACKGROUND: This article describes the rationale and contents of an intervention program aimed at strengthening students' social relations in order to reduce dropout from vocational schools in Denmark. Taking its theoretical cue from the concept of 'social participation', a qualitative study...... on ethnographic methods, including 22 qualitative interviews with students 17-19 years old and fieldwork with participant observations at four vocational schools over 40 days, including informal interviews and discussion meetings with managers, teachers, counselors and students. As part of the fieldwork, four...... additional qualitative interviews and four group interviews were conducted with students 16-25 years old. RESULTS: The qualitative data collection resulted in seven major themes to be addressed in the intervention: social relations, sole focus on professional skills, institutionalized individualization...
f(R)-gravity from Killing tensors
Paliathanasis, Andronikos
2016-04-01
We consider f(R)-gravity in a Friedmann-Lemaître-Robertson-Walker spacetime with zero spatial curvature. We apply the Killing tensors of the minisuperspace in order to specify the functional form of f(R) and for the field equations to be invariant under Lie-Bäcklund transformations, which are linear in momentum (contact symmetries). Consequently, the field equations to admit quadratic conservation laws given by Noether’s theorem. We find three new integrable f(R)-models, for which, with the application of the conservation laws, we reduce the field equations to a system of two first-order ordinary differential equations. For each model we study the evolution of the cosmological fluid. We find that for each integrable model the cosmological fluid has an equation of state parameter, in which there is linear behavior in terms of the scale factor which describes the Chevallier, Polarski and Linder parametric dark energy model.
Related research on corneal higher-order aberrations after different ways refractive surgery
Shu-Xi He
2015-08-01
Full Text Available AIM:To evaluate the changes of corneal high-order aberration(including Coma, Spab, RMShafter laser in situ keratomileusis(LASIKwith femtosecond laser, sub-Bowman keratomileusis(SBKand laser epithelial keratomileusis(LASEK.METHODS: Of 82 myopic patients(164 eyes, 31 patients(62 eyeswere treated by FS-LASIK, 31 patients(62 eyeswere treated by SBK, 20 patients(40 eyeswere treated by LASEK. Sirius system was used for measuring the coma aberration, spherical aberration, and high order aberration at 1, 15d,1, 3mo after surgery.RESULTS: 1Vision: The uncorrected visual acuity of the three groups had no differences(P>0.05. 2Corneal aberrations: Three kinds of surgical procedure for patients with corneal aberration had significant impact. The C7, C8, C12 and RMSh of three groups were increased significantly(P0.05. The C7, C8, C12 and RMSh were not recovered to preoperative levels after 3mo. But the increase of patients after FS-LASIK was smaller than the other two groups, with statistical significance(P0.05.CONCLUSION: Compared with SBK and LASEK,FS-LASIK has better visual acuity in the early postoperative and corneal higher-order aberrations increase is relatively small.
Beam-plasma dielectric tensor with Mathematica
Bret, A.
2007-03-01
We present a Mathematica notebook allowing for the symbolic calculation of the 3×3 dielectric tensor of an electron-beam plasma system in the fluid approximation. Calculation is detailed for a cold relativistic electron beam entering a cold magnetized plasma, and for arbitrarily oriented wave vectors. We show how one can elaborate on this example to account for temperatures, arbitrarily oriented magnetic field or a different kind of plasma. Program summaryTitle of program: Tensor Catalog identifier: ADYT_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADYT_v1_0 Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Computer for which the program is designed and others on which it has been tested: Computers: Any computer running Mathematica 4.1. Tested on DELL Dimension 5100 and IBM ThinkPad T42. Installations: ETSI Industriales, Universidad Castilla la Mancha, Ciudad Real, Spain Operating system under which the program has been tested: Windows XP Pro Programming language used: Mathematica 4.1 Memory required to execute with typical data: 7.17 Mbytes No. of bytes in distributed program, including test data, etc.: 33 439 No. of lines in distributed program, including test data, etc.: 3169 Distribution format: tar.gz Nature of the physical problem: The dielectric tensor of a relativistic beam plasma system may be quite involved to calculate symbolically when considering a magnetized plasma, kinetic pressure, collisions between species, and so on. The present Mathematica notebook performs the symbolic computation in terms of some usual dimensionless variables. Method of solution: The linearized relativistic fluid equations are directly entered and solved by Mathematica to express the first-order expression of the current. This expression is then introduced into a combination of Faraday and Ampère-Maxwell's equations to give the dielectric tensor. Some additional manipulations are needed to express the result in terms of the
2006-01-01
Full Text Available We considered the problem on transversal oscillations of two-layer straight bar, which is under the action of the lengthwise random forces. It is assumed that the layers of the bar were made of nonhomogenous continuously creeping material and the corresponding modulus of elasticity and creeping fractional order derivative of constitutive relation of each layer are continuous functions of the length coordinate and thickness coordinates. Partial fractional differential equation and particular solutions for the case of natural vibrations of the beam of creeping material of a fractional derivative order constitutive relation in the case of the influence of rotation inertia are derived. For the case of natural creeping vibrations, eigenfunction and time function, for different examples of boundary conditions, are determined. By using the derived partial fractional differential equation of the beam vibrations, the almost sure stochastic stability of the beam dynamic shapes, corresponding to the n th shape of the beam elastic form, forced by a bounded axially noise excitation, is investigated. By the use of S. T. Ariaratnam's idea, as well as of the averaging method, the top Lyapunov exponent is evaluated asymptotically when the intensity of excitation process is small.
Bilayer linearized tensor renormalization group approach for thermal tensor networks
Dong, Yong-Liang; Chen, Lei; Liu, Yun-Jing; Li, Wei
2017-04-01
Thermal tensor networks constitute an efficient and versatile representation for quantum lattice models at finite temperatures. By Trotter-Suzuki decomposition, one obtains a D +1 dimensional TTN for the D -dimensional quantum system and then employs efficient renormalizaton group (RG) contractions to obtain the thermodynamic properties with high precision. The linearized tensor renormalization group (LTRG) method, which can be used to contract TTN efficiently and calculate the thermodynamics, is briefly reviewed and then generalized to a bilayer form. We dub this bilayer algorithm as LTRG++ and explore its performance in both finite- and infinite-size systems, finding the numerical accuracy significantly improved compared to single-layer algorithm. Moreover, we show that the LTRG++ algorithm in an infinite-size system is in essence equivalent to transfer-matrix renormalization group method, while reformulated in a tensor network language. As an application of LTRG++, we simulate an extended fermionic Hubbard model numerically, where the phase separation phenomenon, ground-state phase diagram, as well as quantum criticality-enhanced magnetocaloric effects, are investigated.
Counterpart of the Weyl tensor for Rarita-Schwinger type fields
Brandt, Friedemann
2017-04-01
In dimensions larger than 3 a modified field strength for Rarita-Schwinger type fields is constructed whose components are not constrained by the field equations. In supergravity theories the result provides a modified (supercovariant) gravitino field strength related by supersymmetry to the (supercovariantized) Weyl tensor. In various cases, such as for free Rarita-Schwinger type gauge fields and for gravitino fields in several supergravity theories, the modified field strength coincides on-shell with the usual field strength. A corresponding result for first order derivatives of Dirac type spinor fields is also presented.
Stability of Horndeski vector-tensor interactions
Jiménez, Jose Beltrán [Centre for Cosmology, Particle Physics and Phenomenology, Institute of Mathematics and Physics, Louvain University, 2 Chemin du Cyclotron, Louvain-la-Neuve, 1348 (Belgium); Durrer, Ruth; Heisenberg, Lavinia [Département de Physique Théorique and Center for Astroparticle Physics, Université de Genève, 24 quai Ansermet, Genève 4, CH-1211 (Switzerland); Thorsrud, Mikjel, E-mail: jose.beltran@uclouvain.be, E-mail: ruth.durrer@unige.ch, E-mail: lavinia.heisenberg@unige.ch, E-mail: mikjel.thorsrud@astro.uio.no [Institute of Theoretical Astrophysics, University of Oslo, P.O. Box 1029 Blindern, Oslo, N-0315 (Norway)
2013-10-01
We study the Horndeski vector-tensor theory that leads to second order equations of motion and contains a non-minimally coupled abelian gauge vector field. This theory is remarkably simple and consists of only 2 terms for the vector field, namely: the standard Maxwell kinetic term and a coupling to the dual Riemann tensor. Furthermore, the vector sector respects the U(1) gauge symmetry and the theory contains only one free parameter, M{sup 2}, that controls the strength of the non-minimal coupling. We explore the theory in a de Sitter spacetime and study the presence of instabilities and show that it corresponds to an attractor solution in the presence of the vector field. We also investigate the cosmological evolution and stability of perturbations in a general FLRW spacetime. We find that a sufficient condition for the absence of ghosts is M{sup 2} > 0. Moreover, we study further constraints coming from imposing the absence of Laplacian instabilities. Finally, we study the stability of the theory in static and spherically symmetric backgrounds (in particular, Schwarzschild and Reissner-Nordström-de Sitter). We find that the theory, quite generally, do have ghosts or Laplacian instabilities in regions of spacetime where the non-minimal interaction dominates over the Maxwell term. We also calculate the propagation speed in these spacetimes and show that superluminality is a quite generic phenomenon in this theory.
Stability of Horndeski vector-tensor interactions
Jiménez, Jose Beltrán; Heisenberg, Lavinia; Thorsrud, Mikjel
2013-01-01
We study the Horndeski vector-tensor theory that leads to second order equations of motion and contains a non-minimally coupled abelian gauge vector field. This theory is remarkably simple and consists of only 2 terms for the vector field, namely: the standard Maxwell kinetic term and a coupling to the dual Riemann tensor. Furthermore, the vector sector respects the U(1) gauge symmetry and the theory contains only one free parameter, M^2, that controls the strength of the non-minimal coupling. We explore the theory in a de Sitter spacetime and study the presence of instabilities and show that it corresponds to an attractor solution in the presence of the vector field. We also investigate the cosmological evolution and stability of perturbations in a general FLRW spacetime. We find that a sufficient condition for the absence of ghosts is M^2>0. Moreover, we study further constraints coming from imposing the absence of Laplacian instabilities. Finally, we study the stability of the theory in static and spherica...
Stability of Horndeski vector-tensor interactions
Beltrán Jiménez, Jose; Durrer, Ruth; Heisenberg, Lavinia; Thorsrud, Mikjel
2013-10-01
We study the Horndeski vector-tensor theory that leads to second order equations of motion and contains a non-minimally coupled abelian gauge vector field. This theory is remarkably simple and consists of only 2 terms for the vector field, namely: the standard Maxwell kinetic term and a coupling to the dual Riemann tensor. Furthermore, the vector sector respects the U(1) gauge symmetry and the theory contains only one free parameter, M2, that controls the strength of the non-minimal coupling. We explore the theory in a de Sitter spacetime and study the presence of instabilities and show that it corresponds to an attractor solution in the presence of the vector field. We also investigate the cosmological evolution and stability of perturbations in a general FLRW spacetime. We find that a sufficient condition for the absence of ghosts is M2 > 0. Moreover, we study further constraints coming from imposing the absence of Laplacian instabilities. Finally, we study the stability of the theory in static and spherically symmetric backgrounds (in particular, Schwarzschild and Reissner-Nordström-de Sitter). We find that the theory, quite generally, do have ghosts or Laplacian instabilities in regions of spacetime where the non-minimal interaction dominates over the Maxwell term. We also calculate the propagation speed in these spacetimes and show that superluminality is a quite generic phenomenon in this theory.
A Renormalizable 4-Dimensional Tensor Field Theory
Geloun, Joseph Ben
2011-01-01
We prove that an integrated version of the Gurau colored tensor model supplemented with the usual Bosonic propagator on $U(1)^4$ is renormalizable to all orders in perturbation theory. The model is of the type expected for quantization of space-time in 4D Euclidean gravity and is the first example of a renormalizable model of this kind. Its vertex and propagator are four-stranded like in 4D group field theories, but without gauge averaging on the strands. Surprisingly perhaps, the model is of the $\\phi^6$ rather than of the $\\phi^4$ type, since two different $\\phi^6$-type interactions are log-divergent, i.e. marginal in the renormalization group sense. The renormalization proof relies on a multiscale analysis. It identifies all divergent graphs through a power counting theorem. These divergent graphs have internal and external structure of a particular kind called melonic. Melonic graphs dominate the 1/N expansion of colored tensor models and generalize the planar ribbon graphs of matrix models. A new localit...
Phases of antisymmetric tensor field theories
Quevedo, Fernando; Quevedo, Fernando; Trugenberger, Carlo
1997-01-01
We study the different phases of field theories of compact antisymmetric tensors of rank h-1 in arbitrary space-time dimensions D=d+1. Starting in a `Coulomb' phase, topological defects of dimension d-h-1 ((d-h-1)-branes) may condense leading to a generalized `confinement' phase. If the dual theory is also compact the model may also have a third, generalized `Higgs' phase, driven by the condensation of the dual (h-2)-branes. Developing on the work of Julia and Toulouse for ordered solid-state media, we obtain the low energy effective action for these phases. Each phase has two dual descriptions in terms of antisymmetric tensors of different ranks, which are massless for the Coulomb phase but massive for the Higgs and confinement phases. We illustrate our prescription in detail for compact QED in 4D. Compact QED and O(2) models in 3D, as well as a periodic scalar field in 2D (strings on a circle), are also discussed. In this last case we show how T-duality is maintained if one considers both worldsheet instant...
MOMENT TENSOR SOLUTIONS OF RECENT EARTHQUAKES IN THE CALABRIAN REGION (SOUTH ITALY)
Orecchio, B.; D'Amico, S.; Gervasi, A.; Guerra, I.; Presti, D.; Zhu, L.; Herrmann, R. B.; Neri, G.
2009-12-01
The aim of this study is to provide moment tensor solutions for recent events occurred in the Calabrian region (South Italy), an area struck by several destructive earthquakes in the last centuries. The seismicity of the area under investigation is actually characterized by low to moderate magnitude earthquakes (up to 4.5) not properly represented in the Italian national catalogues of focal mechanisms like RCMT (Regional Centroid Moment Tensor, Pondrelli et al., PEPI, 2006) and TDMT (Time Domain Moment Tensors, Dreger and Helmerger, BSSA, 1993). Also, the solutions estimated from P-onset polarities are often poorly constrained due to network geometry in the study area. We computed the moment tensor solutions using the “Cut And Paste” method originally proposed by Zhao and Helmerger (BSSA, 1994) and later modified by Zhu and Helmerger (BSSA, 1996). Each waveform is broken into the Pnl and surface wave segments and the source depth and focal mechanisms are determined using a grid search technique. The technique allows time shifts between synthetics and observed data in order to reduce dependence of the solution on the assumed velocity model and earthquake locations. This method has shown to provide good-quality solutions for earthquakes of magnitude as small as 2.5. The data set of the present study consists of waveforms from more than 100 earthquakes that were recorded by the permanent seismic network run by Istituto Nazionale di Geofisica e Vulcanologia (INGV) and about 40 stations of the NSF CAT/SCAN project. The results concur to check and better detail the regional geodynamic model assuming subduction of the Ionian lithosphere beneath the Tyrrhenian one and related response of the shallow structures in terms of normal and strike-slip faulting seismicity.
Killing(-Yano) Tensors in String Theory
Chervonyi, Yuri
2015-01-01
We construct the Killing(-Yano) tensors for a large class of charged black holes in higher dimensions and study general properties of such tensors, in particular, their behavior under string dualities. Killing(-Yano) tensors encode the symmetries beyond isometries, which lead to insights into dynamics of particles and fields on a given geometry by providing a set of conserved quantities. By analyzing the eigenvalues of the Killing tensor, we provide a prescription for constructing several conserved quantities starting from a single object, and we demonstrate that Killing tensors in higher dimensions are always associated with ellipsoidal coordinates. We also determine the transformations of the Killing(-Yano) tensors under string dualities, and find the unique modification of the Killing-Yano equation consistent with these symmetries. These results are used to construct the explicit form of the Killing(-Yano) tensors for the Myers-Perry black hole in arbitrary number of dimensions and for its charged version.
White matter degeneration in schizophrenia: a comparative diffusion tensor analysis
Ingalhalikar, Madhura A.; Andreasen, Nancy C.; Kim, Jinsuh; Alexander, Andrew L.; Magnotta, Vincent A.
2010-03-01
Schizophrenia is a serious and disabling mental disorder. Diffusion tensor imaging (DTI) studies performed on schizophrenia have demonstrated white matter degeneration either due to loss of myelination or deterioration of fiber tracts although the areas where the changes occur are variable across studies. Most of the population based studies analyze the changes in schizophrenia using scalar indices computed from the diffusion tensor such as fractional anisotropy (FA) and relative anisotropy (RA). The scalar measures may not capture the complete information from the diffusion tensor. In this paper we have applied the RADTI method on a group of 9 controls and 9 patients with schizophrenia. The RADTI method converts the tensors to log-Euclidean space where a linear regression model is applied and hypothesis testing is performed between the control and patient groups. Results show that there is a significant difference in the anisotropy between patients and controls especially in the parts of forceps minor, superior corona radiata, anterior limb of internal capsule and genu of corpus callosum. To check if the tensor analysis gives a better idea of the changes in anisotropy, we compared the results with voxelwise FA analysis as well as voxelwise geodesic anisotropy (GA) analysis.
The Cauchy Problem of Scalar Tensor Theories of Gravity
Salgado, M
2006-01-01
The 3+1 formulation of scalar-tensor theories of gravity (STT) is obtained in the physical (Jordan) frame departing from the 4+0 covariant field equations. Contrary to the common believe (folklore), the new system of ADM-like equations shows that the Cauchy problem of STT is well formulated (in the sense that the whole system is of first order in the time-derivative). This is the first step towards a full first order (in time and space) formulation from which a subsequent hyperbolicity analysis (a well-posedness determination) can be performed. Several gauge (lapse and shift) conditions are considered and implemented for STT. In particular, a generalization of the harmonic gauge for STT allows to prove the well posedness of the STT using a second order analysis which is very similar to the one used in general relativity. Some spacetimes of astrophysical and cosmological interest are considered as specific applications. Several appendices complement the ideas of the main part of the paper.
Constructing higher-order hydrodynamics: The third order
Grozdanov, Sašo; Kaplis, Nikolaos
2016-03-01
Hydrodynamics can be formulated as the gradient expansion of conserved currents in terms of the fundamental fields describing the near-equilibrium fluid flow. In the relativistic case, the Navier-Stokes equations follow from the conservation of the stress-energy tensor to first order in derivatives. In this paper, we go beyond the presently understood second-order hydrodynamics and discuss the systematization of obtaining the hydrodynamic expansion to an arbitrarily high order. As an example of the algorithm that we present, we fully classify the gradient expansion at third order for neutral fluids in four dimensions, thus finding the most general next-to-leading-order corrections to the relativistic Navier-Stokes equations in curved space-time. In doing so, we list 20 new transport coefficient candidates in the conformal case and 68 in the nonconformal case. As we do not consider any constraints that could potentially arise from the local entropy current analysis, this is the maximal possible set of neutral third-order transport coefficients. To investigate the physical implications of these new transport coefficients, we obtain the third-order corrections to the linear dispersion relations that describe the propagation of diffusion and sound waves in relativistic fluids. We also compute the corrections to the scalar (spin-2) two-point correlation function of the third-order stress-energy tensor. Furthermore, as an example of a nonlinear hydrodynamic flow, we calculate the third-order corrections to the energy density of a boost-invariant Bjorken flow. Finally, we apply our field theoretic results to the N =4 supersymmetric Yang-Mills fluid at infinite 't Hooft coupling and an infinite number of colors to find the values of five new linear combinations of the conformal transport coefficients.
Scalar-tensor linear inflation
Artymowski, Michal
2016-01-01
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 any form of the non-minimal coupling to gravity of the form of $f(\\varphi)R/2$; b) the particle physics approach, where we motivate the form of the Jordan frame potential by the loop corrections to the inflaton field. In both cases the Jordan frame potentials are modifications of the induced inflation, but instead of the Starobinsky attractor they lead to the linear inflation in the strong coupling limit.
Scalar-tensor linear inflation
Artymowski, Michał; Racioppi, Antonio
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(varphi)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.
Extended vector-tensor theories
Kimura, Rampei; Naruko, Atsushi; Yoshida, Daisuke
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.
Estimation of tensors and tensor-derived measures in diffusional kurtosis imaging.
Tabesh, Ali; Jensen, Jens H; Ardekani, Babak A; Helpern, Joseph A
2011-03-01
This article presents two related advancements to the diffusional kurtosis imaging estimation framework to increase its robustness to noise, motion, and imaging artifacts. The first advancement substantially improves the estimation of diffusion and kurtosis tensors parameterizing the diffusional kurtosis imaging model. Rather than utilizing conventional unconstrained least squares methods, the tensor estimation problem is formulated as linearly constrained linear least squares, where the constraints ensure physically and/or biologically plausible tensor estimates. The exact solution to the constrained problem is found via convex quadratic programming methods or, alternatively, an approximate solution is determined through a fast heuristic algorithm. The computationally more demanding quadratic programming-based method is more flexible, allowing for an arbitrary number of diffusion weightings and different gradient sets for each diffusion weighting. The heuristic algorithm is suitable for real-time settings such as on clinical scanners, where run time is crucial. The advantage offered by the proposed constrained algorithms is demonstrated using in vivo human brain images. The proposed constrained methods allow for shorter scan times and/or higher spatial resolution for a given fidelity of the diffusional kurtosis imaging parametric maps. The second advancement increases the efficiency and accuracy of the estimation of mean and radial kurtoses by applying exact closed-form formulae.
Estimation of Tensors and Tensor-Derived Measures in Diffusional Kurtosis Imaging1
Tabesh, Ali; Jensen, Jens H.; Ardekani, Babak A.; Helpern, Joseph A.
2010-01-01
This paper presents two related advancements to the diffusional kurtosis imaging (DKI) estimation framework to increase its robustness to noise, motion, and imaging artifacts. The first advancement substantially improves the estimation of diffusion and kurtosis tensors parameterizing the DKI model. Rather than utilizing conventional unconstrained least squares (LS) methods, the tensor estimation problem is formulated as linearly constrained linear LS, where the constraints ensure physically and/or biologically plausible tensor estimates. The exact solution to the constrained problem is found via convex quadratic programming methods or, alternatively, an approximate solution is determined through a fast heuristic algorithm. The computationally more demanding quadratic programming-based method is more flexible, allowing for an arbitrary number of diffusion weightings and different gradient sets for each diffusion weighting. The heuristic algorithm is suitable for real-time settings such as on clinical scanners, where run time is crucial. The advantage offered by the proposed constrained algorithms is demonstrated using in vivo human brain images. The proposed constrained methods allow for shorter scan times and/or higher spatial resolution for a given fidelity of the DKI parametric maps. The second advancement increases the efficiency and accuracy of the estimation of mean and radial kurtoses by applying exact closed-form formulae. PMID:21337412
On the Decomposition of the Spacetime Metric Tensor and of Tensor Fields in Strained Spacetime
Millette P. A.
2012-10-01
Full Text Available We propose a natural decomposition of the spacetime metric tensor of General Relativ- ity into a background and a dynamical part based on an analysis from first principles of the effect of a test mass on the background metric. We find that the presence of mass results in strains in the spacetime continuum. Those strains correspond to the dy- namical part of the spacetime metric tensor. We then apply the stress-strain relation of Continuum Mechanics to the spacetime continuum to show that rest-mass energy den- sity arises from the volume dilatation of the spacetime continuum. Finally we propose a natural decomposition of tensor fields in strained spacetime, in terms of dilatations and distortions. We show that dilatations correspond to rest-mass energy density, while distortions correspond to massless shear transverse waves. We note that this decom- position in a massive dilatation and a massless transverse wave distortion, where both are present in spacetime continuum deformations, is somewhat reminiscent of wave- particle duality. We note that these results are considered to be local effects in the particular reference frame of the observer. In addition, the applicability of the proposed metric to the Einstein field equations remains open.
FaRe: A Mathematica package for tensor reduction of Feynman integrals
Re Fiorentin, Michele
2016-08-01
In this paper, we present FaRe, a package for Mathematica that implements the decomposition of a generic tensor Feynman integral, with arbitrary loop number, into scalar integrals in higher dimension. In order for FaRe to work, the package FeynCalc is needed, so that the tensor structure of the different contributions is preserved and the obtained scalar integrals are grouped accordingly. FaRe can prove particularly useful when it is preferable to handle Feynman integrals with free Lorentz indices and tensor reduction of high-order integrals is needed. This can then be achieved with several powerful existing tools.
FaRe: a Mathematica package for tensor reduction of Feynman integrals
Fiorentin, Michele Re
2015-01-01
We present FaRe, a package for Mathematica that implements the decomposition of a generic tensor Feynman integral, with arbitrary loop number, into scalar integrals in higher dimension. In order for FaRe to work, the package FeynCalc is needed, so that the tensor structure of the different contributions is preserved and the obtained scalar integrals are grouped accordingly. FaRe can prove particularly useful when it is preferable to handle Feynman integrals with free Lorentz indices and tensor reduction of high-order integrals is needed. This can then be achieved with several powerful existing tools.
Globalization by the Souths. Chinese-African Relations and International Order
Julien Rajaoson
2014-11-01
Full Text Available This study focuses on worldwide governance. It will be related to the Assian approach of international relationships. This approach claiming by the Chinese is closed to the David Miller Nationalist and liberal way of thinking. But it remains very restrictive because it is only based on the liberal economic point of view. We will do a critical study of the principles which are regulating the governances and we will analyse a special sectorial field: the Sino-African relations. These thoughts and statements need to have a sectorial dimension of approaching matters. The management of the different governments can have effects on local realities of people's life and on investments. In thirty years China passed from an emerging country to the second worldwide economically powerful country just behind the United States. Now, they must have an interdependance relationship with the United States. It is very important and necessary to undermine this interdependance relationship in order to understand how its economic strategy has an influence upon the worldwide market. And from this study, we will understand how the Chinese relate to the balance of power they are dealing with.
European Security through EU-Russian Relations: Towards a New Multilateral Order?
Sandra Fernandes
2011-05-01
Full Text Available Since the end of the Cold War, the EU and Russia have managed to create an original framework for institutionalised cooperation despite asymmetric characteristics. Yet, the way these two main security actors interact has an impact on the (non-resolution of security issues in Europe, ranging from ‘‘frozen conflicts’’ to the discussion of the security architecture. Since the second mandate of President Putin, the relation has been characterised by two paradoxical features. On the one hand, the methodology and the domains of cooperation have reached a high degree of achievement. On the other hand, the political quality of the relationship has deteriorated and it is not able to achieve the desired ‘‘strategic partnership’’ that should be based on a common set of values and principles. This article aims to define multilateralism as a paradigm applicable to EU-Russian relations. It examines their relationship in the security and defence realm and the Union’s reactions to a new security approach by Russia since the 2008 Medvedev proposal. The article questions how the EU-Russian political dialogue impacts on multilateralism in the security field. The conclusion considers EU-Russian relations as a peculiar multilateral playground addressing common security challenges, which still needs to be developed further in order to be instrumental in the search for collective and legitimate solutions.
Local virial and tensor theorems.
Cohen, Leon
2011-11-17
We show that for any wave function and potential the local virial theorem can always be satisfied 2K(r) = r·ΔV by choosing a particular expression for the local kinetic energy. In addition, we show that for each choice of local kinetic energy there are an infinite number of quasi-probability distributions which will generate the same expression. We also consider the local tensor virial theorem.
Holographic duality from random tensor networks
Hayden, Patrick; Nezami, Sepehr; Qi, Xiao-Liang; Thomas, Nathaniel; Walter, Michael; Yang, Zhao [Stanford Institute for Theoretical Physics, Department of Physics, Stanford University,382 Via Pueblo, Stanford, CA 94305 (United States)
2016-11-02
Tensor networks provide a natural framework for exploring holographic duality because they obey entanglement area laws. They have been used to construct explicit toy models realizing many of the interesting structural features of the AdS/CFT correspondence, including the non-uniqueness of bulk operator reconstruction in the boundary theory. In this article, we explore the holographic properties of networks of random tensors. We find that our models naturally incorporate many features that are analogous to those of the AdS/CFT correspondence. When the bond dimension of the tensors is large, we show that the entanglement entropy of all boundary regions, whether connected or not, obey the Ryu-Takayanagi entropy formula, a fact closely related to known properties of the multipartite entanglement of assistance. We also discuss the behavior of Rényi entropies in our models and contrast it with AdS/CFT. Moreover, we find that each boundary region faithfully encodes the physics of the entire bulk entanglement wedge, i.e., the bulk region enclosed by the boundary region and the minimal surface. Our method is to interpret the average over random tensors as the partition function of a classical ferromagnetic Ising model, so that the minimal surfaces of Ryu-Takayanagi appear as domain walls. Upon including the analog of a bulk field, we find that our model reproduces the expected corrections to the Ryu-Takayanagi formula: the bulk minimal surface is displaced and the entropy is augmented by the entanglement of the bulk field. Increasing the entanglement of the bulk field ultimately changes the minimal surface behavior topologically, in a way similar to the effect of creating a black hole. Extrapolating bulk correlation functions to the boundary permits the calculation of the scaling dimensions of boundary operators, which exhibit a large gap between a small number of low-dimension operators and the rest. While we are primarily motivated by the AdS/CFT duality, the main
Tensor Interaction Effect in Dibaryon
CHEN Ling-Zhi; PANG Hou-Rong; PING Jia-Lun; WANG Fan
2005-01-01
The gluon and Goldstone boson induced tensor interaction effect on the dibaryon mass and the D-wave decay width has been studied in the quark delocalization, color screening model. The effective S-D wave transition interactions induced by gluon and Goldstone boson exchanges decrease quickly as the increasing of the channel strangeness. The K and η meson tensor contribution is negligible in this model. No six-quark state in the light flavor world can become a bound one by the help of these tensor interactions except the deuteron. The partial D-wave decay width of Ijp = 1/2 2+NΩ state to spin 0, 1 ∧([1]) final state is 20.7 keV and 63.1 keV respectively. It is a very narrow dibaryon resonance and might be detected in the relativistic heavy ion reaction by the existing RHIC detectors through the reconstruction of the ∧([1]) vertex mass and the future COMPAS detector at CERN and FAIR project in Germany.
Frequency-domain generelaized singular peruturbation method for relative error model order reduction
Hamid Reza SHAKER
2009-01-01
A new mixed method for relative error model order reduction is proposed.In the proposed method the frequency domain balanced stochastic truncation method is improved by applying the generalized singular perturbation method to the frequency domain balanced system in the reduction procedure.The frequency domain balanced stochastic truncation method,which was proposed in [15] and [17] by the author,is based on two recently developed methods,namely frequency domain balanced truncation within a desired frequency bound and inner-outer factorization techniques.The proposed method in this paper is a carry over of the frequency-domain balanced stochastic truncation and is of interest for practical model order reduction because in this context it shows to keep the accuracy of the approximation as high as possible without sacrificing the computational efficiency and important system properties.It is shown that some important properties of the frequency domain stochastic balanced reduction technique are extended to the proposed reduction method by using the concept and properties of the reciprocal systems.Numerical results show the accuracy,simplicity and flexibility enhancement of the method.
Estimating the Relative Order of Speciation or Coalescence Events on a Given Phylogeny
Rutger Vos
2006-01-01
Full Text Available The reconstruction of large phylogenetic trees from data that violates clocklike evolution (or as a supertree constructed from any m input trees raises a difficult question for biologists– how can one assign relative dates to the vertices of the tree? In this paper we investigate this problem, assuming a uniform distribution on the order of the inner vertices of the tree (which includes, but is more general than, the popular Yule distribution on trees. We derive fast algorithms for computing the probability that (i any given vertex in the tree was the j–th speciation event (for each j, and (ii any one given vertex is earlier in the tree than a second given vertex. We show how the first algorithm can be used to calculate the expected length of any given interior edge in any given tree that has been generated under either a constant- rate speciation model, or the coalescent model.
Financial Brownian Particle in the Layered Order-Book Fluid and Fluctuation-Dissipation Relations
Yura, Yoshihiro; Takayasu, Hideki; Sornette, Didier; Takayasu, Misako
2014-03-01
We introduce a novel description of the dynamics of the order book of financial markets as that of an effective colloidal Brownian particle embedded in fluid particles. The analysis of comprehensive market data enables us to identify all motions of the fluid particles. Correlations between the motions of the Brownian particle and its surrounding fluid particles reflect specific layering interactions; in the inner layer the correlation is strong and with short memory, while in the outer layer it is weaker and with long memory. By interpreting and estimating the contribution from the outer layer as a drag resistance, we demonstrate the validity of the fluctuation-dissipation relation in this nonmaterial Brownian motion process.
Du, Yigang; Fan, Rui; Li, Yong
2016-01-01
An ultrasound imaging framework modeled with the first order nonlinear pressure–velocity relations (NPVR) based simulation and implemented by a half-time staggered solution and pseudospectral method is presented in this paper. The framework is capable of simulating linear and nonlinear ultrasound...... propagation and reflections in a heterogeneous medium with different sound speeds and densities. It can be initialized with arbitrary focus, excitation and apodization for multiple individual channels in both 2D and 3D spatial fields. The simulated channel data can be generated using this framework......, and ultrasound image can be obtained by beamforming the simulated channel data. Various results simulated by different algorithms are illustrated for comparisons. The root mean square (RMS) errors for each compared pulses are calculated. The linear propagation is validated by an angular spectrum approach (ASA...
M. A. Hussain
2014-01-01
Full Text Available This paper discusses the discrete-time stability analysis of a neural network inverse model control strategy for a relative order two nonlinear system. The analysis is done by representing the closed loop system in state space format and then analyzing the time derivative of the state trajectory using Lyapunov’s direct method. The analysis shows that the tracking output error of the states is confined to a ball in the neighborhood of the equilibrium point where the size of the ball is partly dependent on the accuracy of the neural network model acting as the controller. Simulation studies on the two-tank-in-series system were done to complement the stability analysis and to demonstrate some salient results of the study.
Tensor analysis and elementary differential geometry for physicists and engineers
Nguyen-Schäfer, Hung
2014-01-01
Tensors and methods of differential geometry are very useful mathematical tools in many fields of modern physics and computational engineering including relativity physics, electrodynamics, computational fluid dynamics (CFD), continuum mechanics, aero and vibroacoustics, and cybernetics. This book comprehensively presents topics, such as bra-ket notation, tensor analysis, and elementary differential geometry of a moving surface. Moreover, authors intentionally abstain from giving mathematically rigorous definitions and derivations that are however dealt with as precisely as possible. The reader is provided with hands-on calculations and worked-out examples at which he will learn how to handle the bra-ket notation, tensors and differential geometry and to use them in the physical and engineering world. The target audience primarily comprises graduate students in physics and engineering, research scientists, and practicing engineers.
Robust Estimation of Trifocal Tensor Using Messy Genetic Algorithm
HUMingxing; YUANBaozong; TANGXiaofang
2003-01-01
Given three partially overlapping views of a scene from which a set of point or line correspondences have been extracted, 3D structure and camera motion pa-rameters can be represented by the trifocal tensor, which is the key to many problems of computer vision among three views. This paper addresses the problem of robust esti-mating the trifocal tensor employing a new method based on messy genetic algorithm, which uses each gene to stand for a triplet of correspondences, and takes every chromo-some as a minimum subset for trifocal tensor estimation.The method would eventually converge to a near optimal solution and is relatively unaffected by the outliers. Exper-iments with both synthetic data and real images show that our method is more robust and precise than other typical methods because it can efficiently detect and delete the bad corresponding points, which include both bad loca-tions and false matches.
Three-dimensional diffusion tensor microscopy of fixed mouse hearts.
Jiang, Yi; Pandya, Kumar; Smithies, Oliver; Hsu, Edward W
2004-09-01
The relative utility of 3D, microscopic resolution assessments of fixed mouse myocardial structure via diffusion tensor imaging is demonstrated in this study. Isotropic 100-microm resolution fiber orientation mapping within 5.5 degrees accuracy was achieved in 9.1 hr scan time. Preliminary characterization of the diffusion tensor primary eigenvector reveals a smooth and largely linear angular rotation across the left ventricular wall. Moreover, a higher level of structural hierarchy is evident from the organized secondary and tertiary eigenvector fields. These findings are consistent with the known myocardial fiber and laminar structures reported in the literature and suggest an essential role of diffusion tensor microscopy in developing quantitative atlases for studying the structure-function relationships of mouse hearts.
Extended Tensor Products and Generalization of the Notion of Entanglement
Khrennikov, Andrei
2012-01-01
Motivated by the novel applications of the mathematical formalism of quantum theory and its generalizations in cognitive science, psychology, social and political sciences, and economics, we extend the notion of the tensor product and entanglement. We also study the relation between conventional entanglement of complex qubits and our generalized entanglement. Our construction can also be used to describe entanglement in the framework of non-Archimedean physics. It is also possible to construct tensor products of non-Archimedean (e.g., $p$-adic) and complex Hilbert spaces.
Analytical stress tensor and pressure calculations with the CRYSTAL code
Doll, K.
2010-02-01
The calculation of the stress tensor and related properties and its implementation in the CRYSTAL code are described. The stress tensor is obtained from the earlier implemented analytical gradients with respect to the cell parameters. Subsequently, the pressure and enthalpy are computed, and a test concerning the pressure-driven phase transition in KI is used as an illustration. Finally, the possibility of applying external pressure is implemented. The constant-pressure optimization offers an alternative optimization method in addition to the already implemented optimization at constant volume.
Proposal for the proper gravitational energy-momentum tensor
Shimizu, Katsutaro
2016-08-01
We propose a gravitational energy-momentum (GEMT) tensor of the general relativity obtained using Noether’s theorem. It transforms as a tensor under general coordinate transformations. One of the two indices of the GEMT labels a local Lorentz frame that satisfies the energy-momentum conservation law. The energies for a gravitational wave, a Schwarzschild black hole and a Friedmann-Lemaitre-Robertson-Walker (FLRW) universe are calculated as examples. The gravitational energy of the Schwarzschild black hole exists only outside the horizon, its value being the negative of the black hole mass.
Extended tensor products and generalization of the notion of entanglement
Khrennikov, Andrei; Rosinger, Elemer E.
2012-03-01
Motivated by the novel applications of the mathematical formalism of quantum theory and its generalizations in cognitive science, psychology, social and political sciences, and economics, we extend the notion of the tensor product and entanglement. We also study the relation between conventional entanglement of complex qubits and our generalized entanglement. Our construction can also be used to describe entanglement in the framework of non-Archimedean physics. It is also possible to construct tensor products of non-Archimedean (e.g., p-adic) and complex Hilbert spaces.
Tensor network quotient takes the vacuum to the thermal state
Czech, Bartłomiej; Evenbly, Glen; Lamprou, Lampros; McCandlish, Samuel; Qi, Xiao-liang; Sully, James; Vidal, Guifré
2016-08-01
In 1+1-dimensional conformal-field theory, the thermal state on a circle is related to a certain quotient of the vacuum on a line. We explain how to take this quotient in the MERA tensor network representation of the vacuum and confirm the validity of the construction in the critical Ising model. This result suggests that the tensors comprising MERA can be interpreted as performing local scale transformations, so that adding or removing them emulates conformal maps. In this sense, the optimized MERA recovers local conformal invariance that is broken by the choice of lattice.
An optimization approach for fitting canonical tensor decompositions.
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.
Faster identification of optimal contraction sequences for tensor networks.
Pfeifer, Robert N C; Haegeman, Jutho; Verstraete, Frank
2014-09-01
The efficient evaluation of tensor expressions involving sums over multiple indices is of significant importance to many fields of research, including quantum many-body physics, loop quantum gravity, and quantum chemistry. The computational cost of evaluating an expression may depend strongly on the order in which the index sums are evaluated, and determination of the operation-minimizing contraction sequence for a single tensor network (single term, in quantum chemistry) is known to be NP-hard. The current preferred solution is an exhaustive search, using either an iterative depth-first approach with pruning or dynamic programming and memoization, but these approaches are impractical for many of the larger tensor network ansätze encountered in quantum many-body physics. We present a modified search algorithm with enhanced pruning which exhibits a performance increase of several orders of magnitude while still guaranteeing identification of an optimal operation-minimizing contraction sequence for a single tensor network. A reference implementation for matlab, compatible with the ncon() and multienv() network contractors of arXiv:1402.0939 and Evenbly and Pfeifer, Phys. Rev. B 89, 245118 (2014), respectively, is supplied.
Diffusion tensor imaging of hippocampal network plasticity.
Sierra, Alejandra; Laitinen, Teemu; Gröhn, Olli; Pitkänen, Asla
2015-03-01
Diffusion tensor imaging (DTI) has become a valuable tool to investigate white matter integrity in the brain. DTI also gives contrast in gray matter, which has been relatively little explored in studies assessing post-injury structural abnormalities. The present study was designed to compare white and gray matter reorganization in the rat hippocampus after two epileptogenic brain injuries, status epilepticus (SE) and traumatic brain injury (TBI), using ex vivo high-resolution DTI. Imaging was performed at 6-12 months post-injury and findings were compared to histological analyses of Nissl, myelin, and Timm-stained preparations from the same animals. In agreement with the severity of histological damage, fractional anisotropy (FA), axial (D ||) and radial (D ⊥) diffusivities, and mean diffusivity (MD) measurements were altered in the order SE > TBI ipsilaterally > TBI contralaterally. After SE, the most severe abnormalities were found in the dentate gyrus and CA3b-c subfields, in which the mean FA was increased to 125 % (p < 0.001) and 143 % (p < 0.001) of that in controls, respectively. In both subfields, the change in FA was associated with an increase in D || (p < 0.01). In the stratum radiatum of the CA1, FA was decreased to 81 % of that in controls (p < 0.05) which was associated with an increase in D ⊥ (p < 0.01). After TBI, DTI did not reveal any major abnormalities in the dentate gyrus. In the ipsilateral CA3b-c, however, FA was increased to 126 % of that in controls (p < 0.01) and associated with a mild decrease in D ⊥ (p < 0.05). In the stratum radiatum of the ipsilateral CA1, FA was decreased to 88 % of that in controls (p < 0.05). Our data demonstrate that DTI reveals subfield-specific abnormalities in the hippocampus with remarkable qualitative and quantitative differences between the two epileptogenic etiologies, suggesting that DTI could be a valuable tool for follow-up of focal circuitry reorganization during the post
Sparse alignment for robust tensor learning.
Lai, Zhihui; Wong, Wai Keung; Xu, Yong; Zhao, Cairong; Sun, Mingming
2014-10-01
Multilinear/tensor extensions of manifold learning based algorithms have been widely used in computer vision and pattern recognition. This paper first provides a systematic analysis of the multilinear extensions for the most popular methods by using alignment techniques, thereby obtaining a general tensor alignment framework. From this framework, it is easy to show that the manifold learning based tensor learning methods are intrinsically different from the alignment techniques. Based on the alignment framework, a robust tensor learning method called sparse tensor alignment (STA) is then proposed for unsupervised tensor feature extraction. Different from the existing tensor learning methods, L1- and L2-norms are introduced to enhance the robustness in the alignment step of the STA. The advantage of the proposed technique is that the difficulty in selecting the size of the local neighborhood can be avoided in the manifold learning based tensor feature extraction algorithms. Although STA is an unsupervised learning method, the sparsity encodes the discriminative information in the alignment step and provides the robustness of STA. Extensive experiments on the well-known image databases as well as action and hand gesture databases by encoding object images as tensors demonstrate that the proposed STA algorithm gives the most competitive performance when compared with the tensor-based unsupervised learning methods.
TIMER: tensor image morphing for elastic registration.
Yap, Pew-Thian; Wu, Guorong; Zhu, Hongtu; Lin, Weili; Shen, Dinggang
2009-08-15
We propose a novel diffusion tensor imaging (DTI) registration algorithm, called Tensor Image Morphing for Elastic Registration (TIMER), which leverages the hierarchical guidance of regional distributions and local boundaries, both extracted directly from the tensors. Currently available DTI registration methods generally extract tensor scalar features from each tensor to construct scalar maps. Subsequently, regional integration and other operations such as edge detection are performed to extract more features to guide the registration. However, there are two major limitations with these approaches. First, the computed regional features might not reflect the actual regional tensor distributions. Second, by the same token, gradient maps calculated from the tensor-derived scalar feature maps might not represent the actual tissue tensor boundaries. To overcome these limitations, we propose a new approach which extracts regional and edge information directly from a tensor neighborhood. Regional tensor distribution information, such as mean and variance, is computed in a multiscale fashion directly from the tensors by taking into account the voxel neighborhood of different sizes, and hence capturing tensor information at different scales, which in turn can be employed to hierarchically guide the registration. Such multiscale scheme can help alleviate the problem of local minimum and is also more robust to noise since one can better determine the statistical properties of each voxel by taking into account the properties of its surrounding. Also incorporated in our method is edge information extracted directly from the tensors, which is crucial to facilitate registration of tissue boundaries. Experiments involving real subjects, simulated subjects, fiber tracking, and atrophy detection indicate that TIMER performs better than the other methods (Yang et al., 2008; Zhang et al., 2006).
On the performance of tensor methods for solving ill-conditioned problems.
Schnabel, Robert B. (University of Colorado at Boulder, Boulder, CO); Bader, Brett William
2004-09-01
This paper investigates the performance of tensor methods for solving small- and large-scale systems of nonlinear equations where the Jacobian matrix at the root is ill-conditioned or singular. This condition occurs on many classes of problems, such as identifying or approaching turning points in path following problems. The singular case has been studied more than the highly ill-conditioned case, for both Newton and tensor methods. It is known that Newton-based methods do not work well with singular problems because they converge linearly to the solution and, in some cases, with poor accuracy. On the other hand, direct tensor methods have performed well on singular problems and have superlinear convergence on such problems under certain conditions. This behavior originates from the use of a special, restricted form of the second-order term included in the local tensor model that provides information lacking in a (nearly) singular Jacobian. With several implementations available for large-scale problems, tensor methods now are capable of solving larger problems. We compare the performance of tensor methods and Newton-based methods for both small- and large-scale problems over a range of conditionings, from well-conditioned to ill-conditioned to singular. Previous studies with tensor methods only concerned the ends of this spectrum. Our results show that tensor methods are increasingly superior to Newton-based methods as the problem grows more ill-conditioned.
Misra, Avijit; Biswas, Anindya; Pati, Arun K; Sen De, Aditi; Sen, Ujjwal
2015-05-01
Quantum discord is a measure of quantum correlations beyond the entanglement-separability paradigm. It is conceptualized by using the von Neumann entropy as a measure of disorder. We introduce a class of quantum correlation measures as differences between total and classical correlations, in a shared quantum state, in terms of the sandwiched relative Rényi and Tsallis entropies. We compare our results with those obtained by using the traditional relative entropies. We find that the measures satisfy all the plausible axioms for quantum correlations. We evaluate the measures for shared pure as well as paradigmatic classes of mixed states. We show that the measures can faithfully detect the quantum critical point in the transverse quantum Ising model and find that they can be used to remove an unquieting feature of nearest-neighbor quantum discord in this respect. Furthermore, the measures provide better finite-size scaling exponents of the quantum critical point than the ones for other known order parameters, including entanglement and information-theoretic measures of quantum correlations.
Xiuling Liang
2016-12-01
Full Text Available The processing of causal relations has been constantly found to be asymmetrical once the roles of cause and effect are assigned to objects in interactions. We used a relationship recognition paradigm and recorded electroencephalographic (EEG signals to explore the neural mechanism underlying the asymmetrical representations of causal relations in semantic memory. The results revealed that the verification of causal relations is faster if two words appear in cause–effect order (e.g., virus-epidemic than if they appear in effect–cause order (e.g., epidemic-virus, whereas no such asymmetrical representation was found for the verification of hierarchical relations with reverse orders (e.g., bird-sparrow v. sparrow-bird in Experiment 1. Furthermore, the P2 amplitude elicited by superordinate-subordinate order was larger than that when in reverse order, whereas the N400 effect elicited by cause-effect order was smaller (more positive than when in reverse order. However, no such asymmetry, as well as P2 and N400 components, were observed when verifying the existence of a general associative relation in Experiment 2. We suggested that the smaller N400 in cause-effect order indicates their increased salience in semantic memory relative to the effect-cause order. These results provide evidence for dissociable neural processes, which are related to role binding, contributing to the generation of causal asymmetry.
Liang, Xiuling; Xiao, Feng; Wu, Lijun; Chen, Qingfei; Lei, Yi; Li, Hong
2016-01-01
The processing of causal relations has been constantly found to be asymmetrical once the roles of cause and effect are assigned to objects in interactions. We used a relationship recognition paradigm and recorded electroencephalographic (EEG) signals to explore the neural mechanism underlying the asymmetrical representations of causal relations in semantic memory. The results revealed that the verification of causal relations is faster if two words appear in "cause-effect" order (e.g., virus-epidemic) than if they appear in "effect-cause" order (e.g., epidemic-virus), whereas no such asymmetrical representation was found for the verification of hierarchical relations with reverse orders (e.g., bird-sparrow vs. sparrow-bird) in Experiment 1. Furthermore, the P2 amplitude elicited by "superordinate-subordinate" order was larger than that when in reverse order, whereas the N400 effect elicited by "cause-effect" order was smaller (more positive) than when in reverse order. However, no such asymmetry, as well as P2 and N400 components, were observed when verifying the existence of a general associative relation in Experiment 2. We suggested that the smaller N400 in cause-effect order indicates their increased salience in semantic memory relative to the effect-cause order. These results provide evidence for dissociable neural processes, which are related to role binding, contributing to the generation of causal asymmetry.
Nucleon tensor charges and electric dipole moments
Pitschmann, Mario; Seng, Chien-Yeah; Roberts, Craig D.; Schmidt, Sebastian M.
2015-04-01
A symmetry-preserving Dyson-Schwinger equation treatment of a vector-vector contact interaction is used to compute dressed-quark-core contributions to the nucleon σ -term and tensor charges. The latter enable one to directly determine the effect of dressed-quark electric dipole moments (EDMs) on neutron and proton EDMs. The presence of strong scalar and axial-vector diquark correlations within ground-state baryons is a prediction of this approach. These correlations are active participants in all scattering events and thereby modify the contribution of the singly represented valence quark relative to that of the doubly represented quark. Regarding the proton σ -term and that part of the proton mass which owes to explicit chiral symmetry breaking, with a realistic d -u mass splitting, the singly represented d quark contributes 37% more than the doubly represented u quark; and in connection with the proton's tensor charges, δTu , δTd , the ratio δTd /δTu is 18% larger than anticipated from simple quark models. Of particular note, the size of δTu is a sensitive measure of the strength of dynamical chiral symmetry breaking; and δTd measures the amount of axial-vector diquark correlation within the proton, vanishing if such correlations are absent.
Correlation of proton MR spectroscopy and diffusion tensor imaging
Irwan, R; Sijens, PE; Potze, JH; Oudkerk, M
2005-01-01
Proton magnetic resonance spectroscopy (H-1-MRS) provides indices of neuronal damage. Diffusion tensor imaging (DTI) relates to water diffusivity and fiber tract orientation. A method to compare H-1-MRS and DTI findings was developed, tested on phantom and applied on normal brain. Point-resolved spe
Energy in class of scalar-tensor theories of gravity
Barraco, D.; Hamity, V. (Universidad Nacional de Cordoba, Cordoba (Antigua and Barbuda)); Calvo, A.; Seco, J. (Departamento de Fisica General de la Atmosfera, Universidad de Salamanca, Salamanca (Spain))
1994-01-01
We investigate the equality of inertial and gravitational mass in a wide class of scalar tensor theories. We derive a general expression for the active mass (gravitational mass) and the inertial mass related by a term which can be seen as the energy of the scalar field. (Author) 13 refs.
2013-02-21
... seq. \\2\\ Order Granting Exemptions from Certain Rules of Regulation SHO Related to Hurricane Sandy... Hurricane Sandy made landfall and whose settlement depends on the delivery of such physical certificates (or... COMMISSION Order Extending Temporary Exemptions From Certain Rules of Regulation SHO Related to...
Ali A. Ismail
2014-07-01
Full Text Available In this study a general form of recurrence relations of continuous function for doubly truncated modified Makeham distribution is obtained. Recurrence relations between single and product moments of order statistics from doubly truncated modified Makeham distribution are given. Also, a characterization of modified Makeham distribution from the right and the left is discussed through the properties of order statistics.
Walder, Brennan J.; Davis, Michael C.; Grandinetti, Philip J. [Department of Chemistry, Ohio State University, 100 West 18th Avenue, Columbus, Ohio 43210 (United States); Dey, Krishna K. [Department of Physics, Dr. H. S. Gour University, Sagar, Madhya Pradesh 470003 (India); Baltisberger, Jay H. [Division of Natural Science, Mathematics, and Nursing, Berea College, Berea, Kentucky 40403 (United States)
2015-01-07
A new two-dimensional Nuclear Magnetic Resonance (NMR) experiment to separate and correlate the first-order quadrupolar and chemical/paramagnetic shift interactions is described. This experiment, which we call the shifting-d echo experiment, allows a more precise determination of tensor principal components values and their relative orientation. It is designed using the recently introduced symmetry pathway concept. A comparison of the shifting-d experiment with earlier proposed methods is presented and experimentally illustrated in the case of {sup 2}H (I = 1) paramagnetic shift and quadrupolar tensors of CuCl{sub 2}⋅2D{sub 2}O. The benefits of the shifting-d echo experiment over other methods are a factor of two improvement in sensitivity and the suppression of major artifacts. From the 2D lineshape analysis of the shifting-d spectrum, the {sup 2}H quadrupolar coupling parameters are 〈C{sub q}〉 = 118.1 kHz and 〈η{sub q}〉 = 0.88, and the {sup 2}H paramagnetic shift tensor anisotropy parameters are 〈ζ{sub P}〉 = − 152.5 ppm and 〈η{sub P}〉 = 0.91. The orientation of the quadrupolar coupling principal axis system (PAS) relative to the paramagnetic shift anisotropy principal axis system is given by (α,β,γ)=((π)/2 ,(π)/2 ,0). Using a simple ligand hopping model, the tensor parameters in the absence of exchange are estimated. On the basis of this analysis, the instantaneous principal components and orientation of the quadrupolar coupling are found to be in excellent agreement with previous measurements. A new point dipole model for predicting the paramagnetic shift tensor is proposed yielding significantly better agreement than previously used models. In the new model, the dipoles are displaced from nuclei at positions associated with high electron density in the singly occupied molecular orbital predicted from ligand field theory.
Reconstruction of convex bodies from surface tensors
Kousholt, Astrid; Kiderlen, Markus
The set of all surface tensors of a convex body K (Minkowski tensors derived from the surface area measure of K) determine K up to translation, and hereby, the surface tensors of K contain all information on the shape of K. Here, shape means the equivalence class of all convex bodies...... 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....... 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...
Derivatives on the isotropic tensor functions
DUI; Guansuo; WANG; Zhengdao; JIN; Ming
2006-01-01
The derivative of the isotropic tensor function plays an important part in continuum mechanics and computational mechanics, and also it is still an opening problem. By means of a scalar response function and solving a tensor equation, this problem is well studied. A compact explicit expression for the derivative of the isotropic tensor function is presented, which is valid for both distinct and repeated eigenvalue cases. Throughout the analysis, the formulation holds for general isotropic tensor functions without need to solve eigenvector problems or determine coefficients. On the theoretical side, a very simple solution of a tensor equation is obtained. As an application to continuum mechanics, a base-free expression for the Hill's strain rate is given, which is more compact than the existent results. Finally, with an example we compute the derivative of an exponent tensor function. And the efficiency of the present formulations is demonstrated.
Seamless warping of diffusion tensor fields
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...
Ichikawa, Kazuhide; Kurokawa, Yusaku I; Sakaki, Shigeyoshi; Tachibana, Akitomo
2011-01-01
We study the electronic structure of two types of transition metal complexes, the inverted-sandwich-type and open-lantern-type, by the electronic stress tensor. In particular, the bond order b_e measured by the energy density which is defined from the electronic stress tensor is studied and compared with the conventional MO based bond order. We also examine the patterns found in the largest eigenvalue of the stress tensor and corresponding eigenvector field, the "spindle structure" and "pseudo-spindle structure". As for the inverted-sandwich-type complex, our bond order b_e calculation shows that relative strength of the metal-benzene bond among V, Cr and Mn complexes is V > Cr > Mn which is consistent with the MO based bond order. As for the open-lantern-type complex, we find that our energy density based bond order can properly describe the relative strength of Cr--Cr and Mo--Mo bonds by the surface integration of the energy density over the "Lagrange surface" which can take into account the spatial extent ...
Tensor Effect on Bubble Nuclei
WANG Yan-Zhao; GU Jian-Zhong; ZHANG Xi-Zhen; DONG Jian-Min
2011-01-01
In the framework of the Hartree-Fock-Bogoliubov (HFB) approach with Skyrme interactions SLy5+T, SLy5+Tw and several sets of TIJ parametrizations, I.e. The Skyrme interaction parametrizations including the tensor terms, the proton density distribution in 34Si and 46Ar nuclei is calculated with and without the tensor force. It is shown that the bubble effect in 34Si does not depend a great deal on the Skyrme parametrization and the proton density distribution in 34Si is hardly influenced by the tensor force. As to 46Ar, the SLy5+Tw parametrization favors the formation of the bubble structure due to the inversion between the 2s1/2 and 1d3/2 orbits (2s1/2-ld3/2 inversion). The inversion mechanism induced by the SLy5+Tw interaction is analyzed based on the proton single-particle spectra obtained from the SLy5 and SLy5+Tw interactions as well as the wave functions of the 2s1/2 and 1d3/2 states.%In the framework of the Hartree-Fock-Bogoliubov (HFB) approach with Skyrme interactions SLy5+ T,SLy5+ Tω and several sets of TIJ parametrizations,i.e.the Skyrme interaction pararmetrizations including the tensor terms,the proton density distribution in 34Si and 46 Ar nuclei is calculated with and without the tensor force.It is shown that the bubble effect in 34Si does not depend a great deal on the Skyrme parametrization and the proton density distribution in 34Si is hardly influenced by the tensor force.As to 46Ar,the SLy5+ Tω parametrization favors the formation of the bubble structure due to the inversion between the 2s1/2 and 1d3/2 orbits (2s1/2-1d3/2 inversion).The inversion mechanism induced by the SLy5+ Tω interaction is analyzed based on the proton single-particle spectra obtained from the SLy5 and SLy5+ Tω interactions as well as the wave functions of the 2s1/2 and 1d3/2 states.The study of exotic nuclear structures has been a hot topic in nuclear physics.[1-4] Exotic nuclei are unstabile,superheavy nuclei,halo nuclei and so forth,whose structures are quite different
Early Age-Related Functional Connectivity Decline in High-Order Cognitive Networks
Siman-Tov, Tali; Bosak, Noam; Sprecher, Elliot; Paz, Rotem; Eran, Ayelet; Aharon-Peretz, Judith; Kahn, Itamar
2017-01-01
As the world ages, it becomes urgent to unravel the mechanisms underlying brain aging and find ways of intervening with them. While for decades cognitive aging has been related to localized brain changes, growing attention is now being paid to alterations in distributed brain networks. Functional connectivity magnetic resonance imaging (fcMRI) has become a particularly useful tool to explore large-scale brain networks; yet, the temporal course of connectivity lifetime changes has not been established. Here, an extensive cross-sectional sample (21–85 years old, N = 887) from a public fcMRI database was used to characterize adult lifespan connectivity dynamics within and between seven brain networks: the default mode, salience, dorsal attention, fronto-parietal control, auditory, visual and motor networks. The entire cohort was divided into young (21–40 years, mean ± SD: 25.5 ± 4.8, n = 543); middle-aged (41–60 years, 50.6 ± 5.4, n = 238); and old (61 years and above, 69.0 ± 6.3, n = 106) subgroups. Correlation matrices as well as a mixed model analysis of covariance indicated that within high-order cognitive networks a considerable connectivity decline is already evident by middle adulthood. In contrast, a motor network shows increased connectivity in middle adulthood and a subsequent decline. Additionally, alterations in inter-network interactions are noticeable primarily in the transition between young and middle adulthood. These results provide evidence that aging-related neural changes start early in adult life. PMID:28119599
Hard Exclusive Production of Tensor Mesons
Braun, V M
2001-01-01
We point out that hard exclusive production of tensor mesons $f_2(1270)$ with helicity $\\lambda=\\pm 2$ is dominated by the gluon component in the meson wave function and can be used to determine gluon admixture in tensor mesons in a theoretically clean manner. We present a detailed analysis of the tensor meson distribution amplitudes and calculate the transition form factor $\\gamma+\\gamma^*\\to f_2(1270)$ for one real and one virtual photon.
Li, Xi-Zeng; Su, Bao-Xia
1994-01-01
It is found that two-mode output quantum electromagnetic field in two-mode squeezed states exhibits higher-order squeezing to all even orders. And the generalized uncertainty relations are also presented for the first time. The concept of higher-order squeezing of the single-mode quantum electromagnetic field was first introduced and applied to several processes by Hong and Mandel in 1985. Lately Li Xizeng and Shan Ying have calculated the higher-order squeezing in the process of degenerate four-wave mixing and presented the higher-order uncertainty relations of the fields in single-mode squeezed states. In this paper we generalize the above work to the higher-order squeezing in two-mode squeezed states. The generalized uncertainty relations are also presented for the first time.
Non abelian tensor square of non abelian prime power groups
2010-01-01
For every $p$-group of order $p^n$ with the derived subgroup of order $p^m$, Rocco in \\cite{roc} has shown that the order of tensor square of $G$ is at most $p^{n(n-m)}$. In the present paper not only we improve his bound for non-abelian $p$-groups but also we describe the structure of all non-abelian $p$-groups when the bound is attained for a special case. Moreover, our results give as well an upper bound for the order of $\\pi_3(SK(G, 1))$.
The tensor network theory library
Al-Assam, S.; Clark, S. R.; Jaksch, D.
2017-09-01
In this technical paper we introduce the tensor network theory (TNT) library—an open-source software project aimed at providing a platform for rapidly developing robust, easy to use and highly optimised code for TNT calculations. The objectives of this paper are (i) to give an overview of the structure of TNT library, and (ii) to help scientists decide whether to use the TNT library in their research. We show how to employ the TNT routines by giving examples of ground-state and dynamical calculations of one-dimensional bosonic lattice system. We also discuss different options for gaining access to the software available at www.tensornetworktheory.org.
Numerical evaluation of tensor Feynman integrals in Euclidean kinematics
Gluza, J.; Kajda [Silesia Univ., Katowice (Poland). Inst. of Physics; Riemann, T.; Yundin, V. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany)
2010-10-15
For the investigation of higher order Feynman integrals, potentially with tensor structure, it is highly desirable to have numerical methods and automated tools for dedicated, but sufficiently 'simple' numerical approaches. We elaborate two algorithms for this purpose which may be applied in the Euclidean kinematical region and in d=4-2{epsilon} dimensions. One method uses Mellin-Barnes representations for the Feynman parameter representation of multi-loop Feynman integrals with arbitrary tensor rank. Our Mathematica package AMBRE has been extended for that purpose, and together with the packages MB (M. Czakon) or MBresolve (A. V. Smirnov and V. A. Smirnov) one may perform automatically a numerical evaluation of planar tensor Feynman integrals. Alternatively, one may apply sector decomposition to planar and non-planar multi-loop {epsilon}-expanded Feynman integrals with arbitrary tensor rank. We automatized the preparations of Feynman integrals for an immediate application of the package sectordecomposition (C. Bogner and S. Weinzierl) so that one has to give only a proper definition of propagators and numerators. The efficiency of the two implementations, based on Mellin-Barnes representations and sector decompositions, is compared. The computational packages are publicly available. (orig.)
Tensor methods for large sparse systems of nonlinear equations
Bouaricha, A. [Argonne National Lab., IL (United States). Mathematics and Computer Science Div.; Schnabel, R.B. [Colorado Univ., Boulder, CO (United States). Dept. of Computer Science
1996-12-31
This paper introduces censor methods for solving, large sparse systems of nonlinear equations. Tensor methods for nonlinear equations were developed in the context of solving small to medium- sized dense problems. They base each iteration on a quadratic model of the nonlinear equations. where the second-order term is selected so that the model requires no more derivative or function information per iteration than standard linear model-based methods, and hardly more storage or arithmetic operations per iteration. Computational experiments on small to medium-sized problems have shown censor methods to be considerably more efficient than standard Newton-based methods, with a particularly large advantage on singular problems. This paper considers the extension of this approach to solve large sparse problems. The key issue that must be considered is how to make efficient use of sparsity in forming and solving the censor model problem at each iteration. Accomplishing this turns out to require an entirely new way of solving the tensor model that successfully exploits the sparsity of the Jacobian, whether the Jacobian is nonsingular or singular. We develop such an approach and, based upon it, an efficient tensor method for solving large sparse systems of nonlinear equations. Test results indicate that this tensor method is significantly more efficient and robust than an efficient sparse Newton-based method. in terms of iterations, function evaluations. and execution time.
Tensor power spectrum and disformal transformations
Fumagalli, Jacopo; Postma, Marieke
2016-01-01
In a general effective theory description of inflation a disformal transformation can be used to set the tensor sound speed to one. After the transformation, the tensor power spectrum then automatically only depends on the Hubble parameter. We show that this disformal transformation, however, is nothing else than a change of units. It is a very useful tool for simplifying and interpreting computations, but it cannot change any physics. While the apparent parametrical dependence of the tensor power spectrum does change under a disformal transformation, the physics described is frame invariant. We further illustrate the frame invariance of the tensor power spectrum by writing it exclusively in terms of separately invariant quantities.
Loop Optimization for Tensor Network Renormalization
Yang, Shuo; Gu, Zheng-Cheng; Wen, Xiao-Gang
2017-03-01
We introduce a tensor renormalization group scheme for coarse graining a two-dimensional tensor network that can be successfully applied to both classical and quantum systems on and off criticality. The key innovation in our scheme is to deform a 2D tensor network into small loops and then optimize the 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.
Reconstruction of convex bodies from surface tensors
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...
Loop Optimization for Tensor Network Renormalization.
Yang, Shuo; Gu, Zheng-Cheng; Wen, Xiao-Gang
2017-03-17
We introduce a tensor renormalization group scheme for coarse graining a two-dimensional tensor network that can be successfully applied to both classical and quantum systems on and off criticality. The key innovation in our scheme is to deform a 2D tensor network into small loops and then optimize the 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.
Ezquiaga, Jose María; García-Bellido, Juan; Zumalacárregui, Miguel
2016-07-01
We use a description based on differential forms to systematically explore the space of scalar-tensor theories of gravity. Within this formalism, we propose a basis for the scalar sector at the lowest order in derivatives of the field and in any number of dimensions. This minimal basis is used to construct a finite and closed set of Lagrangians describing general scalar-tensor theories invariant under local Lorentz transformations in a pseudo-Riemannian manifold, which contains ten physically distinct elements in four spacetime dimensions. Subsequently, we compute their corresponding equations of motion and find which combinations are at most second order in derivatives in four as well as an arbitrary number of dimensions. By studying the possible exact forms (total derivatives) and algebraic relations between the basis components, we discover that there are only four Lagrangian combinations producing second-order equations, which can be associated with Horndeski's theory. In this process, we identify a new second-order Lagrangian, named kinetic Gauss-Bonnet, that was not previously considered in the literature. However, we show that its dynamics is already contained in Horndeski's theory. Finally, we provide a full classification of the relations between different second-order theories. This allows us to clarify, for instance, the connection between different covariantizations of Galileons theory. In conclusion, our formulation affords great computational simplicity with a systematic structure. As a first step, we focus on theories with second-order equations of motion. However, this new formalism aims to facilitate advances towards unveiling the most general scalar-tensor theories.
Tensor dissimilarity based adaptive seeding algorithm for DT-MRI visualization with streamtubes
Weldeselassie, Yonas T.; Hamarneh, Ghassan; Weiskopf, Daniel
2007-03-01
In this paper, we propose an adaptive seeding strategy for visualization of diffusion tensor magnetic resonance imaging (DT-MRI) data using streamtubes. DT-MRI is a medical imaging modality that captures unique water diffusion properties and fiber orientation information of the imaged tissues. Visualizing DT-MRI data using streamtubes has the advantage that not only the anisotropic nature of the diffusion is visualized but also the underlying anatomy of biological structures is revealed. This makes streamtubes significant for the analysis of fibrous tissues in medical images. In order to avoid rendering multiple similar streamtubes, an adaptive seeding strategy is employed which takes into account similarity of tensors in a given region. The goal is to automate the process of generating seed points such that regions with dissimilar tensors are assigned more seed points compared to regions with similar tensors. The algorithm is based on tensor dissimilarity metrics that take into account both diffusion magnitudes and directions to optimize the seeding positions and density of streamtubes in order to reduce the visual clutter. Two recent advances in tensor calculus and tensor dissimilarity metrics are utilized: the Log-Euclidean and the J-divergence. Results show that adaptive seeding not only helps to cull unnecessary streamtubes that would obscure visualization but also do so without having to compute the culled streamtubes, which makes the visualization process faster.
Semi-analytic stellar structure in scalar-tensor gravity
Horbatsch, M. W.; Burgess, C. P.
2011-08-01
Precision tests of gravity can be used to constrain the properties of hypothetical very light scalar fields, but these tests depend crucially on how macroscopic astrophysical objects couple to the new scalar field. We study the equations of stellar structure using scalar-tensor gravity, with the goal of seeing how stellar properties depend on assumptions made about the scalar coupling at a microscopic level. In order to make the study relatively easy for different assumptions about microscopic couplings, we develop quasi-analytic approximate methods for solving the stellar-structure equations rather than simply integrating them numerically. (The approximation involved assumes the dimensionless scalar coupling at the stellar center is weak, and we compare our results with numerical integration in order to establish its domain of validity.) We illustrate these methods by applying them to Brans-Dicke scalars, and their generalization in which the scalar-matter coupling slowly runs — or `walks' — as a function of the scalar field: a(phi) simeq as+bsphi. (Such couplings can arise in extra-dimensional applications, for instance.) The four observable parameters that characterize the fields external to a spherically symmetric star are the stellar radius, R, mass, M, scalar `charge', Q, and the scalar's asymptotic value, phi∞. These are subject to two relations because of the matching to the interior solution, generalizing the usual mass-radius, M(R), relation of General Relativity. Since phi∞ is common to different stars in a given region (such as a binary pulsar), all quantities can be computed locally in terms of the stellar masses. We identify how these relations depend on the microscopic scalar couplings, agreeing with earlier workers when comparisons are possible. Explicit analytical solutions are obtained for the instructive toy model of constant-density stars, whose properties we compare to more realistic equations of state for neutron star models.
Lewis, Cannada A; Valeev, Edward F
2015-01-01
Clustered Low Rank (CLR) framework for block-sparse and block-low-rank tensor representation and computation is described. The CLR framework depends on 2 parameters that control precision: one controlling the CLR block rank truncation and another that controls screening of small contributions in arithmetic operations on CLR tensors. As these parameters approach zero CLR representation and arithmetic become exact. There are no other ad-hoc heuristics, such as domains. Use of the CLR format for the order-2 and order-3 tensors that appear in the context of density fitting (DF) evaluation of the Hartree-Fock (exact) exchange significantly reduced the storage and computational complexities below their standard $\\mathcal{O}(N^3)$ and $\\mathcal{O}(N^4)$ figures. Even for relatively small systems and realistic basis sets CLR-based DF HF becomes more efficient than the standard DF approach, and significantly more efficient than the conventional non-DF HF, while negligibly affecting molecular energies and properties.
Conservation Laws and Stress-energy-momentum Tensors for Systems with Background Fields
Gratus, Jonathan; Tucker, Robin W
2012-01-01
This article attempts to delineate the roles played by non-dynamical background structures and Killing symmetries in the construction of stress-energy-momentum tensors generated from a diffeomorphism invariant action density. An intrinsic coordinate independent approach puts into perspective a number of spurious arguments that have historically lead to the main contenders, viz the Belinfante-Rosenfeld stress-energy-momentum tensor derived from a Noether current and the Einstein-Hilbert stress-energy-momentum tensor derived in the context of Einstein's theory of general relativity. Emphasis is placed on the role played by non-dynamical background (phenomenological) structures that discriminate between properties of these tensors particularly in the context of electrodynamics in media. These tensors are used to construct conservation laws in the presence of Killing Lie-symmetric background fields.
On the relative importance of second-order terms in relativistic dissipative fluid dynamics
Molnár, E; Denicol, G S; Rischke, D H
2013-01-01
In Denicol et al., Phys. Rev. D 85, 114047 (2012), the equations of motion of relativistic dissipative fluid dynamics were derived from the relativistic Boltzmann equation. These equations contain a multitude of terms of second order in Knudsen number, in inverse Reynolds number, or their product. Terms of second order in Knudsen number give rise to non-hyperbolic (and thus acausal) behavior and must be neglected in (numerical) solutions of relativistic dissipative fluid dynamics. The coefficients of the terms which are of the order of the product of Knudsen and inverse Reynolds numbers have been explicitly computed in the above reference, in the limit of a massless Boltzmann gas. Terms of second order in inverse Reynolds number arise from the collision term in the Boltzmann equation, upon expansion to second order in deviations from the single-particle distribution function in local thermodynamical equilibrium. In this work, we compute these second-order terms for a massless Boltzmann gas with constant scatt...
New Operator Ordering Formulas Related to Hermite Polynomials Derived by Virtue of IWOP Technique
FAN Hong-Yi
2004-01-01
By virtue of the technique of integration within an ordered product of operators and the fundamentaloperator identity Hn(X) = 2n : Xn :, where X is the coordinate operator and Hn is the n-order Hermite polynomials,:: is the normal ordering symbol, we not only simplify the derivation of the main properties of Hermite polynomials,but also directly derive some new operator identities regarding to Hn(X). Operation for transforming f(X) → :f(X) :is also discussed.