Local recovery of lithospheric stress tensor from GOCE gravitational tensor
Eshagh, Mehdi
2017-04-01
The sublithospheric stress due to mantle convection can be computed from gravity data and propagated through the lithosphere by solving the boundary-value problem of elasticity for the Earth's lithosphere. In this case, a full tensor of stress can be computed at any point inside this elastic layer. Here, we present mathematical foundations for recovering such a tensor from gravitational tensor measured at satellite altitudes. The mathematical relations will be much simpler in this way than the case of using gravity data as no derivative of spherical harmonics (SHs) or Legendre polynomials is involved in the expressions. Here, new relations between the SH coefficients of the stress and gravitational tensor elements are presented. Thereafter, integral equations are established from them to recover the elements of stress tensor from those of the gravitational tensor. The integrals have no closed-form kernels, but they are easy to invert and their spatial truncation errors are reducible. The integral equations are used to invert the real data of the gravity field and steady-state ocean circulation explorer mission (GOCE), in 2009 November, over the South American plate and its surroundings to recover the stress tensor at a depth of 35 km. The recovered stress fields are in good agreement with the tectonic and geological features of the area.
Electromagnetic stress tensor for an amorphous metamaterial medium
Wang, Neng; Wang, Shubo; Ng, Jack
2018-03-01
We analytically and numerically investigated the internal optical forces exerted by an electromagnetic wave inside an amorphous metamaterial medium. We derived, by using the principle of virtual work, the Helmholtz stress tensor, which takes into account the electrostriction effect. Several examples of amorphous media are considered, and different electromagnetic stress tensors, such as the Einstein-Laub tensor and Minkowski tensor, are also compared. It is concluded that the Helmholtz stress tensor is the appropriate tensor for such systems.
Magnetic hydrodynamics with asymmetric stress tensor
Billig, Yuly
2005-04-01
In this paper we study equations of magnetic hydrodynamics with a stress tensor. We interpret this system as the generalized Euler equation associated with an Abelian extension of the Lie algebra of vector fields with a nontrivial 2-cocycle. We use the Lie algebra approach to prove the energy conservation law and the conservation of cross-helicity.
Magnetic hydrodynamics with asymmetric stress tensor
Billig, Yuly
2004-01-01
In this paper we study equations of magnetic hydrodynamics with a stress tensor. We interpret this system as the generalized Euler equation associated with an abelian extension of the Lie algebra of vector fields with a non-trivial 2-cocycle. We use the Lie algebra approach to prove the energy conservation law and the conservation of cross-helicity.
Radiation Forces and Torques without Stress (Tensors)
Bohren, Craig F.
2011-01-01
To understand radiation forces and torques or to calculate them does not require invoking photon or electromagnetic field momentum transfer or stress tensors. According to continuum electromagnetic theory, forces and torques exerted by radiation are a consequence of electric and magnetic fields acting on charges and currents that the fields induce…
Theoretical study of lithium clusters by electronic stress tensor
International Nuclear Information System (INIS)
Ichikawa, Kazuhide; Nozaki, Hiroo; Komazawa, Naoya; Tachibana, Akitomo
2012-01-01
We study the electronic structure of small lithium clusters Li n (n = 2 ∼ 8) using the electronic stress tensor. We find that the three eigenvalues of the electronic stress tensor of the Li clusters are negative and degenerate, just like the stress tensor of liquid. This leads us to propose that we may characterize a metallic bond in terms of the electronic stress tensor. Our proposal is that in addition to the negativity of the three eigenvalues of the electronic stress tensor, their degeneracy characterizes some aspects of the metallic nature of chemical bonding. To quantify the degree of degeneracy, we use the differential eigenvalues of the electronic stress tensor. By comparing the Li clusters and hydrocarbon molecules, we show that the sign of the largest eigenvalue and the differential eigenvalues could be useful indices to evaluate the metallicity or covalency of a chemical bond.
Analysis and interpretation of stress indicators in deviated wells of the Coso Geothermal Field
Schoenball, Martin; Glen, Jonathan M. G.; Davatzes, Nicholas C.
2016-04-01
Characterizing the tectonic stress field is an integral part for the development of hydrothermal systems, especially enhanced geothermal systems (EGS). With a known stress field, critically stressed faults can be identified. Faults that are critically oriented with respect to the in-situ stress field exhibit a high tendency for slip, and thus are likely candidates for reactivation during the creation of an EGS. Reactivated faults are known to serve as dominant fluid pathways during hydrothermal circulation and the characteristics of this process determine the potential for damaging earthquakes; should extensive portions of well-oriented, large features be reactivated. As part of the FORGE initiative at the West Flank of the Coso Geothermal Field, we analyze a large set of image logs obtained from wells distributed across the geothermal field for details about the stress state revealed by indicators such as borehole breakouts and drilling-induced tensile fractures. Previous stress analyses at Coso have ignored deviated well sections, since their interpretation for the orientation of the stress tensor is non-unique with respect to varying stress magnitudes. Using interpreted borehole-induced structures, we perform a grid search over all possible Andersonian stress states and find a best fitting vertical stress tensor for each stress state characterized by principal stress magnitudes. By including deviated well sections and recently drilled wells, we considerably expand the suite of stress measurements in the Coso Geothermal Field. Along individual wells, this analysis also reveals local meter length-scale deviations from the best-fitting mean stress orientation. While most wells show consistent horizontal principal stress orientations with standard deviations of about 10°, other wells show large standard deviations on the order of 25°. Several regions have logged well trajectories with lateral spacing below 1 km. This enables us to trace changes of the stress
Holographic stress tensor for non-relativistic theories
International Nuclear Information System (INIS)
Ross, Simon F.; Saremi, Omid
2009-01-01
We discuss the calculation of the field theory stress tensor from the dual geometry for two recent proposals for gravity duals of non-relativistic conformal field theories. The first of these has a Schroedinger symmetry including Galilean boosts, while the second has just an anisotropic scale invariance (the Lifshitz case). For the Lifshitz case, we construct an appropriate action principle. We propose a definition of the non-relativistic stress tensor complex for the field theory as an appropriate variation of the action in both cases. In the Schroedinger case, we show that this gives physically reasonable results for a simple black hole solution and agrees with an earlier proposal to determine the stress tensor from the familiar AdS prescription. In the Lifshitz case, we solve the linearised equations of motion for a general perturbation around the background, showing that our stress tensor is finite on-shell.
Analysis and interpretation of stress indicators in deviated wells of the Coso Geothermal Field
Schoenball, Martin; Glen, Jonathan M. G.; Davatzes, Nicholas C.
2016-01-01
Characterizing the tectonic stress field is an integral part of the development of hydrothermal systems and especially for enhanced geothermal systems (EGS). With a well characterized stress field the propensity of fault slip on faults with known location and orientation can be identified. Faults that are critically oriented for faulting with respect to the stress field are known to provide natural fluid pathways. A high slip tendency makes a fault a likely candidate for reactivation during the creation of an EGS. Similarly, the stress state provides insight for the potential of larger, damaging earthquakes should extensive portions of well-oriented, larger faults be reactivated.The analysis of stress indicators such as drilling-induced fractures and borehole breakouts is the main tool to infer information on the stress state of a geothermal reservoir. The standard procedure is applicable to sub-vertical wellbore sections and highly deviated sections have to be discarded. However, in order to save costs and reduce the environmental impact most recent wells are directionally drilled with deviations that require appropriate consideration of the deviated trajectory. Here we present an analysis scheme applicable to arbitrary well trajectories or a combination of wells to infer the stress state. Through the sampling of the stress tensor along several directions additional information on the stress regime and even relative stress magnitudes can be obtained. We apply this method on image logs from the pair of wells 58-10 and 58A-10 that were drilled from the same well pad. Both wells have image logs of about 2km of their trajectories that are separated by less than 300m. For both wells we obtain a mean orientation of SHmax of N23° with large standard deviations of locations of stress indicators of 24° and 26°, respectively. While the local stress direction is highly variable along both wells with dominant wavelengths from around 50 to 500m, the mean directions are very
Lithospheric Stress Tensor from Gravity and Lithospheric Structure Models
Eshagh, Mehdi; Tenzer, Robert
2017-07-01
In this study we investigate the lithospheric stresses computed from the gravity and lithospheric structure models. The functional relation between the lithospheric stress tensor and the gravity field parameters is formulated based on solving the boundary-value problem of elasticity in order to determine the propagation of stresses inside the lithosphere, while assuming the horizontal shear stress components (computed at the base of the lithosphere) as lower boundary values for solving this problem. We further suppress the signature of global mantle flow in the stress spectrum by subtracting the long-wavelength harmonics (below the degree of 13). This numerical scheme is applied to compute the normal and shear stress tensor components globally at the Moho interface. The results reveal that most of the lithospheric stresses are accumulated along active convergent tectonic margins of oceanic subductions and along continent-to-continent tectonic plate collisions. These results indicate that, aside from a frictional drag caused by mantle convection, the largest stresses within the lithosphere are induced by subduction slab pull forces on the side of subducted lithosphere, which are coupled by slightly less pronounced stresses (on the side of overriding lithospheric plate) possibly attributed to trench suction. Our results also show the presence of (intra-plate) lithospheric loading stresses along Hawaii islands. The signature of ridge push (along divergent tectonic margins) and basal shear traction resistive forces is not clearly manifested at the investigated stress spectrum (between the degrees from 13 to 180).
Stress-tensor OPE in N=2 superconformal theories
International Nuclear Information System (INIS)
Liendo, Pedro; Ramírez, Israel; Seo, Jihye
2016-01-01
We carry out a detailed superspace analysis of the OPE of two N=2 stress-tensor multiplets. Knowledge of the multiplets appearing in the expansion, together with the two-dimensional chiral algebra description of N=2 SCFTs, imply an analytic bound on the central charge c. This bound is valid for any N=2 SCFT regardless of its matter content and flavor symmetries, and is saturated by the simplest Argyres-Douglas fixed point. We also present a partial conformal block analysis for the scalar superconformal primary of the multiplet.
Quantum stress tensor in Schwarzschild space-time
International Nuclear Information System (INIS)
Howard, K.W.; Candelas, P.
1984-01-01
The vacuum expectation value of the stress-energy tensor for the Hartle-Hawking state in Schwartzschild space-time has been calculated for the conformal scalar field. separates naturally into the sum of two terms. The first coincides with an approximate expression suggested by Page. The second term is a ''remainder'' that may be evaluated numerically. The total expression is in good qualitative agreement with Page's approximation. These results are at variance with earlier results given by Fawcett whose error is explained
Gravity waves from quantum stress tensor fluctuations in inflation
International Nuclear Information System (INIS)
Wu, Chun-Hsien; Hsiang, Jen-Tsung; Ford, L. H.; Ng, Kin-Wang
2011-01-01
We consider the effects of the quantum stress tensor fluctuations of a conformal field in generating gravity waves in inflationary models. We find a nonscale invariant, non-Gaussian contribution which depends upon the total expansion factor between an initial time and the end of inflation. This spectrum of gravity wave perturbations is an illustration of a negative power spectrum, which is possible in quantum field theory. We discuss possible choices for the initial conditions. If the initial time is taken to be sufficiently early, the fluctuating gravity waves are potentially observable both in the CMB radiation and in gravity wave detectors, and could offer a probe of trans-Planckian physics. The fact that they have not yet been observed might be used to constrain the duration and energy scale of inflation. However, this conclusion is contingent upon including the contribution of modes which were trans-Planckian at the beginning of inflation.
Gravity waves from quantum stress tensor fluctuations in inflation
Wu, Chun-Hsien; Hsiang, Jen-Tsung; Ford, L. H.; Ng, Kin-Wang
2011-11-01
We consider the effects of the quantum stress tensor fluctuations of a conformal field in generating gravity waves in inflationary models. We find a nonscale invariant, non-Gaussian contribution which depends upon the total expansion factor between an initial time and the end of inflation. This spectrum of gravity wave perturbations is an illustration of a negative power spectrum, which is possible in quantum field theory. We discuss possible choices for the initial conditions. If the initial time is taken to be sufficiently early, the fluctuating gravity waves are potentially observable both in the CMB radiation and in gravity wave detectors, and could offer a probe of trans-Planckian physics. The fact that they have not yet been observed might be used to constrain the duration and energy scale of inflation. However, this conclusion is contingent upon including the contribution of modes which were trans-Planckian at the beginning of inflation.
Stress-energy tensors for vector fields outside a static black hole
International Nuclear Information System (INIS)
Barrios, F.A.; Vaz, C.
1989-01-01
We obtain new, approximate stress-energy tensors to describe gauge fields in the neighborhood of a Schwarzschild black hole. We assume that the coefficient of ∇ 2 R in the trace anomaly is correctly given by ζ-function regularization. Our approximation differs from that of Page and of Brown and Ottewill and relies upon a new, improved ansatz for the form of the stress-energy tensor in the ultrastatic optical metric of the black hole. The Israel-Hartle-Hawking thermal tensor is constructed to be regular on the horizon and possess the correct asymptotic behavior. Our approximation of Unruh's tensor is likewise constructed to be regular on the future horizon and exhibit a luminosity which agrees with Page's numerically obtained value. Geometric expressions for the approximate tensors are given, and the approximate energy density of the thermal tensor on the horizon is compared with recent numerical estimates
Effect of stress on energy flux deviation of ultrasonic waves in GR/EP composites
Prosser, William H.; Kriz, R. D.; Fitting, Dale W.
1990-01-01
Ultrasonic waves suffer energy flux deviation in graphite/epoxy because of the large anisotropy. The angle of deviation is a function of the elastic coefficients. For nonlinear solids, these coefficients and thus the angle of deviation is a function of stress. Acoustoelastic theory was used to model the effect of stress on flux deviation for unidirectional T300/5208 using previously measured elastic coefficients. Computations were made for uniaxial stress along the x3 axis (fiber axis) and the x1 for waves propagating in the x1x3 plane. These results predict a shift as large as three degrees for the quasi-transverse wave. The shift in energy flux offers a new nondestructive technique of evaluating stress in composites.
Stress tensor computations at Mount St. Helens (1995-1998
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S. Gresta
2000-06-01
Full Text Available Fault plane solutions of 459 events occurring between 1995 and 1998 at Mount St. Helens (State of Washington, Northwest U.S.A. were considered in order to infer the state of stress beneath the volcano. These events occurred in two distinct depth zones. The shallower zone is between 2 and 5.5 km, with shocks clustering in a tight cylindrical distribution about 1 km in radius directly beneath the crater. The deeper events are spread over a larger volume from 5.5 to 10 km depth and surround an aseismic zone below and slightly west of the lava dome. Faulting is characterized by a mixture of strike-slip, reverse and normal faults with maximum compression axes which do not cluster around a single direction. In the deep zone, between 5.5 and 10 km, P axes define a wheel-spoke pattern pointing radially away from the center of the aseismic zone. The 459 fault plane solutions were inverted for stress tensor parameters using the algorithm of Gephart and Forsyth. The inversion of the whole data set revealed that faulting was not produced by a uniform stress distribution. The subdivision of the zone into smaller volumes significantly reduced misfit and confidence areas of the solutions, whereas temporal subdivision of the sample did not lead to significant improvements in terms of stress uniformity. We suggest that the inhomogeneous stress field is consistent with a varying pressure source originating from the inferred crustal magma chamber and a thin conduit extending above it.
Realizability conditions for the turbulent stress tensor in large-eddy simulation
Vreman, A.W.; Geurts, Bernardus J.; Kuerten, Johannes G.M.
1994-01-01
The turbulent stress tensor in large-eddy simulation is examined from a theoretical point of view. Realizability conditions for the components of this tensor are derived, which hold if and only if the filter function is positive. The spectral cut-off, one of the filters frequently used in large-eddy
Characteristics of the Residual Stress tensor when filter width is larger than the Ozmidov scale
de Bragança Alves, Felipe Augusto; de Bruyn Kops, Stephen
2017-11-01
In stratified turbulence, the residual stress tensor is statistically anisotropic unless the smallest resolved length scale is smaller than the Ozmidov scale and the buoyancy Reynolds number is sufficiently high for there to exist a range of scales that is statistically isotropic. We present approximations to the residual stress tensor that are derived analytically. These approximations are evaluated by filtering data from direct numerical simulations of homogeneous stratified turbulence, with unity Prandtl number, resolved on up to 8192 × 8192 × 4096 grid points along with an isotropic homogeneous case resolved on 81923 grid points. It is found that the best possible scaling of the strain rate tensor yields a residual stress tensor (RST) that is less well statistically aligned with the exact RST than a randomly generated tensor. It is also found that, while a scaling of the strain rate tensor can dissipate the right amount of energy, it produces incorrect anisotropic dissipation, removing energy from the wrong components of the velocity vector. We find that a combination of the strain rate tensor and a tensor related to energy redistribution caused by a Newtonian fluid viscous stress yields an excellent tensorial basis for modelling the RST.
Membrane stress tensor in the presence of lipid density and composition inhomogeneities.
Bitbol, A-F; Peliti, L; Fournier, J-B
2011-05-01
We derive the expression of the stress tensor for one- and two-component lipid membranes with density and composition inhomogeneities. We first express the membrane stress tensor as a function of the free-energy density by means of the principle of virtual work. We then apply this general result to a monolayer model which is shown to be a local version of the area-difference elasticity (ADE) model. The resulting stress tensor expression generalizes the one associated with the Helfrich model, and can be specialized to obtain the one associated with the ADE model. Our stress tensor directly gives the force exchanged through a boundary in a monolayer with density and composition inhomogeneities. Besides, it yields the force density, which is also directly obtained in covariant formalism. We apply our results to study the forces induced in a membrane by a local perturbation.
Study of the characteristics of crust stress field in East China by inversion of stress tensor
International Nuclear Information System (INIS)
Huilan, Z.; Rugang, D.
1991-12-01
This paper combines the search procedure with the optimization procedure to inverse the average stress tensor, and applies this method to study the crustal stress field using data of the solution of P wave first motion. By dealing with the data of Haicheng, Tangshan, Xingtai, Anyang, Liyang, Taiwan, Fujian and Guangdong areas, we obtain the characteristics of crust stress field of East China. The directions of the principal pressure stress always possess a small dip angle, but the azimuths vary from NEE (in north part of East China) to SEE (in the south part). This frame probably is related to the push-extrusive effects of the northwestern Pacific plate from NEE and the Philippine plate from SEE. (author). 5 refs, 8 figs, 4 tabs
International Nuclear Information System (INIS)
Glowka, D.A.
1990-09-01
This report investigates the effects of borehole deviation on the useability of lined boreholes for the disposal of high-level nuclear waste at the proposed Yucca Mountain Repository in Nevada. Items that lead to constraints on borehole deviation include excessive stresses that could cause liner failure and possible binding of a waste container inside the liner during waste emplacement and retrieval operations. Liner stress models are developed for two general borehole configurations, one for boreholes drilled with a steerable bit and one for boreholes drilled with a non-steerable bit. Procedures are developed for calculating liner stresses that arise both during insertion of the liner into a borehole and during the thermal expansion process that follows waste emplacement. The effects of borehole curvature on the ability of the waste container to pass freely inside the liner without binding are also examined. Based on the results, specifications on borehole deviation allowances are developed for specific vertical and horizontal borehole configurations of current interest. 11 refs., 22 figs., 4 tabs
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.
Beijeren, H. van
1984-01-01
It is conjectured that the large values at intermediate times of the stress tensor autocorrelation function, found in computer simulations, may be caused by a coupling of the stress tensor to pairs of slowly decaying extended heat modes of large wave number. Approximate expressions, amenable to
Coupled ADCPs can yield complete Reynolds stress tensor profiles in geophysical surface flows
Vermeulen, B.; Hoitink, A.J.F.; Sassi, M.G.
2011-01-01
We introduce a new technique to measure profiles of each term in the Reynolds stress tensor using coupled acoustic Doppler current profilers (ADCPs). The technique is based on the variance method which is extended to the case with eight acoustic beams. Methods to analyze turbulence from a single
Electromagnetic energy density and stress tensor in a warm plasma with finite flow velocity
International Nuclear Information System (INIS)
Choi, Cheong R.; Lee, Nam C.
2004-01-01
The expressions of the average of energy density and the average stress tensor of the electromagnetic field in a warm collisionless plasma moving with a finite velocity are obtained by using a microscopic method that uses the fluid description of plasma. The result contains terms involved with derivatives of the dielectric tensor with respect to the velocity, which explicitly represent the effects of the finite velocity of the medium. In the zero-velocity limit, the results reduce to the well-known expressions for a plasma at rest with temporal and spatial dispersion
The existence of a symmetric stress tensor in a non-local description of continuum mechanics
Schwarz, G.
1993-12-01
Among the foundations of continuum mechanics is the description of the constitutive forces in terms of a symmetric tensor. Noll showed that this is a consequence of the axiom of material frame indifference, what in turn means a local invariance of the system under the Euclidean group. Here we will prove, in order to obtain the same result, that the assumption of locality in this axiom is redundant. We model a non-local system by means of a virtual work principle. Under the global demand that the corresponding functional does not respond on rigid infinitesimal motions, we show the existence of a symmetric stress tensor as a local result.
Prosser, William H.; Kriz, R. D.; Fitting, Dale W.
1990-01-01
Ultrasonic waves suffer energy flux deviation in graphite/epoxy because of the large anisotropy. The angle of deviation is a function of the elastic coefficients. For nonlinear solids, these coefficients and thus the angle of deviation is a function of stress. Acoustoelastic theory was used to model the effect of stress on flux deviation for unidirectional T300/5208 using previously measured elastic coefficients. Computations were made for uniaxial stress along the x3 axis fiber axis) and the x1 axis for waves propagating in the x1x3 plane. These results predict a shift as large as three degrees for the quasi-transverse wave. The shift in energy flux offers new nondestructive technique of evaluating stress in composites.
Four-point correlation function of stress-energy tensors in N=4 superconformal theories
Korchemsky, G P
2015-01-01
We derive the explicit expression for the four-point correlation function of stress-energy tensors in four-dimensional N=4 superconformal theory. We show that it has a remarkably simple and suggestive form allowing us to predict a large class of four-point correlation functions involving the stress-energy tensor and other conserved currents. We then apply the obtained results on the correlation functions to computing the energy-energy correlations, which measure the flow of energy in the final states created from the vacuum by a source. We demonstrate that they are given by a universal function independent of the choice of the source. Our analysis relies only on N=4 superconformal symmetry and does not use the dynamics of the theory.
International Nuclear Information System (INIS)
Iwanicki, T.; Maurer, W.; Heinz, W.
1983-01-01
For the calculation of mechanical properties of large magnet systems in 3-dimensional space, a very fine subdivision of the magnet structure is necessary. In the finite element programmes, this will lead to unacceptable long computing times and to the limits of computer-storage capacity. This limitation requires a simplification of the structure model. This problem can be solved by the numerical method, called ''numerical simulation'', by which an effective elasticity tensor will be obtained for a composite material. The structure has to perform a homogeneity condition, i.e. it must be possible to define a ''representative volume element'' (RVE). With the effective elasticity tensor, which can be found for such RVE, it is possible to calculate the average stress and with the interpolation of a surface displacement also the peak stresses in each point of the structure. A good agreement is found between experimental and theoretical moduli of elasticity. (author)
Stress-energy tensor of quantized massive fields in static wormhole spacetimes
Kocuper, Ewa; Matyjasek, Jerzy; Zwierzchowska, Kasia
2017-11-01
In order to be traversable, the static Lorentzian wormhole must be made out of some exotic matter that violates the weak energy condition. The quantized fields are the natural candidates as their stress-energy tensor, in many cases, possesses desired properties. In this paper we construct and examine the stress-energy tensor of the quantized massive scalar, spinor and vector fields in six static wormhole spacetimes. We find that in all considered cases the quantum fields violate the Morris-Thorne conditions and do not have the form necessary to support the wormhole throat. This is in concord with the previous results and indicates that the massive quantum fields make the wormholes less operable.
Quantum stress tensor fluctuations of a conformal field and inflationary cosmology
International Nuclear Information System (INIS)
Ford, L. H.; Miao, S. P.; Ng, Kin-Wang; Woodard, R. P.; Wu, C.-H.
2010-01-01
We discuss the additional perturbation introduced during inflation by quantum stress tensor fluctuations of a conformally invariant field such as the photon. We consider both a kinematical model, which deals only with the expansion fluctuations of geodesics, and a dynamical model which treats the coupling of the stress tensor fluctuations to a scalar inflaton. In neither model do we find any growth at late times, in accordance with a theorem due to Weinberg. What we find instead is a correction which becomes larger the earlier one starts inflation. This correction is non-Gaussian and highly scale dependent, so the absence of such effects from the observed power spectra may imply a constraint on the total duration of inflation. We discuss different views about the validity of perturbation theory at very early times during which currently observable modes are trans-Planckian.
Vacuum stress tensor of a scalar field in a rectangular waveguide
International Nuclear Information System (INIS)
Rodrigues, R.B.; Svaiter, N.F.; Paola, R.D.M. de
2001-11-01
Using the heat Kernel method and the analytical continuation of the zeta function, we calculate the canonical and improved vacuum stress tensors, {T μν (vector x)} and {Θ μν (vector x)}, associated with a massless scalar field confined in the interior of an infinity long rectangular waveguide. The local depence of the renormalized energy for two special configurations when the total energy is positive and negative are presented using {T 00 (vector x)} and {Θ 00 (vector x)}. From the stress tensors we obtain the local casimir forces in all walls by introducing a particular external configuration. It is hown that this external configuration cannot give account of the edge divergences of the local forces. The local form of the forces is obtained for three special configurations. (author)
Stress tensor correlators of CCFT{sub 2} using flat-space holography
Energy Technology Data Exchange (ETDEWEB)
Asadi, Mohammad; Baghchesaraei, Omid; Fareghbal, Reza [Shahid Beheshti University, Department of Physics, Tehran (Iran, Islamic Republic of)
2017-11-15
We use the correspondence between three-dimensional asymptotically flat spacetimes and two-dimensional contracted conformal field theories (CCFTs) to derive the stress tensor correlators of CCFT{sub 2}. On the gravity side we use the metric formulation instead of the Chern-Simons formulation of three-dimensional gravity. This method can also be used for the four-dimensional case, where there is no Chern-Simons formulation for the bulk theory. (orig.)
The stress-energy tensor of flavor fields from AdS/CFT
Karch, Andreas; O'Bannon, Andy; Thompson, Ethan
2009-04-01
We use the AdS/CFT correspondence to study the transport properties of massive Script N = 2 hypermultiplet fields in an Script N = 4 SU(Nc) super-Yang-Mills theory plasma in the large Nc, large 't Hooft coupling limit, and in the presence of a baryon number chemical potential and external electric and magnetic fields. In particular, we compute the flavor fields' contribution to the stress-energy tensor. We find infrared divergences in the stress-energy tensor, arising from the flavor fields' constant rate of energy and momentum loss. We regulate these divergences and extract the energy and momentum loss rates from the divergent terms. We also check our result in various limits in which the divergences are absent. The supergravity dual is a system of D7-branes, with a particular configuration of worldvolume fields, probing an AdS-Schwarzschild background. The supergravity calculation amounts to computing the stress-energy tensor of the D7-branes.
International Nuclear Information System (INIS)
Adler, S.L.; Lieberman, J.
1978-01-01
We reanalyze the problem of regularization of the stress-energy tensor for massless vector particles propating in a general background metric, using covariant point separation techniques applied to the Hadamard elementary solution. We correct an error, point out by Wald, in the earlier formulation of Adler, Lieberman, and Ng, and find a stress-energy tensor trace anomaly agreeing with that found by other regularization methods
Radiative processes for Rindler and accelerating observers and the stress-tensor detector
International Nuclear Information System (INIS)
Paola, R. De; Svaiter, N.F.
1996-04-01
It is considered a monopole detector interacting with a massive scalar field. Using the rotating wave approximation the radiative processes is discussed from the accelerated frame point of view. After this, it is obtained the Minkowski vacuum stress tensor measured by the accelerated observer using a non-gravitational stress sensor detector. Finally we analyse radiative processes of the monopole detector travelling in a world line that is inertial in the infinite past and has a constant proper acceleration in the infinite future. (author). 30 refs
Directory of Open Access Journals (Sweden)
Yugov Anatoliy Mikhaylovich
2017-11-01
Full Text Available Subject: In this article we review and analyze structural forms and methods for accounting for deviations in metal roof structures. The article also reviews and analyzes previously performed works and methods for accounting for deviations in the design of metal structures. Research objectives: analysis of deviation values and mounting stress-strain state (MSSS of the transverse diaphragm of a single-chord hinge-rod metal shell. A comparative calculation of deviations and calculation results analysis was made on the example of a transverse diaphragm of a single-chord hinge-rod metal shell of the roof structure for different technological assembly-mounting schemes: from the supports to the arch center, and vice versa, from the arch center to its supports. Materials and methods: geometrical method for determining deviations is implemented in the the author’s computer program - computing complex of dimensional analysis (CP CCDA; method of finite elements (FEM is used for determining mounting stress-strain state and is implemented in SCAD 11.5. Results: The calculation and analysis of the mounting stress-strain state (MSSS of the diaphragm was performed. Out of two assembly schemes considered in the paper we recommend the second technological scheme of assembly-mounting and also possible ways of compensation for the assembly deviations in the end diaphragm of the cylindrical roof structure of the hangar. We suggest possible options for modeling deviations of individual members of rod systems for several types of profiles and we propose possible cross sections of diaphragms of arched roof structures. Conclusions: the methodology for determining the installation deviations and the method for determining the MSSS, proposed in this article, can be used to determine deviations in a variety of large-span hinge-rod metal structures.
Milton, Kimball A.; Fulling, Stephen A.; Parashar, Prachi; Kalauni, Pushpa; Murphy, Taylor
2016-04-01
Motivated by a desire to understand quantum fluctuation energy densities and stress within a spatially varying dielectric medium, we examine the vacuum expectation value for the stress tensor of a scalar field with arbitrary conformal parameter, in the background of a given potential that depends on only one spatial coordinate. We regulate the expressions by incorporating a temporal-spatial cutoff in the (imaginary) time and transverse-spatial directions. The divergences are captured by the zeroth- and second-order WKB approximations. Then the stress tensor is "renormalized" by omitting the terms that depend on the cutoff. The ambiguities that inevitably arise in this procedure are both duly noted and restricted by imposing certain physical conditions; one result is that the renormalized stress tensor exhibits the expected trace anomaly. The renormalized stress tensor exhibits no pressure anomaly, in that the principle of virtual work is satisfied for motions in a transverse direction. We then consider a potential that defines a wall, a one-dimensional potential that vanishes for z 0 , for z >0 . Previously, the stress tensor had been computed outside of the wall, whereas now we compute all components of the stress tensor in the interior of the wall. The full finite stress tensor is computed numerically for the two cases where explicit solutions to the differential equation are available, α =1 and 2. The energy density exhibits an inverse linear divergence as the boundary is approached from the inside for a linear potential, and a logarithmic divergence for a quadratic potential. Finally, the interaction between two such walls is computed, and it is shown that the attractive Casimir pressure between the two walls also satisfies the principle of virtual work (i.e., the pressure equals the negative derivative of the energy with respect to the distance between the walls).
Reduced Stress Tensor and Dissipation and the Transport of Lamb Vector
Wu, Jie-Zhi; Zhou, Ye; Wu, Jian-Ming
1996-01-01
We develop a methodology to ensure that the stress tensor, regardless of its number of independent components, can be reduced to an exactly equivalent one which has the same number of independent components as the surface force. It is applicable to the momentum balance if the shear viscosity is constant. A direct application of this method to the energy balance also leads to a reduction of the dissipation rate of kinetic energy. Following this procedure, significant saving in analysis and computation may be achieved. For turbulent flows, this strategy immediately implies that a given Reynolds stress model can always be replaced by a reduced one before putting it into computation. Furthermore, we show how the modeling of Reynolds stress tensor can be reduced to that of the mean turbulent Lamb vector alone, which is much simpler. As a first step of this alternative modeling development, we derive the governing equations for the Lamb vector and its square. These equations form a basis of new second-order closure schemes and, we believe, should be favorably compared to that of traditional Reynolds stress transport equation.
Quantum fields interacting with colliding plane waves: the stress-energy tensor and backreaction
International Nuclear Information System (INIS)
Dorca, M.; Verdaguer, E.
1997-01-01
Following a previous work on the quantization of a massless scalar field in a space-time representing the head on collision of two plane waves which focus into a Killing-Cauchy horizon, we compute the renormalized expectation value of the stress-energy tensor of the quantum field near that horizon in the physical state which corresponds to the Minkowski vacuum before the collision of the waves. It is found that for minimally coupled and conformally coupled scalar fields the respective stress-energy tensors are unbounded in the horizon. The specific form of the divergences suggests that when the semiclassical Einstein equations describing the backreaction of the quantum fields on the space-time geometry are taken into account, the horizon will acquire a curvature singularity. Thus the Killing-Cauchy horizon which is known to be unstable under ''generic'' classical perturbations is also unstable by vacuum polarization. The calculation is done following the point-splitting regularization technique. The dynamical colliding wave space-time has four quite distinct space-time regions, namely, one flat region, two single plane wave regions, and one interaction region. Exact mode solutions of the quantum field equation cannot be found exactly, but the blueshift suffered by the initial modes in the plane wave and interaction regions makes the use of the WKB expansion a suitable method of solution. To ensure the correct regularization of the stress-energy tensor, the initial flat modes propagated into the interaction region must be given to a rather high adiabatic order of approximation. (orig.)
TensorLy: Tensor Learning in Python
Kossaifi, Jean; Panagakis, Yannis; Pantic, Maja
2016-01-01
Tensor methods are gaining increasing traction in machine learning. However, there are scant to no resources available to perform tensor learning and decomposition in Python. To answer this need we developed TensorLy. TensorLy is a state of the art general purpose library for tensor learning.
Energy Technology Data Exchange (ETDEWEB)
Glowka, D.A.
1990-09-01
This report investigates the effects of borehole deviation on the useability of lined boreholes for the disposal of high-level nuclear waste at the proposed Yucca Mountain Repository in Nevada. Items that lead to constraints on borehole deviation include excessive stresses that could cause liner failure and possible binding of a waste container inside the liner during waste emplacement and retrieval operations. Liner stress models are developed for two general borehole configurations, one for boreholes drilled with a steerable bit and one for boreholes drilled with a non-steerable bit. Procedures are developed for calculating liner stresses that arise both during insertion of the liner into a borehole and during the thermal expansion process that follows waste emplacement. The effects of borehole curvature on the ability of the waste container to pass freely inside the liner without binding are also examined. Based on the results, specifications on borehole deviation allowances are developed for specific vertical and horizontal borehole configurations of current interest. 11 refs., 22 figs., 4 tabs.
Renormalized Stress-Energy Tensor of an Evaporating Spinning Black Hole.
Levi, Adam; Eilon, Ehud; Ori, Amos; van de Meent, Maarten
2017-04-07
We provide the first calculation of the renormalized stress-energy tensor (RSET) of a quantum field in Kerr spacetime (describing a stationary spinning black hole). More specifically, we employ a recently developed mode-sum regularization method to compute the RSET of a minimally coupled massless scalar field in the Unruh vacuum state, the quantum state corresponding to an evaporating black hole. The computation is done here for the case a=0.7M, using two different variants of the method: t splitting and φ splitting, yielding good agreement between the two (in the domain where both are applicable). We briefly discuss possible implications of the results for computing semiclassical corrections to certain quantities, and also for simulating dynamical evaporation of a spinning black hole.
Correlation functions of the chiral stress-tensor multiplet in $ \\mathcal{N}=4 $ SYM
Chicherin, Dmitry; Eden, Burkhard; Heslop, Paul; Korchemsky, Gregory P.; Mason, Lionel; Sokatchev, Emery
2015-01-01
We give a new method for computing the correlation functions of the chiral part of the stress-tensor supermultiplet that relies on the reformulation of N=4 SYM in twistor space. It yields the correlation functions in the Born approximation as a sum of Feynman diagrams on twistor space that involve only propagators and no integration vertices. We use this unusual feature of the twistor Feynman rules to compute the correlation functions in terms of simple building blocks which we identify as a new class of N=4 off-shell superconformal invariants. Making use of the duality between correlation functions and planar scattering amplitudes, we demonstrate that these invariants represent an off-shell generalisation of the on-shell invariants defining tree-level scattering amplitudes in N=4 SYM.
Correlation functions of the chiral stress-tensor multiplet in N=4 SYM
Energy Technology Data Exchange (ETDEWEB)
Chicherin, Dmitry [LAPTH (Laboratoire d’Annecy-le-Vieux de Physique Théorique, UMR 5108),Université de Savoie, CNRS, B.P. 110, F-74941 Annecy-le-Vieux (France); Doobary, Reza [Science Laboratories, Mathematics Department, Durham University, South Rd, Durham DH1 3LE (United Kingdom); Eden, Burkhard [Institut für Mathematik und Physik, Humboldt-Universität,Zum großen Windkanal 6, 12489 Berlin (Germany); Heslop, Paul [Science Laboratories, Mathematics Department, Durham University, South Rd, Durham DH1 3LE (United Kingdom); Korchemsky, Gregory P. [Institut de Physique Théorique, Unité Mixte de Recherche du CNRS, UMR 3681,CEA Saclay, 91191 Gif-sur-Yvette Cedex (France); Mason, Lionel [Mathematics Department, Oxford University,Woodstock Road, OX2 6GG (United Kingdom); Sokatchev, Emery [LAPTH (Laboratoire d’Annecy-le-Vieux de Physique Théorique, UMR 5108),Université de Savoie, CNRS, B.P. 110, F-74941 Annecy-le-Vieux (France); Physics Department, Theory Unit, CERN,CH -1211, Geneva 23 (Switzerland); Institut Universitaire de France,103, bd Saint-Michel F-75005 Paris (France)
2015-06-29
We give a new method for computing the correlation functions of the chiral part of the stress-tensor supermultiplet that relies on the reformulation of N=4 SYM in twistor space. It yields the correlation functions in the Born approximation as a sum of Feynman diagrams on twistor space that involve only propagators and no integration vertices. We use this unusual feature of the twistor Feynman rules to compute the correlation functions in terms of simple building blocks which we identify as a new class of N=4 off-shell superconformal invariants. Making use of the duality between correlation functions and planar scattering amplitudes, we demonstrate that these invariants represent an off-shell generalisation of the on-shell invariants defining tree-level scattering amplitudes in N=4 SYM.
Jongschaap, R.J.J.
1987-01-01
The so-called generalized Kramers-Kirkwood expression for the average stress tensor of a system of interacting point particles, derived by Bird and Curtiss on using a phase-space-kinetic formalism has been reconsidered from different points of view. First a derivation based upon volume averaging is
International Nuclear Information System (INIS)
Christensen, S.M.
1976-01-01
A method known as covariant geodesic point separation is developed to calculate the vacuum expectation value of the stress tensor for a massive scalar field in an arbitrary gravitational field. The vacuum expectation value will diverge because the stress-tensor operator is constructed from products of field operators evaluated at the same space-time point. To remedy this problem, one of the field operators is taken to a nearby point. The resultant vacuum expectation value is finite and may be expressed in terms of the Hadamard elementary function. This function is calculated using a curved-space generalization of Schwinger's proper-time method for calculating the Feynman Green's function. The expression for the Hadamard function is written in terms of the biscalar of geodetic interval which gives a measure of the square of the geodesic distance between the separated points. Next, using a covariant expansion in terms of the tangent to the geodesic, the stress tensor may be expanded in powers of the length of the geodesic. Covariant expressions for each divergent term and for certain terms in the finite portion of the vacuum expectation value of the stress tensor are found. The properties, uses, and limitations of the results are discussed
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...
Stress tensor and viscosity of water: Molecular dynamics and generalized hydrodynamics results
Bertolini, Davide; Tani, Alessandro
1995-08-01
The time correlation functions (CF's) of diagonal and off-diagonal components of the stress tensor of water have been calculated at 245 and 298 K in a molecular dynamics (MD) study on 343 molecules in the microcanonical ensemble. We present results obtained at wave number k=0 and at a few finite values of k, in the atomic and molecular formalism. In all cases, more than 98% of these functions are due to the potential term of the stress tensor. At k=0, their main features are a fast oscillatory initial decay, followed by a long-time tail more apparent in the supercooled region. Bulk and shear viscosities, calculated via Green-Kubo integration of the relevant CF at k=0, are underestimated with respect to experimental data, mainly at low temperature, but their ratio (~=2) is correctly reproduced. Both shear and bulk viscosity decrease as a function of k, the latter more rapidly, so that they become almost equal at ~=1 Å-1. Also, both viscosities drop rapidly from their maximum at ω=0. This behavior has been related to the large narrowing observed in the acoustic band, mainly in the supercooled region. The infinite frequency bulk and shear rigidity moduli have been shown to be in fair agreement with the experimental data, provided the MD value used for comparison is that corresponding to the frequency range relevant to ultrasonic measurements. The MD results of stress-stress CF's compare well with those predicted by Bertolini and Tani [Phys. Rev. E 51, 1091 (1995)] at k=0, by an application of generalized hydrodynamics [de Schepper et al., Phys. Rev. A 38, 271 (1988)] in the molecular formalism, to the same model of water (TIP4P) [Jorgensen et al., J. Chem. Phys. 79, 926 (1983)]. These CF's are essentially equal in the atomic and molecular formalism, the only minor difference being restricted to the high frequency librational region of the shear function. By a comparison of atomic and molecular results, we show here that neglecting libration has no effect on the
Boundary stress-energy tensor and Newton-Cartan geometry in Lifshitz holography
International Nuclear Information System (INIS)
Christensen, Morten H.; Hartong, Jelle; Obers, Niels A.; Rollier, Blaise
2014-01-01
For a specific action supporting z=2 Lifshitz geometries we identify the Lifshitz UV completion by solving for the most general solution near the Lifshitz boundary. We identify all the sources as leading components of bulk fields which requires a vielbein formalism. This includes two linear combinations of the bulk gauge field and timelike vielbein where one asymptotes to the boundary timelike vielbein and the other to the boundary gauge field. The geometry induced from the bulk onto the boundary is a novel extension of Newton-Cartan geometry that we call torsional Newton-Cartan (TNC) geometry. There is a constraint on the sources but its pairing with a Ward identity allows one to reduce the variation of the on-shell action to unconstrained sources. We compute all the vevs along with their Ward identities and derive conditions for the boundary theory to admit conserved currents obtained by contracting the boundary stress-energy tensor with a TNC analogue of a conformal Killing vector. We also obtain the anisotropic Weyl anomaly that takes the form of a Hořava-Lifshitz action defined on a TNC geometry. The Fefferman-Graham expansion contains a free function that does not appear in the variation of the on-shell action. We show that this is related to an irrelevant deformation that selects between two different UV completions
On the equivalence among stress tensors in a gauge-fluid system
Mitra, Arpan Krishna; Banerjee, Rabin; Ghosh, Subir
2017-12-01
In this paper, we bring out the subtleties involved in the study of a first-order relativistic field theory with auxiliary field variables playing an essential role. In particular, we discuss the nonisentropic Eulerian (or Hamiltonian) fluid model. Interactions are introduced by coupling the fluid to a dynamical Maxwell (U(1)) gauge field. This dynamical nature of the gauge field is crucial in showing the equivalence, on the physical subspace, of the stress tensor derived from two definitions, i.e. the canonical (Noether) one and the symmetric one. In the conventional equal-time formalism, we have shown that the generators of the space-time transformations obtained from these two definitions agree modulo the Gauss constraint. This equivalence in the physical sector has been achieved only because of the dynamical nature of the gauge fields. Subsequently, we have explicitly demonstrated the validity of the Schwinger condition. A detailed analysis of the model in lightcone formalism has also been done where several interesting features are revealed.
International Nuclear Information System (INIS)
Dappiagi, Claudio; Hack, Thomas-Paul; Pinamonti, Nicola
2009-03-01
We discuss from scratch the classical structure of Dirac spinors on an arbitrary globally hyperbolic, Lorentzian spacetime, their formulation as a locally covariant quantum field theory, and the associated notion of a Hadamard state. Eventually, we develop the notion of Wick polynomials for spinor fields, and we employ the latter to construct a covariantly conserved stress-energy tensor suited for back-reaction computations. We explicitly calculate its trace anomaly in particular. (orig.)
Levashov, V A
2016-03-07
It is possible to associate with every atom or molecule in a liquid its own atomic stress tensor. These atomic stress tensors can be used to describe liquids' structures and to investigate the connection between structural and dynamic properties. In particular, atomic stresses allow to address atomic scale correlations relevant to the Green-Kubo expression for viscosity. Previously correlations between the atomic stresses of different atoms were studied using the Cartesian representation of the stress tensors or the representation based on spherical harmonics. In this paper we address structural correlations in a 3D model binary liquid using the eigenvalues and eigenvectors of the atomic stress tensors. This approach allows to interpret correlations relevant to the Green-Kubo expression for viscosity in a simple geometric way. On decrease of temperature the changes in the relevant stress correlation function between different atoms are significantly more pronounced than the changes in the pair density function. We demonstrate that this behaviour originates from the orientational correlations between the eigenvectors of the atomic stress tensors. We also found correlations between the eigenvalues of the same atomic stress tensor. For the studied system, with purely repulsive interactions between the particles, the eigenvalues of every atomic stress tensor are positive and they can be ordered: λ1 ≥ λ2 ≥ λ3 ≥ 0. We found that, for the particles of a given type, the probability distributions of the ratios (λ2/λ1) and (λ3/λ2) are essentially identical to each other in the liquids state. We also found that λ2 tends to be equal to the geometric average of λ1 and λ3. In our view, correlations between the eigenvalues may represent "the Poisson ratio effect" at the atomic scale.
Varadhan, S R S
2016-01-01
The theory of large deviations deals with rates at which probabilities of certain events decay as a natural parameter in the problem varies. This book, which is based on a graduate course on large deviations at the Courant Institute, focuses on three concrete sets of examples: (i) diffusions with small noise and the exit problem, (ii) large time behavior of Markov processes and their connection to the Feynman-Kac formula and the related large deviation behavior of the number of distinct sites visited by a random walk, and (iii) interacting particle systems, their scaling limits, and large deviations from their expected limits. For the most part the examples are worked out in detail, and in the process the subject of large deviations is developed. The book will give the reader a flavor of how large deviation theory can help in problems that are not posed directly in terms of large deviations. The reader is assumed to have some familiarity with probability, Markov processes, and interacting particle systems.
Hollander, Frank den
2008-01-01
This book is an introduction to the theory and applications of large deviations, a branch of probability theory that describes the probability of rare events in terms of variational problems. By focusing the theory, in Part A of the book, on random sequences, the author succeeds in conveying the main ideas behind large deviations without a need for technicalities, thus providing a concise and accessible entry to this challenging and captivating subject. The selection of modern applications, described in Part B of the book, offers a good sample of what large deviation theory is able to achieve
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.
Jenkins, Samantha; Blancafort, Lluís; Kirk, Steven R; Bearpark, Michael J
2014-04-21
New insights into the double bond isomerization of fulvene in the ground and excited electronic states are provided by newly developed QTAIM and stress tensor tools. The S0 and S1 states follow the 'biradical' torsion model, but the double bond is stiffer in the S0 state; by contrast, the S2 state follows the 'zwitterionic' torsion. Differences are explained in terms of the ellipticity and bond critical point (BCP) stiffness for both QTAIM and the stress tensor. Overall, the wave-function based analysis is found to be in agreement with the work of Bonačić-Koutecký and Michl that the bond-twisted species can have biradical or zwitterionic character, depending on the state. Using QTAIM and the stress tensor a new understanding of bond torsion is revealed; the electronic charge density around the twisted bond is found not to rotate in concert with the nuclei of the rotated -CH2 methylene group. The ability to visualize how the bond stiffness varies between individual electronic states and how this correlates with the QTAIM and stress tensor bond stiffness is highlighted. In addition, the most and least preferred morphologies of bond-path torsion are visualized. Briefly we discuss the prospects for using this new QTAIM and stress tensor analysis for excited state chemistry.
De Hoop, A.T.; Abubakar, A.; Habashy, T.M.
2009-01-01
The contrast-source stress-velocity integral-equation formulation of three-dimensional time-domain elastodynamic scattering problems is discussed. A novel feature of the formulation is a tensor partitioning of the relevant dynamic stress and the contrast source volume density of deformation rate.
Deuschel, Jean-Dominique; Deuschel, Jean-Dominique
2001-01-01
This is the second printing of the book first published in 1988. The first four chapters of the volume are based on lectures given by Stroock at MIT in 1987. They form an introduction to the basic ideas of the theory of large deviations and make a suitable package on which to base a semester-length course for advanced graduate students with a strong background in analysis and some probability theory. A large selection of exercises presents important material and many applications. The last two chapters present various non-uniform results (Chapter 5) and outline the analytic approach that allow
Directory of Open Access Journals (Sweden)
C. Musumeci
1997-06-01
Full Text Available Fault-plane solutions of some tens of local earthquakes which occurred at Mt. Etna volcano during 1983-1986 have been inverted for stress tensor parameters by the algorithm of Gephart and Forsyth (1984. Three seismic sequences were focused on which respectively occurred during a flank eruption (June 1983, just after the end of a subterminal eruption (October 1984 and during an inter-eruptive period (May 1986. The application to the three sets of data of both the "approximate" and the "exact" methods evidenced the stability of results, and the stress directions are well defined in spite of the small number of events used for the inversion. The s1 obtained agrees with the regional tectonic framework, nearly horizontal and oriented N-S, only in the shallow crust, and just after the 1984 eruption. This supports the hypothesis of a tectonic control on the end of the eruptive activities at Mt. Etna. Conversely, results concerning the depth range 10-30 km are in apparent disagreement with other investigations (Cocina et al., 1997, as well as with the regional tectonics. The stress was here found homogeneous, but with s1 respectively trending ENE-WSW (June 1983 and E-W (May 1986. We suggest that the stress field could be temporarily modified by a local stress regime driven by the intrusion of uprising magma.
Li, Jiahui; Xu, Tianlv; Ping, Yang; van Mourik, Tanja; Früchtl, Herbert; Kirk, Steven R.; Jenkins, Samantha
2018-03-01
QTAIM and the stress tensor were used to provide a detailed analysis of the topology of the molecular graph, BCP and bond-path properties, including the new introduced helicity length H, of a Tyr-Gly dipeptide conformer subjected to a torsion with four levels of theory; MP2, M06-2X, B3LYP-D3 and B3LYP and a modest-sized basis set, 6-31+G(d). Structural effects and bonding properties are quantified and reflect differences in the BSSE and lack of inclusion of dispersion effects in the B3LYP calculations. The helicity length H demonstrated that MP2 produced a unique response to the torsion suggesting future use as a diagnostic tool.
The stress energy tensor of a locally supersymmetric quantum field on a curved spacetime
International Nuclear Information System (INIS)
Koehler, M.
1995-04-01
For an analogon of the free Wess-Zumino model on Ricci flat spacetimes, the relation between a conserved 'supercurrent' and the point-separated improved energy momentum tensor is investigated and a similar relation as on Minkowski space is established. The expectation value of the latter in any globally Hadamard product state is found to be a priori finite in the coincidence limit if the theory is massive. On arbitrary globally hyperbolic spacetimes the 'supercurrent' is shown to be a well defined operator valued distribution on the GNS Hilbertspace of any globally Hadamard product state. Viewed as a new field, all n-point distributions exist, giving a new example for a Wightman field on that manifold. Moreover, it is shown that this field satisfies a new wave front set spectrum condition in a nontrivial way. (orig.)
Levitas, Valery I; Attariani, Hamed
2013-01-01
Si is a promising anode material for Li-ion batteries, since it absorbs large amounts of Li. However, insertion of Li leads to 334% of volumetric expansion, huge stresses, and fracture; it can be suppressed by utilizing nanoscale anode structures. Continuum approaches to stress relaxation in LixSi, based on plasticity theory, are unrealistic, because the yield strength of LixSi is much higher than the generated stresses. Here, we suggest that stress relaxation is due to anisotropic (tensorial) compositional straining that occurs during insertion-extraction at any deviatoric stresses. Developed theory describes known experimental and atomistic simulation data. A method to reduce stresses is predicted and confirmed by known experiments. Chemical potential has an additional contribution due to deviatoric stresses, which leads to increases in the driving force both for insertion and extraction. The results have conceptual and general character and are applicable to any material systems.
A new deteriorated energy-momentum tensor
International Nuclear Information System (INIS)
Duff, M.J.
1982-01-01
The stress-tensor of a scalar field theory is not unique because of the possibility of adding an 'improvement term'. In supersymmetric field theories the stress-tensor will appear in a super-current multiplet along with the sypersymmetry current. The general question of the supercurrent multiplet for arbitrary deteriorated stress tensors and their relationship to supercurrent multiplets for models with gauge antisymmetric tensors is answered for various models of N = 1, 2 and 4 supersymmetry. (U.K.)
Tensor surgery and tensor rank
M. Christandl (Matthias); J. Zuiddam (Jeroen)
2018-01-01
textabstractWe introduce a method for transforming low-order tensors into higher-order tensors and apply it to tensors defined by graphs and hypergraphs. The transformation proceeds according to a surgery-like procedure that splits vertices, creates and absorbs virtual edges and inserts new vertices
DEFF Research Database (Denmark)
Pessah, Martin Elias; Chan, Chi-kwan; Psaltis, Dimitrios
2006-01-01
The magnetorotational instability is thought to be responsible for the generation of magnetohydrodynamic turbulence that leads to enhanced outward angular momentum transport in accretion discs. Here, we present the first formal analytical proof showing that, during the exponential growth...... of the instability, the mean (averaged over the disc scale-height) Reynolds stress is always positive, the mean Maxwell stress is always negative, and hence the mean total stress is positive and leads to a net outward flux of angular momentum. More importantly, we show that the ratio of the Maxwell to the Reynolds...
Stress tensor analysis in the Taiwan area from focal mechanisms of earthquakes
Yih-Hsiung, Yeh; Eric, Barrier; Cheng-Horng Lin; Jacques, Angelier
1991-12-01
We produce a map of the stress pattern in and around Taiwan based on 200 earthquake focal mechanism solutions. These solutions were determined by using data from Taiwan Telemetered Seismographic Network, microearthquake surveys and WWSSN. The stresses are derived through a minimization of angles between the slip vector and the shear stress on each nodal plane considered as a fault, employing appropriate weighting factors. The whole set of focal mechanisms is divided into several groups, mainly according to apparent clustering of the event locations. The results show that the direction of maximum principal stress in Taiwan area is nearly horizontal and SE-NW on average. This is in good agreement with the direction of relative motion between the Philippine Sea plate and the Eurasian plate. In western Taiwan, the fan-shaped distribution of the maximum principal stress is consistent with the direction of Philippine Sea-Eurasian plate convergence through a simple model of viscous material indented by a rigid wedge. In the northeastern part of Taiwan, a nearly horizontal minimum principal stress oriented N-S is found for shallow depths; it occurs in a region of low seismic velocities, probably related to the back-arc activity of the Okinawa Trough. Down-dip compressional and down-dip extensional stresses have been identified in different depth ranges within the subducting slab of the Philippine Sea plate in the northern Taiwan; this may reflect the slab characteristics in this area. A complex stress pattern prevails in the Hualien area, at the junction between the Ryukyu subduction system and the Taiwan collision zone.
(Ln-bar, g)-spaces. Special tensor fields
International Nuclear Information System (INIS)
Manoff, S.; Dimitrov, B.
1998-01-01
The Kronecker tensor field, the contraction tensor field, as well as the multi-Kronecker and multi-contraction tensor fields are determined and the action of the covariant differential operator, the Lie differential operator, the curvature operator, and the deviation operator on these tensor fields is established. The commutation relations between the operators Sym and Asym and the covariant and Lie differential operators are considered acting on symmetric and antisymmetric tensor fields over (L n bar, g)-spaces
Hamilton, Nicholas; Cal, Raúl Bayoán
2015-01-01
A 4 × 3 wind turbine array in a Cartesian arrangement was constructed in a wind tunnel setting with four configurations based on the rotational sense of the rotor blades. The fourth row of devices is considered to be in the fully developed turbine canopy for a Cartesian arrangement. Measurements of the flow field were made with stereo particle-image velocimetry immediately upstream and downstream of the selected model turbines. Rotational sense of the turbine blades is evident in the mean spanwise velocity W and the Reynolds shear stress - v w ¯ . The flux of kinetic energy is shown to be of greater magnitude following turbines in arrays where direction of rotation of the blades varies. Invariants of the normalized Reynolds stress anisotropy tensor (η and ξ) are plotted in the Lumley triangle and indicate that distinct characters of turbulence exist in regions of the wake following the nacelle and the rotor blade tips. Eigendecomposition of the tensor yields principle components and corresponding coordinate system transformations. Characteristic spheroids representing the balance of components in the normalized anisotropy tensor are composed with the eigenvalues yielding shapes predicted by the Lumley triangle. Rotation of the coordinate system defined by the eigenvectors demonstrates trends in the streamwise coordinate following the rotors, especially trailing the top-tip of the rotor and below the hub. Direction of rotation of rotor blades is shown by the orientation of characteristic spheroids according to principle axes. In the inflows of exit row turbines, the normalized Reynolds stress anisotropy tensor shows cumulative effects of the upstream turbines, tending toward prolate shapes for uniform rotational sense, oblate spheroids for streamwise organization of rotational senses, and a mixture of characteristic shapes when the rotation varies by row. Comparison between the invariants of the Reynolds stress anisotropy tensor and terms from the mean
DEFF Research Database (Denmark)
Vaage-Nilsen, M; Rasmussen, Verner; Sørum, C
1999-01-01
discovered ST-segment deviation in asymptomatic healthy persons. METHODS AND RESULTS: The occurrence of ST-segment deviation was studied in a population of 63 clinically healthy male subjects 51 to 75 years of age, with the use of 24-hour Holter monitoring and exercise stress testing. The subjects were......BACKGROUND: Although ST-segment deviation has been evaluated and used during many years both on continuous electrocardiographic Holter monitoring and during exercise stress testing, considerable controversy still remains concerning the prevalence and diagnostic significance of fortuitously......-segment deviation during Holter monitoring and exercise stress testing, indicated with a specificity of 1.0 or 0.95 according to choice of criterion, implies that the person is in a healthy state....
Buchner, Abel-John; Lozano-Durán, Adrián; Kitsios, Vassili; Atkinson, Callum; Soria, Julio
2016-04-01
Previous works have shown that momentum transfer in the wall-normal direction within turbulent wall-bounded flows occurs primarily within coherent structures defined by regions of intense Reynolds stress [1]. Such structures may be classified into wall-attached and wall-detached structures with the latter being typically weak, small-scale, and isotropically oriented, while the former are larger and carry most of the Reynolds stresses. The mean velocity fluctuation within each structure may also be used to separate structures by their dynamic properties. This study aims to extract information regarding the scales, kinematics and dynamics of these structures within the topological framework of the invariants of the velocity gradient tensor (VGT). The local topological characteristics of these intense Reynolds stress structures are compared to the topological characteristics of vortex clusters defined by the discriminant of the velocity gradient tensor. The alignment of vorticity with the principal strain directions within these structures is also determined, and the implications of these findings are discussed.
DEFF Research Database (Denmark)
Vaage-Nilsen, M; Rasmussen, Verner; Sørum, C
1999-01-01
BACKGROUND: Although ST-segment deviation has been evaluated and used during many years both on continuous electrocardiographic Holter monitoring and during exercise stress testing, considerable controversy still remains concerning the prevalence and diagnostic significance of fortuitously...... discovered ST-segment deviation in asymptomatic healthy persons. METHODS AND RESULTS: The occurrence of ST-segment deviation was studied in a population of 63 clinically healthy male subjects 51 to 75 years of age, with the use of 24-hour Holter monitoring and exercise stress testing. The subjects were...... in healthy subjects without disease, was 1.0 when using as criterion for significant ST-segment deviation a horizontal or descending ST-segment depression of >0.20 mV or ST-segment elevation >/=0.15 mV during Holter monitoring, and acceptable, for example, 0.95, when using as criterion a horizontal...
The Distance Standard Deviation
Edelmann, Dominic; Richards, Donald; Vogel, Daniel
2017-01-01
The distance standard deviation, which arises in distance correlation analysis of multivariate data, is studied as a measure of spread. New representations for the distance standard deviation are obtained in terms of Gini's mean difference and in terms of the moments of spacings of order statistics. Inequalities for the distance variance are derived, proving that the distance standard deviation is bounded above by the classical standard deviation and by Gini's mean difference. Further, it is ...
Wéber, Zoltán
2016-01-01
We have successfully estimated the full moment tensors of 22 local earthquakes with local magnitude ranging from 1.2 to 4.8 that occurred in the Hungarian part of the Pannonian basin between 1995 and 2014. We used a probabilistic waveform inversion procedure that takes into account the effects of the random noise contained in the seismograms, the uncertainty of the hypocentre determined from arrival times and the inaccurate knowledge of the velocity structure, while estimating the error affecting the derived focal parameters. The applied probabilistic approach maps the posterior probability density functions (PPDFs) for both the hypocentral coordinates and the moment tensor components. The final estimates are given by the maximum likelihood points of the PPDFs, while solution uncertainties are presented by histogram plots. The estimated uncertainties in the moment tensor components are plotted on the focal sphere in such a way, that the significance of the double couple (DC), the compensated linear vector dipole (CLVD) and the isotropic (ISO) parts of the source can be assessed. We have shown that the applied waveform inversion method is equally suitable to recover the source mechanism for low-magnitude events using short-period local waveforms as well as for moderate-size earthquakes using long-period seismograms. The non-DC components of the retrieved focal mechanisms are statistically insignificant for all the analysed earthquakes. The negligible amount of the ISO component implies the tectonic nature of the investigated events. The moment tensor solutions reported by other agencies for five of the ML > 4 earthquakes studied in this paper are very similar to those calculated by the applied waveform inversion algorithm. We have found only strike-slip and thrust faulting events, giving further support to the hypothesis that the Pannonian basin is currently experiencing a compressional regime of deformation. The orientations of the obtained focal mechanisms are in
Chicherin, Dmitry
2017-03-09
We study the multipoint super-correlation functions of the full non-chiral stress-tensor multiplet in N=4 super-Yang-Mills theory in the Born approximation. We derive effective supergraph Feynman rules for them. Surprisingly, the Feynman rules for the non-chiral correlators differ only slightly from those for the chiral correlators. We rely on the formulation of the theory in Lorentz harmonic chiral (LHC) superspace elaborated in the twin paper \\cite{PartI}. In this approach only the chiral half of the supersymmetry is manifest. The other half is realized by nonlinear and nonlocal transformations of the LHC superfields. However, at Born level only the simple linear part of the transformations is relevant. It corresponds to effectively working in the self-dual sector of the theory. Our method is also applicable to a wider class of supermultiplets like all the half-BPS operators and the Konishi multiplet.
Tensor Transpose and Its Properties
Pan, Ran
2014-01-01
Tensor transpose is a higher order generalization of matrix transpose. In this paper, we use permutations and symmetry group to define? the tensor transpose. Then we discuss the classification and composition of tensor transposes. Properties of tensor transpose are studied in relation to tensor multiplication, tensor eigenvalues, tensor decompositions and tensor rank.
Moran, S.C.
2003-01-01
The volcanological significance of seismicity within Katmai National Park has been debated since the first seismograph was installed in 1963, in part because Katmai seismicity consists almost entirely of high-frequency earthquakes that can be caused by a wide range of processes. I investigate this issue by determining 140 well-constrained first-motion fault-plane solutions for shallow (depth regions within the park. Earthquakes removed by several kilometers from the volcanic axis occur in a stress field characterized by horizontally oriented ??1 and ??3 axes, with ??1 rotated slightly (12??) relative to the NUVELIA subduction vector, indicating that these earthquakes are occurring in response to regional tectonic forces. On the other hand, stress tensors for earthquake clusters beneath several Katmai cluster volcanoes have vertically oriented ??1 axes, indicating that these events are occuring in response to local, not regional, processes. At Martin-Mageik, vertically oriented ??1 is most consistent with failure under edifice loading conditions in conjunction with localized pore pressure increases associated with hydrothermal circulation cells. At Trident-Novarupta, it is consistent with a number of possible models, including occurence along fractures formed during the 1912 eruption that now serve as horizontal conduits for migrating fluids and/or volatiles from nearby degassing and cooling magma bodies. At Mount Katmai, it is most consistent with continued seismicity along ring-fracture systems created in the 1912 eruption, perhaps enhanced by circulating hydrothermal fluids and/or seepage from the caldera-filling lake.
Hess, Siegfried
2015-01-01
This book presents the science of tensors in a didactic way. The various types and ranks of tensors and the physical basis is presented. Cartesian Tensors are needed for the description of directional phenomena in many branches of physics and for the characterization the anisotropy of material properties. The first sections of the book provide an introduction to the vector and tensor algebra and analysis, with applications to physics, at undergraduate level. Second rank tensors, in particular their symmetries, are discussed in detail. Differentiation and integration of fields, including generalizations of the Stokes law and the Gauss theorem, are treated. The physics relevant for the applications in mechanics, quantum mechanics, electrodynamics and hydrodynamics is presented. The second part of the book is devoted to tensors of any rank, at graduate level. Special topics are irreducible, i.e. symmetric traceless tensors, isotropic tensors, multipole potential tensors, spin tensors, integration and spin-...
Gurau, Razvan
2017-01-01
Written by the creator of the modern theory of random tensors, this book is the first self-contained introductory text to this rapidly developing theory. Starting from notions familiar to the average researcher or PhD student in mathematical or theoretical physics, the book presents in detail the theory and its applications to physics. The recent detections of the Higgs boson at the LHC and gravitational waves at LIGO mark new milestones in Physics confirming long standing predictions of Quantum Field Theory and General Relativity. These two experimental results only reinforce today the need to find an underlying common framework of the two: the elusive theory of Quantum Gravity. Over the past thirty years, several alternatives have been proposed as theories of Quantum Gravity, chief among them String Theory. While these theories are yet to be tested experimentally, key lessons have already been learned. Whatever the theory of Quantum Gravity may be, it must incorporate random geometry in one form or another....
Tensor rank is not multiplicative under the tensor product
M. Christandl (Matthias); A. K. Jensen (Asger Kjærulff); J. Zuiddam (Jeroen)
2018-01-01
textabstractThe tensor rank of a tensor t is the smallest number r such that t can be decomposed as a sum of r simple tensors. Let s be a k-tensor and let t be an ℓ-tensor. The tensor product of s and t is a (k+ℓ)-tensor. Tensor rank is sub-multiplicative under the tensor product. We revisit the
Tensor rank is not multiplicative under the tensor product
M. Christandl (Matthias); A. K. Jensen (Asger Kjærulff); J. Zuiddam (Jeroen)
2017-01-01
textabstractThe tensor rank of a tensor is the smallest number r such that the tensor can be decomposed as a sum of r simple tensors. Let s be a k-tensor and let t be an l-tensor. The tensor product of s and t is a (k + l)-tensor (not to be confused with the "tensor Kronecker product" used in
Taguchi, Y-H
2017-12-21
Although post-traumatic stress disorder (PTSD) is primarily a mental disorder, it can cause additional symptoms that do not seem to be directly related to the central nervous system, which PTSD is assumed to directly affect. PTSD-mediated heart diseases are some of such secondary disorders. In spite of the significant correlations between PTSD and heart diseases, spatial separation between the heart and brain (where PTSD is primarily active) prevents researchers from elucidating the mechanisms that bridge the two disorders. Our purpose was to identify genes linking PTSD and heart diseases. In this study, gene expression profiles of various murine tissues observed under various types of stress or without stress were analyzed in an integrated manner using tensor decomposition (TD). Based upon the obtained features, ∼ 400 genes were identified as candidate genes that may mediate heart diseases associated with PTSD. Various gene enrichment analyses supported biological reliability of the identified genes. Ten genes encoding protein-, DNA-, or mRNA-interacting proteins-ILF2, ILF3, ESR1, ESR2, RAD21, HTT, ATF2, NR3C1, TP53, and TP63-were found to be likely to regulate expression of most of these ∼ 400 genes and therefore are candidate primary genes that cause PTSD-mediated heart diseases. Approximately 400 genes in the heart were also found to be strongly affected by various drugs whose known adverse effects are related to heart diseases and/or fear memory conditioning; these data support the reliability of our findings. TD-based unsupervised feature extraction turned out to be a useful method for gene selection and successfully identified possible genes causing PTSD-mediated heart diseases.
DEFF Research Database (Denmark)
Rocha, Vera; Van Praag, Mirjam; Carneiro, Anabela
survival? The analysis is based on a matched employer-employee dataset and covers about 17,500 startups in manufacturing and services. We adopt a new procedure to estimate individual benchmarks for the quantity and quality of initial human resources, acknowledging correlations between hiring decisions......This paper studies three related questions: To what extent otherwise similar startups employ different quantities and qualities of human capital at the moment of entry? How persistent are initial human capital choices over time? And how does deviating from human capital benchmarks influence firm......, founders human capital, and the ownership structure of startups (solo entrepreneurs versus entrepreneurial teams). We then study the survival implications of exogenous deviations from these benchmarks, based on spline models for survival data. Our results indicate that (especially negative) deviations from...
Deviations from exponential decay
Petridis, Athanasios; Staunton, Lawrence; Luban, Marshall; Vermedahl, Jon
2003-10-01
We study deviations from exponetial decay in cases when the initial wavefunction is set in a potential well and is not an eigenstate of this potential. We numerically solve the time-dependent Schroedinger equation and observe a decaying but oscillatory behavior of the survival probability. Analytical calculations have been performed proving that even in the case of a simple finite square-well potential deviations from exponential decay persist for large times. Possible explanations for the limiting exponential decay for many-particle systems are developed.
Ye, Qian; Lin, Haoze
2017-07-01
Though extensively used in calculating optical force and torque acting on a material object illuminated by laser, the Maxwell stress tensor (MST) method follows the electromagnetic linear and angular momentum balance that is usually derived in most textbooks for a continuous volume charge distribution in free space, if not resorting to the application of Noether’s theorem in electrodynamics. To cast the conservation laws into a physically appealing form involving the current densities of linear and angular momentum, on which the MST method is based, the divergence theorem is employed to transform a volume integral into a surface integral. When a material object of finite volume is put into the field, it brings about a discontinuity of field across its surface, due to the presence of induced surface charge and surface current. Ambiguity arises among students in whether the divergence theorem can still be directly used without any justification. By taking into account the effect of the induced surface charge and current, we present a simple pedagogical derivation for the MST method for calculating the optical force and torque on an object immersed in monochromatic optical field, without resorting to Noether’s theorem. Although the results turn out to be identical to those given in the standard textbooks, our derivation avoids the direct use of the divergence theorem on a discontinuous function.
Energy Technology Data Exchange (ETDEWEB)
Chicherin, Dmitry [LAPTH, Université de Savoie, CNRS,B.P. 110, F-74941 Annecy-le-Vieux (France); Sokatchev, Emery [LAPTH, Université de Savoie, CNRS,B.P. 110, F-74941 Annecy-le-Vieux (France); Theoretical Physics Department, CERN,CH-1211, Geneva 23 (Switzerland)
2017-03-09
We study the multipoint super-correlation functions of the full non-chiral stress-tensor multiplet in N=4 super-Yang-Mills theory in the Born approximation. We derive effective supergraph Feynman rules for them. Surprisingly, the Feynman rules for the non-chiral correlators are obtained from those for the chiral correlators by a simple Grassmann shift of the space-time variables. We rely on the formulation of the theory in Lorentz harmonic chiral (LHC) superspace elaborated in the twin paper arXiv:1601.06803. In this approach only the chiral half of the supersymmetry is manifest. The other half is realized by nonlinear and nonlocal transformations of the LHC superfields. However, at Born level only the simple linear part of the transformations is relevant. It corresponds to effectively working in the self-dual sector of the theory. Our method is also applicable to a wider class of supermultiplets like all the half-BPS operators and the Konishi multiplet.
Chicherin, Dmitry; Sokatchev, Emery
2017-03-01
We study the multipoint super-correlation functions of the full non-chiral stress-tensor multiplet in N = 4 super-Yang-Mills theory in the Born approximation. We derive effective supergraph Feynman rules for them. Surprisingly, the Feynman rules for the non-chiral correlators are obtained from those for the chiral correlators by a simple Grassmann shift of the space-time variables. We rely on the formulation of the theory in Lorentz harmonic chiral (LHC) superspace elaborated in the twin paper arXiv:1601.06803. In this approach only the chiral half of the supersymmetry is manifest. The other half is realized by nonlinear and nonlocal transformations of the LHC superfields. However, at Born level only the simple linear part of the transformations is relevant. It corresponds to effectively working in the self-dual sector of the theory. Our method is also applicable to a wider class of supermultiplets like all the half-BPS operators and the Konishi multiplet.
Tensor rank is not multiplicative under the tensor product
Christandl, Matthias; Jensen, Asger Kjærulff; Zuiddam, Jeroen
2017-01-01
The tensor rank of a tensor t is the smallest number r such that t can be decomposed as a sum of r simple tensors. Let s be a k-tensor and let t be an l-tensor. The tensor product of s and t is a (k + l)-tensor. Tensor rank is sub-multiplicative under the tensor product. We revisit the connection between restrictions and degenerations. A result of our study is that tensor rank is not in general multiplicative under the tensor product. This answers a question of Draisma and Saptharishi. Specif...
Tensor structure for Nori motives
Barbieri-Viale, Luca; Huber, Annette; Prest, Mike
2018-01-01
We construct a tensor product on Freyd's universal abelian category attached to an additive tensor category or a tensor quiver and establish a universal property. This is used to give an alternative construction for the tensor product on Nori motives.
INDICATIVE MODEL OF DEVIATIONS IN PROJECT
Directory of Open Access Journals (Sweden)
Олена Борисівна ДАНЧЕНКО
2016-02-01
Full Text Available The article shows the process of constructing the project deviations indicator model. It based on a conceptual model of project deviations integrated management (PDIM. During the project different causes (such as risks, changes, problems, crises, conflicts, stress lead to deviations of integrated project indicators - time, cost, quality, and content. For a more detailed definition of where in the project deviations occur and how they are dangerous for the whole project, it needs to develop an indicative model of project deviations. It allows identifying the most dangerous deviations that require PDIM. As a basis for evaluation of project's success has been taken famous model IPMA Delta. During the evaluation, IPMA Delta estimated project management competence of organization in three modules: I-Module ("Individuals" - a self-assessment personnel, P-module ("Projects" - self-assessment of projects and/or programs, and O-module ("Organization" - used to conduct interviews with selected people during auditing company. In the process of building an indicative model of deviations in the project, the first step is the assessment of project management in the organization by IPMA Delta. In the future, built cognitive map and matrix of system interconnections of the project, which conducted simulations and built a scale of deviations for the selected project. They determined a size and place of deviations. To identify the detailed causes of deviations in the project management has been proposed to use the extended system of indicators, which is based on indicators of project management model Project Excellence. The proposed indicative model of deviations in projects allows to estimate the size of variation and more accurately identify the place of negative deviations in the project and provides the project manager information for operational decision making for the management of deviations in the implementation of the project
Haack, Jason; Papel, Ira D
2009-06-01
The nasal septum is a structure poorly understood and appreciated by the lay public and the nonotolaryngologist--head and neck surgeon alike. Deviation of the caudal portion of the nasal septum may result in nasal obstruction, a crooked nose, and columellar irregularities. The correction of a severely deviated caudal septum is one of the most difficult challenges of the otolaryngologist and facial plastic surgeon. A variety of options are available for correction of mild, to the most severe, deflections. This condition, as with all challenges in medicine, should not be a one size fits all or one surgery fits all situation. The skilled surgeon should understand the multiple options available for surgical correction and tailor fit the procedure to the deformity.
Tensor eigenvalues and their applications
Qi, Liqun; Chen, Yannan
2018-01-01
This book offers an introduction to applications prompted by tensor analysis, especially by the spectral tensor theory developed in recent years. It covers applications of tensor eigenvalues in multilinear systems, exponential data fitting, tensor complementarity problems, and tensor eigenvalue complementarity problems. It also addresses higher-order diffusion tensor imaging, third-order symmetric and traceless tensors in liquid crystals, piezoelectric tensors, strong ellipticity for elasticity tensors, and higher-order tensors in quantum physics. This book is a valuable reference resource for researchers and graduate students who are interested in applications of tensor eigenvalues.
Comon, Pierre
2014-01-01
International audience; Tensor decompositions are at the core of many Blind Source Separation (BSS) algorithms, either explicitly or implicitly. In particular, the Canonical Polyadic (CP) tensor decomposition plays a central role in identification of underdetermined mixtures. Despite some similarities, CP and Singular value Decomposition (SVD) are quite different. More generally, tensors and matrices enjoy different properties, as pointed out in this brief survey.
Local Tensor Radiation Conditions For Elastic Waves
DEFF Research Database (Denmark)
Krenk, S.; Kirkegaard, Poul Henning
2001-01-01
A local boundary condition is formulated, representing radiation of elastic waves from an arbitrary point source. The boundary condition takes the form of a tensor relation between the stress at a point on an arbitrarily oriented section and the velocity and displacement vectors at the point....... The tensor relation generalizes the traditional normal incidence impedance condition by accounting for the angle between wave propagation and the surface normal and by including a generalized stiffness term due to spreading of the waves. The effectiveness of the local tensor radiation condition...
International Nuclear Information System (INIS)
Beig, Robert; Krammer, Werner
2004-01-01
For a conformally flat 3-space, we derive a family of linear second-order partial differential operators which sends vectors into trace-free, symmetric 2-tensors. These maps, which are parametrized by conformal Killing vectors on the 3-space, are such that the divergence of the resulting tensor field depends only on the divergence of the original vector field. In particular, these maps send source-free electric fields into TT tensors. Moreover, if the original vector field is the Coulomb field on R 3 {0}, the resulting tensor fields on R 3 {0} are nothing but the family of TT tensors originally written by Bowen and York
DEFF Research Database (Denmark)
Rocha, Vera; Van Praag, Mirjam; Carneiro, Anabela
This paper studies three related questions: To what extent otherwise similar startups employ different quantities and qualities of human capital at the moment of entry? How persistent are initial human capital choices over time? And how does deviating from human capital benchmarks influence firm...... survival? The analysis is based on a matched employer-employee dataset and covers about 17,500 startups in manufacturing and services. We adopt a new procedure to estimate individual benchmarks for the quantity and quality of initial human resources, acknowledging correlations between hiring decisions...... the benchmark can be substantial, are persistent over time, and hinder the survival of firms. The implications may, however, vary according to the sector and the ownership structure at entry. Given the stickiness of initial choices, wrong human capital decisions at entry turn out to be a close to irreversible...
Segmentation Using Symmetry Deviation
DEFF Research Database (Denmark)
Hollensen, Christian; Højgaard, L.; Specht, L.
2011-01-01
and evaluate the method. The method uses deformable registration on computed tomography(CT) to find anatomical symmetry deviations of Head & Neck squamous cell carcinoma and combining it with positron emission tomography (PET) images. The method allows the use anatomical and symmetrical information of CT scans...... segmentations on manual contours was evaluated using concordance index and sensitivity for the hypopharyngeal patients. The resulting concordance index and sensitivity was compared with the result of using a threshold of 3 SUV using a paired t-test. Results: The anatomical and symmetrical atlas was constructed...... and sensitivity of respectively 0.43±0.15 and 0.56±0.18 was acquired. It was compared to the concordance index of segmentation using absolute threshold of 3 SUV giving respectively 0.41±0.16 and 0.51±0.19 for concordance index and sensitivity yielding p-values of 0.33 and 0.01 for a paired t-test respectively....
Direct tensor rendering using a bidirectional reflectance model
Nagasawa, Mikio; Suzuki, Yoshio
2000-02-01
For the multi variable volumetric tensor field visualization, an efficient direct rendering technique without using geometrical primitive is proposed. The bi- directional reflectance shading model is used to map the anisotropy stress shear tensor components in direct volume rendering. We model the sub-pixel-sized microfacet at tensor sampling points. The nine component of 3D tensor field are mapped onto grid deformation, opacity mapping, color specification, and normal directions of these microfacets. The ray integration is executed though these irregular infinitesimal microfacets distribution. This direct tensor rendering was applied for at-a-glance tensor visualization of earthquake simulation. That realized a view of deformed structure, stress distribution, local shear discontinuity and the shock front, integrated in a single image. The characteristic P- and S-wave modes are distinguished in the rendered earthquake simulations. Compared with the glyph representation of tensor features, the direct tensor rendering gives the general and total image of tensor field even for the low resolution pixel planes, because the sampling object is assumed as infinitesimally small. the computational cost of direct tensor rendering is not so high than that of scalar volume rendering because the modifications are only ins hading calculation but not in the ray integration.
Tensor rank is not multiplicative under the tensor product
DEFF Research Database (Denmark)
Christandl, Matthias; Jensen, Asger Kjærulff; Zuiddam, Jeroen
2018-01-01
The tensor rank of a tensor t is the smallest number r such that t can be decomposed as a sum of r simple tensors. Let s be a k-tensor and let t be an ℓ-tensor. The tensor product of s and t is a (k+ℓ)-tensor. Tensor rank is sub-multiplicative under the tensor product. We revisit the connection...... between restrictions and degenerations. A result of our study is that tensor rank is not in general multiplicative under the tensor product. This answers a question of Draisma and Saptharishi. Specifically, if a tensor t has border rank strictly smaller than its rank, then the tensor rank of t...... is not multiplicative under taking a sufficiently hight tensor product power. The “tensor Kronecker product” from algebraic complexity theory is related to our tensor product but different, namely it multiplies two k-tensors to get a k-tensor. Nonmultiplicativity of the tensor Kronecker product has been known since...
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
Linear Invariant Tensor Interpolation Applied to Cardiac Diffusion Tensor MRI
Gahm, Jin Kyu; Wisniewski, Nicholas; Kindlmann, Gordon; Kung, Geoffrey L.; Klug, William S.; Garfinkel, Alan; Ennis, Daniel B.
2015-01-01
Purpose Various methods exist for interpolating diffusion tensor fields, but none of them linearly interpolate tensor shape attributes. Linear interpolation is expected not to introduce spurious changes in tensor shape. Methods Herein we define a new linear invariant (LI) tensor interpolation method that linearly interpolates components of tensor shape (tensor invariants) and recapitulates the interpolated tensor from the linearly interpolated tensor invariants and the eigenvectors of a linearly interpolated tensor. The LI tensor interpolation method is compared to the Euclidean (EU), affine-invariant Riemannian (AI), log-Euclidean (LE) and geodesic-loxodrome (GL) interpolation methods using both a synthetic tensor field and three experimentally measured cardiac DT-MRI datasets. Results EU, AI, and LE introduce significant microstructural bias, which can be avoided through the use of GL or LI. Conclusion GL introduces the least microstructural bias, but LI tensor interpolation performs very similarly and at substantially reduced computational cost. PMID:23286085
Soibelman, Yan
1997-01-01
We introduce the notion of meromorphic tensor category and illustrate it in several examples. They include representations of quantum affine algebras, chiral algebras of Beilinson and Drinfeld, G-vertex algebras of Borcherds, and representations of GL over a local field. Hopefully the formalism will accomodate various tensor structures arising in relation to the quantized Knizhnik-Zamolodchikov equations and deformed CFT
Group Cohesiveness, Deviation, Stress, and Conformity
1993-08-11
basic 19 result was similar to Asch’s; subject responses were influenced str ~ngly by the judgments of others in the group. Determinants of Conformity...Cola number of cups, __ Chocolate , cocoa, wine, beer/alcohol, decaffeinated coffee. Breads containing raisins, prunes, orange peel, banana, or...cream, anchovies. Cheese omelets, spanish omelets with aged cheese. Macaroni and cheese, spaghetti in tomato sauce. Walnuts, chocolate or coffee
Robust tensor estimation in diffusion tensor imaging
Maximov, Ivan I.; Grinberg, Farida; Jon Shah, N.
2011-12-01
The signal response measured in diffusion tensor imaging is subject to detrimental influences caused by noise. Noise fields arise due to various contributions such as thermal and physiological noise and sources related to the hardware imperfection. As a result, diffusion tensors estimated by different linear and non-linear least squares methods in absence of a proper noise correction tend to be substantially corrupted. In this work, we propose an advanced tensor estimation approach based on the least median squares method of the robust statistics. Both constrained and non-constrained versions of the method are considered. The performance of the developed algorithm is compared to that of the conventional least squares method and of the alternative robust methods proposed in the literature. Two examples of simulated diffusion attenuations and experimental in vivo diffusion data sets were used as a basis for comparison. The robust algorithms were shown to be advantageous compared to the least squares method in the cases where elimination of the outliers is desirable. Additionally, the constraints were applied in order to prevent generation of the non-positive definite tensors and reduce related artefacts in the maps of fractional anisotropy. The developed method can potentially be exploited also by other MR techniques where a robust regression or outlier localisation is required.
Tensor spherical harmonics and tensor multipoles. II. Minkowski space
International Nuclear Information System (INIS)
Daumens, M.; Minnaert, P.
1976-01-01
The bases of tensor spherical harmonics and of tensor multipoles discussed in the preceding paper are generalized in the Hilbert space of Minkowski tensor fields. The transformation properties of the tensor multipoles under Lorentz transformation lead to the notion of irreducible tensor multipoles. We show that the usual 4-vector multipoles are themselves irreducible, and we build the irreducible tensor multipoles of the second order. We also give their relations with the symmetric tensor multipoles defined by Zerilli for application to the gravitational radiation
Ford, S. R.; Dreger, D. S.; Walter, W. R.
2006-12-01
Seismic moment tensor analysis at regional distances commonly involves solving for the deviatoric moment tensor and decomposing it to characterize the tectonic earthquake source. The full seismic moment tensor solution can also recover the isotropic component of the seismic source, which is theoretically dominant in explosions and collapses, and present in volcanic events. Analysis of events with demonstrably significant isotropic energy can aid in understanding the source processes of volcanic and geothermal seismic events and the monitoring of nuclear explosions. Using a regional time-domain waveform inversion for the complete moment tensor we calculate the deviatoric and isotropic source components for several explosions at the Nevada Test Site (NTS) and earthquakes, collapses, and volcanic events in the surrounding region of the NTS (Western US). The events separate into specific populations according to their deviation from a pure double-couple and ratio of isotropic to deviatoric energy. The separation allows for anomalous event identification and discrimination of explosions, earthquakes, and collapses. Analysis of the source principal axes can characterize the regional stress field, and tectonic release due to explosions. Error in the moment tensor solutions and source parameters is also calculated. We investigate the sensitivity of the moment tensor solutions to Green's functions calculated with imperfect Earth models, inaccurate event locations, and data with a low signal-to-noise ratio. We also test the performance of the method under a range of recording conditions from excellent azimuthal coverage to cases of sparse coverage as might be expected for smaller events. This analysis will be used to determine the magnitude range where well-constrained solutions can be obtained.
Tensors and their applications
Islam, Nazrul
2006-01-01
About the Book: The book is written is in easy-to-read style with corresponding examples. The main aim of this book is to precisely explain the fundamentals of Tensors and their applications to Mechanics, Elasticity, Theory of Relativity, Electromagnetic, Riemannian Geometry and many other disciplines of science and engineering, in a lucid manner. The text has been explained section wise, every concept has been narrated in the form of definition, examples and questions related to the concept taught. The overall package of the book is highly useful and interesting for the people associated with the field. Contents: Preliminaries Tensor Algebra Metric Tensor and Riemannian Metric Christoffel`s Symbols and Covariant Differentiation Riemann-Christoffel Tensor The e-Systems and the Generalized Krönecker Deltas Geometry Analytical Mechanics Curvature of a Curve, Geodesic Parallelism of Vectors Ricci`s Coefficients of Rotation and Congruence Hyper Surfaces
Symmetric Tensor Decomposition
DEFF Research Database (Denmark)
Brachat, Jerome; Comon, Pierre; Mourrain, Bernard
2010-01-01
We present an algorithm for decomposing a symmetric tensor, of dimension n and order d, as a sum of rank-1 symmetric tensors, extending the algorithm of Sylvester devised in 1886 for binary forms. We recall the correspondence between the decomposition of a homogeneous polynomial in n variables...... of polynomial equations of small degree in non-generic cases. We propose a new algorithm for symmetric tensor decomposition, based on this characterization and on linear algebra computations with Hankel matrices. The impact of this contribution is two-fold. First it permits an efficient computation...... of the decomposition of any tensor of sub-generic rank, as opposed to widely used iterative algorithms with unproved global convergence (e.g. Alternate Least Squares or gradient descents). Second, it gives tools for understanding uniqueness conditions and for detecting the rank....
International Nuclear Information System (INIS)
Scheunert, M.
1982-10-01
We develop a graded tensor calculus corresponding to arbitrary Abelian groups of degrees and arbitrary commutation factors. The standard basic constructions and definitions like tensor products, spaces of multilinear mappings, contractions, symmetrization, symmetric algebra, as well as the transpose, adjoint, and trace of a linear mapping, are generalized to the graded case and a multitude of canonical isomorphisms is presented. Moreover, the graded versions of the classical Lie algebras are introduced and some of their basic properties are described. (orig.)
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...
Killing tensors and conformal Killing tensors from conformal Killing vectors
International Nuclear Information System (INIS)
Rani, Raffaele; Edgar, S Brian; Barnes, Alan
2003-01-01
Koutras has proposed some methods to construct reducible proper conformal Killing tensors and Killing tensors (which are, in general, irreducible) when a pair of orthogonal conformal Killing vectors exist in a given space. We give the completely general result demonstrating that this severe restriction of orthogonality is unnecessary. In addition, we correct and extend some results concerning Killing tensors constructed from a single conformal Killing vector. A number of examples demonstrate that it is possible to construct a much larger class of reducible proper conformal Killing tensors and Killing tensors than permitted by the Koutras algorithms. In particular, by showing that all conformal Killing tensors are reducible in conformally flat spaces, we have a method of constructing all conformal Killing tensors, and hence all the Killing tensors (which will in general be irreducible) of conformally flat spaces using their conformal Killing vectors
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...
DEFF Research Database (Denmark)
Ziegel, Johanna; Nyengaard, Jens Randel; Jensen, Eva B. Vedel
In the present paper, statistical procedures for estimating shape and orientation of arbitrary three-dimensional particles are developed. The focus of this work is on the case where the particles cannot be observed directly, but only via sections. Volume tensors are used for describing particle...... shape and orientation, and stereological estimators of the tensors are derived. It is shown that these estimators can be combined to provide consistent estimators of the moments of the so-called particle cover density. The covariance structure associated with the particle cover density depends...... may be analysed using a generalized methods of moments in which the volume tensors enter. The developed methods are used to study the cell organization in the human brain cortex....
International Nuclear Information System (INIS)
Malyshev, C
2007-01-01
A translational gauge approach of the Einstein type is proposed for obtaining the stresses that are due to non-singular screw dislocation. The stress distribution of the second order around the screw dislocation is classically known for the hollow circular cylinder with traction-free external and internal boundaries. The inner boundary surrounds the dislocation's core, which is not captured by the conventional solution. The present gauge approach enables us to continue the classically known quadratic stresses inside the core. The gauge equation is chosen in the Hilbert-Einstein form, and it plays the role of non-conventional incompatibility law. The stress function method is used, and it leads to the modified stress potential given by two constituents: the conventional one, say, the 'background' and a short-ranged gauge contribution. The latter just causes additional stresses, which are localized. The asymptotic properties of the resulting stresses are studied. Since the gauge contributions are short-ranged, the background stress field dominates sufficiently far from the core. The outer cylinder's boundary is traction-free. At sufficiently moderate distances, the second-order stresses acquire regular continuation within the core region, and the cut-off at the core does not occur. Expressions for the asymptotically far stresses provide self-consistently new length scales dependent on the elastic parameters. These lengths could characterize an exteriority of the dislocation core region
Visualizing Tensor Normal Distributions at Multiple Levels of Detail.
Abbasloo, Amin; Wiens, Vitalis; Hermann, Max; Schultz, Thomas
2016-01-01
Despite the widely recognized importance of symmetric second order tensor fields in medicine and engineering, the visualization of data uncertainty in tensor fields is still in its infancy. A recently proposed tensorial normal distribution, involving a fourth order covariance tensor, provides a mathematical description of how different aspects of the tensor field, such as trace, anisotropy, or orientation, vary and covary at each point. However, this wealth of information is far too rich for a human analyst to take in at a single glance, and no suitable visualization tools are available. We propose a novel approach that facilitates visual analysis of tensor covariance at multiple levels of detail. We start with a visual abstraction that uses slice views and direct volume rendering to indicate large-scale changes in the covariance structure, and locations with high overall variance. We then provide tools for interactive exploration, making it possible to drill down into different types of variability, such as in shape or orientation. Finally, we allow the analyst to focus on specific locations of the field, and provide tensor glyph animations and overlays that intuitively depict confidence intervals at those points. Our system is demonstrated by investigating the effects of measurement noise on diffusion tensor MRI, and by analyzing two ensembles of stress tensor fields from solid mechanics.
Tensor Calculus: Unlearning Vector Calculus
Lee, Wha-Suck; Engelbrecht, Johann; Moller, Rita
2018-01-01
Tensor calculus is critical in the study of the vector calculus of the surface of a body. Indeed, tensor calculus is a natural step-up for vector calculus. This paper presents some pitfalls of a traditional course in vector calculus in transitioning to tensor calculus. We show how a deeper emphasis on traditional topics such as the Jacobian can…
The evolution of tensor polarization
International Nuclear Information System (INIS)
Huang, H.; Lee, S.Y.; Ratner, L.
1993-01-01
By using the equation of motion for the vector polarization, the spin transfer matrix for spin tensor polarization, the spin transfer matrix for spin tensor polarization is derived. The evolution equation for the tensor polarization is studied in the presence of an isolate spin resonance and in the presence of a spin rotor, or snake
Diffusion tensor image registration using hybrid connectivity and tensor features.
Wang, Qian; Yap, Pew-Thian; Wu, Guorong; Shen, Dinggang
2014-07-01
Most existing diffusion tensor imaging (DTI) registration methods estimate structural correspondences based on voxelwise matching of tensors. The rich connectivity information that is given by DTI, however, is often neglected. In this article, we propose to integrate complementary information given by connectivity features and tensor features for improved registration accuracy. To utilize connectivity information, we place multiple anchors representing different brain anatomies in the image space, and define the connectivity features for each voxel as the geodesic distances from all anchors to the voxel under consideration. The geodesic distance, which is computed in relation to the tensor field, encapsulates information of brain connectivity. We also extract tensor features for every voxel to reflect the local statistics of tensors in its neighborhood. We then combine both connectivity features and tensor features for registration of tensor images. From the images, landmarks are selected automatically and their correspondences are determined based on their connectivity and tensor feature vectors. The deformation field that deforms one tensor image to the other is iteratively estimated and optimized according to the landmarks and their associated correspondences. Experimental results show that, by using connectivity features and tensor features simultaneously, registration accuracy is increased substantially compared with the cases using either type of features alone. Copyright © 2013 Wiley Periodicals, Inc.
Evaluation of Bayesian tensor estimation using tensor coherence
Kim, Dae-Jin; Kim, In-Young; Jeong, Seok-Oh; Park, Hae-Jeong
2009-06-01
Fiber tractography, a unique and non-invasive method to estimate axonal fibers within white matter, constructs the putative streamlines from diffusion tensor MRI by interconnecting voxels according to the propagation direction defined by the diffusion tensor. This direction has uncertainties due to the properties of underlying fiber bundles, neighboring structures and image noise. Therefore, robust estimation of the diffusion direction is essential to reconstruct reliable fiber pathways. For this purpose, we propose a tensor estimation method using a Bayesian framework, which includes an a priori probability distribution based on tensor coherence indices, to utilize both the neighborhood direction information and the inertia moment as regularization terms. The reliability of the proposed tensor estimation was evaluated using Monte Carlo simulations in terms of accuracy and precision with four synthetic tensor fields at various SNRs and in vivo human data of brain and calf muscle. Proposed Bayesian estimation demonstrated the relative robustness to noise and the higher reliability compared to the simple tensor regression.
Evaluation of Bayesian tensor estimation using tensor coherence
Energy Technology Data Exchange (ETDEWEB)
Kim, Dae-Jin; Park, Hae-Jeong [Laboratory of Molecular Neuroimaging Technology, Brain Korea 21 Project for Medical Science, Yonsei University, College of Medicine, Seoul (Korea, Republic of); Kim, In-Young [Department of Biomedical Engineering, Hanyang University, Seoul (Korea, Republic of); Jeong, Seok-Oh [Department of Statistics, Hankuk University of Foreign Studies, Yongin (Korea, Republic of)], E-mail: parkhj@yuhs.ac
2009-06-21
Fiber tractography, a unique and non-invasive method to estimate axonal fibers within white matter, constructs the putative streamlines from diffusion tensor MRI by interconnecting voxels according to the propagation direction defined by the diffusion tensor. This direction has uncertainties due to the properties of underlying fiber bundles, neighboring structures and image noise. Therefore, robust estimation of the diffusion direction is essential to reconstruct reliable fiber pathways. For this purpose, we propose a tensor estimation method using a Bayesian framework, which includes an a priori probability distribution based on tensor coherence indices, to utilize both the neighborhood direction information and the inertia moment as regularization terms. The reliability of the proposed tensor estimation was evaluated using Monte Carlo simulations in terms of accuracy and precision with four synthetic tensor fields at various SNRs and in vivo human data of brain and calf muscle. Proposed Bayesian estimation demonstrated the relative robustness to noise and the higher reliability compared to the simple tensor regression.
Deviations from Newton's law in supersymmetric large extra dimensions
International Nuclear Information System (INIS)
Callin, P.; Burgess, C.P.
2006-01-01
Deviations from Newton's inverse-squared law at the micron length scale are smoking-gun signals for models containing supersymmetric large extra dimensions (SLEDs), which have been proposed as approaches for resolving the cosmological constant problem. Just like their non-supersymmetric counterparts, SLED models predict gravity to deviate from the inverse-square law because of the advent of new dimensions at sub-millimeter scales. However SLED models differ from their non-supersymmetric counterparts in three important ways: (i) the size of the extra dimensions is fixed by the observed value of the dark energy density, making it impossible to shorten the range over which new deviations from Newton's law must be seen; (ii) supersymmetry predicts there to be more fields in the extra dimensions than just gravity, implying different types of couplings to matter and the possibility of repulsive as well as attractive interactions; and (iii) the same mechanism which is purported to keep the cosmological constant naturally small also keeps the extra-dimensional moduli effectively massless, leading to deviations from general relativity in the far infrared of the scalar-tensor form. We here explore the deviations from Newton's law which are predicted over micron distances, and show the ways in which they differ and resemble those in the non-supersymmetric case
Moderate deviations for bounded subsequences
Directory of Open Access Journals (Sweden)
George Stoica
2006-01-01
Full Text Available We study Davis' series of moderate deviations probabilities for Lp-bounded sequences of random variables (p>2. A certain subseries therein is convergent for the same range of parameters as in the case of martingale difference or i.i.d. sequences.
Gogny interactions with tensor terms
Energy Technology Data Exchange (ETDEWEB)
Anguiano, M.; Lallena, A.M.; Bernard, R.N. [Universidad de Granada, Departamento de Fisica Atomica, Molecular y Nuclear, Granada (Spain); Co' , G. [INFN, Lecce (Italy); De Donno, V. [Universita del Salento, Dipartimento di Matematica e Fisica ' ' E. De Giorgi' ' , Lecce (Italy); Grasso, M. [Universite Paris-Sud, Institut de Physique Nucleaire, IN2P3-CNRS, Orsay (France)
2016-07-15
We present a perturbative approach to include tensor terms in the Gogny interaction. We do not change the values of the usual parameterisations, with the only exception of the spin-orbit term, and we add tensor terms whose only free parameters are the strengths of the interactions. We identify observables sensitive to the presence of the tensor force in Hartree-Fock, Hartree-Fock-Bogoliubov and random phase approximation calculations. We show the need of including two tensor contributions, at least: a pure tensor term and a tensor-isospin term. We show results relevant for the inclusion of the tensor term for single-particle energies, charge-conserving magnetic excitations and Gamow-Teller excitations. (orig.)
The geomagnetic field gradient tensor
DEFF Research Database (Denmark)
Kotsiaros, Stavros; Olsen, Nils
2012-01-01
We develop the general mathematical basis for space magnetic gradiometry in spherical coordinates. The magnetic gradient tensor is a second rank tensor consisting of 3 × 3 = 9 spatial derivatives. Since the geomagnetic field vector B is always solenoidal (∇ · B = 0) there are only eight independent...... tensor elements. Furthermore, in current free regions the magnetic gradient tensor becomes symmetric, further reducing the number of independent elements to five. In that case B is a Laplacian potential field and the gradient tensor can be expressed in series of spherical harmonics. We present properties...... of the magnetic gradient tensor and provide explicit expressions of its elements in terms of spherical harmonics. Finally we discuss the benefit of using gradient measurements for exploring the Earth’s magnetic field from space, in particular the advantage of the various tensor elements for a better determination...
Large deviations of Lyapunov exponents
International Nuclear Information System (INIS)
Laffargue, Tanguy; Tailleur, Julien; Lam, Khanh-Dang Nguyen Thu; Kurchan, Jorge
2013-01-01
Generic dynamical systems have ‘typical’ Lyapunov exponents, measuring the sensitivity to small perturbations of almost all trajectories. A generic system also has trajectories with exceptional values of the exponents, corresponding to unusually stable or chaotic situations. From a more mathematical point of view, large deviations of Lyapunov exponents characterize phase-space topological structures such as separatrices, homoclinic trajectories and degenerate tori. Numerically sampling such large deviations using the Lyapunov Weighted Dynamics allows one to pinpoint, for example, stable configurations in celestial mechanics or collections of interacting chaotic ‘breathers’ in nonlinear media. Furthermore, we show that this numerical method allows one to compute the topological pressure of extended dynamical systems, a central quantity in the thermodynamic of trajectories of Ruelle. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Lyapunov analysis: from dynamical systems theory to applications’. (paper)
Large deviations of Lyapunov exponents
Laffargue, Tanguy; Nguyen Thu Lam, Khanh-Dang; Kurchan, Jorge; Tailleur, Julien
2013-06-01
Generic dynamical systems have ‘typical’ Lyapunov exponents, measuring the sensitivity to small perturbations of almost all trajectories. A generic system also has trajectories with exceptional values of the exponents, corresponding to unusually stable or chaotic situations. From a more mathematical point of view, large deviations of Lyapunov exponents characterize phase-space topological structures such as separatrices, homoclinic trajectories and degenerate tori. Numerically sampling such large deviations using the Lyapunov Weighted Dynamics allows one to pinpoint, for example, stable configurations in celestial mechanics or collections of interacting chaotic ‘breathers’ in nonlinear media. Furthermore, we show that this numerical method allows one to compute the topological pressure of extended dynamical systems, a central quantity in the thermodynamic of trajectories of Ruelle. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Lyapunov analysis: from dynamical systems theory to applications’.
Dillon, Joshua V.; Langmore, Ian; Tran, Dustin; Brevdo, Eugene; Vasudevan, Srinivas; Moore, Dave; Patton, Brian; Alemi, Alex; Hoffman, Matt; Saurous, Rif A.
2017-01-01
The TensorFlow Distributions library implements a vision of probability theory adapted to the modern deep-learning paradigm of end-to-end differentiable computation. Building on two basic abstractions, it offers flexible building blocks for probabilistic computation. Distributions provide fast, numerically stable methods for generating samples and computing statistics, e.g., log density. Bijectors provide composable volume-tracking transformations with automatic caching. Together these enable...
Large Deviations for Random Trees.
Bakhtin, Yuri; Heitsch, Christine
2008-08-01
We consider large random trees under Gibbs distributions and prove a Large Deviation Principle (LDP) for the distribution of degrees of vertices of the tree. The LDP rate function is given explicitly. An immediate consequence is a Law of Large Numbers for the distribution of vertex degrees in a large random tree. Our motivation for this study comes from the analysis of RNA secondary structures.
Simultaneous Invariants of Strain and Rotation Rate Tensors and Their Admitted Region
Directory of Open Access Journals (Sweden)
Igor Vigdorovich
2015-01-01
Full Text Available The purpose of this paper is to establish the admitted region for five simultaneous, functionally independent invariants of the strain rate tensor S and rotation rate tensor Ω and calculate some simultaneous invariants of these tensors which are encountered in the theory of constitutive relations for turbulent flows. Such a problem, as far as we know, has not yet been considered, though it is obviously an integral part of any problem in which scalar functions of the tensors S and Ω are studied. The theory provided inside this paper is the building block for a derivation of new algebraic constitutive relations for three-dimensional turbulent flows in the form of expansions of the Reynolds-stress tensor in a tensorial basis formed by the tensors S and Ω, in which the scalar coefficients depend on simultaneous invariants of these tensors.
Tensor Permutation Matrices in Finite Dimensions
Christian, Rakotonirina
2005-01-01
We have generalised the properties with the tensor product, of one 4x4 matrix which is a permutation matrix, and we call a tensor commutation matrix. Tensor commutation matrices can be constructed with or without calculus. A formula allows us to construct a tensor permutation matrix, which is a generalisation of tensor commutation matrix, has been established. The expression of an element of a tensor commutation matrix has been generalised in the case of any element of a tensor permutation ma...
Tensor Factorization for Low-Rank Tensor Completion.
Zhou, Pan; Lu, Canyi; Lin, Zhouchen; Zhang, Chao
2018-03-01
Recently, a tensor nuclear norm (TNN) based method was proposed to solve the tensor completion problem, which has achieved state-of-the-art performance on image and video inpainting tasks. However, it requires computing tensor singular value decomposition (t-SVD), which costs much computation and thus cannot efficiently handle tensor data, due to its natural large scale. Motivated by TNN, we propose a novel low-rank tensor factorization method for efficiently solving the 3-way tensor completion problem. Our method preserves the low-rank structure of a tensor by factorizing it into the product of two tensors of smaller sizes. In the optimization process, our method only needs to update two smaller tensors, which can be more efficiently conducted than computing t-SVD. Furthermore, we prove that the proposed alternating minimization algorithm can converge to a Karush-Kuhn-Tucker point. Experimental results on the synthetic data recovery, image and video inpainting tasks clearly demonstrate the superior performance and efficiency of our developed method over state-of-the-arts including the TNN and matricization methods.
48 CFR 2901.404 - Class deviations.
2010-10-01
... ACQUISITION REGULATION SYSTEM Deviations From the FAR and DOLAR 2901.404 Class deviations. (a) The Senior Procurement Executive is authorized to approve class deviations from FAR or DOLAR provisions which affect more...
Optimal hedging via large deviation
Stutzer, Michael
2013-08-01
The criterion of minimizing the cumulative hedged returns’ probability of underperforming a benchmark provides a framework for evaluating short-term hedges that are rolled over to produce longer-term hedges. Large deviations theory can be used to either parametrically or nonparametrically estimate underperformance probabilities for cumulative hedged returns produced by roll-overs, providing a straightforward way to find optimal hedge ratios. Optimal hedges using soybean futures are constructed to illustrate the procedures, and their relationship to the popular hedging criteria that are motivated by normality.
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
Notes on super Killing tensors
Energy Technology Data Exchange (ETDEWEB)
Howe, P.S. [Department of Mathematics, King’s College London,The Strand, London WC2R 2LS (United Kingdom); Lindström, University [Department of Physics and Astronomy, Theoretical Physics, Uppsala University,SE-751 20 Uppsala (Sweden); Theoretical Physics, Imperial College London,Prince Consort Road, London SW7 2AZ (United Kingdom)
2016-03-14
The notion of a Killing tensor is generalised to a superspace setting. Conserved quantities associated with these are defined for superparticles and Poisson brackets are used to define a supersymmetric version of the even Schouten-Nijenhuis bracket. Superconformal Killing tensors in flat superspaces are studied for spacetime dimensions 3,4,5,6 and 10. These tensors are also presented in analytic superspaces and super-twistor spaces for 3,4 and 6 dimensions. Algebraic structures associated with superconformal Killing tensors are also briefly discussed.
Tensor Train Neighborhood Preserving Embedding
Wang, Wenqi; Aggarwal, Vaneet; Aeron, Shuchin
2018-05-01
In this paper, we propose a Tensor Train Neighborhood Preserving Embedding (TTNPE) to embed multi-dimensional tensor data into low dimensional tensor subspace. Novel approaches to solve the optimization problem in TTNPE are proposed. For this embedding, we evaluate novel trade-off gain among classification, computation, and dimensionality reduction (storage) for supervised learning. It is shown that compared to the state-of-the-arts tensor embedding methods, TTNPE achieves superior trade-off in classification, computation, and dimensionality reduction in MNIST handwritten digits and Weizmann face datasets.
Large deviations and portfolio optimization
Sornette, Didier
Risk control and optimal diversification constitute a major focus in the finance and insurance industries as well as, more or less consciously, in our everyday life. We present a discussion of the characterization of risks and of the optimization of portfolios that starts from a simple illustrative model and ends by a general functional integral formulation. A major item is that risk, usually thought of as one-dimensional in the conventional mean-variance approach, has to be addressed by the full distribution of losses. Furthermore, the time-horizon of the investment is shown to play a major role. We show the importance of accounting for large fluctuations and use the theory of Cramér for large deviations in this context. We first treat a simple model with a single risky asset that exemplifies the distinction between the average return and the typical return and the role of large deviations in multiplicative processes, and the different optimal strategies for the investors depending on their size. We then analyze the case of assets whose price variations are distributed according to exponential laws, a situation that is found to describe daily price variations reasonably well. Several portfolio optimization strategies are presented that aim at controlling large risks. We end by extending the standard mean-variance portfolio optimization theory, first within the quasi-Gaussian approximation and then using a general formulation for non-Gaussian correlated assets in terms of the formalism of functional integrals developed in the field theory of critical phenomena.
Herman, Matthew W.; Herrmann, Robert B.; Benz, Harley M.; Furlong, Kevin P.
2014-01-01
On September 3, 2010, a MW 7.0 (U.S. Geological Survey moment magnitude) earthquake ruptured across the Canterbury Plains in South Island, New Zealand. Since then, New Zealand GNS Science has recorded over 10,000 aftershocks ML 2.0 and larger, including three destructive ~ MW 6.0 earthquakes near Christchurch. We treat the Canterbury earthquake sequence as an intraplate earthquake sequence, and compare its kinematics to an Andersonian model for fault slip in a uniform stress field. We determined moment magnitudes and double couple solutions for 150 earthquakes having MW 3.7 and larger through the use of a waveform inversion technique using data from broadband seismic stations on South Island, New Zealand. The majority (126) of these double couple solutions have strike-slip focal mechanisms, with right-lateral slip on ENE fault planes or equivalently left-lateral slip on SSE fault planes. The remaining focal mechanisms indicate reverse faulting, except for two normal faulting events. The strike-slip segments have compatible orientations for slip in a stress field with a horizontal σ1 oriented ~ N115°E, and horizontal σ3. The preference for right lateral strike-slip earthquakes suggests that these structures are inherited from previous stages of deformation. Reverse slip is interpreted to have occurred on previously existing structures in regions with an absence of existing structures optimally oriented for strike-slip deformation. Despite the variations in slip direction and faulting style, most aftershocks had nearly the same P-axis orientation, consistent with the regional σ1. There is no evidence for significant changes in these stress orientations throughout the Canterbury earthquake sequence.
Asymptotic tensor rank of graph tensors: beyond matrix multiplication
M. Christandl (Matthias); P. Vrana (Péter); J. Zuiddam (Jeroen)
2016-01-01
textabstractWe present an upper bound on the exponent of the asymptotic behaviour of the tensor rank of a family of tensors defined by the complete graph on $k$ vertices. For $k\\geq4$, we show that the exponent per edge is at most 0.77, outperforming the best known upper bound on the exponent per
FOOT POSTURAL DEVIATIONS IN FEMALE KATHAK DANCERS
Directory of Open Access Journals (Sweden)
Roopika Sabharwal
2017-09-01
Full Text Available Background: Kathak is a very complex dance form in which greater emphasis is laid on foot work thus putting substantial amount of stress over the feet. The purpose of this study was to investigate the foot postural deviations amongst the Kathak dancers. Methods: Screening of 40 Female Kathak Dancers was done for the study from Department of Dance, Punjabi University, Patiala on the basis of inclusion criteria. Subjects were assessed for Postural deviations via. Foot Posture Index, Medial Longitudinal Arch Angle, Navicular Drop, Rearfoot angle and Forefoot angle. Results: Percentile analysis of Foot Posture index scores suggested that a large population of kathak dancers (approx 92.5 % have pronated feet. Most of the Kathak dancers showed increase in Rearfoot angle (approx. 90%, Forefoot angle (approx.75% and Navicular drop (approx. 97% and decrease in Medial Longitudinal Arch angle (approx. 95%. Analysis of Coefficient of Correlation suggested a significant positive relationship of Foot Posture Index scores with Rearfoot angle (r = 0.40, p= 0.0087, Navicular Drop (r = 0.62, p= < 0.0001 and Forefoot angle (r = 0.51, p=0.0007 and a significant negative correlation with Medial Longitudinal Arch angle (r = -0.42, p= 0.0059. Conclusion: From the observations, it can be concluded that with time kathak dancers start developing certain Postural Deviations at Foot which can lead to hyperpronation. These changes if not treated on time may lead to various degenerative changes in the Foot and Ankle thus leading to the instabilities and can also make them susceptible to foot and ankle injuries, shin pain, etc. Thus, the study recommends that the dancers should be educated and trained about the foot problems associated with kathak dance and their prevention.
Indicial tensor manipulation on MACSYMA
International Nuclear Information System (INIS)
Bogen, R.A.; Pavelle, R.
1977-01-01
A new computational tool for physical calculations is described. It is the first computer system capable of performing indicial tensor calculus (as opposed to component tensor calculus). It is now operational on the symbolic manipulation system MACSYMA. The authors outline the capabilities of the system and describe some of the physical problems considered as well as others being examined at this time. (Auth.)
Core Polarization and Tensor Coupling Effects on Magnetic Moments of Hypernuclei
International Nuclear Information System (INIS)
Jiang-Ming, Yao; Jie, Meng; Hong-Feng, Lü; Greg, Hillhouse
2008-01-01
Effects of core polarization and tensor coupling on the magnetic moments in Λ 13 C, Λ 17 O, and Λ 41 Ca Λ-hypernuclei are studied by employing the Dirac equation with scalar, vector and tensor potentials. It is found that the effect of core polarization on the magnetic moments is suppressed by Λ tensor coupling. The Λ tensor potential reduces the spin-orbit splitting of p Λ states considerably. However, almost the same magnetic moments are obtained using the hyperon wavefunction obtained via the Dirac equation either with or without the A tensor potential in the electromagnetic current vertex. The deviations of magnetic moments for p Λ states from the Schmidt values are found to increase with nuclear mass number. (nuclear physics)
Killing-Yano tensors and Nambu mechanics
International Nuclear Information System (INIS)
Baleanu, D.
1998-01-01
Killing-Yano tensors were introduced in 1952 by Kentaro-Yano from mathematical point of view. The physical interpretation of Killing-Yano tensors of rank higher than two was unclear. We found that all Killing-Yano tensors η i 1 i 2 . .. i n with covariant derivative zero are Nambu tensors. We found that in the case of flat space case all Killing-Yano tensors are Nambu tensors. In the case of Taub-NUT and Kerr-Newmann metric Killing-Yano tensors of order two generate Nambu tensors of rank 3
X-ray strain tensor imaging: FEM simulation and experiments with a micro-CT.
Kim, Jae G; Park, So E; Lee, Soo Y
2014-01-01
In tissue elasticity imaging, measuring the strain tensor components is necessary to solve the inverse problem. However, it is impractical to measure all the tensor components in ultrasound or MRI elastography because of their anisotropic spatial resolution. The objective of this study is to compute 3D strain tensor maps from the 3D CT images of a tissue-mimicking phantom. We took 3D micro-CT images of the phantom twice with applying two different mechanical compressions to it. Applying the 3D image correlation technique to the CT images under different compression, we computed 3D displacement vectors and strain tensors at every pixel. To evaluate the accuracy of the strain tensor maps, we made a 3D FEM model of the phantom, and we computed strain tensor maps through FEM simulation. Experimentally obtained strain tensor maps showed similar patterns to the FEM-simulated ones in visual inspection. The correlation between the strain tensor maps obtained from the experiment and the FEM simulation ranges from 0.03 to 0.93. Even though the strain tensor maps suffer from high level noise, we expect the x-ray strain tensor imaging may find some biomedical applications such as malignant tissue characterization and stress analysis inside the tissues.
MATLAB tensor classes for fast algorithm prototyping.
Energy Technology Data Exchange (ETDEWEB)
Bader, Brett William; Kolda, Tamara Gibson (Sandia National Laboratories, Livermore, CA)
2004-10-01
Tensors (also known as mutidimensional arrays or N-way arrays) are used in a variety of applications ranging from chemometrics to psychometrics. We describe four MATLAB classes for tensor manipulations that can be used for fast algorithm prototyping. The tensor class extends the functionality of MATLAB's multidimensional arrays by supporting additional operations such as tensor multiplication. The tensor as matrix class supports the 'matricization' of a tensor, i.e., the conversion of a tensor to a matrix (and vice versa), a commonly used operation in many algorithms. Two additional classes represent tensors stored in decomposed formats: cp tensor and tucker tensor. We descibe all of these classes and then demonstrate their use by showing how to implement several tensor algorithms that have appeared in the literature.
Random SU(2) invariant tensors
Li, Youning; Han, Muxin; Ruan, Dong; Zeng, Bei
2018-04-01
SU(2) invariant tensors are states in the (local) SU(2) tensor product representation but invariant under the global group action. They are of importance in the study of loop quantum gravity. A random tensor is an ensemble of tensor states. An average over the ensemble is carried out when computing any physical quantities. The random tensor exhibits a phenomenon known as ‘concentration of measure’, which states that for any bipartition the average value of entanglement entropy of its reduced density matrix is asymptotically the maximal possible as the local dimensions go to infinity. We show that this phenomenon is also true when the average is over the SU(2) invariant subspace instead of the entire space for rank-n tensors in general. It is shown in our earlier work Li et al (2017 New J. Phys. 19 063029) that the subleading correction of the entanglement entropy has a mild logarithmic divergence when n = 4. In this paper, we show that for n > 4 the subleading correction is not divergent but a finite number. In some special situation, the number could be even smaller than 1/2, which is the subleading correction of random state over the entire Hilbert space of tensors.
Black holes in vector-tensor theories
Energy Technology Data Exchange (ETDEWEB)
Heisenberg, Lavinia [Institute for Theoretical Studies, ETH Zurich, Clausiusstrasse 47, 8092 Zurich (Switzerland); Kase, Ryotaro; Tsujikawa, Shinji [Department of Physics, Faculty of Science, Tokyo University of Science, 1-3, Kagurazaka, Shinjuku-ku, Tokyo 162-8601 (Japan); Minamitsuji, Masato, E-mail: lavinia.heisenberg@eth-its.ethz.ch, E-mail: r.kase@rs.tus.ac.jp, E-mail: masato.minamitsuji@tecnico.ulisboa.pt, E-mail: shinji@rs.kagu.tus.ac.jp [Centro Multidisciplinar de Astrofisica—CENTRA, Departamento de Fisica, Instituto Superior Tecnico—IST, Universidade de Lisboa—UL, Avenida Rovisco Pais 1, 1049-001 Lisboa (Portugal)
2017-08-01
We study static and spherically symmetric black hole (BH) solutions in second-order generalized Proca theories with nonminimal vector field derivative couplings to the Ricci scalar, the Einstein tensor, and the double dual Riemann tensor. We find concrete Lagrangians which give rise to exact BH solutions by imposing two conditions of the two identical metric components and the constant norm of the vector field. These exact solutions are described by either Reissner-Nordström (RN), stealth Schwarzschild, or extremal RN solutions with a non-trivial longitudinal mode of the vector field. We then numerically construct BH solutions without imposing these conditions. For cubic and quartic Lagrangians with power-law couplings which encompass vector Galileons as the specific cases, we show the existence of BH solutions with the difference between two non-trivial metric components. The quintic-order power-law couplings do not give rise to non-trivial BH solutions regular throughout the horizon exterior. The sixth-order and intrinsic vector-mode couplings can lead to BH solutions with a secondary hair. For all the solutions, the vector field is regular at least at the future or past horizon. The deviation from General Relativity induced by the Proca hair can be potentially tested by future measurements of gravitational waves in the nonlinear regime of gravity.
Calculating contracted tensor Feynman integrals
International Nuclear Information System (INIS)
Fleischer, J.; Riemann, T.
2011-01-01
A recently derived approach to the tensor reduction of 5-point one-loop Feynman integrals expresses the tensor coefficients by scalar 1-point to 4-point Feynman integrals completely algebraically. In this Letter we derive extremely compact algebraic expressions for the contractions of the tensor integrals with external momenta. This is based on sums over signed minors weighted with scalar products of the external momenta. With these contractions one can construct the invariant amplitudes of the matrix elements under consideration, and the evaluation of one-loop contributions to massless and massive multi-particle production at high energy colliders like LHC and ILC is expected to be performed very efficiently.
Metric Tensor Vs. Metric Extensor
Fernández, V. V.; Moya, A. M.; Rodrigues Jr, Waldyr A.
2002-01-01
In this paper we give a comparison between the formulation of the concept of metric for a real vector space of finite dimension in terms of \\emph{tensors} and \\emph{extensors}. A nice property of metric extensors is that they have inverses which are also themselves metric extensors. This property is not shared by metric tensors because tensors do \\emph{not} have inverses. We relate the definition of determinant of a metric extensor with the classical determinant of the corresponding matrix as...
Calculating contracted tensor Feynman integrals
International Nuclear Information System (INIS)
Fleischer, J.
2011-05-01
A recently derived approach to the tensor reduction of 5-point one-loop Feynman integrals expresses the tensor coefficients by scalar 1-point to 4-point Feynman integrals completely algebraically. In this letter we derive extremely compact algebraic expressions for the contractions of the tensor integrals with externalmomenta. This is based on sums over signedminors weighted with scalar products of the external momenta. With these contractions one can construct the invariant amplitudes of the matrix elements under consideration, and the evaluation of one-loop contributions to massless and massive multi-particle production at high energy colliders like LHC and ILC is expected to be performed very efficiently. (orig.)
A tensor approach to the estimation of hydraulic conductivities in ...
African Journals Online (AJOL)
2006-07-03
Jul 3, 2006 ... coefficients, i.e. the fracture roughness and combined stress conditions, are adapted to calibrate the tensor model application. The application ... Darcy's law is always used to estimate the groundwater flow in both porous and ... Inverse analysis on continuous or discontinuous problems dependent on ...
Tensor Product of Polygonal Cell Complexes
Chien, Yu-Yen
2017-01-01
We introduce the tensor product of polygonal cell complexes, which interacts nicely with the tensor product of link graphs of complexes. We also develop the unique factorization property of polygonal cell complexes with respect to the tensor product, and study the symmetries of tensor products of polygonal cell complexes.
2010-01-01
... 10 Energy 4 2010-01-01 2010-01-01 false Deviations. 961.4 Section 961.4 Energy DEPARTMENT OF ENERGY STANDARD CONTRACT FOR DISPOSAL OF SPENT NUCLEAR FUEL AND/OR HIGH-LEVEL RADIOACTIVE WASTE General... the deviation and nuclear power reactor(s) affected; (e) A statement as to whether the deviation has...
Colored Tensor Models - a Review
Directory of Open Access Journals (Sweden)
Razvan Gurau
2012-04-01
Full Text Available Colored tensor models have recently burst onto the scene as a promising conceptual and computational tool in the investigation of problems of random geometry in dimension three and higher. We present a snapshot of the cutting edge in this rapidly expanding research field. Colored tensor models have been shown to share many of the properties of their direct ancestor, matrix models, which encode a theory of fluctuating two-dimensional surfaces. These features include the possession of Feynman graphs encoding topological spaces, a 1/N expansion of graph amplitudes, embedded matrix models inside the tensor structure, a resumable leading order with critical behavior and a continuum large volume limit, Schwinger-Dyson equations satisfying a Lie algebra (akin to the Virasoro algebra in two dimensions, non-trivial classical solutions and so on. In this review, we give a detailed introduction of colored tensor models and pointers to current and future research directions.
[Vertical and tortional deviations in early strabismus].
Spielmann, A
1990-04-01
The occlusion of one eye may trigger two types of deviation: 1) Heterophorias: the occluded eye deviates towards a horizontal, vertical or torsional abnormal position of rest. Fusion keeps the eyes straight during binocular fixation. 2) Dissociated deviations, horizontal (DHD), vertical (DVD), torsional (DTD): they are found in infantile strabismus. The deviation without fixation is always smaller than the deviation of the occluded eye. The more typical cases are the ones where the position of rest without fixation is an orthoposition. Normal binocular vision is lacking. Most of the time, an alternant neutralisation is found: the occlusion deviation is not the return of the occluded eye to an abnormal position of rest. The deviation is caused by a disequilibrium of binocular retinal stimulations. Horizontal and vertical deviations are easy to study. It is not the case in dissociated torsional deviation (DTD) where the incyclotorsion does not exist when fixation is absent. An indirect proof of extorsion is given by the study of horizontal and vertical deviations determined in the cardinal position of gaze. Extorsion of the globus leeds always to abnormal actions of the recti. This give a typical synoptometer chart which is found in any extorsion whatever its origins: paralysis, alphabetic patterns or infantile strabismus. Dissociated extorsions are always associated with a bilateral elevation in the primary position. Dissociated deviations are found in infantile strabismus with the other dissociations phenomenon such as nystagmus, optokinetic nystagmus asymmetry, fixation in adduction preference (and incyclotorsion).
Physical and Geometric Interpretations of the Riemann Tensor, Ricci Tensor, and Scalar Curvature
Loveridge, Lee C.
2004-01-01
Various interpretations of the Riemann Curvature Tensor, Ricci Tensor, and Scalar Curvature are described. Also, the physical meanings of the Einstein Tensor and Einstein's Equations are discussed. Finally a derivation of Newtonian Gravity from Einstein's Equations is given.
Theoretical study of the relativistic molecular rotational g-tensor
International Nuclear Information System (INIS)
Aucar, I. Agustín; Gomez, Sergio S.; Giribet, Claudia G.; Ruiz de Azúa, Martín C.
2014-01-01
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 + (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 + systems. Only for the sixth-row Rn atom a significant deviation of this relation is found
Theoretical study of the relativistic molecular rotational g-tensor
Energy Technology Data Exchange (ETDEWEB)
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.
Teh, Irvin; McClymont, Darryl; Zdora, Marie-Christine; Whittington, Hannah J; Davidoiu, Valentina; Lee, Jack; Lygate, Craig A; Rau, Christoph; Zanette, Irene; Schneider, Jürgen E
2017-03-10
Diffusion tensor imaging (DTI) is widely used to assess tissue microstructure non-invasively. Cardiac DTI enables inference of cell and sheetlet orientations, which are altered under pathological conditions. However, DTI is affected by many factors, therefore robust validation is critical. Existing histological validation is intrinsically flawed, since it requires further tissue processing leading to sample distortion, is routinely limited in field-of-view and requires reconstruction of three-dimensional volumes from two-dimensional images. In contrast, synchrotron radiation imaging (SRI) data enables imaging of the heart in 3D without further preparation following DTI. The objective of the study was to validate DTI measurements based on structure tensor analysis of SRI data. One isolated, fixed rat heart was imaged ex vivo with DTI and X-ray phase contrast SRI, and reconstructed at 100 μm and 3.6 μm isotropic resolution respectively. Structure tensors were determined from the SRI data and registered to the DTI data. Excellent agreement in helix angles (HA) and transverse angles (TA) was observed between the DTI and structure tensor synchrotron radiation imaging (STSRI) data, where HA DTI-STSRI = -1.4° ± 23.2° and TA DTI-STSRI = -1.4° ± 35.0° (mean ± 1.96 standard deviation across all voxels in the left ventricle). STSRI confirmed that the primary eigenvector of the diffusion tensor corresponds with the cardiomyocyte long-axis across the whole myocardium. We have used STSRI as a novel and high-resolution gold standard for the validation of DTI, allowing like-with-like comparison of three-dimensional tissue structures in the same intact heart free of distortion. This represents a critical step forward in independently verifying the structural basis and informing the interpretation of cardiac DTI data, thereby supporting the further development and adoption of DTI in structure-based electro-mechanical modelling and routine clinical
Calibration of magnetic gradient tensor measurement array in magnetic anomaly detection
Chen, Jinfei; Zhang, Qi; Pan, Mengchun; Weng, Feibing; Chen, Dixiang; Pang, Hongfeng
2013-01-01
Magnetic anomaly detection based on magnetic gradient tensor has become more and more important in civil and military applications. Compared with methods based on magnetic total field or components measurement, magnetic gradient tensor has some unique advantages. Usually, a magnetic gradient tensor measurement array is constituted by four three-axis magnetometers. The prominent problem of magnetic gradient tensor measurement array is the misalignment of sensors. In order to measure the magnetic gradient tensor accurately, it is quite essential to calibrate the measurement array. The calibration method, which is proposed in this paper, is divided into two steps. In the first step, each sensor of the measurement array should be calibrated, whose error is mainly caused by constant biases, scale factor deviations and nonorthogonality of sensor axes. The error of measurement array is mainly caused by the misalignment of sensors, so that triplets' deviation in sensors array coordinates is calibrated in the second step. In order to verify the effectiveness of the proposed method, simulation was taken and the result shows that the proposed method improves the measurement accuracy of magnetic gradient tensor greatly.
The tensor rank of tensor product of two three-qubit W states is eight
Chen, Lin; Friedland, Shmuel
2017-01-01
We show that the tensor rank of tensor product of two three-qubit W states is not less than eight. Combining this result with the recent result of M. Christandl, A. K. Jensen, and J. Zuiddam that the tensor rank of tensor product of two three-qubit W states is at most eight, we deduce that the tensor rank of tensor product of two three-qubit W states is eight. We also construct the upper bound of the tensor rank of tensor product of many three-qubit W states.
DUCASSE , Eric; YAACOUBI , Slah
2010-01-01
International audience; A tensor Hankel transform'' (THT) is defined for vector fields, such as displacement, and second-order tensor fields, such as stress or strain. The THT establishes a bijection between the real space and the wave-vector domain, and, remarkably, cannot be reduced to a scalar transform applied separately to each component. One of the advantages of this approach is that some standard elasticity problems can be concisely rewritten by applying this tensor integral transform ...
Moderate Deviations for Recursive Stochastic Algorithms
2014-08-02
There are also results for martingale di¤erences such as Dembo [9], Gao [16], and Djellout [11]. For various reasons, the issues previously mentioned...deviations approach to design and analysis. Stoch. Proc. Appl., 119:562� 587, 2009. [9] A. Dembo. Moderate deviations for martingales with bounded jumps...H. Djellout. Moderate deviations for martingale di¤erences and applic- ations to -mixing sequences. Stoch. Stoch. Rep., 73:37�63, 2002. [12] P
Tensor Target Polarization at TRIUMF
Energy Technology Data Exchange (ETDEWEB)
Smith, G
2014-10-27
The first measurements of tensor observables in $\\pi \\vec{d}$ scattering experiments were performed in the mid-80's at TRIUMF, and later at SIN/PSI. The full suite of tensor observables accessible in $\\pi \\vec{d}$ elastic scattering were measured: $T_{20}$, $T_{21}$, and $T_{22}$. The vector analyzing power $iT_{11}$ was also measured. These results led to a better understanding of the three-body theory used to describe this reaction. %Some measurements were also made in the absorption and breakup channels. A direct measurement of the target tensor polarization was also made independent of the usual NMR techniques by exploiting the (nearly) model-independent result for the tensor analyzing power at 90$^\\circ _{cm}$ in the $\\pi \\vec{d} \\rightarrow 2p$ reaction. This method was also used to check efforts to enhance the tensor polarization by RF burning of the NMR spectrum. A brief description of the methods developed to measure and analyze these experiments is provided.
Link prediction via generalized coupled tensor factorisation
DEFF Research Database (Denmark)
Ermiş, Beyza; Evrim, Acar Ataman; Taylan Cemgil, A.
2012-01-01
and higher-order tensors. We propose to use an approach based on probabilistic interpretation of tensor factorisation models, i.e., Generalised Coupled Tensor Factorisation, which can simultaneously fit a large class of tensor models to higher-order tensors/matrices with com- mon latent factors using...... different loss functions. Numerical experiments demonstrate that joint analysis of data from multiple sources via coupled factorisation improves the link prediction performance and the selection of right loss function and tensor model is crucial for accurately predicting missing links....
41 CFR 115-1.110 - Deviations.
2010-07-01
... 41 Public Contracts and Property Management 3 2010-07-01 2010-07-01 false Deviations. 115-1.110 Section 115-1.110 Public Contracts and Property Management Federal Property Management Regulations System (Continued) ENVIRONMENTAL PROTECTION AGENCY 1-INTRODUCTION 1.1-Regulation System § 115-1.110 Deviations...
2010-07-01
... 41 Public Contracts and Property Management 3 2010-07-01 2010-07-01 false Deviation. 105-1.110 Section 105-1.110 Public Contracts and Property Management Federal Property Management Regulations System (Continued) GENERAL SERVICES ADMINISTRATION 1-INTRODUCTION 1.1-Regulations System § 105-1.110 Deviation. (a...
2010-07-01
... 41 Public Contracts and Property Management 2 2010-07-01 2010-07-01 true Deviation. 101-1.110 Section 101-1.110 Public Contracts and Property Management Federal Property Management Regulations System FEDERAL PROPERTY MANAGEMENT REGULATIONS GENERAL 1-INTRODUCTION 1.1-Regulation System § 101-1.110 Deviation...
Tensor product of quantum logics
Pulmannová, Sylvia
1985-01-01
A quantum logic is the couple (L,M) where L is an orthomodular σ-lattice and M is a strong set of states on L. The Jauch-Piron property in the σ-form is also supposed for any state of M. A ``tensor product'' of quantum logics is defined. This definition is compared with the definition of a free orthodistributive product of orthomodular σ-lattices. The existence and uniqueness of the tensor product in special cases of Hilbert space quantum logics and one quantum and one classical logic are studied.
Phase transition in tensor models
Energy Technology Data Exchange (ETDEWEB)
Delepouve, Thibault [Laboratoire de Physique Théorique, CNRS UMR 8627, Université Paris Sud,91405 Orsay Cedex (France); Centre de Physique Théorique, CNRS UMR 7644, École Polytechnique,91128 Palaiseau Cedex (France); Gurau, Razvan [Centre de Physique Théorique, CNRS UMR 7644, École Polytechnique,91128 Palaiseau Cedex (France); Perimeter Institute for Theoretical Physics,31 Caroline St. N, N2L 2Y5, Waterloo, ON (Canada)
2015-06-25
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.
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...
The 'gravitating' tensor in the dualistic theory
International Nuclear Information System (INIS)
Mahanta, M.N.
1989-01-01
The exact microscopic system of Einstein-type field equations of the dualistic gravitation theory is investigated as well as an analysis of the modified energy-momentum tensor or so called 'gravitating' tensor is presented
Reciprocal mass tensor : a general form
International Nuclear Information System (INIS)
Roy, C.L.
1978-01-01
Using the results of earlier treatment of wave packets, a general form of reciprocal mass tensor has been obtained. The elements of this tensor are seen to be dependent on momentum as well as space coordinates of the particle under consideration. The conditions under which the tensor would reduce to the usual space-independent form, are discussed and the impact of the space-dependence of this tensor on the motion of Bloch electrons, is examined. (author)
Tensor-based spatiotemporal saliency detection
Dou, Hao; Li, Bin; Deng, Qianqian; Zhang, LiRui; Pan, Zhihong; Tian, Jinwen
2018-03-01
This paper proposes an effective tensor-based spatiotemporal saliency computation model for saliency detection in videos. First, we construct the tensor representation of video frames. Then, the spatiotemporal saliency can be directly computed by the tensor distance between different tensors, which can preserve the complete temporal and spatial structure information of object in the spatiotemporal domain. Experimental results demonstrate that our method can achieve encouraging performance in comparison with the state-of-the-art methods.
Akkerman, Erik M.
2010-01-01
Both in diffusion tensor imaging (DTI) and in generalized diffusion tensor imaging (GDTI) the relation between the diffusion tensor and the measured apparent diffusion coefficients is given by a tensorial equation, which needs to be inverted in order to solve the diffusion tensor. The traditional
Bridging scales of crustal stress patterns using the new World Stress Map
Heidbach, O.; Rajabi, M.; Cui, X.; Fuchs, K. W.; Mueller, B.; Reinecker, J.; Reiter, K.; Tingay, M. R. P.; Wenzel, F.; Xie, F.; Ziegler, M.; Zoback, M. D.; Zoback, M. L.
2017-12-01
Knowledge of the contemporary crustal stress field is a key parameter for the understanding of geodynamic processes such as global plate tectonics and the earthquake cycle. It is also an essential parameter for our sustainable and safe usage of Earth's resources, which is a major challenge for energy security in the 21st century. Since 1986, the World Stress Map (WSM) project has systematically compiled present-day stress information and provides a unique public domain global database. It is a long-term project based on an international network of partners from academia and industry. All data are public and available on the project website at world-stress-map.org. For the 30th anniversary of the project a new database has been compiled, containing double the amount of data records (n=42,870) including new data records from almost 4,000 deep boreholes. The new compilation focused on areas with previously sparse data coverage in order to resolve the stress pattern on different spatial scales. The significantly higher data density can now be used to resolve stress pattern heterogeneities on regional and local scales, as well as with depth in some regions. We present three results derived from the new WSM compilation: 1.) The global comparison between absolute plate motion and the mean of the orientation of maximum horizontal stress SHmax on a regular grid shows that there is still a correlation for the North and South America plate, but deviations from this general trend are now also clearly resolved. 2.) The variability of the crustal stress pattern changes when zooming in from plate-wide scale down to basin scale at 100 km. We show examples for Eastern Australia, Oklahoma and Central Europe. This regional and local variability of the stress pattern can be used as a proxy to identify and quantify regional and local stress sources by means of geomechanical-numerical models of the 3D stress tensor. 3.) Finally we present briefly the general concept of a multi-stage 3D
Entanglement transitions induced by large deviations
Bhosale, Udaysinh T.
2017-12-01
The probability of large deviations of the smallest Schmidt eigenvalue for random pure states of bipartite systems, denoted as A and B , is computed analytically using a Coulomb gas method. It is shown that this probability, for large N , goes as exp[-β N2Φ (ζ ) ] , where the parameter β is the Dyson index of the ensemble, ζ is the large deviation parameter, while the rate function Φ (ζ ) is calculated exactly. Corresponding equilibrium Coulomb charge density is derived for its large deviations. Effects of the large deviations of the extreme (largest and smallest) Schmidt eigenvalues on the bipartite entanglement are studied using the von Neumann entropy. Effect of these deviations is also studied on the entanglement between subsystems 1 and 2, obtained by further partitioning the subsystem A , using the properties of the density matrix's partial transpose ρ12Γ. The density of states of ρ12Γ is found to be close to the Wigner's semicircle law with these large deviations. The entanglement properties are captured very well by a simple random matrix model for the partial transpose. The model predicts the entanglement transition across a critical large deviation parameter ζ . Log negativity is used to quantify the entanglement between subsystems 1 and 2. Analytical formulas for it are derived using the simple model. Numerical simulations are in excellent agreement with the analytical results.
Weyl tensors for asymmetric complex curvatures
International Nuclear Information System (INIS)
Oliveira, C.G.
Considering a second rank Hermitian field tensor and a general Hermitian connection the associated complex curvature tensor is constructed. The Weyl tensor that corresponds to this complex curvature is determined. The formalism is applied to the Weyl unitary field theory and to the Moffat gravitational theory. (Author) [pt
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.
TERMINOLOGY MANAGEMENT FRAMEWORK DEVIATIONS IN PROJECTS
Directory of Open Access Journals (Sweden)
Олена Борисівна ДАНЧЕНКО
2015-05-01
Full Text Available The article reviews new approaches to managing projects deviations (risks, changes, problems. By offering integrated control these parameters of the project and by analogy with medical terminological systems building a new system for managing terminological variations in the projects. With an improved method of triads system definitions are analyzed medical terms that make up terminological basis. Using the method of analogy proposed new definitions for managing deviations in projects. By using triad integrity built a new system triad in project management, which will subsequently also analogous to develop a new methodology of deviations in projects.
Projectors and seed conformal blocks for traceless mixed-symmetry tensors
Energy Technology Data Exchange (ETDEWEB)
Costa, Miguel S. [Centro de Física do Porto, Departamento de Física e Astronomia, Faculdade de Ciências da Universidade do Porto, Rua do Campo Alegre 687, 4169-007 Porto (Portugal); Theory Division, Department of Physics, CERN, CH-1211 Genève 23 (Switzerland); Hansen, Tobias [Centro de Física do Porto, Departamento de Física e Astronomia, Faculdade de Ciências da Universidade do Porto, Rua do Campo Alegre 687, 4169-007 Porto (Portugal); II. Institut für Theoretische Physik, Universität Hamburg, Luruper Chaussee 149, D-22761 Hamburg (Germany); Penedones, João [Centro de Física do Porto, Departamento de Física e Astronomia, Faculdade de Ciências da Universidade do Porto, Rua do Campo Alegre 687, 4169-007 Porto (Portugal); Theory Division, Department of Physics, CERN, CH-1211 Genève 23 (Switzerland); Fields and Strings Laboratory, Institute of Physics, EPFL, CH-1015 Lausanne (Switzerland); Trevisani, Emilio [Centro de Física do Porto, Departamento de Física e Astronomia, Faculdade de Ciências da Universidade do Porto, Rua do Campo Alegre 687, 4169-007 Porto (Portugal)
2016-07-05
In this paper we derive the projectors to all irreducible SO(d) representations (traceless mixed-symmetry tensors) that appear in the partial wave decomposition of a conformal correlator of four stress-tensors in d dimensions. These projectors are given in a closed form for arbitrary length l{sub 1} of the first row of the Young diagram. The appearance of Gegenbauer polynomials leads directly to recursion relations in l{sub 1} for seed conformal blocks. Further results include a differential operator that generates the projectors to traceless mixed-symmetry tensors and the general normalization constant of the shadow operator.
Projectors and seed conformal blocks for traceless mixed-symmetry tensors
Costa, Miguel S.; Penedones, João; Trevisani, Emilio
2016-01-01
In this paper we derive the projectors to all irreducible SO(d) representations (traceless mixed-symmetry tensors) that appear in the partial wave decomposition of a conformal correlator of four stress-tensors in d dimensions. These projectors are given in a closed form for arbitrary length $l_1$ of the first row of the Young diagram. The appearance of Gegenbauer polynomials leads directly to recursion relations in $l_1$ for seed conformal blocks. Further results include a differential operator that generates the projectors to traceless mixed-symmetry tensors and the general normalization constant of the shadow operator.
Ion density deviations in semipermeable ionic microcapsules.
Tang, Qiyun; Denton, Alan R
2015-04-28
By implementing the nonlinear Poisson-Boltzmann theory in a cell model, we theoretically investigate the influence of polyelectrolye gel permeability on ion densities and pH deviations inside the cavities of ionic microcapsules. Our calculations show that variations in permeability of a charged capsule shell cause a redistribution of ion densities within the capsule, which ultimately affects the pH deviation and Donnan potential induced by the electric field of the shell. We find that semipermeable capsules can induce larger pH deviations inside their cavities that can permeable capsules. Furthermore, with increasing capsule charge, the influence of permeability on pH deviations progressively increases. Our theory, while providing a self-consistent method for modeling the influence of permeability on fundamental properties of ionic microgels, makes predictions of practical significance for the design of microcapsules loaded with fluorescent dyes, which can serve as biosensors for diagnostic purposes.
48 CFR 3001.403 - Individual deviations.
2010-10-01
... CFR 30.201-3, 30.201-4; the requirements of the Cost Accounting Standards board rules and regulations..., including complete documentation of the justification for the deviation (See HSAM 3001.403). ...
Comparison of Magnetic Susceptibility Tensor and Diffusion Tensor of the Brain.
Li, Wei; Liu, Chunlei
2013-10-01
Susceptibility tensor imaging (STI) provides a novel approach for noninvasive assessment of the white matter pathways of the brain. Using mouse brain ex vivo , we compared STI with diffusion tensor imaging (DTI), in terms of tensor values, principal tensor values, anisotropy values, and tensor orientations. Despite the completely different biophysical underpinnings, magnetic susceptibility tensors and diffusion tensors show many similarities in the tensor and principal tensor images, for example, the tensors perpendicular to the fiber direction have the highest gray-white matter contrast, and the largest principal tensor is along the fiber direction. Comparison to DTI fractional anisotropy, the susceptibility anisotropy provides much higher sensitivity to the chemical composition of the white matter, especially myelin. The high sensitivity can be further enhanced with the perfusion of ProHance, a gadolinium-based contrast agent. Regarding the tensor orientations, the direction of the largest principal susceptibility tensor agrees with that of diffusion tensors in major white matter fiber bundles. The STI fiber tractography can reconstruct the fiber pathways for the whole corpus callosum and for white matter fiber bundles that are in close contact but in different orientations. There are some differences between susceptibility and diffusion tensor orientations, which are likely due to the limitations in the current STI reconstruction. With the development of more accurate reconstruction methods, STI holds the promise for probing the white matter micro-architectures with more anatomical details and higher chemical sensitivity.
Tensor Fields for Use in Fractional-Order Viscoelasticity
Freed, Alan D.; Diethelm, Kai
2003-01-01
To be able to construct viscoelastic material models from fractional0order differentegral equations that are applicable for 3D finite-strain analysis requires definitions for fractional derivatives and integrals for symmetric tensor fields, like stress and strain. We define these fields in the body manifold. We then map them ito spatial fields expressed in terms of an Eulerian or Lagrangian reference frame where most analysts prefer to solve boundary problems.
Evaluation of the tensor polynomial failure criterion for composite materials
Tennyson, R. C.; Macdonald, D.; Nanyaro, A. P.
1978-01-01
A comprehensive experimental and analytical evaluation of the tensor polynomial failure criterion was undertaken to determine its capability for predicting the ultimate strength of laminated composite structures subject to a plane stress state. Results are presented demonstrating that a quadratic formulation is too conservative and a cubic representation is required. Strength comparisons with test data derived from glass/epoxy and graphite/epoxy tubular specimens are also provided to validate the cubic strength criterion.
The large deviations theorem and ergodicity
International Nuclear Information System (INIS)
Gu Rongbao
2007-01-01
In this paper, some relationships between stochastic and topological properties of dynamical systems are studied. For a continuous map f from a compact metric space X into itself, we show that if f satisfies the large deviations theorem then it is topologically ergodic. Moreover, we introduce the topologically strong ergodicity, and prove that if f is a topologically strongly ergodic map satisfying the large deviations theorem then it is sensitively dependent on initial conditions
The Physical Interpretation of the Lanczos Tensor
Roberts, Mark D.
1999-01-01
The field equations of general relativity can be written as first order differential equations in the Weyl tensor, the Weyl tensor in turn can be written as a first order differential equation in a three index tensor called the Lanczos tensor. The Lanczos tensor plays a similar role in general relativity to that of the vector potential in electro-magnetic theory. The Aharonov-Bohm effect shows that when quantum mechanics is applied to electro-magnetic theory the vector potential is dynamicall...
The large deviation approach to statistical mechanics
Touchette, Hugo
2009-07-01
The theory of large deviations is concerned with the exponential decay of probabilities of large fluctuations in random systems. These probabilities are important in many fields of study, including statistics, finance, and engineering, as they often yield valuable information about the large fluctuations of a random system around its most probable state or trajectory. In the context of equilibrium statistical mechanics, the theory of large deviations provides exponential-order estimates of probabilities that refine and generalize Einstein’s theory of fluctuations. This review explores this and other connections between large deviation theory and statistical mechanics, in an effort to show that the mathematical language of statistical mechanics is the language of large deviation theory. The first part of the review presents the basics of large deviation theory, and works out many of its classical applications related to sums of random variables and Markov processes. The second part goes through many problems and results of statistical mechanics, and shows how these can be formulated and derived within the context of large deviation theory. The problems and results treated cover a wide range of physical systems, including equilibrium many-particle systems, noise-perturbed dynamics, nonequilibrium systems, as well as multifractals, disordered systems, and chaotic systems. This review also covers many fundamental aspects of statistical mechanics, such as the derivation of variational principles characterizing equilibrium and nonequilibrium states, the breaking of the Legendre transform for nonconcave entropies, and the characterization of nonequilibrium fluctuations through fluctuation relations.
The large deviation approach to statistical mechanics
International Nuclear Information System (INIS)
Touchette, Hugo
2009-01-01
The theory of large deviations is concerned with the exponential decay of probabilities of large fluctuations in random systems. These probabilities are important in many fields of study, including statistics, finance, and engineering, as they often yield valuable information about the large fluctuations of a random system around its most probable state or trajectory. In the context of equilibrium statistical mechanics, the theory of large deviations provides exponential-order estimates of probabilities that refine and generalize Einstein's theory of fluctuations. This review explores this and other connections between large deviation theory and statistical mechanics, in an effort to show that the mathematical language of statistical mechanics is the language of large deviation theory. The first part of the review presents the basics of large deviation theory, and works out many of its classical applications related to sums of random variables and Markov processes. The second part goes through many problems and results of statistical mechanics, and shows how these can be formulated and derived within the context of large deviation theory. The problems and results treated cover a wide range of physical systems, including equilibrium many-particle systems, noise-perturbed dynamics, nonequilibrium systems, as well as multifractals, disordered systems, and chaotic systems. This review also covers many fundamental aspects of statistical mechanics, such as the derivation of variational principles characterizing equilibrium and nonequilibrium states, the breaking of the Legendre transform for nonconcave entropies, and the characterization of nonequilibrium fluctuations through fluctuation relations.
Conformal correlators of mixed-symmetry tensors
Costa, Miguel S
2015-01-01
We generalize the embedding formalism for conformal field theories to the case of general operators with mixed symmetry. The index-free notation encoding symmetric tensors as polynomials in an auxiliary polarization vector is extended to mixed-symmetry tensors by introducing a new commuting or anticommuting polarization vector for each row or column in the Young diagram that describes the index symmetries of the tensor. We determine the tensor structures that are allowed in n-point conformal correlation functions and give an algorithm for counting them in terms of tensor product coefficients. We show, with an example, how the new formalism can be used to compute conformal blocks of arbitrary external fields for the exchange of any conformal primary and its descendants. The matching between the number of tensor structures in conformal field theory correlators of operators in d dimensions and massive scattering amplitudes in d+1 dimensions is also seen to carry over to mixed-symmetry tensors.
Antisymmetric tensor generalizations of affine vector fields.
Houri, Tsuyoshi; Morisawa, Yoshiyuki; Tomoda, Kentaro
2016-02-01
Tensor generalizations of affine vector fields called symmetric and antisymmetric affine tensor fields are discussed as symmetry of spacetimes. We review the properties of the symmetric ones, which have been studied in earlier works, and investigate the properties of the antisymmetric ones, which are the main theme in this paper. It is shown that antisymmetric affine tensor fields are closely related to one-lower-rank antisymmetric tensor fields which are parallelly transported along geodesics. It is also shown that the number of linear independent rank- p antisymmetric affine tensor fields in n -dimensions is bounded by ( n + 1)!/ p !( n - p )!. We also derive the integrability conditions for antisymmetric affine tensor fields. Using the integrability conditions, we discuss the existence of antisymmetric affine tensor fields on various spacetimes.
Koch, Saskia B. J.; van Zuiden, Mirjam; Nawijn, Laura; Frijling, Jessie L.; Veltman, Dick J.; Olff, Miranda
2017-01-01
Background: Posttraumatic stress disorder (PTSD) is a disabling psychiatric disorder that has been associated with lower white matter integrity of tracts connecting the prefrontal cortex with limbic regions. However, previous diffusion tensor imaging (DTI) findings have been inconsistent, showing
Spectral Tensor-Train Decomposition
DEFF Research Database (Denmark)
Bigoni, Daniele; Engsig-Karup, Allan Peter; Marzouk, Youssef M.
2016-01-01
discretizations of the target function. We assess the performance of the method on a range of numerical examples: a modified set of Genz functions with dimension up to 100, and functions with mixed Fourier modes or with local features. We observe significant improvements in performance over an anisotropic......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...
Diffusion tensor optical coherence tomography
Marks, Daniel L.; Blackmon, Richard L.; Oldenburg, Amy L.
2018-01-01
In situ measurements of diffusive particle transport provide insight into tissue architecture, drug delivery, and cellular function. Analogous to diffusion-tensor magnetic resonance imaging (DT-MRI), where the anisotropic diffusion of water molecules is mapped on the millimeter scale to elucidate the fibrous structure of tissue, here we propose diffusion-tensor optical coherence tomography (DT-OCT) for measuring directional diffusivity and flow of optically scattering particles within tissue. Because DT-OCT is sensitive to the sub-resolution motion of Brownian particles as they are constrained by tissue macromolecules, it has the potential to quantify nanoporous anisotropic tissue structure at micrometer resolution as relevant to extracellular matrices, neurons, and capillaries. Here we derive the principles of DT-OCT, relating the detected optical signal from a minimum of six probe beams with the six unique diffusion tensor and three flow vector components. The optimal geometry of the probe beams is determined given a finite numerical aperture, and a high-speed hardware implementation is proposed. Finally, Monte Carlo simulations are employed to assess the ability of the proposed DT-OCT system to quantify anisotropic diffusion of nanoparticles in a collagen matrix, an extracellular constituent that is known to become highly aligned during tumor development.
Transposes, L-Eigenvalues and Invariants of Third Order Tensors
Qi, Liqun
2017-01-01
Third order tensors have wide applications in mechanics, physics and engineering. The most famous and useful third order tensor is the piezoelectric tensor, which plays a key role in the piezoelectric effect, first discovered by Curie brothers. On the other hand, the Levi-Civita tensor is famous in tensor calculus. In this paper, we study third order tensors and (third order) hypermatrices systematically, by regarding a third order tensor as a linear operator which transforms a second order t...
Transport Coefficients from Large Deviation Functions
Directory of Open Access Journals (Sweden)
Chloe Ya Gao
2017-10-01
Full Text Available We describe a method for computing transport coefficients from the direct evaluation of large deviation functions. This method is general, relying on only equilibrium fluctuations, and is statistically efficient, employing trajectory based importance sampling. Equilibrium fluctuations of molecular currents are characterized by their large deviation functions, which are scaled cumulant generating functions analogous to the free energies. A diffusion Monte Carlo algorithm is used to evaluate the large deviation functions, from which arbitrary transport coefficients are derivable. We find significant statistical improvement over traditional Green–Kubo based calculations. The systematic and statistical errors of this method are analyzed in the context of specific transport coefficient calculations, including the shear viscosity, interfacial friction coefficient, and thermal conductivity.
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.
Tensor SOM and tensor GTM: Nonlinear tensor analysis by topographic mappings.
Iwasaki, Tohru; Furukawa, Tetsuo
2016-05-01
In this paper, we propose nonlinear tensor analysis methods: the tensor self-organizing map (TSOM) and the tensor generative topographic mapping (TGTM). TSOM is a straightforward extension of the self-organizing map from high-dimensional data to tensorial data, and TGTM is an extension of the generative topographic map, which provides a theoretical background for TSOM using a probabilistic generative model. These methods are useful tools for analyzing and visualizing tensorial data, especially multimodal relational data. For given n-mode relational data, TSOM and TGTM can simultaneously organize a set of n-topographic maps. Furthermore, they can be used to explore the tensorial data space by interactively visualizing the relationships between modes. We present the TSOM algorithm and a theoretical description from the viewpoint of TGTM. Various TSOM variations and visualization techniques are also described, along with some applications to real relational datasets. Additionally, we attempt to build a comprehensive description of the TSOM family by adapting various data structures. Copyright © 2016 Elsevier Ltd. All rights reserved.
Evolutionary implications of genetic code deviations
International Nuclear Information System (INIS)
Chela Flores, J.
1986-07-01
By extending the standard genetic code into a temperature dependent regime, we propose a train of molecular events leading to alternative coding. The first few examples of these deviations have already been reported in some ciliated protozoans and Gram positive bacteria. A possible range of further alternative coding, still within the context of universality, is pointed out. (author)
Bodily Deviations and Body Image in Adolescence
Vilhjalmsson, Runar; Kristjansdottir, Gudrun; Ward, Dianne S.
2012-01-01
Adolescents with unusually sized or shaped bodies may experience ridicule, rejection, or exclusion based on their negatively valued bodily characteristics. Such experiences can have negative consequences for a person's image and evaluation of self. This study focuses on the relationship between bodily deviations and body image and is based on a…
48 CFR 201.404 - Class deviations.
2010-10-01
..., and the Defense Logistics Agency, may approve any class deviation, other than those described in 201...) Diminish any preference given small business concerns by the FAR or DFARS; or (D) Extend to requirements imposed by statute or by regulations of other agencies such as the Small Business Administration and the...
Seamless warping of diffusion tensor fields
DEFF Research Database (Denmark)
Xu, Dongrong; Hao, Xuejun; Bansal, Ravi
2008-01-01
To warp diffusion tensor fields accurately, tensors must be reoriented in the space to which the tensors are warped based on both the local deformation field and the orientation of the underlying fibers in the original image. Existing algorithms for warping tensors typically use forward mapping...... of seams, including voxels in which the deformation is extensive. Backward mapping, however, cannot reorient tensors in the template space because information about the directional orientation of fiber tracts is contained in the original, unwarped imaging space only, and backward mapping alone cannot...... transfer that information to the template space. To combine the advantages of forward and backward mapping, we propose a novel method for the spatial normalization of diffusion tensor (DT) fields that uses a bijection (a bidirectional mapping with one-to-one correspondences between image spaces) to warp DT...
Numerical Approximation of Elasticity Tensor Associated With Green-Naghdi Rate.
Liu, Haofei; Sun, Wei
2017-08-01
Objective stress rates are often used in commercial finite element (FE) programs. However, deriving a consistent tangent modulus tensor (also known as elasticity tensor or material Jacobian) associated with the objective stress rates is challenging when complex material models are utilized. In this paper, an approximation method for the tangent modulus tensor associated with the Green-Naghdi rate of the Kirchhoff stress is employed to simplify the evaluation process. The effectiveness of the approach is demonstrated through the implementation of two user-defined fiber-reinforced hyperelastic material models. Comparisons between the approximation method and the closed-form analytical method demonstrate that the former can simplify the material Jacobian evaluation with satisfactory accuracy while retaining its computational efficiency. Moreover, since the approximation method is independent of material models, it can facilitate the implementation of complex material models in FE analysis using shell/membrane elements in abaqus.
Schrimpf, Martin
2016-01-01
Google's Machine Learning framework TensorFlow was open-sourced in November 2015 [1] and has since built a growing community around it. TensorFlow is supposed to be flexible for research purposes while also allowing its models to be deployed productively. This work is aimed towards people with experience in Machine Learning considering whether they should use TensorFlow in their environment. Several aspects of the framework important for such a decision are examined, such as the heterogenity,...
Dictionary-Based Tensor Canonical Polyadic Decomposition
Cohen, Jeremy Emile; Gillis, Nicolas
2018-04-01
To ensure interpretability of extracted sources in tensor decomposition, we introduce in this paper a dictionary-based tensor canonical polyadic decomposition which enforces one factor to belong exactly to a known dictionary. A new formulation of sparse coding is proposed which enables high dimensional tensors dictionary-based canonical polyadic decomposition. The benefits of using a dictionary in tensor decomposition models are explored both in terms of parameter identifiability and estimation accuracy. Performances of the proposed algorithms are evaluated on the decomposition of simulated data and the unmixing of hyperspectral images.
Bayesian regularization of diffusion tensor images
DEFF Research Database (Denmark)
Frandsen, Jesper; Hobolth, Asger; Østergaard, Leif
2007-01-01
Diffusion tensor imaging (DTI) is a powerful tool in the study of the course of nerve fibre bundles in the human brain. Using DTI, the local fibre orientation in each image voxel can be described by a diffusion tensor which is constructed from local measurements of diffusion coefficients along...... several directions. The measured diffusion coefficients and thereby the diffusion tensors are subject to noise, leading to possibly flawed representations of the three dimensional fibre bundles. In this paper we develop a Bayesian procedure for regularizing the diffusion tensor field, fully utilizing...
Inflationary cosmology and 4-index tensor fields
International Nuclear Information System (INIS)
Moorhouse, R.G.; Nixon, J.
1985-01-01
We show how an arbitrarily large expansion of the ordinary dimensions in the very early universe can be achieved in the d=11 supergravity theory where the 4-index anti-symmetric tensor field supplies the energy-momentum tensor. However, the decrease of the extra dimensions is too fast to give a satisfactory inflationary cosmology. If a 4-index tensor field is similar used to provide the energy-momentum tensor in dimensions significantly greater than 11 the inflationary outlook is more hopeful. (orig.)
A RENORMALIZATION PROCEDURE FOR TENSOR MODELS AND SCALAR-TENSOR THEORIES OF GRAVITY
SASAKURA, NAOKI
2010-01-01
Tensor models are more-index generalizations of the so-called matrix models, and provide models of quantum gravity with the idea that spaces and general relativity are emergent phenomena. In this paper, a renormalization procedure for the tensor models whose dynamical variable is a totally symmetric real three-tensor is discussed. It is proven that configurations with certain Gaussian forms are the attractors of the three-tensor under the renormalization procedure. Since these Gaussian config...
Deviations from LTE in a stellar atmosphere
Kalkofen, W.; Klein, R. I.; Stein, R. F.
1979-01-01
Deviations for LTE are investigated in an atmosphere of hydrogen atoms with one bound level, satisfying the equations of radiative, hydrostatic, and statistical equilibrium. The departure coefficient and the kinetic temperature as functions of the frequency dependence of the radiative cross section are studied analytically and numerically. Near the outer boundary of the atmosphere, the departure coefficient is smaller than unity when the radiative cross section grows with frequency faster than with the square of frequency; it exceeds unity otherwise. Far from the boundary the departure coefficient tends to exceed unity for any frequency dependence of the radiative cross section. Overpopulation always implies that the kinetic temperature in the statistical-equilibrium atmosphere is higher than the temperature in the corresponding LTE atmosphere. Upper and lower bounds on the kinetic temperature are given for an atmosphere with deviations from LTE only in the optically shallow layers when the emergent intensity can be described by a radiation temperature.
Deviations from LTE in a stellar atmosphere
International Nuclear Information System (INIS)
Kalkofen, W.; Klein, R.I.; Stein, R.F.
1979-01-01
Deviations from LTE are investigated in an atmosphere of hydrogen atoms with one bound level, satisfying the equations of radiative, hydrostatic, and statistical equilibrium. The departure coefficient and the kinetic temperature as functions of the frequency dependence of the radiative cross section are studied analytically and numerically. Near the outer boundary of the atmosphere, the departure coefficient b is smaller than unity when the radiative cross section αsub(ν) grows with frequency ν faster than ν 2 ; b exceeds unity otherwise. Far from the boundary the departure coefficient tends to exceed unity for any frequency dependence of αsub(ν). Overpopulation (b > 1) always implies that the kinetic temperature in the statistical equilibrium atmosphere is higher than the temperature in the corresponding LTE atmosphere. Upper and lower bounds on the kinetic temperature are given for an atmosphere with deviations from LTE only in the optically shallow layers when the emergent intensity can be described by a radiation temperature. (author)
Large Deviations for Gaussian Diffusions with Delay
Azencott, Robert; Geiger, Brett; Ott, William
2018-01-01
Dynamical systems driven by nonlinear delay SDEs with small noise can exhibit important rare events on long timescales. When there is no delay, classical large deviations theory quantifies rare events such as escapes from metastable fixed points. Near such fixed points, one can approximate nonlinear delay SDEs by linear delay SDEs. Here, we develop a fully explicit large deviations framework for (necessarily Gaussian) processes X_t driven by linear delay SDEs with small diffusion coefficients. Our approach enables fast numerical computation of the action functional controlling rare events for X_t and of the most likely paths transiting from X_0 = p to X_T=q. Via linear noise local approximations, we can then compute most likely routes of escape from metastable states for nonlinear delay SDEs. We apply our methodology to the detailed dynamics of a genetic regulatory circuit, namely the co-repressive toggle switch, which may be described by a nonlinear chemical Langevin SDE with delay.
Large deviations for tandem queueing systems
Directory of Open Access Journals (Sweden)
Roland L. Dobrushin
1994-01-01
Full Text Available The crude asymptotics of the large delay probability in a tandem queueing system is considered. The main result states that one of the two channels in the tandem system defines the crude asymptotics. The constant that determines the crude asymptotics is given. The results obtained are based on the large deviation principle for random processes with independent increments on an infinite interval recently established by the authors.
What is "Standard" About the Standard Deviation
Newberger, Florence; Safer, Alan M.; Watson, Saleem
2010-01-01
The choice of the formula for standard deviation is explained in elementary statistics textbooks in various ways. We give an explanation for this formula by representing the data as a vector in $\\mathbb R^n$ and considering its distance from a central tendency vector. In this setting the "standard" formula represents a shortest distance in the standard metric. We also show that different metrics lead to different measures of central tendency.
3D reconstruction of tensors and vectors
Energy Technology Data Exchange (ETDEWEB)
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.
Note onset deviations as musical piece signatures.
Serrà, Joan; Özaslan, Tan Hakan; Arcos, Josep Lluis
2013-01-01
A competent interpretation of a musical composition presents several non-explicit departures from the written score. Timing variations are perhaps the most important ones: they are fundamental for expressive performance and a key ingredient for conferring a human-like quality to machine-based music renditions. However, the nature of such variations is still an open research question, with diverse theories that indicate a multi-dimensional phenomenon. In the present study, we consider event-shift timing variations and show that sequences of note onset deviations are robust and reliable predictors of the musical piece being played, irrespective of the performer. In fact, our results suggest that only a few consecutive onset deviations are already enough to identify a musical composition with statistically significant accuracy. We consider a mid-size collection of commercial recordings of classical guitar pieces and follow a quantitative approach based on the combination of standard statistical tools and machine learning techniques with the semi-automatic estimation of onset deviations. Besides the reported results, we believe that the considered materials and the methodology followed widen the testing ground for studying musical timing and could open new perspectives in related research fields.
Note onset deviations as musical piece signatures.
Directory of Open Access Journals (Sweden)
Joan Serrà
Full Text Available A competent interpretation of a musical composition presents several non-explicit departures from the written score. Timing variations are perhaps the most important ones: they are fundamental for expressive performance and a key ingredient for conferring a human-like quality to machine-based music renditions. However, the nature of such variations is still an open research question, with diverse theories that indicate a multi-dimensional phenomenon. In the present study, we consider event-shift timing variations and show that sequences of note onset deviations are robust and reliable predictors of the musical piece being played, irrespective of the performer. In fact, our results suggest that only a few consecutive onset deviations are already enough to identify a musical composition with statistically significant accuracy. We consider a mid-size collection of commercial recordings of classical guitar pieces and follow a quantitative approach based on the combination of standard statistical tools and machine learning techniques with the semi-automatic estimation of onset deviations. Besides the reported results, we believe that the considered materials and the methodology followed widen the testing ground for studying musical timing and could open new perspectives in related research fields.
Bound-Preserving Reconstruction of Tensor Quantities for Remap in ALE Fluid Dynamics
Energy Technology Data Exchange (ETDEWEB)
Klima, Matej [Czech Technical Univ. in Prague, Praha (Czech Republic); Kucharik, MIlan [Czech Technical Univ. in Prague, Praha (Czech Republic); Shashkov, Mikhail Jurievich [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Velechovsky, Jan [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2017-01-06
We analyze several new and existing approaches for limiting tensor quantities in the context of deviatoric stress remapping in an ALE numerical simulation of elastic flow. Remapping and limiting of the tensor component-by-component is shown to violate radial symmetry of derived variables such as elastic energy or force. Therefore, we have extended the symmetry-preserving Vector Image Polygon algorithm, originally designed for limiting vector variables. This limiter constrains the vector (in our case a vector of independent tensor components) within the convex hull formed by the vectors from surrounding cells – an equivalent of the discrete maximum principle in scalar variables. We compare this method with a limiter designed specifically for deviatoric stress limiting which aims to constrain the J_{2} invariant that is proportional to the specific elastic energy and scale the tensor accordingly. We also propose a method which involves remapping and limiting the J_{2} invariant independently using known scalar techniques. The deviatoric stress tensor is then scaled to match this remapped invariant, which guarantees conservation in terms of elastic energy.
Constraints on the tensor-to-scalar ratio for non-power-law models
International Nuclear Information System (INIS)
Vázquez, J. Alberto; Bridges, M.; Ma, Yin-Zhe; Hobson, M.P.
2013-01-01
Recent cosmological observations hint at a deviation from the simple power-law form of the primordial spectrum of curvature perturbations. In this paper we show that in the presence of a tensor component, a turn-over in the initial spectrum is preferred by current observations, and hence non-power-law models ought to be considered. For instance, for a power-law parameterisation with both a tensor component and running parameter, current data show a preference for a negative running at more than 2.5σ C.L. As a consequence of this deviation from a power-law, constraints on the tensor-to-scalar ratio r are slightly broader. We also present constraints on the inflationary parameters for a model-independent reconstruction and the Lasenby and Doran (LD) model. In particular, the constraints on the tensor-to-scalar ratio from the LD model are: r LD = 0.11±0.024. In addition to current data, we show expected constraints from Planck-like and CMB-Pol sensitivity experiments by using Markov-Chain-Monte-Carlo sampling chains. For all the models, we have included the Bayesian Evidence to perform a model selection analysis. The Bayes factor, using current observations, shows a strong preference for the LD model over the standard power-law parameterisation, and provides an insight into the accuracy of differentiating models through future surveys
Algebraic classification of the Weyl tensor in higher dimensions based on its 'superenergy' tensor
International Nuclear Information System (INIS)
Senovilla, Jose M M
2010-01-01
The algebraic classification of the Weyl tensor in the arbitrary dimension n is recovered by means of the principal directions of its 'superenergy' tensor. This point of view can be helpful in order to compute the Weyl aligned null directions explicitly, and permits one to obtain the algebraic type of the Weyl tensor by computing the principal eigenvalue of rank-2 symmetric future tensors. The algebraic types compatible with states of intrinsic gravitational radiation can then be explored. The underlying ideas are general, so that a classification of arbitrary tensors in the general dimension can be achieved. (fast track communication)
Unique characterization of the Bel-Robinson tensor
International Nuclear Information System (INIS)
Bergqvist, G; Lankinen, P
2004-01-01
We prove that a completely symmetric and trace-free rank-4 tensor is, up to sign, a Bel-Robinson-type tensor, i.e., the superenergy tensor of a tensor with the same algebraic symmetries as the Weyl tensor, if and only if it satisfies a certain quadratic identity. This may be seen as the first Rainich theory result for rank-4 tensors
Differential invariants for higher-rank tensors. A progress report
International Nuclear Information System (INIS)
Tapial, V.
2004-07-01
We outline the construction of differential invariants for higher-rank tensors. In section 2 we outline the general method for the construction of differential invariants. A first result is that the simplest tensor differential invariant contains derivatives of the same order as the rank of the tensor. In section 3 we review the construction for the first-rank tensors (vectors) and second-rank tensors (metrics). In section 4 we outline the same construction for higher-rank tensors. (author)
Friction tensor concept for textured surfaces
Indian Academy of Sciences (India)
This paper proposes the concept of a friction tensor analogous to the heat conduc- tion tensor in anisotropic media. This implies that there exists two principal friction coefficients μ1,2 analogous to the principal conductivities k1,2. For symmetrically textured surfaces the principal directions are orthogonal with atleast one ...
Gravitational Metric Tensor Exterior to Rotating Homogeneous ...
African Journals Online (AJOL)
The covariant and contravariant metric tensors exterior to a homogeneous spherical body rotating uniformly about a common φ axis with constant angular velocity ω is constructed. The constructed metric tensors in this gravitational field have seven non-zero distinct components.The Lagrangian for this gravitational field is ...
Friction tensor concept for textured surfaces
Indian Academy of Sciences (India)
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 ...
Directory of Open Access Journals (Sweden)
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.
Morphometric study of tensor of vastus intermedius in South Indian population.
Veeramani, Raveendranath; Gnanasekaran, Dhivyalakshmi
2017-03-01
Tensor of vastus intermedius is a newly discovered muscle located between vastus lateralis and vastus intermedius. The purpose of this study was to investigate the detailed morphology of tensor of vastus intermedius, specifically to provide data pertaining to the attachments, innervations, variation in the types and its morphometry in South Indian population. The tensor of vastus intermedius was studied in thirty six cadaveric lower limbs using macrodissection techniques. The origin of the muscle was from upper part of intertrochanteric line and anterior part of greater trochanter of femur inserted to medial aspect of upper border of patella. The muscle was classified into four types based on the origin and also the aponeurosis course with independent type (type 1) being common. The mean and standard deviation of the length of tensor of vastus intermedius and aponeurosis were 145.40±37.55 mm and 193.55±42.32 mm, respectively. The results of the study suggest that tensor of vastus intermedius is variable and the information provided regarding the attachments, types and quantitative data will contribute to the existing knowledge of the muscle.
Tensor completion and low-n-rank tensor recovery via convex optimization
International Nuclear Information System (INIS)
Gandy, Silvia; Yamada, Isao; Recht, Benjamin
2011-01-01
In this paper we consider sparsity on a tensor level, as given by the n-rank of a tensor. In an important sparse-vector approximation problem (compressed sensing) and the low-rank matrix recovery problem, using a convex relaxation technique proved to be a valuable solution strategy. Here, we will adapt these techniques to the tensor setting. We use the n-rank of a tensor as a sparsity measure and consider the low-n-rank tensor recovery problem, i.e. the problem of finding the tensor of the lowest n-rank that fulfills some linear constraints. We introduce a tractable convex relaxation of the n-rank and propose efficient algorithms to solve the low-n-rank tensor recovery problem numerically. The algorithms are based on the Douglas–Rachford splitting technique and its dual variant, the alternating direction method of multipliers
Weyl curvature tensor in static spherical sources
International Nuclear Information System (INIS)
Ponce de Leon, J.
1988-01-01
The role of the Weyl curvature tensor in static sources of the Schwarzschild field is studied. It is shown that in general the contribution from the Weyl curvature tensor (the ''purely gravitational field energy'') to the mass-energy inside the body may be positive, negative, or zero. It is proved that a positive (negative) contribution from the Weyl tensor tends to increase (decrease) the effective gravitational mass, the red-shift (from a point in the sphere to infinity), as well as the gravitational force which acts on a constituent matter element of a body. It is also proved that the contribution from the Weyl tensor always is negative in sources with surface gravitational potential larger than (4/9. It is pointed out that large negative contributions from the Weyl tensor could give rise to the phenomenon of gravitational repulsion. A simple example which illustrates the results is discussed
A recursive reduction of tensor Feynman integrals
International Nuclear Information System (INIS)
Diakonidis, T.; Riemann, T.; Tausk, J.B.; Fleischer, J.
2009-07-01
We perform a recursive reduction of one-loop n-point rank R tensor Feynman integrals [in short: (n,R)-integrals] for n≤6 with R≤n by representing (n,R)-integrals in terms of (n,R-1)- and (n-1,R-1)-integrals. We use the known representation of tensor integrals in terms of scalar integrals in higher dimension, which are then reduced by recurrence relations to integrals in generic dimension. With a systematic application of metric tensor representations in terms of chords, and by decomposing and recombining these representations, we find the recursive reduction for the tensors. The procedure represents a compact, sequential algorithm for numerical evaluations of tensor Feynman integrals appearing in next-to-leading order contributions to massless and massive three- and four-particle production at LHC and ILC, as well as at meson factories. (orig.)
Seamless warping of diffusion tensor fields
DEFF Research Database (Denmark)
Xu, Dongrong; Hao, Xuejun; Bansal, Ravi
2008-01-01
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......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...... deformations in an attempt to ensure that the local deformations in the warped image remains true to the orientation of the underlying fibers; forward mapping, however, can also create "seams" or gaps and consequently artifacts in the warped image by failing to define accurately the voxels in the template...
On Lovelock analogs of the Riemann tensor
Energy Technology Data Exchange (ETDEWEB)
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.)
Tensor Minkowski Functionals: first application to the CMB
Energy Technology Data Exchange (ETDEWEB)
Ganesan, Vidhya [Indian Institute of Astrophysics, Koramangala II Block, Bangalore 560 034 (India); Chingangbam, Pravabati, E-mail: vidhya@iiap.res.in, E-mail: prava@iiap.res.in [Indian Institute of Science, C.V. Raman Ave, Bangalore 560 012 (India)
2017-06-01
Tensor Minkowski Functionals (TMFs) are tensor generalizations of the usual Minkowski Functionals which are scalar quantities. We introduce them here for use in cosmological analysis, in particular to analyze the Cosmic Microwave Background (CMB) radiation. They encapsulate information about the shapes of structures and the orientation of distributions of structures. We focus on one of the TMFs, namely W {sub 2}{sup 1,1}, which is the (1,1) rank tensor generalization of the genus. The ratio of the eigenvalues of the average of W {sub 2}{sup 1,1} over all structures, α, encodes the net orientation of the structures; and the average of the ratios of the eigenvalues of W {sub 2}{sup 1,1} for each structure, β, encodes the net intrinsic anisotropy of the structures. We have developed a code that computes W {sub 2}{sup 1,1}, and from it α and β, for a set of structures on the 2-dimensional Euclidean plane. We use it to compute α and β as functions of chosen threshold levels for simulated Gaussian and isotropic CMB temperature and E mode fields. We obtain the value of α to be one for both temperature and E mode, which means that we recover the statistical isotropy of density fluctuations that we input in the simulations. We find that the standard ΛCDM model predicts a charateristic shape of β for temperature and E mode as a function of the threshold, and the average over thresholds is β∼ 0.62 for temperature and β∼ 0.63 for E mode. Accurate measurements of α and β can be used to test the standard model of cosmology and to search for deviations from it. For this purpose we compute α and β for temperature and E mode data of various data sets from PLANCK mission. We compare the values measured from observed data with those obtained from simulations to which instrument beam and noise characteristics of the 44GHz frequency channel have been added (which are provided as part of the PLANCK data release). We find very good agreement of β and α between all
Examining the consistency relations describing the three-point functions involving tensors
International Nuclear Information System (INIS)
Sreenath, V.; Sriramkumar, L.
2014-01-01
It is well known that the non-Gaussianity parameter f NL characterizing the scalar bi-spectrum can be expressed in terms of the scalar spectral index in the squeezed limit, a property that is referred to as the consistency relation. In contrast to the scalar bi-spectrum, the three-point cross-correlations involving scalars and tensors and the tensor bi-spectrum have not received adequate attention, which can be largely attributed to the fact that the tensors had remained undetected at the level of the power spectrum until very recently. The detection of the imprints of the primordial tensor perturbations by BICEP2 and its indication of a rather high tensor-to-scalar ratio, if confirmed, can open up a new window for understanding the tensor perturbations, not only at the level of the power spectrum, but also in the realm of non-Gaussianities. In this work, we consider the consistency relations associated with the three-point cross-correlations involving scalars and tensors as well as the tensor bi-spectrum in inflationary models driven by a single, canonical, scalar field. Characterizing the cross-correlations in terms of the dimensionless non-Gaussianity parameters C NL R and C NL γ that we had introduced earlier, we express the consistency relations governing the cross-correlations as relations between these non-Gaussianity parameters and the scalar or tensor spectral indices, in a fashion similar to that of the purely scalar case. We also discuss the corresponding relation for the non-Gaussianity parameter h NL used to describe the tensor bi-spectrum. We analytically establish these consistency relations explicitly in the following two situations: a simple example involving a specific case of power law inflation and a non-trivial scenario in the so-called Starobinsky model that is governed by a linear potential with a sharp change in its slope. We also numerically verify the consistency relations in three types of inflationary models that permit deviations from
Standard deviation of the longest common subsequence
Lember, Jüri; Matzinger, Heinrich
2009-01-01
Let Ln be the length of the longest common subsequence of two independent i.i.d. sequences of Bernoulli variables of length n. We prove that the order of the standard deviation of Ln is $\\sqrt{n}$ , provided the parameter of the Bernoulli variables is small enough. This validates Waterman’s conjecture in this situation [Philos. Trans. R. Soc. Lond. Ser. B 344 (1994) 383–390]. The order conjectured by Chvatal and Sankoff [J. Appl. Probab. 12 (1975) 306–315], however, is different.
International Nuclear Information System (INIS)
Montesinos, M.; Flores, E.
2006-01-01
The symmetric and gauge-invariant energy-momentum tensors for source-free Maxwell and Yang-Mills theories are obtained by means of translations in spacetime via a systematic implementation of Noether's theorem. For the source-free neutral Proca field, the same procedure yields also the symmetric energy-momentum tensor. In all cases, the key point to get the right expressions for the energy-momentum tensors is the appropriate handling of their equations of motion and the Bianchi identities. It must be stressed that these results are obtained without using Belinfante's symmetrization techniques which are usually employed to this end. (Author)
Dislocations, the elastic energy momentum tensor and crack propagation
International Nuclear Information System (INIS)
Lung, Chi-wei
1979-07-01
Based upon dislocation theory, some stress intensity factors can be calculated for practical cases. The results obtained by this method have been found to agree fairly well with the results obtained by the conventional fracture mechanics. The elastic energy momentum tensor has been used to calculate the force acting on the crack tip. A discussion on the kinetics of migration of impurities to the crack tip was given. It seems that the crack tip sometimes may be considered as a singularity in an elastic field and the fundamental law of classical field theory is applicable on the problem in fracture of materials. (author)
Efficient Tensor Completion for Color Image and Video Recovery: Low-Rank Tensor Train.
Bengua, Johann A; Phien, Ho N; Tuan, Hoang Duong; Do, Minh N
2017-05-01
This paper proposes a novel approach to tensor completion, which recovers missing entries of data represented by tensors. The approach is based on the tensor train (TT) rank, which is able to capture hidden information from tensors thanks to its definition from a well-balanced matricization scheme. Accordingly, new optimization formulations for tensor completion are proposed as well as two new algorithms for their solution. The first one called simple low-rank tensor completion via TT (SiLRTC-TT) is intimately related to minimizing a nuclear norm based on TT rank. The second one is from a multilinear matrix factorization model to approximate the TT rank of a tensor, and is called tensor completion by parallel matrix factorization via TT (TMac-TT). A tensor augmentation scheme of transforming a low-order tensor to higher orders is also proposed to enhance the effectiveness of SiLRTC-TT and TMac-TT. Simulation results for color image and video recovery show the clear advantage of our method over all other methods.
Conformal field theories and tensor categories. Proceedings
Energy Technology Data Exchange (ETDEWEB)
Bai, Chengming [Nankai Univ., Tianjin (China). Chern Institute of Mathematics; Fuchs, Juergen [Karlstad Univ. (Sweden). Theoretical Physics; Huang, Yi-Zhi [Rutgers Univ., Piscataway, NJ (United States). Dept. of Mathematics; Kong, Liang [Tsinghua Univ., Beijing (China). Inst. for Advanced Study; Runkel, Ingo; Schweigert, Christoph (eds.) [Hamburg Univ. (Germany). Dept. of Mathematics
2014-08-01
First book devoted completely to the mathematics of conformal field theories, tensor categories and their applications. Contributors include both mathematicians and physicists. Some long expository articles are especially suitable for beginners. The present volume is a collection of seven papers that are either based on the talks presented at the workshop ''Conformal field theories and tensor categories'' held June 13 to June 17, 2011 at the Beijing International Center for Mathematical Research, Peking University, or are extensions of the material presented in the talks at the workshop. These papers present new developments beyond rational conformal field theories and modular tensor categories and new applications in mathematics and physics. The topics covered include tensor categories from representation categories of Hopf algebras, applications of conformal field theories and tensor categories to topological phases and gapped systems, logarithmic conformal field theories and the corresponding non-semisimple tensor categories, and new developments in the representation theory of vertex operator algebras. Some of the papers contain detailed introductory material that is helpful for graduate students and researchers looking for an introduction to these research directions. The papers also discuss exciting recent developments in the area of conformal field theories, tensor categories and their applications and will be extremely useful for researchers working in these areas.
Tensor network method for reversible classical computation
Yang, Zhi-Cheng; Kourtis, Stefanos; Chamon, Claudio; Mucciolo, Eduardo R.; Ruckenstein, Andrei E.
2018-03-01
We develop a tensor network technique that can solve universal reversible classical computational problems, formulated as vertex models on a square lattice [Nat. Commun. 8, 15303 (2017), 10.1038/ncomms15303]. By encoding the truth table of each vertex constraint in a tensor, the total number of solutions compatible with partial inputs and outputs at the boundary can be represented as the full contraction of a tensor network. We introduce an iterative compression-decimation (ICD) scheme that performs this contraction efficiently. The ICD algorithm first propagates local constraints to longer ranges via repeated contraction-decomposition sweeps over all lattice bonds, thus achieving compression on a given length scale. It then decimates the lattice via coarse-graining tensor contractions. Repeated iterations of these two steps gradually collapse the tensor network and ultimately yield the exact tensor trace for large systems, without the need for manual control of tensor dimensions. Our protocol allows us to obtain the exact number of solutions for computations where a naive enumeration would take astronomically long times.
Directory of Open Access Journals (Sweden)
İhsan Çaça
2004-01-01
Full Text Available We evaluated the correlation with success rates and deviation type and degree inhorizontal concomitant deviations. 104 horizontal concomitan strabismus cases whowere operated in our clinic between January 1994 – December 2000 were included in thestudy. 56 cases undergone recession-resection procedure in the same eye 19 cases twomuscle recession and one muscle resection, 20 cases two muscle recession, 9 cases onlyone muscle recession. 10 ± prism diopter deviation in postoperative sixth monthexamination was accepted as surgical success.Surgical success rate was 90% and 89.3% in the cases with deviation angle of 15-30and 31-50 prism diopter respectively. Success rate was 78.9% if the angle was more than50 prism diopter. According to strabismus type when surgical success rate examined; inalternan esotropia 88.33%, in alternan exotropia 84.6%, in monocular esotropia 88%and in monocular exotropia 83.3% success was fixed. Statistically significant differencewas not found between strabismus type and surgical success rate. The binocular visiongaining rate was found as 51.8% after the treatment of cases.In strabismus surgery, preoperative deviation angle was found to be an effectivefactor on the success rate.
Surface tensor estimation from linear sections
DEFF Research Database (Denmark)
Kousholt, Astrid; Kiderlen, Markus; Hug, Daniel
From Crofton's formula for Minkowski tensors we derive stereological estimators of translation invariant surface tensors of convex bodies in the n-dimensional Euclidean space. The estimators are based on one-dimensional linear sections. In a design based setting we suggest three types of estimators....... These are based on isotropic uniform random lines, vertical sections, and non-isotropic random lines, respectively. Further, we derive estimators of the specific surface tensors associated with a stationary process of convex particles in the model based setting....
Abelian gauge theories with tensor gauge fields
International Nuclear Information System (INIS)
Kapuscik, E.
1984-01-01
Gauge fields of arbitrary tensor type are introduced. In curved space-time the gravitational field serves as a bridge joining different gauge fields. The theory of second order tensor gauge field is developed on the basis of close analogy to Maxwell electrodynamics. The notion of tensor current is introduced and an experimental test of its detection is proposed. The main result consists in a coupled set of field equations representing a generalization of Maxwell theory in which the Einstein equivalence principle is not satisfied. (author)
Surface tensor estimation from linear sections
DEFF Research Database (Denmark)
Kousholt, Astrid; Kiderlen, Markus; Hug, Daniel
2015-01-01
From Crofton’s formula for Minkowski tensors we derive stereological estimators of translation invariant surface tensors of convex bodies in the n-dimensional Euclidean space. The estimators are based on one-dimensional linear sections. In a design based setting we suggest three types of estimators....... These are based on isotropic uniform random lines, vertical sections, and non-isotropic random lines, respectively. Further, we derive estimators of the specific surface tensors associated with a stationary process of convex particles in the model based setting....
Why are tensor field theories asymptotically free?
Rivasseau, V.
2015-09-01
In this pedagogic letter we explain the combinatorics underlying the generic asymptotic freedom of tensor field theories. We focus on simple combinatorial models with a 1/p2 propagator and quartic interactions and on the comparison between the intermediate field representations of the vector, matrix and tensor cases. The transition from asymptotic freedom (tensor case) to asymptotic safety (matrix case) is related to the crossing symmetry of the matrix vertex, whereas in the vector case, the lack of asymptotic freedom (“Landau ghost”), as in the ordinary scalar φ^44 case, is simply due to the absence of any wave function renormalization at one loop.
Transmission-type angle deviation microscopy
International Nuclear Information System (INIS)
Chiu, M.-H.; Lai, C.-W.; Tan, C.-T.; Lai, C.-F.
2008-01-01
We present a new microscopy technique that we call transmission angle deviation microscopy (TADM). It is based on common-path heterodyne interferometry and geometrical optics. An ultrahigh sensitivity surface plasmon resonance (SPR) angular sensor is used to expand dynamic measurement ranges and to improve the axial resolution in three-dimensional optical microscopy. When transmitted light is incident upon a specimen, the beam converges or diverges because of refractive and/or surface height variations. Advantages include high axial resolution (∼32 nm), nondestructive and noncontact measurement, and larger measurement ranges (± 80 μm) for a numerical aperture of 0.21in a transparent measurement medium. The technique can be used without conductivity and pretreatment
Network analysis based on large deviation statistics
Miyazaki, Syuji
2007-07-01
A chaotic piecewise linear map whose statistical properties are identical to those of a random walk on directed graphs such as the world wide web (WWW) is constructed, and the dynamic quantity is analyzed in the framework of large deviation statistics. Gibbs measures include the weight factor appearing in the weighted average of the dynamic quantity, which can also quantitatively measure the importance of web sites. Currently used levels of importance in the commercial search engines are independent of search terms, which correspond to the stationary visiting frequency of each node obtained from a random walk on the network or equivalent chaotic dynamics. Levels of importance based on the Gibbs measure depend on each search term which is specified by the searcher. The topological conjugate transformation between one dynamical system with a Gibbs measure and another dynamical system whose standard invariant probability measure is identical to the Gibbs measure is also discussed.
Investigating deviations from norms in court interpreting
DEFF Research Database (Denmark)
Dubslaff, Friedel; Martinsen, Bodil
in Denmark, which involves three researchers affiliated to the same institution (Aarhus School of Business), and includes French, German and Arabic. Apart from recordings of (parts of) authentic courtroom proceedings, the empirical data include questionnaires filled in by the interpreters and most - and......, in some cases, all - professional users involved (judges, lawyers, prosecutors). As far as the non-Danish speaking users are concerned, it has, with one notable exception, unfortunately not been possible to obtain data from this group via questionnaires. As this type of data, however, is important...... deviations and sanctions in every case. By way of example: Several judges, who had given their consent to recordings of authentic data in connection with the research project, reported that they had experienced problems with insufficient language proficiency on the part of untrained interpreters speaking...
Large Deviations and Asymptotic Methods in Finance
Gatheral, Jim; Gulisashvili, Archil; Jacquier, Antoine; Teichmann, Josef
2015-01-01
Topics covered in this volume (large deviations, differential geometry, asymptotic expansions, central limit theorems) give a full picture of the current advances in the application of asymptotic methods in mathematical finance, and thereby provide rigorous solutions to important mathematical and financial issues, such as implied volatility asymptotics, local volatility extrapolation, systemic risk and volatility estimation. This volume gathers together ground-breaking results in this field by some of its leading experts. Over the past decade, asymptotic methods have played an increasingly important role in the study of the behaviour of (financial) models. These methods provide a useful alternative to numerical methods in settings where the latter may lose accuracy (in extremes such as small and large strikes, and small maturities), and lead to a clearer understanding of the behaviour of models, and of the influence of parameters on this behaviour. Graduate students, researchers and practitioners will find th...
Tucker tensor analysis of Matern functions in spatial statistics
Litvinenko, Alexander
2018-04-20
Low-rank Tucker tensor methods in spatial statistics 1. Motivation: improve statistical models 2. Motivation: disadvantages of matrices 3. Tools: Tucker tensor format 4. Tensor approximation of Matern covariance function via FFT 5. Typical statistical operations in Tucker tensor format 6. Numerical experiments
Minimal Gersgorin tensor eigenvalue inclusion set and its numerical approximation
Li, Chaoqian; Li, Yaotang
2015-01-01
For a complex tensor A, Minimal Gersgorin tensor eigenvalue inclusion set of A is presented, and its sufficient and necessary condition is given. Furthermore, we study its boundary by the spectrums of the equimodular set and the extended equimodular set for A. Lastly, for an irreducible tensor, a numerical approximation to Minimal Gersgorin tensor eigenvalue inclusion set is given.
TensorFlow Agents: Efficient Batched Reinforcement Learning in TensorFlow
Hafner, Danijar; Davidson, James; Vanhoucke, Vincent
2017-01-01
We introduce TensorFlow Agents, an efficient infrastructure paradigm for building parallel reinforcement learning algorithms in TensorFlow. We simulate multiple environments in parallel, and group them to perform the neural network computation on a batch rather than individual observations. This allows the TensorFlow execution engine to parallelize computation, without the need for manual synchronization. Environments are stepped in separate Python processes to progress them in parallel witho...
Maritime Group Motion Analysis: Representation, Learning, Recognition, and Deviation Detection
2017-02-01
represent behaviors. Keywords: Group tracks, motion analysis, behavior pattern 1 Introduction Motion activity analysis of single and multiple...its decomposition into anti-symmetric, and symmetric (both with and without trace) elements of the velocity gradient tensor is attributed to Cauchy...orientation of the deformation axis (see Fig.1). These geometric invariants are simply the eigenvalues of the decomposed velocity gradient tensor , and
C%2B%2B tensor toolbox user manual.
Energy Technology Data Exchange (ETDEWEB)
Plantenga, Todd D.; Kolda, Tamara Gibson
2012-04-01
The C++ Tensor Toolbox is a software package for computing tensor decompositions. It is based on the Matlab Tensor Toolbox, and is particularly optimized for sparse data sets. This user manual briefly overviews tensor decomposition mathematics, software capabilities, and installation of the package. Tensors (also known as multidimensional arrays or N-way arrays) are used in a variety of applications ranging from chemometrics to network analysis. The Tensor Toolbox provides classes for manipulating dense, sparse, and structured tensors in C++. The Toolbox compiles into libraries and is intended for use with custom applications written by users.
Degrees of Freedom for Allan Deviation Estimates of Multiple Clocks
2016-04-01
ALLAN VARIANCE The Allan variance is a widely used statistic in the timing community to evaluate the performance of frequency stan- dards [2]. The...Allan deviation . Allan deviation will be represented by σ and standard deviation will be represented by δ. In practice, when the Allan deviation of a...the Allan deviation of standard noise types. Once the number of degrees of freedom is known, an approximate confidence interval can be assigned by
Unsupervised Tensor Mining for Big Data Practitioners.
Papalexakis, Evangelos E; Faloutsos, Christos
2016-09-01
Multiaspect data are ubiquitous in modern Big Data applications. For instance, different aspects of a social network are the different types of communication between people, the time stamp of each interaction, and the location associated to each individual. How can we jointly model all those aspects and leverage the additional information that they introduce to our analysis? Tensors, which are multidimensional extensions of matrices, are a principled and mathematically sound way of modeling such multiaspect data. In this article, our goal is to popularize tensors and tensor decompositions to Big Data practitioners by demonstrating their effectiveness, outlining challenges that pertain to their application in Big Data scenarios, and presenting our recent work that tackles those challenges. We view this work as a step toward a fully automated, unsupervised tensor mining tool that can be easily and broadly adopted by practitioners in academia and industry.
Potentials for transverse trace-free tensors
International Nuclear Information System (INIS)
Conboye, Rory; Murchadha, Niall Ó
2014-01-01
In constructing and understanding initial conditions in the 3 + 1 formalism for numerical relativity, the transverse and trace-free (TT) part of the extrinsic curvature plays a key role. We know that TT tensors possess two degrees of freedom per space point. However, finding an expression for a TT tensor depending on only two scalar functions is a non-trivial task. Assuming either axial or translational symmetry, expressions depending on two scalar potentials alone are derived here for all TT tensors in flat 3-space. In a more general spatial slice, only one of these potentials is found, the same potential given in (Baker and Puzio 1999 Phys. Rev. D 59 044030) and (Dain 2001 Phys. Rev. D 64 124002), with the remaining equations reduced to a partial differential equation, depending on boundary conditions for a solution. As an exercise, we also derive the potentials which give the Bowen-York curvature tensor in flat space. (paper)
Correlators in tensor models from character calculus
Directory of Open Access Journals (Sweden)
A. Mironov
2017-11-01
Full Text Available We explain how the calculations of [20], which provided the first evidence for non-trivial structures of Gaussian correlators in tensor models, are efficiently performed with the help of the (Hurwitz character calculus. This emphasizes a close similarity between technical methods in matrix and tensor models and supports a hope to understand the emerging structures in very similar terms. We claim that the 2m-fold Gaussian correlators of rank r tensors are given by r-linear combinations of dimensions with the Young diagrams of size m. The coefficients are made from the characters of the symmetric group Sm and their exact form depends on the choice of the correlator and on the symmetries of the model. As the simplest application of this new knowledge, we provide simple expressions for correlators in the Aristotelian tensor model as tri-linear combinations of dimensions.
Energy-momentum tensor in scalar QED
International Nuclear Information System (INIS)
Joglekar, S.D.; Misra, A.
1988-01-01
We consider the renormalization of the energy-momentum tensor in scalar quantum electrodynamics. We show the need for adding an improvement term to the conventional energy-momentum tensor. We consider two possible forms for the improvement term: (i) one in which the improvement coefficient is a finite function of bare parameters of the theory (so that the energy-momentum tensor can be obtained from an action that is a finite function of bare quantities); (ii) one in which the improvement coefficient is a finite quantity, i.e., a finite function of renormalized parameters. We establish a negative result; viz., neither form leads to a finite energy-momentum tensor to O(e 2 λ/sup n/). .AE
Reconstruction of convex bodies from surface tensors
DEFF Research Database (Denmark)
Kousholt, Astrid; Kiderlen, Markus
. The output of the reconstruction algorithm is a polytope P, where the surface tensors of P and K are identical up to rank s. We establish a stability result based on a generalization of Wirtinger’s inequality that shows that for large s, two convex bodies are close in shape when they have identical surface...... that are translates of each other. An algorithm for reconstructing an unknown convex body in R 2 from its surface tensors up to a certain rank is presented. Using the reconstruction algorithm, the shape of an unknown convex body can be approximated when only a finite number s of surface tensors are available...... tensors up to rank s. This is used to establish consistency of the developed reconstruction algorithm....
Reconstruction of convex bodies from surface tensors
DEFF Research Database (Denmark)
Kousholt, Astrid; Kiderlen, Markus
2016-01-01
We present two algorithms for reconstruction of the shape of convex bodies in the two-dimensional Euclidean space. The first reconstruction algorithm requires knowledge of the exact surface tensors of a convex body up to rank s for some natural number s. When only measurements subject to noise...... of surface tensors are available for reconstruction, we recommend to use certain values of the surface tensors, namely harmonic intrinsic volumes instead of the surface tensors evaluated at the standard basis. The second algorithm we present is based on harmonic intrinsic volumes and allows for noisy...... measurements. From a generalized version of Wirtinger's inequality, we derive stability results that are utilized to ensure consistency of both reconstruction procedures. Consistency of the reconstruction procedure based on measurements subject to noise is established under certain assumptions on the noise...
An introduction to linear algebra and tensors
Akivis, M A; Silverman, Richard A
1978-01-01
Eminently readable, completely elementary treatment begins with linear spaces and ends with analytic geometry, covering multilinear forms, tensors, linear transformation, and more. 250 problems, most with hints and answers. 1972 edition.
Correlators in tensor models from character calculus
Mironov, A.; Morozov, A.
2017-11-01
We explain how the calculations of [20], which provided the first evidence for non-trivial structures of Gaussian correlators in tensor models, are efficiently performed with the help of the (Hurwitz) character calculus. This emphasizes a close similarity between technical methods in matrix and tensor models and supports a hope to understand the emerging structures in very similar terms. We claim that the 2m-fold Gaussian correlators of rank r tensors are given by r-linear combinations of dimensions with the Young diagrams of size m. The coefficients are made from the characters of the symmetric group Sm and their exact form depends on the choice of the correlator and on the symmetries of the model. As the simplest application of this new knowledge, we provide simple expressions for correlators in the Aristotelian tensor model as tri-linear combinations of dimensions.
Shifted power method for computing tensor eigenpairs.
Energy Technology Data Exchange (ETDEWEB)
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.
Calculus of tensors and differential forms
Sinha, Rajnikant
2014-01-01
Calculus of tensors and differential forms is an introductory-level textbook. Through this book, students will familiarize themselves with tools they need in order to use for further study on general relativity and research, such as affine tensors, tensor calculus on manifolds, relative tensors, Lie derivatives, wedge products, differential forms, and Stokes' theorem. The treatment is concrete and in detail, so that abstract concepts do not deter even physics and engineering students. This self contained book requires undergraduate-level calculus of several variables and linear algebra as prerequisite. Fubini's theorem in real analysis, to be used in Stokes' theorem, has been proved earlier than Stokes' theorem so that students don't have to search elsewhere.
The energy–momentum tensor(s in classical gauge theories
Directory of Open Access Journals (Sweden)
Daniel N. Blaschke
2016-11-01
Full Text Available We give an introduction to, and review of, the energy–momentum tensors in classical gauge field theories in Minkowski space, and to some extent also in curved space–time. For the canonical energy–momentum tensor of non-Abelian gauge fields and of matter fields coupled to such fields, we present a new and simple improvement procedure based on gauge invariance for constructing a gauge invariant, symmetric energy–momentum tensor. The relationship with the Einstein–Hilbert tensor following from the coupling to a gravitational field is also discussed.
The Energy-Momentum Tensor(s) in Classical Gauge Theories
Blaschke, Daniel N.; Gieres, Francois; Reboud, Meril; Schweda, Manfred
2016-01-01
We give an introduction to, and review of, the energy–momentum tensors in classical gauge field theories in Minkowski space, and to some extent also in curved space–time. For the canonical energy–momentum tensor of non-Abelian gauge fields and of matter fields coupled to such fields, we present a new and simple improvement procedure based on gauge invariance for constructing a gauge invariant, symmetric energy–momentum tensor. The relationship with the Einstein–Hilbert tensor following from t...
The energy–momentum tensor(s) in classical gauge theories
Energy Technology Data Exchange (ETDEWEB)
Blaschke, Daniel N., E-mail: dblaschke@lanl.gov [Los Alamos National Laboratory, Los Alamos, NM 87545 (United States); Gieres, François, E-mail: gieres@ipnl.in2p3.fr [Institut de Physique Nucléaire de Lyon, Université de Lyon, Université Claude Bernard Lyon 1 and CNRS/IN2P3, Bat. P. Dirac, 4 rue Enrico Fermi, F-69622 Villeurbanne (France); Reboud, Méril, E-mail: meril.reboud@ens-lyon.fr [Institut de Physique Nucléaire de Lyon, Université de Lyon, Université Claude Bernard Lyon 1 and CNRS/IN2P3, Bat. P. Dirac, 4 rue Enrico Fermi, F-69622 Villeurbanne (France); Ecole Normale Supérieure de Lyon, 46 allée d' Italie, F-69364 Lyon CEDEX 07 (France); Schweda, Manfred, E-mail: mschweda@tph.tuwien.ac.at [Institute for Theoretical Physics, Vienna University of Technology, Wiedner Hauptstraße 8-10, A-1040 Vienna (Austria)
2016-11-15
We give an introduction to, and review of, the energy–momentum tensors in classical gauge field theories in Minkowski space, and to some extent also in curved space–time. For the canonical energy–momentum tensor of non-Abelian gauge fields and of matter fields coupled to such fields, we present a new and simple improvement procedure based on gauge invariance for constructing a gauge invariant, symmetric energy–momentum tensor. The relationship with the Einstein–Hilbert tensor following from the coupling to a gravitational field is also discussed.
Geometric decomposition of the conformation tensor in viscoelastic turbulence
Hameduddin, Ismail; Meneveau, Charles; Zaki, Tamer A.; Gayme, Dennice F.
2018-05-01
This work introduces a mathematical approach to analysing the polymer dynamics in turbulent viscoelastic flows that uses a new geometric decomposition of the conformation tensor, along with associated scalar measures of the polymer fluctuations. The approach circumvents an inherent difficulty in traditional Reynolds decompositions of the conformation tensor: the fluctuating tensor fields are not positive-definite and so do not retain the physical meaning of the tensor. The geometric decomposition of the conformation tensor yields both mean and fluctuating tensor fields that are positive-definite. The fluctuating tensor in the present decomposition has a clear physical interpretation as a polymer deformation relative to the mean configuration. Scalar measures of this fluctuating conformation tensor are developed based on the non-Euclidean geometry of the set of positive-definite tensors. Drag-reduced viscoelastic turbulent channel flow is then used an example case study. The conformation tensor field, obtained using direct numerical simulations, is analysed using the proposed framework.
Effect of Spring-in Deviation on Fatigue Life of Composite Elevator Assembly
Wang, Hua
2017-12-01
The spring-in deviation results in the extra stresses around the joints of the composite C-beam and metallic parts when they are assembled together. These extra stresses affect the composite elevator's fatigue life, which should be explored with the fatigue experimentation. The paper presents the experimental investigation on the effect of spring-in deviation on the fatigue life of the composite elevator assembly. The investigation seeks to build the relationship between the spring-in and the fatigue life in order to determine the spring-in threshold during the course of assembling. The phenomenological model of the composite C-beam is constructed to predict the stresses around the joints. Based on the predicted spring-in induced stresses around the joints, pre-stresses are precisely added to the fatigue specimen when conducting the fatigue experiment. At last, the relationship curve of the spring-in on the composite C-beam's fatigue life is obtained from the experimental data. Giving the fatigue life accepting limits, the maximum accepting spring-in deviation during the course of assembling could be obtained from the relationship curve. The reported work will enhance the understanding of assembling the composites with spring-in deviation in the civil aircraft industry.
Regional Moment Tensor Inversion for Source Type Identification
Dreger, D. S.; Ford, S. R.; Walter, W. R.
2008-12-01
With Green's functions from calibrated seismic velocity models it is possible to use regional distance moment tensor inversion for source-type identification. The deviatoric and isotropic source components for 17 explosions at the Nevada Test Site, as well as 12 earthquakes and 3 collapses in the surrounding region of the western US, are calculated using a regional time-domain full waveform inversion for the complete moment tensor. The events separate into specific populations according to their deviation from a pure double-couple and ratio of isotropic to deviatoric energy. The separation allows for anomalous event identification and discrimination between explosions, earthquakes, and collapses. Confidence regions of the model parameters are estimated from the data misfit by assuming normally distributed parameter values. We investigate the sensitivity of the resolved parameters of an explosion to imperfect Earth models, inaccurate event depths, and data with a low signal-to-noise ratio (SNR) assuming a reasonable azimuthal distribution of stations. In the band of interest (0.02-0.10 Hz) the source-type calculated from complete moment tensor inversion is insensitive to velocity models perturbations that cause less than a half-cycle shift (explosion source-type is insensitive to an incorrect depth assumption (for a true depth of 1 km), and the goodness-of-fit of the inversion result cannot be used to resolve the true depth of the explosion. Noise degrades the explosive character of the result, and a good fit and accurate result are obtained when the signal-to-noise ratio (SNR) is greater than 5. We assess the depth and frequency dependence upon the resolved explosive moment. As the depth decreases from 1 km to 200 m, the isotropic moment is no longer accurately resolved and is in error between 50-200%. However, even at the most shallow depth the resultant moment tensor is dominated by the explosive component when the data has a good SNR. Finally, the sensitivity
Extended obstruction tensors and renormalized volume coefficients
Graham, C. Robin
2009-01-01
The behavior under conformal change of the renormalized volume coefficients associated to a pseudo-Riemannian metric is investigated. It is shown that they define second order fully nonlinear operators in the conformal factor whose algebraic structure is elucidated via the introduction of "extended obstruction tensors". These together with the Schouten tensor constitute building blocks for the coefficients in the ambient metric expansion. The renormalized volume coefficients have recently bee...
Higher-Order Tensors in Diffusion Imaging
Schultz, Thomas; Fuster, Andrea; Ghosh, Aurobrata; Deriche, Rachid; Florack, Luc; Lek-Heng, Lim
2013-01-01
International audience; Diffusion imaging is a noninvasive tool for probing the microstructure of fibrous nerve and muscle tissue. Higher-order tensors provide a powerful mathematical language to model and analyze the large and complex data that is generated by its modern variants such as High Angular Resolution Diffusion Imaging (HARDI) or Diffusional Kurtosis Imaging. This survey gives a careful introduction to the foundations of higher-order tensor algebra, and explains how some concepts f...
Goldsborough, Peter
2016-01-01
Deep learning is a branch of artificial intelligence employing deep neural network architectures that has significantly advanced the state-of-the-art in computer vision, speech recognition, natural language processing and other domains. In November 2015, Google released $\\textit{TensorFlow}$, an open source deep learning software library for defining, training and deploying machine learning models. In this paper, we review TensorFlow and put it in context of modern deep learning concepts and ...
Diffusion tensor MRI: clinical applications
International Nuclear Information System (INIS)
Meli, Francisco; Romero, Carlos; Carpintiero, Silvina; Salvatico, Rosana; Lambre, Hector; Vila, Jose
2005-01-01
Purpose: To evaluate the usefulness of diffusion-tensor imaging (DTI) on different neurological diseases, and to know if this technique shows additional information than conventional Magnetic Resonance Imaging (MRI). Materials and method: Eight patients, with neurological diseases (five patients with brain tumors, one with multiple sclerosis (MS), one with variant Creutzfeldt-Jakob disease (vCJD) and the other with delayed CO intoxication were evaluated. A MR scanner of 1.5 T was used and conventional sequences and DTI with twenty-five directions were done. Quantitative maps were gotten, where the fractional anisotropy (FA) through regions of interest (ROIs) in specific anatomic area were quantified (i.e.: internal and external capsules, frontal and temporal bundles, corpus fibers). Results: In the patients with brain tumors, there was a decrease of FA on intra and peritumoral fibers. Some of them had a disruption in their pattern. In patients with MS and CO intoxication, partial interruption along white matter bundles was demonstrated. However, a 'mismatch' between the findings of FLAIR, Diffusion-weighted images (DWI) and DTI, in the case of CO intoxication, was seen. Conclusions: DTI gave more information compared to conventional sequences about ultrastructural brain tissue in almost all the diseases above mentioned. Therefore, there is a work in progress about DTI acquisition, to evaluate a new technique, called tractography. (author)
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)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.
On the concircular curvature tensor of Riemannian manifolds
International Nuclear Information System (INIS)
Rahman, M.S.; Lal, S.
1990-06-01
Definition of the concircular curvature tensor, Z hijk , along with Z-tensor, Z ij , is given and some properties of Z hijk are described. Tensors identical with Z hijk are shown. A necessary and sufficient condition that a Riemannian V n has zero Z-tensor is found. A number of theorems on concircular symmetric space, concircular recurrent space (Z n -space) and Z n -space with zero Z-tensor are deduced. (author). 6 refs
Tensor Toolbox for MATLAB v. 3.0
Energy Technology Data Exchange (ETDEWEB)
2017-03-07
Tensors (also known as multidimensional arrays or N-way arrays) are used in a variety of applications ranging from chemometrics to network analysis. The Tensor Toolbox provides classes for manipulating dense, sparse, and structured tensors using MATLAB's object-oriented features. It also provides algorithms for tensor decomposition and factorization, algorithms for computing tensor eigenvalues, and methods for visualization of results.
Fledderus, M.
2012-01-01
Twee op de vijf UT-studenten hebben last van ernstige studiestress, zo erg zelfs dat het ze in hun privéleven belemmert. Die cijfers komen overeen met het landelijk beeld van stress onder studenten. Samen met 14 andere universiteits- en hogeschoolbladen enquêteerde UT Nieuws bijna 5500 studenten. Opvallend is dat mannelijke studenten uit Twente zich veel minder druk lijken te maken over hun studie. Onder vrouwen ligt de stress juist erg hoog ten opzichte van het landelijk gemiddelde.
DEFF Research Database (Denmark)
Keller, Hanne Dauer
2015-01-01
Kapitlet handler om stress som følelse, og det trækker primært på de få kvalitative undersøgelser, der er lavet af stressforløb.......Kapitlet handler om stress som følelse, og det trækker primært på de få kvalitative undersøgelser, der er lavet af stressforløb....
Measuring Nematic Susceptibilities from the Elastoresistivity Tensor
Hristov, A. T.; Shapiro, M. C.; Hlobil, Patrick; Maharaj, Akash; Chu, Jiun-Haw; Fisher, Ian
The elastoresistivity tensor mijkl relates changes in resistivity to the strain on a material. As a fourth-rank tensor, it contains considerably more information about the material than the simpler (second-rank) resistivity tensor; in particular, certain elastoresistivity coefficients can be related to thermodynamic susceptibilities and serve as a direct probe of symmetry breaking at a phase transition. The aim of this talk is twofold. First, we enumerate how symmetry both constrains the structure of the elastoresistivity tensor into an easy-to-understand form and connects tensor elements to thermodynamic susceptibilities. In the process, we generalize previous studies of elastoresistivity to include the effects of magnetic field. Second, we describe an approach to measuring quantities in the elastoresistivity tensor with a novel transverse measurement, which is immune to relative strain offsets. These techniques are then applied to BaFe2As2 in a proof of principle measurement. This work is supported by the Department of Energy, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division, under Contract DE-AC02-76SF00515.
Marin Quintero, Maider J.
2013-01-01
The structure tensor for vector valued images is most often defined as the average of the scalar structure tensors in each band. The problem with this definition is the assumption that all bands provide the same amount of edge information giving them the same weights. As a result non-edge pixels can be reinforced and edges can be weakened…
Lepore, N; Brun, C; Chou, Y Y; Chiang, M C; Dutton, R A; Hayashi, K M; Luders, E; Lopez, O L; Aizenstein, H J; Toga, A W; Becker, J T; Thompson, P M
2008-01-01
This paper investigates the performance of a new multivariate method for tensor-based morphometry (TBM). Statistics on Riemannian manifolds are developed that exploit the full information in deformation tensor fields. In TBM, multiple brain images are warped to a common neuroanatomical template via 3-D nonlinear registration; the resulting deformation fields are analyzed statistically to identify group differences in anatomy. Rather than study the Jacobian determinant (volume expansion factor) of these deformations, as is common, we retain the full deformation tensors and apply a manifold version of Hotelling's $T(2) test to them, in a Log-Euclidean domain. In 2-D and 3-D magnetic resonance imaging (MRI) data from 26 HIV/AIDS patients and 14 matched healthy subjects, we compared multivariate tensor analysis versus univariate tests of simpler tensor-derived indices: the Jacobian determinant, the trace, geodesic anisotropy, and eigenvalues of the deformation tensor, and the angle of rotation of its eigenvectors. We detected consistent, but more extensive patterns of structural abnormalities, with multivariate tests on the full tensor manifold. Their improved power was established by analyzing cumulative p-value plots using false discovery rate (FDR) methods, appropriately controlling for false positives. This increased detection sensitivity may empower drug trials and large-scale studies of disease that use tensor-based morphometry.
Tensor network state correspondence and holography
Singh, Sukhwinder
2018-01-01
In recent years, tensor network states have emerged as a very useful conceptual and simulation framework to study quantum many-body systems at low energies. In this paper, we describe a particular way in which any given tensor network can be viewed as a representation of two different quantum many-body states. The two quantum many-body states are said to correspond to each other by means of the tensor network. We apply this "tensor network state correspondence"—a correspondence between quantum many-body states mediated by tensor networks as we describe—to the multi-scale entanglement renormalization ansatz (MERA) representation of ground states of one dimensional (1D) quantum many-body systems. Since the MERA is a 2D hyperbolic tensor network (the extra dimension is identified as the length scale of the 1D system), the two quantum many-body states obtained from the MERA, via tensor network state correspondence, are seen to live in the bulk and on the boundary of a discrete hyperbolic geometry. The bulk state so obtained from a MERA exhibits interesting features, some of which caricature known features of the holographic correspondence of String theory. We show how (i) the bulk state admits a description in terms of "holographic screens", (ii) the conformal field theory data associated with a critical ground state can be obtained from the corresponding bulk state, in particular, how pointlike boundary operators are identified with extended bulk operators. (iii) We also present numerical results to illustrate that bulk states, dual to ground states of several critical spin chains, have exponentially decaying correlations, and that the bulk correlation length generally decreases with increase in central charge for these spin chains.
Fledderus, M.
2012-01-01
Twee op de vijf UT-studenten hebben last van ernstige studiestress, zo erg zelfs dat het ze in hun privéleven belemmert. Die cijfers komen overeen met het landelijk beeld van stress onder studenten. Samen met 14 andere universiteits- en hogeschoolbladen enquêteerde UT Nieuws bijna 5500 studenten.
Susceptibility tensor imaging (STI) of the brain.
Li, Wei; Liu, Chunlei; Duong, Timothy Q; van Zijl, Peter C M; Li, Xu
2017-04-01
Susceptibility tensor imaging (STI) is a recently developed MRI technique that allows quantitative determination of orientation-independent magnetic susceptibility parameters from the dependence of gradient echo signal phase on the orientation of biological tissues with respect to the main magnetic field. By modeling the magnetic susceptibility of each voxel as a symmetric rank-2 tensor, individual magnetic susceptibility tensor elements as well as the mean magnetic susceptibility and magnetic susceptibility anisotropy can be determined for brain tissues that would still show orientation dependence after conventional scalar-based quantitative susceptibility mapping to remove such dependence. Similar to diffusion tensor imaging, STI allows mapping of brain white matter fiber orientations and reconstruction of 3D white matter pathways using the principal eigenvectors of the susceptibility tensor. In contrast to diffusion anisotropy, the main determinant factor of the susceptibility anisotropy in brain white matter is myelin. Another unique feature of the susceptibility anisotropy of white matter is its sensitivity to gadolinium-based contrast agents. Mechanistically, MRI-observed susceptibility anisotropy is mainly attributed to the highly ordered lipid molecules in the myelin sheath. STI provides a consistent interpretation of the dependence of phase and susceptibility on orientation at multiple scales. This article reviews the key experimental findings and physical theories that led to the development of STI, its practical implementations, and its applications for brain research. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd.
Primordial tensor modes of the early Universe
Martínez, Florencia Benítez; Olmedo, Javier
2016-06-01
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 Schrödinger equation similar to the one emerging in the dressed metric approach and, on the other hand, the ones necessary for the effective evolution equations of these primordial tensor modes within the hybrid approach to be valid. Finally, we consider loop quantum cosmology as an example where these quantization techniques can be applied and compare with other approaches.
A Visual Model for the Variance and Standard Deviation
Orris, J. B.
2011-01-01
This paper shows how the variance and standard deviation can be represented graphically by looking at each squared deviation as a graphical object--in particular, as a square. A series of displays show how the standard deviation is the size of the average square.
Patterns of deviation in Niyi Osundare's poetry | Dick | Mgbakoigba ...
African Journals Online (AJOL)
Poetry is generally marked by deviation. But the question that has bothered scholars is whether there is a difference in this deviation in Modern African/ Nigerian poetry in English as opposed to patterns of deviation in Euro-modernists poetry. A critical stylistic study of the poetry of Niyi Osundare from Nigeria reveals that he ...
International Nuclear Information System (INIS)
Huf, P A; Carminati, J
2015-01-01
In this paper we: (1) introduce TensorPack, a software package for the algebraic manipulation of tensors in covariant index format in Maple; (2) briefly demonstrate the use of the package with an orthonormal tensor proof of the shearfree conjecture for dust. TensorPack is based on the Riemann and Canon tensor software packages and uses their functions to express tensors in an indexed covariant format. TensorPack uses a string representation as input and provides functions for output in index form. It extends the functionality to basic algebra of tensors, substitution, covariant differentiation, contraction, raising/lowering indices, symmetry functions and other accessory functions. The output can be merged with text in the Maple environment to create a full working document with embedded dynamic functionality. The package offers potential for manipulation of indexed algebraic tensor expressions in a flexible software environment. (paper)
Seismic sensitivity of normal-mode coupling to Lorentz stresses in the Sun
Hanasoge, Shravan M.
2017-09-01
Understanding the governing mechanism of solar magnetism remains an outstanding challenge in astrophysics. Seismology is the most compelling technique to infer the internal properties of the Sun and stars. Waves in the Sun, nominally acoustic, are sensitive to the emergence and cyclical strengthening of magnetic field, evidenced by measured changes in resonant oscillation frequencies that are correlated with the solar cycle. The inference of internal Lorentz stresses from these measurements has the potential to significantly advance our appreciation of the dynamo. Indeed, seismological inverse theory for the Sun is well understood for perturbations in composition, thermal structure and flows but, is not fully developed for magnetism, owing to the complexity of the ideal magnetohydrodynamic (MHD) equation. Invoking first-Born perturbation theory to characterize departures from spherically symmetric hydrostatic models of the Sun and applying the notation of generalized spherical harmonics, we calculate sensitivity functions of seismic measurements to the general time-varying Lorentz stress tensor. We find that eigenstates of isotropic (I.e. acoustic only) background models are dominantly sensitive to isotropic deviations in the stress tensor and much more weakly than anisotropic stresses (and therefore challenging to infer). The apple cannot fall far from the tree.
(Ln-bar, g)-spaces. Ordinary and tensor differentials
International Nuclear Information System (INIS)
Manoff, S.; Dimitrov, B.
1998-01-01
Different types of differentials as special cases of differential operators acting on tensor fields over (L n bar, g)-spaces are considered. The ordinary differential, the covariant differential as a special case of the covariant differential operator, and the Lie differential as a special case of the Lie differential operator are investigated. The tensor differential and its special types (Covariant tensor differential, and Lie tensor differential) are determined and their properties are discussed. Covariant symmetric and antisymmetric (external) tensor differentials, Lie symmetric, and Lie antisymmetric (external) tensor differentials are determined and considered over (L n bar, g)-spaces
Energy-momentum tensor in the fermion-pairing model
International Nuclear Information System (INIS)
Kawati, S.; Miyata, H.
1980-01-01
The symmetric energy-momentum tensor for the self-interacting fermion theory (psi-barpsi) 2 is expressed in terms of the collective mode within the Hartree approximation. The divergent part of the energy-momentum tensor for the fermion theory induces an effective energy-momentum tensor for the collective mode, and this effective energy-momentum tensor automatically has the Callan-Coleman-Jackiw improved form. The renormalized energy-momentum tensor is structurally equivalent to the Callan-Coleman-Jackiw improved tensor for the Yukawa theory
Encoding !-tensors as !-graphs with neighbourhood orders
Directory of Open Access Journals (Sweden)
David Quick
2015-11-01
Full Text Available Diagrammatic reasoning using string diagrams provides an intuitive language for reasoning about morphisms in a symmetric monoidal category. To allow working with infinite families of string diagrams, !-graphs were introduced as a method to mark repeated structure inside a diagram. This led to !-graphs being implemented in the diagrammatic proof assistant Quantomatic. Having a partially automated program for rewriting diagrams has proven very useful, but being based on !-graphs, only commutative theories are allowed. An enriched abstract tensor notation, called !-tensors, has been used to formalise the notion of !-boxes in non-commutative structures. This work-in-progress paper presents a method to encode !-tensors as !-graphs with some additional structure. This will allow us to leverage the existing code from Quantomatic and quickly provide various tools for non-commutative diagrammatic reasoning.
Federated Tensor Factorization for Computational Phenotyping
Kim, Yejin; Sun, Jimeng; Yu, Hwanjo; Jiang, Xiaoqian
2017-01-01
Tensor factorization models offer an effective approach to convert massive electronic health records into meaningful clinical concepts (phenotypes) for data analysis. These models need a large amount of diverse samples to avoid population bias. An open challenge is how to derive phenotypes jointly across multiple hospitals, in which direct patient-level data sharing is not possible (e.g., due to institutional policies). In this paper, we developed a novel solution to enable federated tensor factorization for computational phenotyping without sharing patient-level data. We developed secure data harmonization and federated computation procedures based on alternating direction method of multipliers (ADMM). Using this method, the multiple hospitals iteratively update tensors and transfer secure summarized information to a central server, and the server aggregates the information to generate phenotypes. We demonstrated with real medical datasets that our method resembles the centralized training model (based on combined datasets) in terms of accuracy and phenotypes discovery while respecting privacy. PMID:29071165
Exploring extra dimensions through inflationary tensor modes
Im, Sang Hui; Nilles, Hans Peter; Trautner, Andreas
2018-03-01
Predictions of inflationary schemes can be influenced by the presence of extra dimensions. This could be of particular relevance for the spectrum of gravitational waves in models where the extra dimensions provide a brane-world solution to the hierarchy problem. Apart from models of large as well as exponentially warped extra dimensions, we analyze the size of tensor modes in the Linear Dilaton scheme recently revived in the discussion of the "clockwork mechanism". The results are model dependent, significantly enhanced tensor modes on one side and a suppression on the other. In some cases we are led to a scheme of "remote inflation", where the expansion is driven by energies at a hidden brane. In all cases where tensor modes are enhanced, the requirement of perturbativity of gravity leads to a stringent upper limit on the allowed Hubble rate during inflation.
Permittivity and permeability tensors for cloaking applications
Choudhury, Balamati; Jha, Rakesh Mohan
2016-01-01
This book is focused on derivations of analytical expressions for stealth and cloaking applications. An optimal version of electromagnetic (EM) stealth is the design of invisibility cloak of arbitrary shapes in which the EM waves can be controlled within the cloaking shell by introducing a prescribed spatial variation in the constitutive parameters. The promising challenge in design of invisibility cloaks lies in the determination of permittivity and permeability tensors for all the layers. This book provides the detailed derivation of analytical expressions of the permittivity and permeability tensors for various quadric surfaces within the eleven Eisenhart co-ordinate systems. These include the cylinders and the surfaces of revolutions. The analytical modeling and spatial metric for each of these surfaces are provided along with their tensors. This mathematical formulation will help the EM designers to analyze and design of various quadratics and their hybrids, which can eventually lead to design of cloakin...
Tensor calculus for engineers and physicists
de Souza Sánchez Filho, Emil
2016-01-01
This textbook provides a rigorous approach to tensor manifolds in several aspects relevant for Engineers and Physicists working in industry or academia. With a thorough, comprehensive, and unified presentation, this book offers insights into several topics of tensor analysis, which covers all aspects of N dimensional spaces. The main purpose of this book is to give a self-contained yet simple, correct and comprehensive mathematical explanation of tensor calculus for undergraduate and graduate students and for professionals. In addition to many worked problems, this book features a selection of examples, solved step by step. Although no emphasis is placed on special and particular problems of Engineering or Physics, the text covers the fundamentals of these fields of science. The book makes a brief introduction into the basic concept of the tensorial formalism so as to allow the reader to make a quick and easy review of the essential topics that enable having the grounds for the subsequent themes, without need...
Tensor pressure tokamak equilibrium and stability
Energy Technology Data Exchange (ETDEWEB)
Cooper, W.A.
1981-03-01
We investigate the equilibrium and magnetohydrodynamic (MHD) stability of tokamaks with tensor pressure and examine, in particular, the effects of anisotropies induced by neutral beam injection. Perpendicular and parallel beam pressure components are evaluated by taking moments of a distribution function obtained from the solution of a Fokker-Planck equation that models the injection of high-energy neutral beams into a tokamak. We numerically generate D-shaped beam-induced tensor pressure equilibria. A double adiabatic energy principle is derived from a modified version of the guiding center plasma energy principle. Finally, we apply the tensor pressure ballooning mode equation to computed equilibria that model experimentally determined ISX-B discharge profiles with high-power neutral beam injection. We predict that the plasma is unstable to flutelike modes in the central core of the discharge as a result of the pressure profile peakedness induced by the beams.
Ambar Ari Astuti
2007-01-01
Average deviation and standard deviation measures included in the distribution of absolute (absolute dispersion), and is one measure of knowledge of the statistics used to describe a set of data that has been made or not made with attention to every value in the corresponding data set.The figures produced in the calculations using the average deviation and standard deviation expressed in the same units as the original data units.
Some late-time asymptotics of general scalar-tensor cosmologies
Energy Technology Data Exchange (ETDEWEB)
Barrow, John D [DAMTP, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA (United Kingdom); Shaw, Douglas J [Astronomy Unit, Queen Mary University, Mile End Rd., London E1 4NS (United Kingdom)
2008-04-21
We study the asymptotic behaviour of isotropic and homogeneous universes in general scalar-tensor gravity theories containing a p = -{rho} vacuum fluid stress and other sub-dominant matter stresses. It is shown that in order for there to be an approach to a de Sitter spacetime at large 4-volumes the coupling function, {omega}({phi}), which defines the scalar-tensor theory, must diverge faster than |{phi}{sub {infinity}} - {phi}|{sup -1+{epsilon}} for all {epsilon} > 0 as {phi} {yields} {phi}{sub {infinity}} {ne} 0 for large values of the time. Thus, for a given theory, specified by {omega}({phi}), there must exist some {phi}{sub {infinity}} element of (0, {infinity}) such that {omega} {yields} {infinity} and {omega}'/{omega}{sup 2+{epsilon}} {yields} 0 as {phi} {yields} {phi}{sub {infinity}} in order for cosmological solutions of the theory to approach de Sitter expansion at late times. We also classify the possible asymptotic time variations of the gravitation 'constant' G(t) at late times in scalar-tensor theories. We show that (unlike in general relativity) the problem of a profusion of 'Boltzmann brains' at late cosmological times can be avoided in scalar-tensor theories, including Brans-Dicke theory, in which {phi} {yields} {infinity} and {omega} {approx}o({phi}{sup 1/2}) at asymptotically late times.
Kronecker-Basis-Representation Based Tensor Sparsity and Its Applications to Tensor Recovery.
Xie, Qi; Zhao, Qian; Meng, Deyu; Xu, Zongben
2017-08-02
It is well known that the sparsity/low-rank of a vector/matrix can be rationally measured by nonzero-entries-number ($l_0$ norm)/nonzero- singular-values-number (rank), respectively. However, data from real applications are often generated by the interaction of multiple factors, which obviously cannot be sufficiently represented by a vector/matrix, while a high order tensor is expected to provide more faithful representation to deliver the intrinsic structure underlying such data ensembles. Unlike the vector/matrix case, constructing a rational high order sparsity measure for tensor is a relatively harder task. To this aim, in this paper we propose a measure for tensor sparsity, called Kronecker-basis-representation based tensor sparsity measure (KBR briefly), which encodes both sparsity insights delivered by Tucker and CANDECOMP/PARAFAC (CP) low-rank decompositions for a general tensor. Then we study the KBR regularization minimization (KBRM) problem, and design an effective ADMM algorithm for solving it, where each involved parameter can be updated with closed-form equations. Such an efficient solver makes it possible to extend KBR to various tasks like tensor completion and tensor robust principal component analysis. A series of experiments, including multispectral image (MSI) denoising, MSI completion and background subtraction, substantiate the superiority of the proposed methods beyond state-of-the-arts.
Diffusion tensor smoothing through weighted Karcher means
Carmichael, Owen; Chen, Jun; Paul, Debashis; Peng, Jie
2014-01-01
Diffusion tensor magnetic resonance imaging (MRI) quantifies the spatial distribution of water Diffusion at each voxel on a regular grid of locations in a biological specimen by Diffusion tensors– 3 × 3 positive definite matrices. Removal of noise from DTI is an important problem due to the high scientific relevance of DTI and relatively low signal to noise ratio it provides. Leading approaches to this problem amount to estimation of weighted Karcher means of Diffusion tensors within spatial neighborhoods, under various metrics imposed on the space of tensors. However, it is unclear how the behavior of these estimators varies with the magnitude of DTI sensor noise (the noise resulting from the thermal e!ects of MRI scanning) as well as the geometric structure of the underlying Diffusion tensor neighborhoods. In this paper, we combine theoretical analysis, empirical analysis of simulated DTI data, and empirical analysis of real DTI scans to compare the noise removal performance of three kernel-based DTI smoothers that are based on Euclidean, log-Euclidean, and affine-invariant metrics. The results suggest, contrary to conventional wisdom, that imposing a simplistic Euclidean metric may in fact provide comparable or superior noise removal, especially in relatively unstructured regions and/or in the presence of moderate to high levels of sensor noise. On the contrary, log-Euclidean and affine-invariant metrics may lead to better noise removal in highly structured anatomical regions, especially when the sensor noise is of low magnitude. These findings emphasize the importance of considering the interplay of sensor noise magnitude and tensor field geometric structure when assessing Diffusion tensor smoothing options. They also point to the necessity for continued development of smoothing methods that perform well across a large range of scenarios. PMID:25419264
Diffusion tensor imaging in spinal cord compression
International Nuclear Information System (INIS)
Wang, Wei; Qin, Wen; Hao, Nanxin; Wang, Yibin; Zong, Genlin
2012-01-01
Background Although diffusion tensor imaging has been successfully applied in brain research for decades, several main difficulties have hindered its extended utilization in spinal cord imaging. Purpose To assess the feasibility and clinical value of diffusion tensor imaging and tractography for evaluating chronic spinal cord compression. Material and Methods Single-shot spin-echo echo-planar DT sequences were scanned in 42 spinal cord compression patients and 49 healthy volunteers. The mean values of the apparent diffusion coefficient and fractional anisotropy were measured in region of interest at the cervical and lower thoracic spinal cord. The patients were divided into two groups according to the high signal on T2WI (the SCC-HI group and the SCC-nHI group for with or without high signal). A one-way ANOVA was used. Diffusion tensor tractography was used to visualize the morphological features of normal and impaired white matter. Results There were no statistically significant differences in the apparent diffusion coefficient and fractional anisotropy values between the different spinal cord segments of the normal subjects. All of the patients in the SCC-HI group had increased apparent diffusion coefficient values and decreased fractional anisotropy values at the lesion level compared to the normal controls. However, there were no statistically significant diffusion index differences between the SCC-nHI group and the normal controls. In the diffusion tensor imaging maps, the normal spinal cord sections were depicted as fiber tracts that were color-encoded to a cephalocaudal orientation. The diffusion tensor images were compressed to different degrees in all of the patients. Conclusion Diffusion tensor imaging and tractography are promising methods for visualizing spinal cord tracts and can provide additional information in clinical studies in spinal cord compression
Tensor network models of multiboundary wormholes
Peach, Alex; Ross, Simon F.
2017-05-01
We study the entanglement structure of states dual to multiboundary wormhole geometries using tensor network models. Perfect and random tensor networks tiling the hyperbolic plane have been shown to provide good models of the entanglement structure in holography. We extend this by quotienting the plane by discrete isometries to obtain models of the multiboundary states. We show that there are networks where the entanglement structure is purely bipartite, extending results obtained in the large temperature limit. We analyse the entanglement structure in a range of examples.
Tensor modes in pure natural inflation
Nomura, Yasunori; Yamazaki, Masahito
2018-05-01
We study tensor modes in pure natural inflation [1], a recently-proposed inflationary model in which an axionic inflaton couples to pure Yang-Mills gauge fields. We find that the tensor-to-scalar ratio r is naturally bounded from below. This bound originates from the finiteness of the number of metastable branches of vacua in pure Yang-Mills theories. Details of the model can be probed by future cosmic microwave background experiments and improved lattice gauge theory calculations of the θ-angle dependence of the vacuum energy.
Reconstruction of convex bodies from surface tensors
DEFF Research Database (Denmark)
Kousholt, Astrid; Kiderlen, Markus
We present two algorithms for reconstruction of the shape of convex bodies in the two-dimensional Euclidean space. The first reconstruction algorithm requires knowledge of the exact surface tensors of a convex body up to rank s for some natural number s. The second algorithm uses harmonic intrinsic...... volumes which are certain values of the surface tensors and allows for noisy measurements. From a generalized version of Wirtinger's inequality, we derive stability results that are utilized to ensure consistency of both reconstruction procedures. Consistency of the reconstruction procedure based...
Improving Tensor Based Recommenders with Clustering
DEFF Research Database (Denmark)
Leginus, Martin; Dolog, Peter; Zemaitis, Valdas
2012-01-01
Social tagging systems (STS) model three types of entities (i.e. tag-user-item) and relationships between them are encoded into a 3-order tensor. Latent relationships and patterns can be discovered by applying tensor factorization techniques like Higher Order Singular Value Decomposition (HOSVD...... of the recommendations and execution time are improved and memory requirements are decreased. The clustering is motivated by the fact that many tags in a tag space are semantically similar thus the tags can be grouped. Finally, promising experimental results are presented...
Observations About the Projective Tensor Product of Banach Spaces
African Journals Online (AJOL)
, 46B, 46E, 47B. Keywords: tensor, Banach, banach space, tensor product, projective norm, greatest crossnorm, semi-embedding, Radon-Nikodym property, absolutely p-summable sequence, strongly p-summable sequence, topological linear ...
Chambers, David W
2008-01-01
We all experience stress as a regular, and sometimes damaging and sometimes useful, part of our daily lives. In our normal ups and downs, we have our share of exhaustion, despondency, and outrage--matched with their corresponding positive moods. But burnout and workaholism are different. They are chronic, dysfunctional, self-reinforcing, life-shortening habits. Dentists, nurses, teachers, ministers, social workers, and entertainers are especially susceptible to burnout; not because they are hard-working professionals (they tend to be), but because they are caring perfectionists who share control for the success of what they do with others and perform under the scrutiny of their colleagues (they tend to). Workaholics are also trapped in self-sealing cycles, but the elements are ever-receding visions of control and using constant activity as a barrier against facing reality. This essay explores the symptoms, mechanisms, causes, and successful coping strategies for burnout and workaholism. It also takes a look at the general stress response on the physiological level and at some of the damage American society inflicts on itself.
Tensor completion for PDEs with uncertain coefficients and Bayesian Update
Litvinenko, Alexander
2017-03-05
In this work, we tried to show connections between Bayesian update and tensor completion techniques. Usually, only a small/sparse vector/tensor of measurements is available. The typical measurement is a function of the solution. The solution of a stochastic PDE is a tensor, the measurement as well. The idea is to use completion techniques to compute all "missing" values of the measurement tensor and only then apply the Bayesian technique.
A preliminary report on the development of MATLAB tensor classes for fast algorithm prototyping.
Energy Technology Data Exchange (ETDEWEB)
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.
Collineations of the curvature tensor in general relativity
Indian Academy of Sciences (India)
physics pp. 43–48. Collineations of the curvature tensor in general relativity. RISHI KUMAR TIWARI. Department of Mathematics and Computer Application, ... and kinematical properties of the models. Keywords. Collineation; Killing vectors; Ricci tensor; Riemannian curvature tensor. PACS No. 98.80. 1. Introduction.
Efficient MATLAB computations with sparse and factored tensors.
Energy Technology Data Exchange (ETDEWEB)
Bader, Brett William; Kolda, Tamara Gibson (Sandia National Lab, Livermore, CA)
2006-12-01
In this paper, the term tensor refers simply to a multidimensional or N-way array, and we consider how specially structured tensors allow for efficient storage and computation. First, we study sparse tensors, which have the property that the vast majority of the elements are zero. We propose storing sparse tensors using coordinate format and describe the computational efficiency of this scheme for various mathematical operations, including those typical to tensor decomposition algorithms. Second, we study factored tensors, which have the property that they can be assembled from more basic components. We consider two specific types: a Tucker tensor can be expressed as the product of a core tensor (which itself may be dense, sparse, or factored) and a matrix along each mode, and a Kruskal tensor can be expressed as the sum of rank-1 tensors. We are interested in the case where the storage of the components is less than the storage of the full tensor, and we demonstrate that many elementary operations can be computed using only the components. All of the efficiencies described in this paper are implemented in the Tensor Toolbox for MATLAB.
[An Improved Spectral Quaternion Interpolation Method of Diffusion Tensor Imaging].
Xu, Yonghong; Gao, Shangce; Hao, Xiaofei
2016-04-01
Diffusion tensor imaging(DTI)is a rapid development technology in recent years of magnetic resonance imaging.The diffusion tensor interpolation is a very important procedure in DTI image processing.The traditional spectral quaternion interpolation method revises the direction of the interpolation tensor and can preserve tensors anisotropy,but the method does not revise the size of tensors.The present study puts forward an improved spectral quaternion interpolation method on the basis of traditional spectral quaternion interpolation.Firstly,we decomposed diffusion tensors with the direction of tensors being represented by quaternion.Then we revised the size and direction of the tensor respectively according to different situations.Finally,we acquired the tensor of interpolation point by calculating the weighted average.We compared the improved method with the spectral quaternion method and the Log-Euclidean method by the simulation data and the real data.The results showed that the improved method could not only keep the monotonicity of the fractional anisotropy(FA)and the determinant of tensors,but also preserve the tensor anisotropy at the same time.In conclusion,the improved method provides a kind of important interpolation method for diffusion tensor image processing.
Tensor based structure estimation in multi-channel images
DEFF Research Database (Denmark)
Schou, Jesper; Dierking, Wolfgang; Skriver, Henning
2000-01-01
. In the second part tensors are used for representing the structure information. This approach has the advantage, that tensors can be averaged either spatially or by applying several images, and the resulting tensor provides information of the average strength as well as orientation of the structure...
The nonabelian tensor square of a bieberbach group with ...
African Journals Online (AJOL)
The main objective of this paper is to compute the nonabelian tensor square of one Bieberbach group with elementary abelian 2-group point group of dimension three by using the computational method of the nonabelian tensor square for polycyclic groups. The finding of the computation showed that the nonabelian tensor ...
Relativistic particles with spin and antisymmetric tensor fields
International Nuclear Information System (INIS)
Sandoval Junior, L.
1990-09-01
A study is made on antisymmetric tensor fields particularly on second order tensor field as far as his equivalence to other fields and quantization through the path integral are concerned. Also, a particle model is studied which has been recently proposed and reveals to be equivalent to antisymmetric tensor fields of any order. (L.C.J.A.)
Superstrings with tensor degrees of freedom
Energy Technology Data Exchange (ETDEWEB)
Amorim, R. (Inst. de Fisica, Univ. Federal do Rio de Janeiro, Rio de Janeiro, RJ (Brazil)); Barcelos-Neto, J. (Inst. de Fisica, Univ. Federal do Rio de Janeiro, Rio de Janeiro, RJ (Brazil))
1994-10-01
We add antisymmetric tensor degrees of freedom to the usual superstring coordinates. We show that super and kappa symmetries are only achieved for the spacetime dimension D = 4. We also address problems related to the quantization of the model and discuss the influences of this extended spacetime in the usual quantum field theory. (orig.)
Norm of the Riemannian Curvature Tensor
Indian Academy of Sciences (India)
We consider the Riemannian functional R p ( g ) = ∫ M | R ( g ) | p d v g defined on the space of Riemannian metrics with unit volume on a closed smooth manifold where R ( g ) and d v g denote the corresponding Riemannian curvature tensor and volume form and p ∈ ( 0 , ∞ ) . First we prove that the Riemannian metrics ...
Abelian tensor models on the lattice
Chaudhuri, Soumyadeep; Giraldo-Rivera, Victor I.; Joseph, Anosh; Loganayagam, R.; Yoon, Junggi
2018-04-01
We consider a chain of Abelian Klebanov-Tarnopolsky fermionic tensor models coupled through quartic nearest-neighbor interactions. We characterize the gauge-singlet spectrum for small chains (L =2 ,3 ,4 ,5 ) and observe that the spectral statistics exhibits strong evidence in favor of quasi-many-body localization.
Primordial tensor modes from quantum corrected inflation
DEFF Research Database (Denmark)
Joergensen, Jakob; Sannino, Francesco; Svendsen, Ole
2014-01-01
. Finally we confront these theories with the Planck and BICEP2 data. We demonstrate that the discovery of primordial tensor modes by BICEP2 require the presence of sizable quantum departures from the $\\phi^4$-Inflaton model for the non-minimally coupled scenario which we parametrize and quantify. We...
Magnetotelluric impedance tensor analysis for identification of ...
Indian Academy of Sciences (India)
G Pavan Kumar
2017-07-18
Jul 18, 2017 ... Magnetotelluric impedance tensor analysis for identification of transverse tectonic feature in the Wagad uplift, Kachchh, northwest India. G Pavan Kumar*, Virender Kumar, Mehul Nagar, Dilip Singh,. E Mahendar, Pruthul Patel and P Mahesh. Institute of Seismological Research (ISR), Raisan, Gandhinagar ...
Dark energy in scalar-tensor theories
International Nuclear Information System (INIS)
Moeller, J.
2007-12-01
We investigate several aspects of dynamical dark energy in the framework of scalar-tensor theories of gravity. We provide a classification of scalar-tensor coupling functions admitting cosmological scaling solutions. In particular, we recover that Brans-Dicke theory with inverse power-law potential allows for a sequence of background dominated scaling regime and scalar field dominated, accelerated expansion. Furthermore, we compare minimally and non-minimally coupled models, with respect to the small redshift evolution of the dark energy equation of state. We discuss the possibility to discriminate between different models by a reconstruction of the equation-of-state parameter from available observational data. The non-minimal coupling characterizing scalar-tensor models can - in specific cases - alleviate fine tuning problems, which appear if (minimally coupled) quintessence is required to mimic a cosmological constant. Finally, we perform a phase-space analysis of a family of biscalar-tensor models characterized by a specific type of σ-model metric, including two examples from recent literature. In particular, we generalize an axion-dilaton model of Sonner and Townsend, incorporating a perfect fluid background consisting of (dark) matter and radiation. (orig.)
Dark energy in scalar-tensor theories
Energy Technology Data Exchange (ETDEWEB)
Moeller, J.
2007-12-15
We investigate several aspects of dynamical dark energy in the framework of scalar-tensor theories of gravity. We provide a classification of scalar-tensor coupling functions admitting cosmological scaling solutions. In particular, we recover that Brans-Dicke theory with inverse power-law potential allows for a sequence of background dominated scaling regime and scalar field dominated, accelerated expansion. Furthermore, we compare minimally and non-minimally coupled models, with respect to the small redshift evolution of the dark energy equation of state. We discuss the possibility to discriminate between different models by a reconstruction of the equation-of-state parameter from available observational data. The non-minimal coupling characterizing scalar-tensor models can - in specific cases - alleviate fine tuning problems, which appear if (minimally coupled) quintessence is required to mimic a cosmological constant. Finally, we perform a phase-space analysis of a family of biscalar-tensor models characterized by a specific type of {sigma}-model metric, including two examples from recent literature. In particular, we generalize an axion-dilaton model of Sonner and Townsend, incorporating a perfect fluid background consisting of (dark) matter and radiation. (orig.)
Tensor network methods for invariant theory
Biamonte, Jacob; Bergholm, Ville; Lanzagorta, Marco
2013-11-01
Invariant theory is concerned with functions that do not change under the action of a given group. Here we communicate an approach based on tensor networks to represent polynomial local unitary invariants of quantum states. This graphical approach provides an alternative to the polynomial equations that describe invariants, which often contain a large number of terms with coefficients raised to high powers. This approach also enables one to use known methods from tensor network theory (such as the matrix product state (MPS) factorization) when studying polynomial invariants. As our main example, we consider invariants of MPSs. We generate a family of tensor contractions resulting in a complete set of local unitary invariants that can be used to express the Rényi entropies. We find that the graphical approach to representing invariants can provide structural insight into the invariants being contracted, as well as an alternative, and sometimes much simpler, means to study polynomial invariants of quantum states. In addition, many tensor network methods, such as MPSs, contain excellent tools that can be applied in the study of invariants.
Seamless warping of diffusion tensor fields
DEFF Research Database (Denmark)
Xu, Dongrong; Hao, Xuejun; Bansal, Ravi
2008-01-01
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...
Visualization and processing of tensor fields
Weickert, Joachim
2007-01-01
Presents information on the visualization and processing of tensor fields. This book serves as an overview for the inquiring scientist, as a basic foundation for developers and practitioners, and as a textbook for specialized classes and seminars for graduate and doctoral students.
Magnetotelluric impedance tensor analysis for identification of ...
Indian Academy of Sciences (India)
We present the results of magnetotelluric (MT) impedance tensors analyses of 18 sites located along a profile cutting various faults in the uplifted Wagad block of the Kachchh basin. The MT time series of 4–5 days recording duration have been processed and the earth response functions are estimated in broad frequency ...
Fermionic topological quantum states as tensor networks
Wille, C.; Buerschaper, O.; Eisert, J.
2017-06-01
Tensor network states, and in particular projected entangled pair states, play an important role in the description of strongly correlated quantum lattice systems. They do not only serve as variational states in numerical simulation methods, but also provide a framework for classifying phases of quantum matter and capture notions of topological order in a stringent and rigorous language. The rapid development in this field for spin models and bosonic systems has not yet been mirrored by an analogous development for fermionic models. In this work, we introduce a tensor network formalism capable of capturing notions of topological order for quantum systems with fermionic components. At the heart of the formalism are axioms of fermionic matrix-product operator injectivity, stable under concatenation. Building upon that, we formulate a Grassmann number tensor network ansatz for the ground state of fermionic twisted quantum double models. A specific focus is put on the paradigmatic example of the fermionic toric code. This work shows that the program of describing topologically ordered systems using tensor networks carries over to fermionic models.
Tensor B mode and stochastic Faraday mixing
Giovannini, Massimo
2014-01-01
This paper investigates the Faraday effect as a different source of B mode polarization. The E mode polarization is Faraday rotated provided a stochastic large-scale magnetic field is present prior to photon decoupling. In the first part of the paper we discuss the case where the tensor modes of the geometry are absent and we argue that the B mode recently detected by the Bicep2 collaboration cannot be explained by a large-scale magnetic field rotating, through the Faraday effect, the well established E mode polarization. In this case, the observed temperature autocorrelations would be excessively distorted by the magnetic field. In the second part of the paper the formation of Faraday rotation is treated as a stationary, random and Markovian process with the aim of generalizing a set of scaling laws originally derived in the absence of the tensor modes of the geometry. We show that the scalar, vector and tensor modes of the brightness perturbations can all be Faraday rotated even if the vector and tensor par...
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.
Tensor algebra and tensor analysis for engineers with applications to continuum mechanics
Itskov, Mikhail
2015-01-01
This is the fourth and revised edition of a well-received book that aims at bridging the gap between the engineering course of tensor algebra on the one side and the mathematical course of classical linear algebra on the other side. In accordance with the contemporary way of scientific publications, a modern absolute tensor notation is preferred throughout. The book provides a comprehensible exposition of the fundamental mathematical concepts of tensor calculus and enriches the presented material with many illustrative examples. In addition, the book also includes advanced chapters dealing with recent developments in the theory of isotropic and anisotropic tensor functions and their applications to continuum mechanics. Hence, this monograph addresses graduate students as well as scientists working in this field. In each chapter numerous exercises are included, allowing for self-study and intense practice. Solutions to the exercises are also provided.
Baust, Maximilian; Weinmann, Andreas; Wieczorek, Matthias; Lasser, Tobias; Storath, Martin; Navab, Nassir
2016-08-01
In this paper, we consider combined TV denoising and diffusion tensor fitting in DTI using the affine-invariant Riemannian metric on the space of diffusion tensors. Instead of first fitting the diffusion tensors, and then denoising them, we define a suitable TV type energy functional which incorporates the measured DWIs (using an inverse problem setup) and which measures the nearness of neighboring tensors in the manifold. To approach this functional, we propose generalized forward- backward splitting algorithms which combine an explicit and several implicit steps performed on a decomposition of the functional. We validate the performance of the derived algorithms on synthetic and real DTI data. In particular, we work on real 3D data. To our knowledge, the present paper describes the first approach to TV regularization in a combined manifold and inverse problem setup.
Estimates of quantum deviations from classical mechanics using large deviation results
International Nuclear Information System (INIS)
Blanchard, P.; Combe, P.; Sirugue, M.; Sirugue-Collin, M.
1984-11-01
Classical and quantum motions of particles are very different. Indeed one cannot assign a trajectory to a quantum particle. However one has the physical intuition that quantum particles wander around the corresponding classical path in phase space by an amount of h. Deviations come from the uncertainty principle. Underlying this picture, there are two ideas: i) there is some kind of probability associated with possible paths; ii) this probability concentrates around the classical path in a region whose magnitude is related to h. We want to show that there exists in phase space a probabilistic schema which accounts in a much more transparent way for the intuitive ideas alluded above. It is convenient to deal with the description of quantum states not in term of wave function but in term of Wigner functions. It allows a more symmetrical treatment of phase-space variables. Also it is expected to be a less singular object than the wave function in the classical limit. Second section is devoted to describe the elementary results concerning Wigner function. It also describes the time development equation of these functions. In the third section we describe the quantum flow which represents the quantum dynamics in phase space. In the last section, we study the asymptotics of this flow showing that it tends in a suitable sense to the classical flow. The most useful tool for this study is the Ventsel's theory of large deviations. This theory already proved to be very efficient in the study of classical limit. However it has not been used for jump processes up to now
Lepore, Natasha; Brun, Caroline; Chou, Yi-Yu; Chiang, Ming-Chang; Dutton, Rebecca A.; Hayashi, Kiralee M.; Luders, Eileen; Lopez, Oscar L.; Aizenstein, Howard J.; Toga, Arthur W.; Becker, James T.; Thompson, Paul M.
2008-01-01
This paper investigates the performance of a new multivariate method for tensor-based morphometry (TBM). Statistics on Riemannian manifolds are developed that exploit the full information in deformation tensor fields. In TBM, multiple brain images are warped to a common neuroanatomical template via 3-D nonlinear registration; the resulting deformation fields are analyzed statistically to identify group differences in anatomy. Rather than study the Jacobian determinant (volume expansion factor...
DEFF Research Database (Denmark)
Martins, R.V.; Margulies, L.; Schmidt, Søren
2004-01-01
in transmission geometry. After each load step diffraction patterns are collected with a large-area X-ray detector system for a series of different angular and lateral sample positions. An automated indexing routine was used to assign sets of diffraction spots to individual grains. The strain tensor components...... as well as the individual grain position within the sample were then fitted from the diffraction spot positions. A maximum tensile load of 48 MPa was applied. Deviations in strain of up to 600 × 10−6 are observed between respective strain components of individual grains....
Energy Technology Data Exchange (ETDEWEB)
Montesinos, M. [CINVESTAV-IPN, 07360 Mexico D.F. (Mexico); Flores, E. [Facultad de Fisica e Inteligencia Artificial, Universidad Veracruzana, 91000 Xalapa, Veracruz (Mexico)]. E-mail: merced@fis.cinvestav.mx
2006-07-01
The symmetric and gauge-invariant energy-momentum tensors for source-free Maxwell and Yang-Mills theories are obtained by means of translations in spacetime via a systematic implementation of Noether's theorem. For the source-free neutral Proca field, the same procedure yields also the symmetric energy-momentum tensor. In all cases, the key point to get the right expressions for the energy-momentum tensors is the appropriate handling of their equations of motion and the Bianchi identities. It must be stressed that these results are obtained without using Belinfante's symmetrization techniques which are usually employed to this end. (Author)
Quantum uncertainty relation based on the mean deviation
Sharma, Gautam; Mukhopadhyay, Chiranjib; Sazim, Sk; Pati, Arun Kumar
2018-01-01
Traditional forms of quantum uncertainty relations are invariably based on the standard deviation. This can be understood in the historical context of simultaneous development of quantum theory and mathematical statistics. Here, we present alternative forms of uncertainty relations, in both state dependent and state independent forms, based on the mean deviation. We illustrate the robustness of this formulation in situations where the standard deviation based uncertainty relation is inapplica...
Some large deviation results for near intermediate random geometric graphs
Doku-Amponsah, Kwabena
2013-01-01
We find large deviation principles for the degree distribution and the proportion of isolated vertices for the near intermediate random geometric graph models on n vertices placed uniformly in [0, 1]^d, for d in N. In the course of the proof of these large deviation results we find joint large deviation principle for the empirical locality measure of the coloured random geometric graphs,(Canning & Penman, 2003).
Two examples of non strictly convex large deviations
De Marco, Stefano; Jacquier, Antoine; Roome, Patrick
2016-01-01
We present two examples of a large deviations principle where the rate function is not strictly convex. This is motivated by a model used in mathematical finance (the Heston model), and adds a new item to the zoology of non strictly convex large deviations. For one of these examples, we show that the rate function of the Cramer-type of large deviations coincides with that of the Freidlin-Wentzell when contraction principles are applied.
Experimental investigation of acoustic emissions and their moment tensors in rock during failure
Czech Academy of Sciences Publication Activity Database
Aker, E.; Kühn, D.; Vavryčuk, Václav; Soldal, M.; Oye, V.
2014-01-01
Roč. 70, September (2014), s. 286-295 ISSN 1365-1609 R&D Projects: GA ČR(CZ) GAP210/12/1491 EU Projects: European Commission(XE) 230669 - AIM Institutional support: RVO:67985530 Keywords : acoustic emissions * focal mechanisms * moment tensors * rock fracturing * hoop stresses * laboratory experiment Subject RIV: DC - Siesmology, Volcanology, Earth Structure Impact factor: 1.686, year: 2014
Massless and massive quanta resulting from a mediumlike metric tensor
International Nuclear Information System (INIS)
Soln, J.
1985-01-01
A simple model of the ''primordial'' scalar field theory is presented in which the metric tensor is a generalization of the metric tensor from electrodynamics in a medium. The radiation signal corresponding to the scalar field propagates with a velocity that is generally less than c. This signal can be associated simultaneously with imaginary and real effective (momentum-dependent) masses. The requirement that the imaginary effective mass vanishes, which we take to be the prerequisite for the vacuumlike signal propagation, leads to the ''spontaneous'' splitting of the metric tensor into two distinct metric tensors: one metric tensor gives rise to masslesslike radiation and the other to a massive particle. (author)
Feature Surfaces in Symmetric Tensor Fields Based on Eigenvalue Manifold.
Palacios, Jonathan; Yeh, Harry; Wang, Wenping; Zhang, Yue; Laramee, Robert S; Sharma, Ritesh; Schultz, Thomas; Zhang, Eugene
2016-03-01
Three-dimensional symmetric tensor fields have a wide range of applications in solid and fluid mechanics. Recent advances in the (topological) analysis of 3D symmetric tensor fields focus on degenerate tensors which form curves. In this paper, we introduce a number of feature surfaces, such as neutral surfaces and traceless surfaces, into tensor field analysis, based on the notion of eigenvalue manifold. Neutral surfaces are the boundary between linear tensors and planar tensors, and the traceless surfaces are the boundary between tensors of positive traces and those of negative traces. Degenerate curves, neutral surfaces, and traceless surfaces together form a partition of the eigenvalue manifold, which provides a more complete tensor field analysis than degenerate curves alone. We also extract and visualize the isosurfaces of tensor modes, tensor isotropy, and tensor magnitude, which we have found useful for domain applications in fluid and solid mechanics. Extracting neutral and traceless surfaces using the Marching Tetrahedra method can cause the loss of geometric and topological details, which can lead to false physical interpretation. To robustly extract neutral surfaces and traceless surfaces, we develop a polynomial description of them which enables us to borrow techniques from algebraic surface extraction, a topic well-researched by the computer-aided design (CAD) community as well as the algebraic geometry community. In addition, we adapt the surface extraction technique, called A-patches, to improve the speed of finding degenerate curves. Finally, we apply our analysis to data from solid and fluid mechanics as well as scalar field analysis.
Glyph-Based Comparative Visualization for Diffusion Tensor Fields.
Zhang, Changgong; Schultz, Thomas; Lawonn, Kai; Eisemann, Elmar; Vilanova, Anna
2016-01-01
Diffusion Tensor Imaging (DTI) is a magnetic resonance imaging modality that enables the in-vivo reconstruction and visualization of fibrous structures. To inspect the local and individual diffusion tensors, glyph-based visualizations are commonly used since they are able to effectively convey full aspects of the diffusion tensor. For several applications it is necessary to compare tensor fields, e.g., to study the effects of acquisition parameters, or to investigate the influence of pathologies on white matter structures. This comparison is commonly done by extracting scalar information out of the tensor fields and then comparing these scalar fields, which leads to a loss of information. If the glyph representation is kept, simple juxtaposition or superposition can be used. However, neither facilitates the identification and interpretation of the differences between the tensor fields. Inspired by the checkerboard style visualization and the superquadric tensor glyph, we design a new glyph to locally visualize differences between two diffusion tensors by combining juxtaposition and explicit encoding. Because tensor scale, anisotropy type, and orientation are related to anatomical information relevant for DTI applications, we focus on visualizing tensor differences in these three aspects. As demonstrated in a user study, our new glyph design allows users to efficiently and effectively identify the tensor differences. We also apply our new glyphs to investigate the differences between DTI datasets of the human brain in two different contexts using different b-values, and to compare datasets from a healthy and HIV-infected subject.
Tensoral for post-processing users and simulation authors
Dresselhaus, Eliot
1993-01-01
The CTR post-processing effort aims to make turbulence simulations and data more readily and usefully available to the research and industrial communities. The Tensoral language, which provides the foundation for this effort, is introduced here in the form of a user's guide. The Tensoral user's guide is presented in two main sections. Section one acts as a general introduction and guides database users who wish to post-process simulation databases. Section two gives a brief description of how database authors and other advanced users can make simulation codes and/or the databases they generate available to the user community via Tensoral database back ends. The two-part structure of this document conforms to the two-level design structure of the Tensoral language. Tensoral has been designed to be a general computer language for performing tensor calculus and statistics on numerical data. Tensoral's generality allows it to be used for stand-alone native coding of high-level post-processing tasks (as described in section one of this guide). At the same time, Tensoral's specialization to a minute task (namely, to numerical tensor calculus and statistics) allows it to be easily embedded into applications written partly in Tensoral and partly in other computer languages (here, C and Vectoral). Embedded Tensoral, aimed at advanced users for more general coding (e.g. of efficient simulations, for interfacing with pre-existing software, for visualization, etc.), is described in section two of this guide.
Energy-momentum tensor of the electromagnetic field
International Nuclear Information System (INIS)
Horndeski, G.W.; Wainwright, J.
1977-01-01
In this paper we investigate the energy-momentum tensor of the most general second-order vector-tensor theory of gravitation and electromagnetism which has field equations which are (i) derivable from a variational principle, (ii) consistent with the notion of conservation of charge, and (iii) compatible with Maxwell's equations in a flat space. This energy-momentum tensor turns out to be quadratic in the first partial derivatives of the electromagnetic field tensor and depends upon the curvature tensor. The asymptotic behavior of this energy-momentum tensor is examined for solutions to Maxwell's equations in Minkowski space, and it is demonstrated that this energy-momentum tensor predicts regions of negative energy density in the vicinity of point sources
Quantum mechanics of Yano tensors: Dirac equation in curved spacetime
International Nuclear Information System (INIS)
Cariglia, Marco
2004-01-01
In spacetimes admitting Yano tensors, the classical theory of the spinning particle possesses enhanced worldline supersymmetry. Quantum mechanically generators of extra supersymmetries correspond to operators that in the classical limit commute with the Dirac operator and generate conserved quantities. We show that the result is preserved in the full quantum theory, that is, Yano symmetries are not anomalous. This was known for Yano tensors of rank 2, but our main result is to show that it extends to Yano tensors of arbitrary rank. We also describe the conformal Yano equation and show that is invariant under Hodge duality. There is a natural relationship between Yano tensors and supergravity theories. As the simplest possible example, we show that when the spacetime admits a Killing spinor then this generates Yano and conformal Yano tensors. As an application, we construct Yano tensors on maximally symmetric spaces: they are spanned by tensor products of Killing vectors
Algebraic and computational aspects of real tensor ranks
Sakata, Toshio; Miyazaki, Mitsuhiro
2016-01-01
This book provides comprehensive summaries of theoretical (algebraic) and computational aspects of tensor ranks, maximal ranks, and typical ranks, over the real number field. Although tensor ranks have been often argued in the complex number field, it should be emphasized that this book treats real tensor ranks, which have direct applications in statistics. The book provides several interesting ideas, including determinant polynomials, determinantal ideals, absolutely nonsingular tensors, absolutely full column rank tensors, and their connection to bilinear maps and Hurwitz-Radon numbers. In addition to reviews of methods to determine real tensor ranks in details, global theories such as the Jacobian method are also reviewed in details. The book includes as well an accessible and comprehensive introduction of mathematical backgrounds, with basics of positive polynomials and calculations by using the Groebner basis. Furthermore, this book provides insights into numerical methods of finding tensor ranks through...
Limitations of the Concept of Stress in Structural Analysis.
Edelman, Steven Harold
1989-01-01
Provides an introduction and explanations of stress-strain relationships, measuring stress, a goal of structural analysis, and legitimate applications of the concept of stress. Diagrams include a derivation of the stress tensor, graphical representations of stress-strain relations, and related problems. (RT)
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.
Limiting values of large deviation probabilities of quadratic statistics
Jeurnink, Gerardus A.M.; Kallenberg, W.C.M.
1990-01-01
Application of exact Bahadur efficiencies in testing theory or exact inaccuracy rates in estimation theory needs evaluation of large deviation probabilities. Because of the complexity of the expressions, frequently a local limit of the nonlocal measure is considered. Local limits of large deviation
Towards a large deviation theory for strongly correlated systems
Energy Technology Data Exchange (ETDEWEB)
Ruiz, Guiomar, E-mail: guiomar.ruiz@upm.es [Centro Brasileiro de Pesquisas Fisicas and National Institute of Science and Technology for Complex Systems, Rua Xavier Sigaud 150, 22290-180 Rio de Janeiro, RJ (Brazil); Departamento de Matemática Aplicada y Estadística, Universidad Politécnica de Madrid, Pza. Cardenal Cisneros s.n., 28040 Madrid (Spain); Tsallis, Constantino, E-mail: tsallis@cbpf.br [Centro Brasileiro de Pesquisas Fisicas and National Institute of Science and Technology for Complex Systems, Rua Xavier Sigaud 150, 22290-180 Rio de Janeiro, RJ (Brazil); Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, NM 87501 (United States)
2012-07-23
A large-deviation connection of statistical mechanics is provided by N independent binary variables, the (N→∞) limit yielding Gaussian distributions. The probability of n≠N/2 out of N throws is governed by e{sup −Nr}, r related to the entropy. Large deviations for a strong correlated model characterized by indices (Q,γ) are studied, the (N→∞) limit yielding Q-Gaussians (Q→1 recovers a Gaussian). Its large deviations are governed by e{sub q}{sup −Nr{sub q}} (∝1/N{sup 1/(q−1)}, q>1), q=(Q−1)/(γ[3−Q])+1. This illustration opens the door towards a large-deviation foundation of nonextensive statistical mechanics. -- Highlights: ► We introduce the formalism of relative entropy for a single random binary variable and its q-generalization. ► We study a model of N strongly correlated binary random variables and their large-deviation probabilities. ► Large-deviation probability of strongly correlated model exhibits a q-exponential decay whose argument is proportional to N, as extensivity requires. ► Our results point to a q-generalized large deviation theory and suggest a large-deviation foundation of nonextensive statistical mechanics.
Moderate deviations principles for the kernel estimator of ...
African Journals Online (AJOL)
Abstract. The aim of this paper is to provide pointwise and uniform moderate deviations principles for the kernel estimator of a nonrandom regression function. Moreover, we give an application of these moderate deviations principles to the construction of condence regions for the regression function. Resume. L'objectif de ...
38 CFR 36.4304 - Deviations; changes of identity.
2010-07-01
... identity. 36.4304 Section 36.4304 Pensions, Bonuses, and Veterans' Relief DEPARTMENT OF VETERANS AFFAIRS... Deviations; changes of identity. A deviation of more than 5 percent between the estimates upon which a... change in the identity of the property upon which the original appraisal was based, will invalidate the...
45 CFR 63.19 - Budget revisions and minor deviations.
2010-10-01
... 45 Public Welfare 1 2010-10-01 2010-10-01 false Budget revisions and minor deviations. 63.19 Section 63.19 Public Welfare DEPARTMENT OF HEALTH AND HUMAN SERVICES GENERAL ADMINISTRATION GRANT PROGRAMS... Budget revisions and minor deviations. Pursuant to § 74.102(d) of this title, paragraphs (b)(3) and (b)(4...
Fluctuations and large deviations in non-equilibrium systems
Indian Academy of Sciences (India)
For systems in contact with two reservoirs at different densities or with two thermostats at different temperatures, the large deviation function of the density gives a possible way of extending the notion of free energy to non-equilibrium systems. This large deviation function of the density can be calculated explicitly for ...
The deviation matrix of a continuous-time Markov chain
Coolen-Schrijner, Pauline; van Doorn, Erik A.
2002-01-01
he deviation matrix of an ergodic, continuous-time Markov chain with transition probability matrix $P(.)$ and ergodic matrix $\\Pi$ is the matrix $D \\equiv \\int_0^{\\infty} (P(t)-\\Pi)dt$. We give conditions for $D$ to exist and discuss properties and a representation of $D$. The deviation matrix of a
The deviation matrix of a continuous-time Markov chain
Coolen-Schrijner, P.; van Doorn, E.A.
2001-01-01
The deviation matrix of an ergodic, continuous-time Markov chain with transition probability matrix $P(.)$ and ergodic matrix $\\Pi$ is the matrix $D \\equiv \\int_0^{\\infty} (P(t)-\\Pi)dt$. We give conditions for $D$ to exist and discuss properties and a representation of $D$. The deviation matrix of a
Statistics as Unbiased Estimators: Exploring the Teaching of Standard Deviation
Wasserman, Nicholas H.; Casey, Stephanie; Champion, Joe; Huey, Maryann
2017-01-01
This manuscript presents findings from a study about the knowledge for and planned teaching of standard deviation. We investigate how understanding variance as an unbiased (inferential) estimator--not just a descriptive statistic for the variation (spread) in data--is related to teachers' instruction regarding standard deviation, particularly…
[The crooked nose: correction of dorsal and caudal septal deviations].
Foda, H M T
2010-09-01
The deviated nose represents a complex cosmetic and functional problem. Septal surgery plays a central role in the successful management of the externally deviated nose. This study included 800 patients seeking rhinoplasty to correct external nasal deviations; 71% of these suffered from variable degrees of nasal obstruction. Septal surgery was necessary in 736 (92%) patients, not only to improve breathing, but also to achieve a straight, symmetric external nose. A graduated surgical approach was adopted to allow correction of the dorsal and caudal deviations of the nasal septum without weakening its structural support to the nasal dorsum or nasal tip. The approach depended on full mobilization of deviated cartilage, followed by straightening of the cartilage and its fixation in the corrected position by using bony splinting grafts through an external rhinoplasty approach.
Hydrodynamic tensor density functional theory with correct susceptibility
Ovchinnikov, Igor V.; Bartell, Lizette A.; Neuhauser, Daniel
2007-04-01
In a previous work the authors developed a family of orbital-free tensor equations for the density functional theory [J. Chem. Phys. 124, 024105 (2006)]. The theory is a combination of the coupled hydrodynamic moment equation hierarchy with a cumulant truncation of the one-body electron density matrix. A basic ingredient in the theory is how to truncate the series of equation of motion for the moments. In the original work the authors assumed that the cumulants vanish above a certain order (N). Here the authors show how to modify this assumption to obtain the correct susceptibilities. This is done for N =3, a level above the previous study. At the desired truncation level a few relevant terms are added, which, with the right combination of coefficients, lead to excellent agreement with the Kohn-Sham Lindhard susceptibilities for an uninteracting system. The approach is also powerful away from linear response, as demonstrated in a nonperturbative study of a jellium with a repulsive core, where excellent matching with Kohn-Sham simulations is obtained, while the Thomas-Fermi and von Weiszacker methods show significant deviations. In addition, time-dependent linear response studies at the new N =3 level demonstrate the author's previous assertion that as the order of the theory is increased new additional transverse sound modes appear mimicking the random phase approximation transverse dispersion region.
Tensor coupling and pseudospin symmetry in nuclei
International Nuclear Information System (INIS)
Alberto, P.; Castro, A.S. de; Lisboa, R.; Malheiro, M.
2005-01-01
In this work we study the contribution of the isoscalar tensor coupling to the realization of pseudospin symmetry in nuclei. Using realistic values for the tensor coupling strength, we show that this coupling reduces noticeably the pseudospin splittings, especially for single-particle levels near the Fermi surface. By using an energy decomposition of the pseudospin energy splittings, we show that the changes in these splittings come mainly through the changes induced in the lower radial wave function for the low-lying pseudospin partners and through changes in the expectation value of the pseudospin-orbit coupling term for surface partners. This allows us to confirm the conclusion already reached in previous studies, namely that the pseudospin symmetry in nuclei is of a dynamical nature
Tensor modes on the string theory landscape
Energy Technology Data Exchange (ETDEWEB)
Westphal, Alexander
2012-06-15
We attempt an estimate for the distribution of the tensor mode fraction r over the landscape of vacua in string theory. The dynamics of eternal inflation and quantum tunneling lead to a kind of democracy on the landscape, providing no bias towards large-field or small-field inflation regardless of the class of measure. The tensor mode fraction then follows the number frequency distributions of inflationary mechanisms of string theory over the landscape. We show that an estimate of the relative number frequencies for small-field vs large-field inflation, while unattainable on the whole landscape, may be within reach as a regional answer for warped Calabi-Yau flux compactifications of type IIB string theory.
International Nuclear Information System (INIS)
Kibler, M.; Grenet, G.
1979-07-01
The SU 2 unit tensor operators tsub(k,α) are studied. In the case where the spinor point group G* coincides with U 1 , then tsub(k α) reduces up to a constant to the Wigner-Racah-Schwinger tensor operator tsub(kqα), an operator which produces an angular momentum state. One first investigates those general properties of tsub(kα) which are independent of their realization. The tsub(kα) in terms of two pairs of boson creation and annihilation operators are realized. This leads to look at the Schwinger calculus relative to one angular momentum of two coupled angular momenta. As a by-product, a procedure is given for producing recursion relationships between SU 2 Wigner coefficients. Finally, some of the properties of the Wigner and Racah operators for an arbitrary compact group and the SU 2 coupling coefficients are studied
Proton hyperfine tensors in nitroxide radicals
Energy Technology Data Exchange (ETDEWEB)
Brustolon, M.; Maniero, A.L.; Segre, U. (Universita di Padova (Italy)); Ottaviani, M.F. (Universita di Firenze (Italy)); Romanelli, M. (Universita della Basilicata (Italy))
1990-08-23
The proton hyperfine tensors of five nitroxide radicals have been obtained by ENDOR spectroscopy in frozen solution. The spectra are interpreted by computing the dipolar hyperfine interaction and simulating the spectra. EPR spectra in solution of the same radicals have been simulated by taking into account the effects of the proton hyperfine tensors. We have been able to reproduce accurately the line broadening effects of the proton hyperfine structures inside each nitrogen hyperfine component and we have determined the correlation times for the rotational motion. In the case of the radical Tempol, our analysis allows discrimination between the effects due to the protons of the axial and equatorial methyl groups. On the basis of experimental evidence we can attribute the larger isotropic hyperfine coupling constant to the axial methyl protons. The possible use of the present results for interpreting the spectra of other nitroxide radicals is discussed.
Tensor modes on the string theory landscape
International Nuclear Information System (INIS)
Westphal, Alexander
2012-06-01
We attempt an estimate for the distribution of the tensor mode fraction r over the landscape of vacua in string theory. The dynamics of eternal inflation and quantum tunneling lead to a kind of democracy on the landscape, providing no bias towards large-field or small-field inflation regardless of the class of measure. The tensor mode fraction then follows the number frequency distributions of inflationary mechanisms of string theory over the landscape. We show that an estimate of the relative number frequencies for small-field vs large-field inflation, while unattainable on the whole landscape, may be within reach as a regional answer for warped Calabi-Yau flux compactifications of type IIB string theory.
Sasakian manifolds with purely transversal Bach tensor
Ghosh, Amalendu; Sharma, Ramesh
2017-10-01
We show that a (2n + 1)-dimensional Sasakian manifold (M, g) with a purely transversal Bach tensor has constant scalar curvature ≥2 n (2 n +1 ) , equality holding if and only if (M, g) is Einstein. For dimension 3, M is locally isometric to the unit sphere S3. For dimension 5, if in addition (M, g) is complete, then it has positive Ricci curvature and is compact with finite fundamental group π1(M).
Anisotropic diffusion tensor applied to temporal mammograms
DEFF Research Database (Denmark)
Karemore, Gopal; Brandt, Sami; Sporring, Jon
2010-01-01
changes related to specific effects like Hormonal Replacement Therapy (HRT) and aging. Given effect-grouped patient data, we demonstrated how anisotropic diffusion tensor and its coherence features computed in an anatomically oriented breast coordinate system followed by statistical learning...
Tensor Networks and Quantum Error Correction
Ferris, Andrew J.; Poulin, David
2014-07-01
We establish several relations between quantum error correction (QEC) and tensor network (TN) methods of quantum many-body physics. We exhibit correspondences between well-known families of QEC codes and TNs, and demonstrate a formal equivalence between decoding a QEC code and contracting a TN. We build on this equivalence to propose a new family of quantum codes and decoding algorithms that generalize and improve upon quantum polar codes and successive cancellation decoding in a natural way.
Numerical CP Decomposition of Some Difficult Tensors
Czech Academy of Sciences Publication Activity Database
Tichavský, Petr; Phan, A. H.; Cichocki, A.
2017-01-01
Roč. 317, č. 1 (2017), s. 362-370 ISSN 0377-0427 R&D Projects: GA ČR(CZ) GA14-13713S Institutional support: RVO:67985556 Keywords : Small matrix multiplication * Canonical polyadic tensor decomposition * Levenberg-Marquardt method Subject RIV: BB - Applied Statistics, Operational Research OBOR OECD: Applied mathematics Impact factor: 1.357, year: 2016 http://library.utia.cas.cz/separaty/2017/SI/tichavsky-0468385.pdf
Bayesian approach to magnetotelluric tensor decomposition
Czech Academy of Sciences Publication Activity Database
Červ, Václav; Pek, Josef; Menvielle, M.
2010-01-01
Roč. 53, č. 2 (2010), s. 21-32 ISSN 1593-5213 R&D Projects: GA AV ČR IAA200120701; GA ČR GA205/04/0746; GA ČR GA205/07/0292 Institutional research plan: CEZ:AV0Z30120515 Keywords : galvanic distortion * telluric distortion * impedance tensor * basic procedure * inversion * noise Subject RIV: DE - Earth Magnetism, Geodesy, Geography Impact factor: 0.336, year: 2010
Monte Carlo Volcano Seismic Moment Tensors
Waite, G. P.; Brill, K. A.; Lanza, F.
2015-12-01
Inverse modeling of volcano seismic sources can provide insight into the geometry and dynamics of volcanic conduits. But given the logistical challenges of working on an active volcano, seismic networks are typically deficient in spatial and temporal coverage; this potentially leads to large errors in source models. In addition, uncertainties in the centroid location and moment-tensor components, including volumetric components, are difficult to constrain from the linear inversion results, which leads to a poor understanding of the model space. In this study, we employ a nonlinear inversion using a Monte Carlo scheme with the objective of defining robustly resolved elements of model space. The model space is randomized by centroid location and moment tensor eigenvectors. Point sources densely sample the summit area and moment tensors are constrained to a randomly chosen geometry within the inversion; Green's functions for the random moment tensors are all calculated from modeled single forces, making the nonlinear inversion computationally reasonable. We apply this method to very-long-period (VLP) seismic events that accompany minor eruptions at Fuego volcano, Guatemala. The library of single force Green's functions is computed with a 3D finite-difference modeling algorithm through a homogeneous velocity-density model that includes topography, for a 3D grid of nodes, spaced 40 m apart, within the summit region. The homogenous velocity and density model is justified by long wavelength of VLP data. The nonlinear inversion reveals well resolved model features and informs the interpretation through a better understanding of the possible models. This approach can also be used to evaluate possible station geometries in order to optimize networks prior to deployment.
FABRIC TENSOR FOR DISCONTINUOUS GEOLOGICAL MATERIALS
小田, 匡寛
1982-01-01
Geometrical property (fabric) of discontinuity in geological materials is discussed in terms of (1) position and density, (2) shape and dimension and (3) orientation of related discontinuities such as joint, fault and discrete particle. By taking into account these geometrical elements, a unique measure called fabric tensor F_ is definitely introduced to embody the fabric concept without loss of generality.The first invariant of F_ is important as an index measure to evaluate the crack intens...
User-transparent Distributed TensorFlow
Vishnu, Abhinav; Manzano, Joseph; Siegel, Charles; Daily, Jeff
2017-01-01
Deep Learning (DL) algorithms have become the {\\em de facto} choice for data analysis. Several DL implementations -- primarily limited to a single compute node -- such as Caffe, TensorFlow, Theano and Torch have become readily available. Distributed DL implementations capable of execution on large scale systems are becoming important to address the computational needs of large data produced by scientific simulations and experiments. Yet, the adoption of distributed DL implementations faces si...
Tensor Fusion Network for Multimodal Sentiment Analysis
Zadeh, Amir; Chen, Minghai; Poria, Soujanya; Cambria, Erik; Morency, Louis-Philippe
2017-01-01
Multimodal sentiment analysis is an increasingly popular research area, which extends the conventional language-based definition of sentiment analysis to a multimodal setup where other relevant modalities accompany language. In this paper, we pose the problem of multimodal sentiment analysis as modeling intra-modality and inter-modality dynamics. We introduce a novel model, termed Tensor Fusion Network, which learns both such dynamics end-to-end. The proposed approach is tailored for the vola...
Large-deviation joint statistics of the finite-time Lyapunov spectrum in isotropic turbulence
Energy Technology Data Exchange (ETDEWEB)
Johnson, Perry L., E-mail: pjohns86@jhu.edu; Meneveau, Charles [Department of Mechanical Engineering and Center for Environmental and Applied Fluid Mechanics, The Johns Hopkins University, 3400 N. Charles Street, Baltimore, Maryland 21218 (United States)
2015-08-15
One of the hallmarks of turbulent flows is the chaotic behavior of fluid particle paths with exponentially growing separation among them while their distance does not exceed the viscous range. The maximal (positive) Lyapunov exponent represents the average strength of the exponential growth rate, while fluctuations in the rate of growth are characterized by the finite-time Lyapunov exponents (FTLEs). In the last decade or so, the notion of Lagrangian coherent structures (which are often computed using FTLEs) has gained attention as a tool for visualizing coherent trajectory patterns in a flow and distinguishing regions of the flow with different mixing properties. A quantitative statistical characterization of FTLEs can be accomplished using the statistical theory of large deviations, based on the so-called Cramér function. To obtain the Cramér function from data, we use both the method based on measuring moments and measuring histograms and introduce a finite-size correction to the histogram-based method. We generalize the existing univariate formalism to the joint distributions of the two FTLEs needed to fully specify the Lyapunov spectrum in 3D flows. The joint Cramér function of turbulence is measured from two direct numerical simulation datasets of isotropic turbulence. Results are compared with joint statistics of FTLEs computed using only the symmetric part of the velocity gradient tensor, as well as with joint statistics of instantaneous strain-rate eigenvalues. When using only the strain contribution of the velocity gradient, the maximal FTLE nearly doubles in magnitude, highlighting the role of rotation in de-correlating the fluid deformations along particle paths. We also extend the large-deviation theory to study the statistics of the ratio of FTLEs. The most likely ratio of the FTLEs λ{sub 1} : λ{sub 2} : λ{sub 3} is shown to be about 4:1:−5, compared to about 8:3:−11 when using only the strain-rate tensor for calculating fluid volume
Effect of Multi-Axial Loading on Residual Strain Tensor for 12L14 Steel Alloy
Bunn, Jeffrey R.; Penumadu, Dayakar; Lou, Xin; Hubbard, Camden R.
2014-08-01
Evaluating the state of residual strain or stress is critically important for structural materials and for reliable design of complex shape components that need to function in extreme environment subjected to large thermo-mechanical loading. When residual stress state is superposed to external loads, it can lead to reduction or increase in failure strength. Past diffraction studies for evaluating the residual strain state involved measuring lattice spacings in three orthogonal directions and do not often correspond to principal directions. To completely resolve the state of strain at a given location, a full strain tensor must be determined. This is especially important when characterizing materials or metallic components exposed to biaxial or complex loading. Neutron diffraction at the second Generation Neutron Residual Stress Facility (NRSF2) at Oak Ridge National Laboratory is used in this study to measure strain tensors associated with different modes of stress path. Hollow cylinder steel samples with 2 mm wall thickness are subjected to either pure axial extension or pure torsion to simulate multi-axial loading conditions. A virgin sample that is not subjected to any deformation, but subjected to identical manufacturing conditions and machining steps involved to obtain hollow cylinder geometry is used for obtaining reference d-spacing for given hkl planes at target spatial location(s). The two samples which are subjected to either pure tension or torsion are loaded to a deformation state that corresponded to equal amount of octahedral shear strain which is an invariant. This procedure is used so that a basis for comparison between the two samples can be made to isolate the stress path effects. A 2-circle Huber orienteer is used to obtain strain measurements on identical gauge volume at a series of φ and ψ values. The residual state of stress tensor corresponding to ex situ (upon unloading) conditions is presented for three lattice planes (211, 110, 200) for
Liu, Chunlei; Murphy, Nicole E.; Li, Wei
2012-01-01
Diffusion MRI has become an invaluable tool for studying white matter microstructure and brain connectivity. The emergence of quantitative susceptibility mapping and susceptibility tensor imaging (STI) has provided another unique tool for assessing the structure of white matter. In the highly ordered white matter structure, diffusion MRI measures hindered water mobility induced by various tissue and cell membranes, while susceptibility sensitizes to the molecular composition and axonal arrangement. Integrating these two methods may produce new insights into the complex physiology of white matter. In this study, we investigated the relationship between diffusion and magnetic susceptibility in the white matter. Experiments were conducted on phantoms and human brains in vivo. Diffusion properties were quantified with the diffusion tensor model and also with the higher order tensor model based on the cumulant expansion. Frequency shift and susceptibility tensor were measured with quantitative susceptibility mapping and susceptibility tensor imaging. These diffusion and susceptibility quantities were compared and correlated in regions of single fiber bundles and regions of multiple fiber orientations. Relationships were established with similarities and differences identified. It is believed that diffusion MRI and susceptibility MRI provide complementary information of the microstructure of white matter. Together, they allow a more complete assessment of healthy and diseased brains. PMID:23507987
Influence of occlusal plane inclination and mandibular deviation on esthetics.
Corte, Cristiane Cherobini Dalla; Silveira, Bruno Lopes da; Marquezan, Mariana
2015-10-01
The aim of this study was to assess the degree of perception of occlusal plane inclination and mandibular deviation in facial esthetics, assessed by laypeople, dentists and orthodontists. A woman with 5.88° of inclination and 5.54 mm of mandibular deviation was selected and, based on her original photograph, four new images were created correcting the deviations and creating more symmetric faces and smiles. Examiners assessed the images by means of a questionnaire. Their opinions were compared by qualitative and quantitative analyses. A total of 45 laypeople, 27 dentists and 31 orthodontists filled out the questionnaires. All groups were able to perceive the asymmetry; however, orthodontists were more sensitive, identifying asymmetries as from 4.32° of occlusal plane inclination and 4.155 mm of mandibular deviation (pocclusal plane inclination and 5.54 mm of mandibular deviation (pOcclusal plane inclination and mandibular deviation were perceived by all groups, but orthodontists presented higher perception of deviations.
Tensor interaction in heavy-ion scattering. Pt. 1
International Nuclear Information System (INIS)
Nishioka, H.; Johnson, R.C.
1985-01-01
The Heidelberg shape-effect model for heavy-ion tensor interactions is reformulated and generalized using the Hooton-Johnson formulation. The generalized semiclassical model (the turning-point model) predicts that the components of the tensor analysing power anti Tsub(2q) have certain relations with each other for each type of tensor interaction (Tsub(R), Tsub(P) and Tsub(L) types). The predicted relations between the anti Tsub(2q) are very simple and have a direct connection with the properties of the tensor interaction at the turning point. The model predictions are satisfied in quantum-mechanical calculations for 7 Li and 23 Na elastic scattering from 58 Ni in the Fresnel-diffraction energy region. As a consequence of this model, it becomes possible to single out effects from a Tsub(P)- or Tsub(L)-type tensor interaction in polarized heavy-ion scattering. The presence of a Tsub(P)-type tensor interaction is suggested by measured anti T 20 /anti T 22 ratios for 7 Li + 58 Ni scattering. In the turning-point model the three types of tensor operator are not independent, and this is found to be true also in a quantum-mechanical calculation. The model also predicts relations between the components of higher-rank tensor analysing power in the presence of a higher-rank tensor interaction. The rank-3 tensor case is discussed in detail. (orig.)
Quantifying the effect of non-Larmor motion of electrons on the pressure tensor
Che, H.; Schiff, C.; Le, G.; Dorelli, J. C.; Giles, B. L.; Moore, T. E.
2018-03-01
In space plasma, various effects of magnetic reconnection and turbulence cause the electron motion to significantly deviate from their Larmor orbits. Collectively these orbits affect the electron velocity distribution function and lead to the appearance of the "non-gyrotropic" elements in the pressure tensor. Quantification of this effect has important applications in space and laboratory plasma, one of which is tracing the electron diffusion region (EDR) of magnetic reconnection in space observations. Three different measures of agyrotropy of pressure tensor have previously been proposed, namely, A ∅ e , Dng, and Q. The multitude of contradictory measures has caused confusion within the community. We revisit the problem by considering the basic properties an agyrotropy measure should have. We show that A ∅ e , Dng, and Q are all defined based on the sum of the principle minors (i.e., the rotation invariant I2) of the pressure tensor. We discuss in detail the problems of I2-based measures and explain why they may produce ambiguous and biased results. We introduce a new measure AG constructed based on the determinant of the pressure tensor (i.e., the rotation invariant I3) which does not suffer from the problems of I2-based measures. We compare AG with other measures in 2- and 3-dimension particle-in-cell magnetic reconnection simulations and show that AG effectively trace the EDR of reconnection in both Harris and force-free current sheets. On the other hand, A ∅ e does not show prominent peaks in the EDR and part of the separatrix in the force-free reconnection simulations, demonstrating that A ∅ e does not measure all the non-gyrotropic effects in this case and is not suitable for studying magnetic reconnection in more general situations other than Harris sheet reconnection.
International Nuclear Information System (INIS)
Provata, A.; Katsaloulis, P.; Verganelakis, D.A.
2012-01-01
Highlights: ► Calculation of human brain multifractal spectra. ► Calculations are based on Diffusion Tensor MRI Images. ► Spectra are modelled by coupled Ikeda map dynamics. ► Coupled lattice Ikeda maps model well only positive multifractal spectra. ► Appropriately modified coupled lattice Ikeda maps give correct spectra. - Abstract: The multifractal spectra of 3d Diffusion Tensor Images (DTI) obtained by magnetic resonance imaging of the human brain are studied. They are shown to deviate substantially from artificial brain images with the same white matter intensity. All spectra, obtained from 12 healthy subjects, show common characteristics indicating non-trivial moments of the intensity. To model the spectra the dynamics of the chaotic Ikeda map are used. The DTI multifractal spectra for positive q are best approximated by 3d coupled Ikeda maps in the fully developed chaotic regime. The coupling constants are as small as α = 0.01. These results reflect not only the white tissue non-trivial architectural complexity in the human brain, but also demonstrate the presence and importance of coupling between neuron axons. The architectural complexity is also mirrored by the deviations in the negative q-spectra, where the rare events dominate. To obtain a good agreement in the DTI negative q-spectrum of the brain with the Ikeda dynamics, it is enough to slightly modify the most rare events of the coupled Ikeda distributions. The representation of Diffusion Tensor Images with coupled Ikeda maps is not unique: similar conclusions are drawn when other chaotic maps (Tent, Logistic or Henon maps) are employed in the modelling of the neuron axons network.
Diffusion tensor imaging tensor shape analysis for assessment of regional white matter differences.
Middleton, Dana M; Li, Jonathan Y; Lee, Hui J; Chen, Steven; Dickson, Patricia I; Ellinwood, N Matthew; White, Leonard E; Provenzale, James M
2017-08-01
Purpose The purpose of this study was to investigate a novel tensor shape plot analysis technique of diffusion tensor imaging data as a means to assess microstructural differences in brain tissue. We hypothesized that this technique could distinguish white matter regions with different microstructural compositions. Methods Three normal canines were euthanized at seven weeks old. Their brains were imaged using identical diffusion tensor imaging protocols on a 7T small-animal magnetic resonance imaging system. We examined two white matter regions, the internal capsule and the centrum semiovale, each subdivided into an anterior and posterior region. We placed 100 regions of interest in each of the four brain regions. Eigenvalues for each region of interest triangulated onto tensor shape plots as the weighted average of three shape metrics at the plot's vertices: CS, CL, and CP. Results The distribution of data on the plots for the internal capsule differed markedly from the centrum semiovale data, thus confirming our hypothesis. Furthermore, data for the internal capsule were distributed in a relatively tight cluster, possibly reflecting the compact and parallel nature of its fibers, while data for the centrum semiovale were more widely distributed, consistent with the less compact and often crossing pattern of its fibers. This indicates that the tensor shape plot technique can depict data in similar regions as being alike. Conclusion Tensor shape plots successfully depicted differences in tissue microstructure and reflected the microstructure of individual brain regions. This proof of principle study suggests that if our findings are reproduced in larger samples, including abnormal white matter states, the technique may be useful in assessment of white matter diseases.
Ma, Ju; Dineva, Savka; Cesca, Simone; Heimann, Sebastian
2018-03-01
Mining induced seismicity is an undesired consequence of mining operations, which poses significant hazard to miners and infrastructures and requires an accurate analysis of the rupture process. Seismic moment tensors of mining-induced events help to understand the nature of mining-induced seismicity by providing information about the relationship between the mining, stress redistribution and instabilities in the rock mass. In this work, we adapt and test a waveform-based inversion method on high frequency data recorded by a dense underground seismic system in one of the largest underground mines in the world (Kiruna mine, Sweden). Stable algorithm for moment tensor inversion for comparatively small mining induced earthquakes, resolving both the double couple and full moment tensor with high frequency data is very challenging. Moreover, the application to underground mining system requires accounting for the 3D geometry of the monitoring system. We construct a Green's function database using a homogeneous velocity model, but assuming a 3D distribution of potential sources and receivers. We first perform a set of moment tensor inversions using synthetic data to test the effects of different factors on moment tensor inversion stability and source parameters accuracy, including the network spatial coverage, the number of sensors and the signal-to-noise ratio. The influence of the accuracy of the input source parameters on the inversion results is also tested. Those tests show that an accurate selection of the inversion parameters allows resolving the moment tensor also in presence of realistic seismic noise conditions. Finally, the moment tensor inversion methodology is applied to 8 events chosen from mining block #33/34 at Kiruna mine. Source parameters including scalar moment, magnitude, double couple, compensated linear vector dipole and isotropic contributions as well as the strike, dip, rake configurations of the double couple term were obtained. The orientations
Density Large Deviations for Multidimensional Stochastic Hyperbolic Conservation Laws
Barré, J.; Bernardin, C.; Chetrite, R.
2018-02-01
We investigate the density large deviation function for a multidimensional conservation law in the vanishing viscosity limit, when the probability concentrates on weak solutions of a hyperbolic conservation law. When the mobility and diffusivity matrices are proportional, i.e. an Einstein-like relation is satisfied, the problem has been solved in Bellettini and Mariani (Bull Greek Math Soc 57:31-45, 2010). When this proportionality does not hold, we compute explicitly the large deviation function for a step-like density profile, and we show that the associated optimal current has a non trivial structure. We also derive a lower bound for the large deviation function, valid for a more general weak solution, and leave the general large deviation function upper bound as a conjecture.
Prosthodontic management of mandibular deviation using palatal ramp appliance
Directory of Open Access Journals (Sweden)
Prince Kumar
2012-08-01
Full Text Available Segmental resection of the mandible generally results in deviation of the mandible to the defective side. This loss of continuity of the mandible destroys the balance of the lower face and leads to decreased mandibular function by deviation of the residual segment toward the surgical site. Prosthetic methods advocated to reduce or eliminate mandibular deviation include intermaxillary fixation, removable mandibular guide flange, palatal ramp, implant-supported prosthesis and palatal guidance restorations which may be useful in reducing mandibular deviation and improving masticatory performance and efficiency. These methods and restorations would be combined with a well organized mandibular exercise regimen. This clinical report describes the rehabilitation following segmental mandibulectomy using palatal ramp prosthesis.
A Note on Standard Deviation and Standard Error
Hassani, Hossein; Ghodsi, Mansoureh; Howell, Gareth
2010-01-01
Many students confuse the standard deviation and standard error of the mean and are unsure which, if either, to use in presenting data. In this article, we endeavour to address these questions and cover some related ambiguities about these quantities.
Management of Contract Waivers and Deviations for Defense Systems
National Research Council Canada - National Science Library
1998-01-01
This report is the fourth and final in a series of reports resulting from our audit of management of contract waivers and deviations for Defense systems and summarizes our overall evaluation. Report...
48 CFR 2901.403 - Individual deviations from the FAR.
2010-10-01
... DEPARTMENT OF LABOR ACQUISITION REGULATION SYSTEM Deviations From the FAR and DOLAR 2901.403 Individual... provisions (see FAR 1.403) or DOLAR provisions, which affect only one contracting action, unless FAR 1.405(e...
Full paleostress tensor reconstruction: case study of the Panasqueira Mine, Portugal.
Pascal, C.; Jaques Ribeiro, L. M.
2017-12-01
Paleostress tensor restoration methods are traditionally limited to reconstructing geometrical parameters and are unable to resolve stress magnitudes. Based on previous studies we further developed a methodology to restore full paleostress tensors. We concentrated on inversion of Mode I fractures and acquired data in Panasqueira Mine, Portugal, where optimal 3D exposures of mineralised quartz veins can be found. To carry out full paleostress restoration we needed to determine (1) pore (paleo)pressure and (2) vein attitudes. To these aims we conducted an extensive fluid inclusion study to derive fluid isochores from the quartz of the studied veins. To further constrain P-T conditions, we combined these isochores with crystallisation temperatures derived from geochemical analyses of coeval arsenopyrite. We also applied the sphalerite geobarometer and considered two other independent pressure indicators. Our results point to pore pressures of 300 MPa and formation depths of 10 km. As a second step, we measured 600 subhorizontal quartz veins in all the levels of the mine. The inversion of the attitudes of the veins allowed for reconstructing the orientations of the principal axes of stress, the unscaled Mohr circle and the relative pore pressure. After merging these results with the previously obtained absolute pore pressure we reconstructed the six parameters of the paleostress tensor.
An introduction to tensors and group theory for physicists
Jeevanjee, Nadir
2011-01-01
An Introduction to Tensors and Group Theory for Physicists provides both an intuitive and rigorous approach to tensors and groups and their role in theoretical physics and applied mathematics. A particular aim is to demystify tensors and provide a unified framework for understanding them in the context of classical and quantum physics. Connecting the component formalism prevalent in physics calculations with the abstract but more conceptual formulation found in many mathematical texts, the work will be a welcome addition to the literature on tensors and group theory. Part I of the text begins with linear algebraic foundations, follows with the modern component-free definition of tensors, and concludes with applications to classical and quantum physics through the use of tensor products. Part II introduces abstract groups along with matrix Lie groups and Lie algebras, then intertwines this material with that of Part I by introducing representation theory. Exercises and examples are provided throughout for go...
Radiative corrections in a vector-tensor model
International Nuclear Information System (INIS)
Chishtie, F.; Gagne-Portelance, M.; Hanif, T.; Homayouni, S.; McKeon, D.G.C.
2006-01-01
In a recently proposed model in which a vector non-Abelian gauge field interacts with an antisymmetric tensor field, it has been shown that the tensor field possesses no physical degrees of freedom. This formal demonstration is tested by computing the one-loop contributions of the tensor field to the self-energy of the vector field. It is shown that despite the large number of Feynman diagrams in which the tensor field contributes, the sum of these diagrams vanishes, confirming that it is not physical. Furthermore, if the tensor field were to couple with a spinor field, it is shown at one-loop order that the spinor self-energy is not renormalizable, and hence this coupling must be excluded. In principle though, this tensor field does couple to the gravitational field
Perception of midline deviations in smile esthetics by laypersons
Directory of Open Access Journals (Sweden)
Jamille Barros Ferreira
Full Text Available ABSTRACT Objective: To evaluate the esthetic perception of upper dental midline deviation by laypersons and if adjacent structures influence their judgment. Methods: An album with 12 randomly distributed frontal view photographs of the smile of a woman with the midline digitally deviated was evaluated by 95 laypersons. The frontal view smiling photograph was modified to create from 1 mm to 5 mm deviations in the upper midline to the left side. The photographs were cropped in two different manners and divided into two groups of six photographs each: group LCN included the lips, chin, and two-thirds of the nose, and group L included the lips only. The laypersons performed the rate of each smile using a visual analog scale (VAS. Wilcoxon test, Student’s t-test and Mann-Whitney test were applied, adopting a 5% level of significance. Results: Laypersons were able to perceive midline deviations starting at 1 mm. Statistically significant results (p< 0.05 were found for all multiple comparisons of the values in photographs of group LCN and for almost all comparisons in photographs of group L. Comparisons between the photographs of groups LCN and L showed statistically significant values (p< 0.05 when the deviation was 1 mm. Conclusions: Laypersons were able to perceive the upper dental midline deviations of 1 mm, and above when the adjacent structures of the smiles were included. Deviations of 2 mm and above when the lips only were included. The visualization of structures adjacent to the smile demonstrated influence on the perception of midline deviation.
Deviations in Ukrainian gender culture: social and systemologic aspect
I. O. Svyatnenko
2017-01-01
The article is devoted to the problem of understanding of traditional (internal) deviations in Ukrainian gender culture, which are developing rapidly under the influence of the spread of foreign cultures’ (mainly European and American ones) gender deviations. As a result of the study, the following conclusion has been made by the author that matriarchy, cultivated by mistrust of men to each other, their mutual demonization due to the idealization of mothers and devaluation of fathers, con...
Moderate deviations for some point measures in geometric probability
Baryshnikov, Yu; Eichelsbacher, P.; Schreiber, T.; Yukich, J. E.
2008-06-01
Functionals in geometric probability are often expressed as sums of bounded functions exhibiting exponential stabilization. Methods based on cumulant techniques and exponential modifications of measures show that such functionals satisfy moderate deviation principles. This leads to moderate deviation principles and laws of the iterated logarithm for random packing models as well as for statistics associated with germ-grain models and $k$ nearest neighbor graphs.
Age-Related Deviation of Gait from Normality in Alkaptonuria.
Barton, Gabor J; King, Stephanie L; Robinson, Mark A; Hawken, Malcolm B; Ranganath, Lakshminarayan R
2015-01-01
Alkaptonuria is a rare metabolic disease leading to systemic changes including early and severe arthropathy which affects mobility. For unknown reasons, the onset of degenerative changes is delayed to around 30 years of age when both objective and subjective symptoms develop. In order to complement description of the structural changes in alkaptonuria with measures of movement function, clinical gait analysis was added to the list of assessments in 2013. The aim of this study was to describe the deviation of gait from normality as a function of age in patients with alkaptonuria. Three-dimensional movement of reflective markers attached to joints were captured during walking in 39 patients and 10 controls. Subsequent to processing the data to emphasise the shape of marker trajectories, the mean Movement Deviation Profile was generated for all participants. This single number measure gives the deviation of a patient's gait from a distributed definition of gait normality. Results showed that gait deviation roughly follows a sigmoid profile with minimal increase of gait deviations in a younger patient group and an abrupt large increase around the second half of the 4th decade of life. Larger variations of gait deviations were found in the older group than in the younger group suggesting a complex interaction of multiple factors which determine gait function after symptoms manifest. Continued gait analysis of adults with AKU, extended to younger adults and children with AKU, is expected to complete understanding of both the natural history of alkaptonuria and how interventions can affect movement function.
Comparison of two global digital algorithms for Minkowski tensor estimation
DEFF Research Database (Denmark)
The geometry of real world objects can be described by Minkowski tensors. Algorithms have been suggested to approximate Minkowski tensors if only a binary image of the object is available. This paper presents implementations of two such algorithms. The theoretical convergence properties...... are confirmed by simulations on test sets, and recommendations for input arguments of the algorithms are given. For increasing resolutions, we obtain more accurate estimators for the Minkowski tensors. Digitisations of more complicated objects are shown to require higher resolutions....
Energy-momentum tensor in the quantum field theory
International Nuclear Information System (INIS)
Azakov, S.I.
1977-01-01
An energy-momentum tensor in the scalar field theory is built. The tensor must satisfy the finiteness requirement of the Green function. The Green functions can always be made finite by renormalizations in the S-matrix by introducing counter terms into the Hamiltonian (or Lagrangian) of the interaction. Such a renormalization leads to divergencies in the Green functions. Elimination of these divergencies requires the introduction of new counter terms, which must be taken into account in the energy-momentum tensor
Introduction to Tensor Decompositions and their Applications in Machine Learning
Rabanser, Stephan; Shchur, Oleksandr; Günnemann, Stephan
2017-01-01
Tensors are multidimensional arrays of numerical values and therefore generalize matrices to multiple dimensions. While tensors first emerged in the psychometrics community in the $20^{\\text{th}}$ century, they have since then spread to numerous other disciplines, including machine learning. Tensors and their decompositions are especially beneficial in unsupervised learning settings, but are gaining popularity in other sub-disciplines like temporal and multi-relational data analysis, too. The...
Scattering of charged tensor bosons in gauge and superstring theories
Antoniadis, Ignatios
2010-01-01
We calculate the leading-order scattering amplitude of one vector and two tensor gauge bosons in a recently proposed non-Abelian tensor gauge field theory and open superstring theory. The linear in momenta part of the superstring amplitude has identical Lorentz structure with the gauge theory, while its cubic in momenta part can be identified with an effective Lagrangian which is constructed using generalized non-Abelian field strength tensors.
Supergravity tensor calculus in 5D from 6D
International Nuclear Information System (INIS)
Kugo, Taichiro; Ohashi, Keisuke
2000-01-01
Supergravity tensor calculus in five spacetime dimensions is derived by dimensional reduction from the d=6 superconformal tensor calculus. In particular, we obtain an off-shell hypermultiplet in 5D from the on-shell hypermultiplet in 6D. Our tensor calculus retains the dilatation gauge symmetry, so that it is a trivial gauge fixing to make the Einstein term canonical in a general matter-Yang-Mills-supergravity coupled system. (author)
The classification of the Ricci tensor in the general theory of relativity
International Nuclear Information System (INIS)
Cormack, W.J.
1979-10-01
A comprehensive classification of the Ricci tensor in General Relativity using several techniques is given and their connection with existing classification studied under the headings; canonical forms for the Ricci tensor, invariant 2-spaces in the classification of the Ricci tensor, Riemannian curvature and the classification of the Riemann and Ricci tensors, and spinor classifications of the Ricci tensor. (U.K.)
CONSTRUCTION A CORING FROM TENSOR PRODUCT OF BIALGEBRA
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Nikken Prima Puspita
2015-01-01
Full Text Available In this Paper introduced a coring from tensor product of bialgebra. An algebra with compatible coalgebrastructure are known as bialgebra. For any bialgebra B we can obtained tensor product between B anditself. Defined a right and left B -action on the tensor product of bialgebra B such that we have tensorproduct of B and itself is a bimodule over B. In this note we expect that the tensor product B anditself becomes a B -coring with comultiplication and counit.Keywords : action, algebra, coalgebra, coring.
Airborne LIDAR Points Classification Based on Tensor Sparse Representation
Li, N.; Pfeifer, N.; Liu, C.
2017-09-01
The common statistical methods for supervised classification usually require a large amount of training data to achieve reasonable results, which is time consuming and inefficient. This paper proposes a tensor sparse representation classification (SRC) method for airborne LiDAR points. The LiDAR points are represented as tensors to keep attributes in its spatial space. Then only a few of training data is used for dictionary learning, and the sparse tensor is calculated based on tensor OMP algorithm. The point label is determined by the minimal reconstruction residuals. Experiments are carried out on real LiDAR points whose result shows that objects can be distinguished by this algorithm successfully.
p-Norm SDD tensors and eigenvalue localization
Directory of Open Access Journals (Sweden)
Qilong Liu
2016-07-01
Full Text Available Abstract We present a new class of nonsingular tensors (p-norm strictly diagonally dominant tensors, which is a subclass of strong H $\\mathcal{H}$ -tensors. As applications of the results, we give a new eigenvalue inclusion set, which is tighter than those provided by Li et al. (Linear Multilinear Algebra 64:727-736, 2016 in some case. Based on this set, we give a checkable sufficient condition for the positive (semidefiniteness of an even-order symmetric tensor.
Joint Tensor Feature Analysis For Visual Object Recognition.
Wong, Wai Keung; Lai, Zhihui; Xu, Yong; Wen, Jiajun; Ho, Chu Po
2015-11-01
Tensor-based object recognition has been widely studied in the past several years. This paper focuses on the issue of joint feature selection from the tensor data and proposes a novel method called joint tensor feature analysis (JTFA) for tensor feature extraction and recognition. In order to obtain a set of jointly sparse projections for tensor feature extraction, we define the modified within-class tensor scatter value and the modified between-class tensor scatter value for regression. The k-mode optimization technique and the L(2,1)-norm jointly sparse regression are combined together to compute the optimal solutions. The convergent analysis, computational complexity analysis and the essence of the proposed method/model are also presented. It is interesting to show that the proposed method is very similar to singular value decomposition on the scatter matrix but with sparsity constraint on the right singular value matrix or eigen-decomposition on the scatter matrix with sparse manner. Experimental results on some tensor datasets indicate that JTFA outperforms some well-known tensor feature extraction and selection algorithms.
TENSOR MODELING BASED FOR AIRBORNE LiDAR DATA CLASSIFICATION
Directory of Open Access Journals (Sweden)
N. Li
2016-06-01
Full Text Available Feature selection and description is a key factor in classification of Earth observation data. In this paper a classification method based on tensor decomposition is proposed. First, multiple features are extracted from raw LiDAR point cloud, and raster LiDAR images are derived by accumulating features or the “raw” data attributes. Then, the feature rasters of LiDAR data are stored as a tensor, and tensor decomposition is used to select component features. This tensor representation could keep the initial spatial structure and insure the consideration of the neighborhood. Based on a small number of component features a k nearest neighborhood classification is applied.
3D Inversion of SQUID Magnetic Tensor Data
DEFF Research Database (Denmark)
Zhdanov, Michael; Cai, Hongzhu; Wilson, Glenn
2012-01-01
Developments in SQUID-based technology have enabled direct measurement of magnetic tensor data for geophysical exploration. For quantitative interpretation, we introduce 3D regularized inversion for magnetic tensor data. For mineral exploration-scale targets, our model studies show that magnetic...... tensor data have significantly improved resolution compared to magnetic vector data for the same model. We present a case study for the 3D regularized inversion of magnetic tensor data acquired over a magnetite skarn at Tallawang, Australia. The results obtained from our 3D regularized inversion agree...
Many-particle quantum hydrodynamics: Exact equations and pressure tensors
Renziehausen, Klaus; Barth, Ingo
2018-01-01
In the first part of this paper, the many-particle quantum hydrodynamics equations for a system containing many particles of different sorts are derived exactly from the many-particle Schrödinger equation, including the derivation of the many-particle continuity equations, many-particle Ehrenfest equations of motion, and many-particle quantum Cauchy equations for any of the different particle sorts and for the total particle ensemble. The new point in our analysis is that we consider a set of arbitrary particles of different sorts in the system. In the many-particle quantum Cauchy equations, there appears a quantity called the pressure tensor. In the second part of this paper, we analyze two versions of this tensor in depth: the Wyatt pressure tensor and the Kuzmenkov pressure tensor. There are different versions because there is a gauge freedom for the pressure tensor similar to that for potentials. We find that the interpretation of all the quantities contributing to the Wyatt pressure tensor is understandable, but for the Kuzmenkov tensor it is difficult. Furthermore, the transformation from Cartesian coordinates to cylindrical coordinates for the Wyatt tensor can be done in a clear way, but for the Kuzmenkov tensor it is rather cumbersome.
On the magnetic polarizability tensor of US coinage
Davidson, John L.; Abdel-Rehim, Omar A.; Hu, Peipei; Marsh, Liam A.; O’Toole, Michael D.; Peyton, Anthony J.
2018-03-01
The magnetic dipole polarizability tensor of a metallic object gives unique information about the size, shape and electromagnetic properties of the object. In this paper, we present a novel method of coin characterization based on the spectroscopic response of the absolute tensor. The experimental measurements are validated using a combination of tests with a small set of bespoke coin surrogates and simulated data. The method is applied to an uncirculated set of US coins. Measured and simulated spectroscopic tensor responses of the coins show significant differences between different coin denominations. The presented results are encouraging as they strongly demonstrate the ability to characterize coins using an absolute tensor approach.
A local potential for the Weyl tensor in all dimensions
International Nuclear Information System (INIS)
Edgar, S Brian; Senovilla, Jose M M
2004-01-01
In all dimensions n ≥ 4 and arbitrary signature, we demonstrate the existence of a new local potential-a double (2, 3)-form, P ab cde -for the Weyl curvature tensor C abcd , and more generally for all tensors W abcd with the symmetry properties of the Weyl tensor. The classical four-dimensional Lanczos potential for a Weyl tensor-a double (2, 1)-form, H ab c -is proven to be a particular case of the new potential: its double dual. (letter to the editor)
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.
Effect of nasal deviation on quality of life.
de Lima Ramos, Sueli; Hochman, Bernardo; Gomes, Heitor Carvalho; Abla, Luiz Eduardo Felipe; Veiga, Daniela Francescato; Juliano, Yara; Dini, Gal Moreira; Ferreira, Lydia Masako
2011-07-01
Nasal deviation is a common complaint in otorhinolaryngology and plastic surgery. This condition not only causes impairment of nasal function but also affects quality of life, leading to psychological distress. The subjective assessment of quality of life, as an important aspect of outcomes research, has received increasing attention in recent decades. Quality of life is measured using standardized questionnaires that have been tested for reliability, validity, and sensitivity. The aim of this study was to evaluate health-related quality of life, self-esteem, and depression in patients with nasal deviation. Sixty patients were selected for the study. Patients with nasal deviation (n = 32) were assigned to the study group, and patients without nasal deviation (n = 28) were assigned to the control group. The diagnosis of nasal deviation was made by digital photogrammetry. Quality of life was assessed using the Medical Outcomes Study 36-Item Short Form Health Survey questionnaire; the Rosenberg Self-Esteem/Federal University of São Paulo, Escola Paulista de Medicina Scale; and the 20-item Self-Report Questionnaire. There were significant differences between groups in the physical functioning and general health subscales of the Medical Outcomes Study 36-Item Short Form Health Survey (p < 0.05). Depression was detected in 11 patients (34.4 percent) in the study group and in two patients in the control group, with a significant difference between groups (p < 0.05). Nasal deviation is an aspect of rhinoplasty of which the surgeon should be aware so that proper psychological diagnosis can be made and suitable treatment can be planned because psychologically the patients with nasal deviation have significantly worse quality of life and are more prone to depression. Risk, II.(Figure is included in full-text article.).
Scalar-tensor cosmology with cosmological constant
International Nuclear Information System (INIS)
Maslanka, K.
1983-01-01
The equations of scalar-tensor theory of gravitation with cosmological constant in the case of homogeneous and isotropic cosmological model can be reduced to dynamical system of three differential equations with unknown functions H=R/R, THETA=phi/phi, S=e/phi. When new variables are introduced the system becomes more symmetrical and cosmological solutions R(t), phi(t), e(t) are found. It is shown that when cosmological constant is introduced large class of solutions which depend also on Dicke-Brans parameter can be obtained. Investigations of these solutions give general limits for cosmological constant and mean density of matter in plane model. (author)
Tensor glueball-meson mixing phenomenology
International Nuclear Information System (INIS)
Burakovsky, L.; Page, P.R.
2000-01-01
The overpopulated isoscalar tensor states are sifted using Schwinger-type mass relations. Two solutions are found: one where the glueball is the f J (2220), and one where the glueball is more distributed, with f 2 (1820) having the largest component. The f 2 (1565) and f J (1710) cannot be accommodated as glueball-(hybrid) meson mixtures in the absence of significant coupling to decay channels. f 2 '(1525)→ππ is in agreement with experiment. The f J (2220) decays neither flavour democratically nor is narrow. (orig.)
Tensor Network Wavefunctions for Topological Phases
Ware, Brayden Alexander
The combination of quantum effects and interactions in quantum many-body systems can result in exotic phases with fundamentally entangled ground state wavefunctions--topological phases. Topological phases come in two types, both of which will be studied in this thesis. In topologically ordered phases, the pattern of entanglement in the ground state wavefunction encodes the statistics of exotic emergent excitations, a universal indicator of a phase that is robust to all types of perturbations. In symmetry protected topological phases, the entanglement instead encodes a universal response of the system to symmetry defects, an indicator that is robust only to perturbations respecting the protecting symmetry. Finding and creating these phases in physical systems is a motivating challenge that tests all aspects--analytical, numerical, and experimental--of our understanding of the quantum many-body problem. Nearly three decades ago, the creation of simple ansatz wavefunctions--such as the Laughlin fractional quantum hall state, the AKLT state, and the resonating valence bond state--spurred analytical understanding of both the role of entanglement in topological physics and physical mechanisms by which it can arise. However, quantitative understanding of the relevant phase diagrams is still challenging. For this purpose, tensor networks provide a toolbox for systematically improving wavefunction ansatz while still capturing the relevant entanglement properties. In this thesis, we use the tools of entanglement and tensor networks to analyze ansatz states for several proposed new phases. In the first part, we study a featureless phase of bosons on the honeycomb lattice and argue that this phase can be topologically protected under any one of several distinct subsets of the crystalline lattice symmetries. We discuss methods of detecting such phases with entanglement and without. In the second part, we consider the problem of constructing fixed-point wavefunctions for
A Case of Tensor Fasciae Suralis Muscle
Miyauchi, Ryosuke; Kurihara, Kazushige; Tachibana, Gen
1985-01-01
An anomalous muscle was found on the dorsum of the right lower limb of a 67-year-old Japanese male. It originated by two heads from the semitendinosus and long head of the biceps femoris and ran distally to insert into the deep surface of the sural fascia. The origin, insertion and location of the muscle were compared with those of the various supernumerary muscles hitherto published. The muscle is consequently regarded as being the tensor fasciae suralis. This is the fifth case in Japan.
Holographic duality from random tensor networks
Energy Technology Data Exchange (ETDEWEB)
Hayden, Patrick; Nezami, Sepehr; Qi, Xiao-Liang; Thomas, Nathaniel; Walter, Michael; Yang, Zhao [Stanford Institute for Theoretical Physics, Department of Physics, Stanford University,382 Via Pueblo, Stanford, CA 94305 (United States)
2016-11-02
Tensor networks provide a natural framework for exploring holographic duality because they obey entanglement area laws. They have been used to construct explicit toy models realizing many of the interesting structural features of the AdS/CFT correspondence, including the non-uniqueness of bulk operator reconstruction in the boundary theory. In this article, we explore the holographic properties of networks of random tensors. We find that our models naturally incorporate many features that are analogous to those of the AdS/CFT correspondence. When the bond dimension of the tensors is large, we show that the entanglement entropy of all boundary regions, whether connected or not, obey the Ryu-Takayanagi entropy formula, a fact closely related to known properties of the multipartite entanglement of assistance. We also discuss the behavior of Rényi entropies in our models and contrast it with AdS/CFT. Moreover, we find that each boundary region faithfully encodes the physics of the entire bulk entanglement wedge, i.e., the bulk region enclosed by the boundary region and the minimal surface. Our method is to interpret the average over random tensors as the partition function of a classical ferromagnetic Ising model, so that the minimal surfaces of Ryu-Takayanagi appear as domain walls. Upon including the analog of a bulk field, we find that our model reproduces the expected corrections to the Ryu-Takayanagi formula: the bulk minimal surface is displaced and the entropy is augmented by the entanglement of the bulk field. Increasing the entanglement of the bulk field ultimately changes the minimal surface behavior topologically, in a way similar to the effect of creating a black hole. Extrapolating bulk correlation functions to the boundary permits the calculation of the scaling dimensions of boundary operators, which exhibit a large gap between a small number of low-dimension operators and the rest. While we are primarily motivated by the AdS/CFT duality, the main
Czech Academy of Sciences Publication Activity Database
Kopský, Vojtěch
2006-01-01
Roč. 62, - (2006), s. 65-76 ISSN 0108-7673 R&D Projects: GA ČR GA202/04/0992 Institutional research plan: CEZ:AV0Z10100520 Keywords : tensor ial covariants * domain states * stability spaces Subject RIV: BE - Theoretical Physics Impact factor: 1.676, year: 2006
Complexity analysis based on generalized deviation for financial markets
Li, Chao; Shang, Pengjian
2018-03-01
In this paper, a new modified method is proposed as a measure to investigate the correlation between past price and future volatility for financial time series, known as the complexity analysis based on generalized deviation. In comparison with the former retarded volatility model, the new approach is both simple and computationally efficient. The method based on the generalized deviation function presents us an exhaustive way showing the quantization of the financial market rules. Robustness of this method is verified by numerical experiments with both artificial and financial time series. Results show that the generalized deviation complexity analysis method not only identifies the volatility of financial time series, but provides a comprehensive way distinguishing the different characteristics between stock indices and individual stocks. Exponential functions can be used to successfully fit the volatility curves and quantify the changes of complexity for stock market data. Then we study the influence for negative domain of deviation coefficient and differences during the volatile periods and calm periods. after the data analysis of the experimental model, we found that the generalized deviation model has definite advantages in exploring the relationship between the historical returns and future volatility.
Wells, Tanya G.
"Utilization of Skills in the Care of Patients with Deviations in Psychosocial Adaptation" (NS 207) is an associate degree nursing course offered at Chattanooga State Technical Community College. The course stresses the individual as a system in his/her psychosocial adaptation to internal and external stressors, and highlights the…
Interactive Volume Rendering of Diffusion Tensor Data
Energy Technology Data Exchange (ETDEWEB)
Hlawitschka, Mario; Weber, Gunther; Anwander, Alfred; Carmichael, Owen; Hamann, Bernd; Scheuermann, Gerik
2007-03-30
As 3D volumetric images of the human body become an increasingly crucial source of information for the diagnosis and treatment of a broad variety of medical conditions, advanced techniques that allow clinicians to efficiently and clearly visualize volumetric images become increasingly important. Interaction has proven to be a key concept in analysis of medical images because static images of 3D data are prone to artifacts and misunderstanding of depth. Furthermore, fading out clinically irrelevant aspects of the image while preserving contextual anatomical landmarks helps medical doctors to focus on important parts of the images without becoming disoriented. Our goal was to develop a tool that unifies interactive manipulation and context preserving visualization of medical images with a special focus on diffusion tensor imaging (DTI) data. At each image voxel, DTI provides a 3 x 3 tensor whose entries represent the 3D statistical properties of water diffusion locally. Water motion that is preferential to specific spatial directions suggests structural organization of the underlying biological tissue; in particular, in the human brain, the naturally occuring diffusion of water in the axon portion of neurons is predominantly anisotropic along the longitudinal direction of the elongated, fiber-like axons [MMM+02]. This property has made DTI an emerging source of information about the structural integrity of axons and axonal connectivity between brain regions, both of which are thought to be disrupted in a broad range of medical disorders including multiple sclerosis, cerebrovascular disease, and autism [Mos02, FCI+01, JLH+99, BGKM+04, BJB+03].
Quantum chaos and holographic tensor models
International Nuclear Information System (INIS)
Krishnan, Chethan; Sanyal, Sambuddha; Subramanian, P.N. Bala
2017-01-01
A class of tensor models were recently outlined as potentially calculable examples of holography: their perturbative large-N behavior is similar to the Sachdev-Ye-Kitaev (SYK) model, but they are fully quantum mechanical (in the sense that there is no quenched disorder averaging). These facts make them intriguing tentative models for quantum black holes. In this note, we explicitly diagonalize the simplest non-trivial Gurau-Witten tensor model and study its spectral and late-time properties. We find parallels to (a single sample of) SYK where some of these features were recently attributed to random matrix behavior and quantum chaos. In particular, the spectral form factor exhibits a dip-ramp-plateau structure after a running time average, in qualitative agreement with SYK. But we also observe that even though the spectrum has a unique ground state, it has a huge (quasi-?)degeneracy of intermediate energy states, not seen in SYK. If one ignores the delta function due to the degeneracies however, there is level repulsion in the unfolded spacing distribution hinting chaos. Furthermore, there are gaps in the spectrum. The system also has a spectral mirror symmetry which we trace back to the presence of a unitary operator with which the Hamiltonian anticommutes. We use it to argue that to the extent that the model exhibits random matrix behavior, it is controlled not by the Dyson ensembles, but by the BDI (chiral orthogonal) class in the Altland-Zirnbauer classification.
Quantum chaos and holographic tensor models
Energy Technology Data Exchange (ETDEWEB)
Krishnan, Chethan [Center for High Energy Physics, Indian Institute of Science,Bangalore 560012 (India); Sanyal, Sambuddha [International Center for Theoretical Sciences, Tata Institute of Fundamental Research,Bangalore 560089 (India); Subramanian, P.N. Bala [Center for High Energy Physics, Indian Institute of Science,Bangalore 560012 (India)
2017-03-10
A class of tensor models were recently outlined as potentially calculable examples of holography: their perturbative large-N behavior is similar to the Sachdev-Ye-Kitaev (SYK) model, but they are fully quantum mechanical (in the sense that there is no quenched disorder averaging). These facts make them intriguing tentative models for quantum black holes. In this note, we explicitly diagonalize the simplest non-trivial Gurau-Witten tensor model and study its spectral and late-time properties. We find parallels to (a single sample of) SYK where some of these features were recently attributed to random matrix behavior and quantum chaos. In particular, the spectral form factor exhibits a dip-ramp-plateau structure after a running time average, in qualitative agreement with SYK. But we also observe that even though the spectrum has a unique ground state, it has a huge (quasi-?)degeneracy of intermediate energy states, not seen in SYK. If one ignores the delta function due to the degeneracies however, there is level repulsion in the unfolded spacing distribution hinting chaos. Furthermore, there are gaps in the spectrum. The system also has a spectral mirror symmetry which we trace back to the presence of a unitary operator with which the Hamiltonian anticommutes. We use it to argue that to the extent that the model exhibits random matrix behavior, it is controlled not by the Dyson ensembles, but by the BDI (chiral orthogonal) class in the Altland-Zirnbauer classification.
Scaling Deviations for Neutrino Reactions in Aysmptotically Free Field Theories
Wilczek, F. A.; Zee, A.; Treiman, S. B.
1974-11-01
Several aspects of deep inelastic neutrino scattering are discussed in the framework of asymptotically free field theories. We first consider the growth behavior of the total cross sections at large energies. Because of the deviations from strict scaling which are characteristic of such theories the growth need not be linear. However, upper and lower bounds are established which rather closely bracket a linear growth. We next consider in more detail the expected pattern of scaling deviation for the structure functions and, correspondingly, for the differential cross sections. The analysis here is based on certain speculative assumptions. The focus is on qualitative effects of scaling breakdown as they may show up in the X and y distributions. The last section of the paper deals with deviations from the Callan-Gross relation.
Mean-deviation analysis in the theory of choice.
Grechuk, Bogdan; Molyboha, Anton; Zabarankin, Michael
2012-08-01
Mean-deviation analysis, along with the existing theories of coherent risk measures and dual utility, is examined in the context of the theory of choice under uncertainty, which studies rational preference relations for random outcomes based on different sets of axioms such as transitivity, monotonicity, continuity, etc. An axiomatic foundation of the theory of coherent risk measures is obtained as a relaxation of the axioms of the dual utility theory, and a further relaxation of the axioms are shown to lead to the mean-deviation analysis. Paradoxes arising from the sets of axioms corresponding to these theories and their possible resolutions are discussed, and application of the mean-deviation analysis to optimal risk sharing and portfolio selection in the context of rational choice is considered. © 2012 Society for Risk Analysis.
Deviation of eyes and head in acute cerebral stroke
Directory of Open Access Journals (Sweden)
Ilg UJ
2006-06-01
Full Text Available Abstract Background It is a well-known phenomenon that some patients with acute left or right hemisphere stroke show a deviation of the eyes (Prévost's sign and head to one side. Here we investigated whether both right- and left-sided brain lesions may cause this deviation. Moreover, we studied the relationship between this phenomenon and spatial neglect. In contrast to previous studies, we determined not only the discrete presence or absence of eye deviation with the naked eye through clinical inspection, but actually measured the extent of horizontal eye-in-head and head-on-trunk deviation. In further contrast, measurements were performed early after stroke onset (1.5 days on average. Methods Eye-in-head and head-on-trunk positions were measured at the bedside in 33 patients with acute unilateral left or right cerebral stroke consecutively admitted to our stroke unit. Results Each single patient with spatial neglect and right hemisphere lesion showed a marked deviation of the eyes and the head to the ipsilesional, right side. The average spontaneous gaze position in this group was 46° right, while it was close to the saggital body midline (0° in the groups with acute left- or right-sided stroke but no spatial neglect as well as in healthy subjects. Conclusion A marked horizontal eye and head deviation observed ~1.5 days post-stroke is not a symptom associated with acute cerebral lesions per se, nor is a general symptom of right hemisphere lesions, but rather is specific for stroke patients with spatial neglect. The evaluation of the patient's horizontal eye and head position thus could serve as a brief and easy way helping to diagnose spatial neglect, in addition to the traditional paper-and-pencil tests.
Dual-phase cardiac diffusion tensor imaging with strain correction.
Directory of Open Access Journals (Sweden)
Christian T Stoeck
Full Text Available In this work we present a dual-phase diffusion tensor imaging (DTI technique that incorporates a correction scheme for the cardiac material strain, based on 3D myocardial tagging.In vivo dual-phase cardiac DTI with a stimulated echo approach and 3D tagging was performed in 10 healthy volunteers. The time course of material strain was estimated from the tagging data and used to correct for strain effects in the diffusion weighted acquisition. Mean diffusivity, fractional anisotropy, helix, transverse and sheet angles were calculated and compared between systole and diastole, with and without strain correction. Data acquired at the systolic sweet spot, where the effects of strain are eliminated, served as a reference.The impact of strain correction on helix angle was small. However, large differences were observed in the transverse and sheet angle values, with and without strain correction. The standard deviation of systolic transverse angles was significantly reduced from 35.9±3.9° to 27.8°±3.5° (p<0.001 upon strain-correction indicating more coherent fiber tracks after correction. Myocyte aggregate structure was aligned more longitudinally in systole compared to diastole as reflected by an increased transmural range of helix angles (71.8°±3.9° systole vs. 55.6°±5.6°, p<0.001 diastole. While diastolic sheet angle histograms had dominant counts at high sheet angle values, systolic histograms showed lower sheet angle values indicating a reorientation of myocyte sheets during contraction.An approach for dual-phase cardiac DTI with correction for material strain has been successfully implemented. This technique allows assessing dynamic changes in myofiber architecture between systole and diastole, and emphasizes the need for strain correction when sheet architecture in the heart is imaged with a stimulated echo approach.
Moderate Deviation Principles for Stochastic Differential Equations with Jumps
2014-01-15
bounded and continuous functions respectively. For Banach spaces B1; B2, L(B1; B2) will denote the space of bounded linear operators from B1 to B2. For...random vectors in a Banach space . Chinese J. Appl. Probab. Statist., 7(1):24�32, 1991. [14] X. Chen. Moderate deviations form-dependent random...variables with Banach space values. Statist. Probab. Lett., 35(2):123�134, 1997. ISSN 0167-7152. [15] X. Chen. Moderate deviations for Markovian occupation
Effect of density deviations of concrete on its attenuation efficiency
International Nuclear Information System (INIS)
Szymendera, L.; Wincel, K.; Blociszewski, S.; Kordyasz, D.; Sobolewska, I.
In the work, the influence of concrete density deviation on shield thickness and total dose ratio outside the reactor shield, has--on the basis of numerical analysis--been considered. It has been noticed the possibility of introducing flexible corrections--without additional shielding calculation--to the design thickness of the shield. It has been also found that in common cases of shield design, where any necessity of minimizing the shield thickness does not exist, the tendency to minimize the value of this deviation is hardly substantiable
Anisotropic cosmological models and generalized scalar tensor theory
Indian Academy of Sciences (India)
physics pp. 669–673. Anisotropic cosmological models and generalized scalar tensor theory. SUBENOY CHAKRABORTY1,*, BATUL CHANDRA SANTRA2 and ... Anisotropic cosmological models; general scalar tensor theory; inflation. PACS Nos 98.80.Hw; 04.50.+h; 98.80.Cq. 1. Introduction. Brans–Dicke theory [1] (BD ...
The ultrarelativistic Kerr geometry and its energy-momentum tensor
Balasin, Herbert; Nachbagauer, Herbert
1995-03-01
The ultrarelativistic limit of the Schwarzschild and the Kerr-geometry together with their respective energy-momentum tensors is derived. The approach is based on tensor-distributions making use of the underlying Kerr-Schild structure, which remains stable under the ultrarelativistic boost.
Exploring the tensor networks/AdS correspondence
Energy Technology Data Exchange (ETDEWEB)
Bhattacharyya, Arpan [Department of Physics and Center for Field Theory and Particle Physics, Fudan University,220 Handan Road, 200433 Shanghai (China); Centre For High Energy Physics, Indian Institute of Science,560012 Bangalore (India); Gao, Zhe-Shen [Department of Physics and Center for Field Theory and Particle Physics, Fudan University,220 Handan Road, 200433 Shanghai (China); Hung, Ling-Yan [Department of Physics and Center for Field Theory and Particle Physics, Fudan University,220 Handan Road, 200433 Shanghai (China); State Key Laboratory of Surface Physics and Department of Physics, Fudan University,220 Handan Road, 200433 Shanghai (China); Collaborative Innovation Center of Advanced Microstructures, Nanjing University,Nanjing, 210093 (China); Liu, Si-Nong [Department of Physics and Center for Field Theory and Particle Physics, Fudan University,220 Handan Road, 200433 Shanghai (China)
2016-08-11
In this paper we study the recently proposed tensor networks/AdS correspondence. We found that the Coxeter group is a useful tool to describe tensor networks in a negatively curved space. Studying generic tensor network populated by perfect tensors, we find that the physical wave function generically do not admit any connected correlation functions of local operators. To remedy the problem, we assume that wavefunctions admitting such semi-classical gravitational interpretation are composed of tensors close to, but not exactly perfect tensors. Computing corrections to the connected two point correlation functions, we find that the leading contribution is given by structures related to geodesics connecting the operators inserted at the boundary physical dofs. Such considerations admit generalizations at least to three point functions. This is highly suggestive of the emergence of the analogues of Witten diagrams in the tensor network. The perturbations alone however do not give the right entanglement spectrum. Using the Coxeter construction, we also constructed the tensor network counterpart of the BTZ black hole, by orbifolding the discrete lattice on which the network resides. We found that the construction naturally reproduces some of the salient features of the BTZ black hole, such as the appearance of RT surfaces that could wrap the horizon, depending on the size of the entanglement region A.
Square Deal: Lower Bounds and Improved Relaxations for Tensor Recovery
2013-08-16
drawn uniformly at random (by the command orth(randn(·, ·)) in Matlab ). The observed entries are chosen uniformly with ratio ρ. We increase the...and 4d pre-stack seismic data completion using tensor nuclear norm (tnn). preprint, 2013. [GQ12] D. Goldfarb and Z. Qin. Robust low-rank tensor
Tensor estimation for double-pulsed diffusional kurtosis imaging.
Shaw, Calvin B; Hui, Edward S; Helpern, Joseph A; Jensen, Jens H
2017-07-01
Double-pulsed diffusional kurtosis imaging (DP-DKI) represents the double diffusion encoding (DDE) MRI signal in terms of six-dimensional (6D) diffusion and kurtosis tensors. Here a method for estimating these tensors from experimental data is described. A standard numerical algorithm for tensor estimation from conventional (i.e. single diffusion encoding) diffusional kurtosis imaging (DKI) data is generalized to DP-DKI. This algorithm is based on a weighted least squares (WLS) fit of the signal model to the data combined with constraints designed to minimize unphysical parameter estimates. The numerical algorithm then takes the form of a quadratic programming problem. The principal change required to adapt the conventional DKI fitting algorithm to DP-DKI is replacing the three-dimensional diffusion and kurtosis tensors with the 6D tensors needed for DP-DKI. In this way, the 6D diffusion and kurtosis tensors for DP-DKI can be conveniently estimated from DDE data by using constrained WLS, providing a practical means for condensing DDE measurements into well-defined mathematical constructs that may be useful for interpreting and applying DDE MRI. Data from healthy volunteers for brain are used to demonstrate the DP-DKI tensor estimation algorithm. In particular, representative parametric maps of selected tensor-derived rotational invariants are presented. Copyright © 2017 John Wiley & Sons, Ltd.
The Twist Tensor Nuclear Norm for Video Completion.
Hu, Wenrui; Tao, Dacheng; Zhang, Wensheng; Xie, Yuan; Yang, Yehui
2017-12-01
In this paper, we propose a new low-rank tensor model based on the circulant algebra, namely, twist tensor nuclear norm (t-TNN). The twist tensor denotes a three-way tensor representation to laterally store 2-D data slices in order. On one hand, t-TNN convexly relaxes the tensor multirank of the twist tensor in the Fourier domain, which allows an efficient computation using fast Fourier transform. On the other, t-TNN is equal to the nuclear norm of block circulant matricization of the twist tensor in the original domain, which extends the traditional matrix nuclear norm in a block circulant way. We test the t-TNN model on a video completion application that aims to fill missing values and the experiment results validate its effectiveness, especially when dealing with video recorded by a nonstationary panning camera. The block circulant matricization of the twist tensor can be transformed into a circulant block representation with nuclear norm invariance. This representation, after transformation, exploits the horizontal translation relationship between the frames in a video, and endows the t-TNN model with a more powerful ability to reconstruct panning videos than the existing state-of-the-art low-rank models.
Multiple M2-branes and the embedding tensor
Bergshoeff, Eric A.; de Roo, Mees; Hohm, Olaf
2008-01-01
We show that the Bagger-Lambert theory of multiple M2-branes fits into the general construction of maximally supersymmetric gauge theories using the embedding tensor technique. We apply the embedding tensor technique in order to systematically obtain the consistent gaugings of N = 8 superconformal
Subtracting a best rank-1 approximation may increase tensor rank
Stegeman, Alwin; Comon, Pierre
2010-01-01
It has been shown that a best rank-R approximation of an order-k tensor may not exist when R >= 2 and k >= 3. This poses a serious problem to data analysts using tensor decompositions it has been observed numerically that, generally, this issue cannot be solved by consecutively computing and
(2, 0) tensor multiplets and conformal supergravity in D = 6
Bergshoeff, Eric; Sezgin, Ergin; Proeyen, Antoine Van
1999-01-01
We construct the supercurrent multiplet that contains the energyâ€“momentum tensor of the (2, 0) tensor multiplet. By coupling this multiplet of currents to the fields of conformal supergravity, we first construct the linearized superconformal transformations rules of the (2, 0) Weyl multiplet.
Data fusion in metabolomics using coupled matrix and tensor factorizations
DEFF Research Database (Denmark)
Evrim, Acar Ataman; Bro, Rasmus; Smilde, Age Klaas
2015-01-01
of heterogeneous (i.e., in the form of higher order tensors and matrices) data sets with shared/unshared factors. In order to jointly analyze such heterogeneous data sets, we formulate data fusion as a coupled matrix and tensor factorization (CMTF) problem, which has already proved useful in many data mining...
Fast evaluation of nonlinear functionals of tensor product wavelet expansions
Schwab, C.; Stevenson, R.
2011-01-01
Abstract For a nonlinear functional f, and a function u from the span of a set of tensor product interpolets, it is shown how to compute the interpolant of f (u) from the span of this set of tensor product interpolets in linear complexity, assuming that the index set has a certain multiple tree
3D inversion of full tensor magnetic gradiometry (FTMG) data
DEFF Research Database (Denmark)
Zhdanov, Michael; Cai, Hongzhu; Wilson, Glenn
2011-01-01
Following recent advances in SQUID technology, full tensor magnetic gradiometry (FTMG) is emerging as a practical exploration method. We introduce 3D regularized focusing inversion for FTMG data. Our model studies show that inversion of magnetic tensor data can significantly improve resolution...
Gauge theories, duality relations and the tensor hierarchy
Bergshoeff, Eric A.; Hartong, Jelle; Hohm, Olaf; Huebscher, Mechthild; Ortin, Tomas; Hübscher, Mechthild
We compute the complete 3- and 4-dimensional tensor hierarchies, i.e. sets of p-form fields, with 1 We construct gauge-invariant actions that include all the fields in the tensor hierarchies. We elucidate the relation between the gauge transformations of the p-form fields in the action and those of
Secoond order parallel tensors on some paracontact manifolds | Liu ...
African Journals Online (AJOL)
The object of the present paper is to study the symmetric and skewsymmetric properties of a second order parallel tensor on paracontact metric (k;μ)- spaces and almost β-para-Kenmotsu (k;μ)-spaces. In this paper, we prove that if there exists a second order symmetric parallel tensor on a paracontact metric (k;μ)- space M, ...
Couplings of self-dual tensor multiplet in six dimensions
Bergshoeff, E.; Sezgin, E.; Sokatchev, E.
1996-01-01
The (1, 0) supersymmetry in six dimensions admits a tensor multiplet which contains a second-rank antisymmetric tensor field with a self-dual field strength and a dilaton. We describe the fully supersymmetric coupling of this multiplet to a Yangâ€“Mills multiplet, in the absence of supergravity. The
Superconformal tensor calculus and matter couplings in six dimensions
Bergshoeff, E.; Sezgin, E.; Proeyen, A. Van
1986-01-01
Using superconformal tensor calculus we construct general interactions of N = 2, d = 6 supergravity with a tensor multiplet and a number of scalar, vector and linear multiplets. We start from the superconformal algebra which we realize on a 40+40 Weyl multiplet and on several matter multiplets. A
A tensor approach to the estimation of hydraulic conductivities in ...
African Journals Online (AJOL)
Based on the field measurements of the physical properties of fractured rocks, the anisotropic properties of hydraulic conductivity (HC) of the fractured rock aquifer can be assessed and presented using a tensor approach called hydraulic conductivity tensor. Three types of HC values, namely point value, axial value and flow ...
Black holes with surrounding matter in scalar-tensor theories.
Cardoso, Vitor; Carucci, Isabella P; Pani, Paolo; Sotiriou, Thomas P
2013-09-13
We uncover two mechanisms that can render Kerr black holes unstable in scalar-tensor gravity, both associated with the presence of matter in the vicinity of the black hole and the fact that this introduces an effective mass for the scalar. Our results highlight the importance of understanding the structure of spacetime in realistic, astrophysical black holes in scalar-tensor theories.
Superspace actions and duality transformations for N=2 tensor multiplets
International Nuclear Information System (INIS)
Galperin, A.; Ivanov, E.; Ogievetsky, V.
1985-01-01
General actions for self-interacting N=2 tensor multiplets are considered in the harmonic superspace approach. All of them are shown to be equivalent, by superfield duality transformations, to some restricted class of the hypermultiplets actions. In particular, the improved tensor multiplet theory is dual to a free hypermultiplet one. Superspace couplings of these improved matter multiplets against conformal supergravity are also constructed
Tensor Basis Neural Network v. 1.0 (beta)
Energy Technology Data Exchange (ETDEWEB)
2017-03-28
This software package can be used to build, train, and test a neural network machine learning model. The neural network architecture is specifically designed to embed tensor invariance properties by enforcing that the model predictions sit on an invariant tensor basis. This neural network architecture can be used in developing constitutive models for applications such as turbulence modeling, materials science, and electromagnetism.
MATLAB tensor classes for fast algorithm prototyping : source code.
Energy Technology Data Exchange (ETDEWEB)
Bader, Brett William; Kolda, Tamara Gibson (Sandia National Laboratories, Livermore, CA)
2004-10-01
We present the source code for three MATLAB classes for manipulating tensors in order to allow fast algorithm prototyping. A tensor is a multidimensional or Nway array. This is a supplementary report; details on using this code are provided separately in SAND-XXXX.
Relativistic interpretation of the nature of the nuclear tensor force
Zong, Yao-Yao; Sun, Bao-Yuan
2018-02-01
The spin-dependent nature of the nuclear tensor force is studied in detail within the relativistic Hartree-Fock approach. The relativistic formalism for the tensor force is supplemented with an additional Lorentz-invariant tensor formalism in the σ-scalar channel, so as to take into account almost fully the nature of the tensor force brought about by the Fock diagrams in realistic nuclei. Specifically, the tensor sum rules are tested for the spin and pseudo-spin partners with and without nodes, to further understand the nature of the tensor force within the relativistic model. It is shown that the interference between the two components of nucleon spinors causes distinct violations of the tensor sum rules in realistic nuclei, mainly due to the opposite signs on the κ quantities of the upper and lower components, as well as the nodal difference. However, the sum rules can be precisely reproduced if the same radial wave functions are taken for the spin/pseudo-spin partners in addition to neglecting the lower/upper components, revealing clearly the nature of the tensor force. Supported by National Natural Science Foundation of China (11375076, 11675065) and the Fundamental Research Funds for the Central Universities (lzujbky-2016-30)
Evaluation of uncertainty in alignment tensors obtained from dipolar couplings
International Nuclear Information System (INIS)
Zweckstetter, Markus; Bax, Ad
2002-01-01
Residual dipolar couplings and their corresponding alignment tensors are useful for structural analysis of macromolecules. The error in an alignment tensor, derived from residual dipolar couplings on the basis of a known structure, is determined not only by the accuracy of the measured couplings but also by the uncertainty in the structure (structural noise). This dependence is evaluated quantitatively on the basis of simulated structures using Monte-Carlo type analyses. When large numbers of dipolar couplings are available, structural noise is found to result in a systematic underestimate of the magnitude of the alignment tensor. Particularly in cases where only few dipolar couplings are available, structural noise can cause significant errors in best-fitted alignment tensor values, making determination of the relative orientation of small fragments and evaluation of local backbone mobility from dipolar couplings difficult. An example for the protein ubiquitin demonstrates the inherent limitations in characterizing motions on the basis of local alignment tensor magnitudes
Coordinate independent expression for transverse trace-free tensors
International Nuclear Information System (INIS)
Conboye, Rory
2016-01-01
The transverse and trace-free (TT) part of the extrinsic curvature represents half of the dynamical degrees of freedom of the gravitational field in the 3 + 1 formalism. As such, it is part of the freely specifiable initial data for numerical relativity. Though TT tensors in three-space possess only two component degrees of freedom, they cannot ordinarily be given solely by two scalar potentials. Such expressions have been derived, however, in coordinate form, for all TT tensors in flat space which are also translationally or axially symmetric (Conboye and Murchadha 2014 Class. Quantum Grav. 31 085019). Since TT tensors are conformally covariant, these also give TT tensors in conformally flat space. In this article, the work above has been extended by giving a coordinate-independent expression for these TT tensors. The translational and axial symmetry conditions have also been generalized to invariance along any hypersurface orthogonal Killing vector. (paper)
On energy-momentum tensors of gravitational field
International Nuclear Information System (INIS)
Nikishov, A.I.
2001-01-01
The phenomenological approach to gravitation is discussed in which the 3-graviton interaction is reduced to the interaction of each graviton with the energy-momentum tensor of two others. If this is so, (and in general relativity this is not so), then the problem of choosing the correct energy-momentum tensor comes to finding the right 3-graviton vertex. Several energy-momentum tensors od gravitational field are considered and compared in the lowest approximation. Each of them together with the energy-momentum tensor of point-like particles satisfies the conservation laws when equations of motion of particles are the same as in general relativity. It is shown that in Newtonian approximation the considered tensors differ one from other in the way their energy density is distributed between energy density of interaction (nonzero only at locations of particles) and energy density of gravitational field. Stating from Lorentz invariance, the Lagrangians for spin-2, mass-0 field are considered [ru
On the energy-momentum tensor in Moyal space
International Nuclear Information System (INIS)
Balasin, Herbert; Schweda, Manfred; Blaschke, Daniel N.; Gieres, Francois
2015-01-01
We study the properties of the energy-momentum tensor of gauge fields coupled to matter in non-commutative (Moyal) space. In general, the non-commutativity affects the usual conservation law of the tensor as well as its transformation properties (gauge covariance instead of gauge invariance). It is well known that the conservation of the energy-momentum tensor can be achieved by a redefinition involving another star-product. Furthermore, for a pure gauge theory it is always possible to define a gauge invariant energy-momentum tensor by means of a Wilson line. We show that the last two procedures are incompatible with each other if couplings of gauge fields to matter fields (scalars or fermions) are considered: The gauge invariant tensor (constructed via Wilson line) does not allow for a redefinition assuring its conservation, and vice versa the introduction of another star-product does not allow for gauge invariance by means of a Wilson line. (orig.)
Decomposition of a symmetric second-order tensor
Heras, José A.
2018-05-01
In the three-dimensional space there are different definitions for the dot and cross products of a vector with a second-order tensor. In this paper we show how these products can uniquely be defined for the case of symmetric tensors. We then decompose a symmetric second-order tensor into its ‘dot’ part, which involves the dot product, and the ‘cross’ part, which involves the cross product. For some physical applications, this decomposition can be interpreted as one in which the dot part identifies with the ‘parallel’ part of the tensor and the cross part identifies with the ‘perpendicular’ part. This decomposition of a symmetric second-order tensor may be suitable for undergraduate courses of vector calculus, mechanics and electrodynamics.
The effects of noise over the complete space of diffusion tensor shape.
Gahm, Jin Kyu; Kindlmann, Gordon; Ennis, Daniel B
2014-01-01
Diffusion tensor magnetic resonance imaging (DT-MRI) is a technique used to quantify the microstructural organization of biological tissues. Multiple images are necessary to reconstruct the tensor data and each acquisition is subject to complex thermal noise. As such, measures of tensor invariants, which characterize components of tensor shape, derived from the tensor data will be biased from their true values. Previous work has examined this bias, but over a narrow range of tensor shape. Herein, we define the mathematics for constructing a tensor from tensor invariants, which permits an intuitive and principled means for building tensors with a complete range of tensor shape and salient microstructural properties. Thereafter, we use this development to evaluate by simulation the effects of noise on characterizing tensor shape over the complete space of tensor shape for three encoding schemes with different SNR and gradient directions. We also define a new framework for determining the distribution of the true values of tensor invariants given their measures, which provides guidance about the confidence the observer should have in the measures. Finally, we present the statistics of tensor invariant estimates over the complete space of tensor shape to demonstrate how the noise sensitivity of tensor invariants varies across the space of tensor shape as well as how the imaging protocol impacts measures of tensor invariants. Copyright © 2013 Elsevier B.V. All rights reserved.
Endoscopic Anatomy of the Tensor Fold and Anterior Attic.
Li, Bin; Doan, Phi; Gruhl, Robert R; Rubini, Alessia; Marchioni, Daniele; Fina, Manuela
2018-02-01
Objectives The objectives of the study were to (1) study the anatomical variations of the tensor fold and its anatomic relation with transverse crest, supratubal recess, and anterior epitympanic space and (2) explore the most appropriate endoscopic surgical approach to each type of the tensor fold variants. Study Design Cadaver dissection study. Setting Temporal bone dissection laboratory. Subjects and Methods Twenty-eight human temporal bones (26 preserved and 2 fresh) were dissected through an endoscopic transcanal approach between September 2016 and June 2017. The anatomical variations of the tensor fold, transverse crest, supratubal recess, and anterior epitympanic space were studied before and after removing ossicles. Results Three different tensor fold orientations were observed: vertical (type A, 11/28, 39.3%) with attachment to the transverse crest, oblique (type B, 13/28, 46.4%) with attachment to the anterior tegmen tympani, and horizontal (type C, 4/28, 14.3%) with attachment to the tensor tympani canal. The tensor fold was a complete membrane in 20 of 28 (71.4%) specimens, preventing direct ventilation between the supratubal recess and anterior epitympanic space. We identified 3 surgical endoscopic approaches, which allowed visualization of the tensor fold without removing the ossicles. Conclusions The orientation of the tensor fold is the determining structure that dictates the conformation and limits of the epitympanic space. We propose a classification of the tensor fold based on 3 anatomical variants. We also describe 3 different minimally invasive endoscopic approaches to identify the orientation of the tensor fold while maintaining ossicular chain continuity.
Liouville action as path-integral complexity: from continuous tensor networks to AdS/CFT
Caputa, Pawel; Kundu, Nilay; Miyaji, Masamichi; Takayanagi, Tadashi; Watanabe, Kento
2017-11-01
We propose an optimization procedure for Euclidean path-integrals that evaluate CFT wave functionals in arbitrary dimensions. The optimization is performed by minimizing certain functional, which can be interpreted as a measure of computational complexity, with respect to background metrics for the path-integrals. In two dimensional CFTs, this functional is given by the Liouville action. We also formulate the optimization for higher dimensional CFTs and, in various examples, find that the optimized hyperbolic metrics coincide with the time slices of expected gravity duals. Moreover, if we optimize a reduced density matrix, the geometry becomes two copies of the entanglement wedge and reproduces the holographic entanglement entropy. Our approach resembles a continuous tensor network renormalization and provides a concrete realization of the proposed interpretation of AdS/CFT as tensor networks. The present paper is an extended version of our earlier report arXiv:1703.00456 and includes many new results such as evaluations of complexity functionals, energy stress tensor, higher dimensional extensions and time evolutions of thermofield double states.
Jaques, Luís; Pascal, Christophe
2017-09-01
Paleostress tensor restoration methods are traditionally limited to reconstructing geometrical parameters and are unable to resolve stress magnitudes. Based on previous studies we further developed a methodology to restore full paleostress tensors. We concentrated on inversion of Mode I fractures and acquired data in Panasqueira Mine, Portugal, where optimal exposures of mineralized quartz veins can be found. To carry out full paleostress restoration we needed to determine (1) pore (paleo)pressure and (2) vein attitudes. The present contribution focuses specifically on the determination of pore pressure. To these aims we conducted an extensive fluid inclusion study to derive fluid isochores from the quartz of the studied veins. To constrain P-T conditions, we combined these isochores with crystallisation temperatures derived from geochemical analyses of coeval arsenopyrite. We also applied the sphalerite geobarometer and considered two other independent pressure indicators. Our results point to pore pressures of ∼300 MPa and formation depths of ∼10 km. Such formation depths are in good agreement with the regional geological evolution. The obtained pore pressure will be merged with vein inversion results, in order to achieve full paleostress tensor restoration, in a forthcoming companion paper.
Process Measurement Deviation Analysis for Flow Rate due to Miscalibration
Energy Technology Data Exchange (ETDEWEB)
Oh, Eunsuk; Kim, Byung Rae; Jeong, Seog Hwan; Choi, Ji Hye; Shin, Yong Chul; Yun, Jae Hee [KEPCO Engineering and Construction Co., Deajeon (Korea, Republic of)
2016-10-15
An analysis was initiated to identify the root cause, and the exemption of high static line pressure correction to differential pressure (DP) transmitters was one of the major deviation factors. Also the miscalibrated DP transmitter range was identified as another major deviation factor. This paper presents considerations to be incorporated in the process flow measurement instrumentation calibration and the analysis results identified that the DP flow transmitter electrical output decreased by 3%. Thereafter, flow rate indication decreased by 1.9% resulting from the high static line pressure correction exemption and measurement range miscalibration. After re-calibration, the flow rate indication increased by 1.9%, which is consistent with the analysis result. This paper presents the brief calibration procedures for Rosemount DP flow transmitter, and analyzes possible three cases of measurement deviation including error and cause. Generally, the DP transmitter is required to be calibrated with precise process input range according to the calibration procedure provided for specific DP transmitter. Especially, in case of the DP transmitter installed in high static line pressure, it is important to correct the high static line pressure effect to avoid the inherent systematic error for Rosemount DP transmitter. Otherwise, failure to notice the correction may lead to indicating deviation from actual value.
Oscillations in deviating difference equations using an iterative technique
Directory of Open Access Journals (Sweden)
George E Chatzarakis
2017-07-01
Full Text Available Abstract The paper deals with the oscillation of the first-order linear difference equation with deviating argument and nonnegative coefficients. New sufficient oscillation conditions, involving limsup, are given, which essentially improve all known results, based on an iterative technique. We illustrate the results and the improvement over other known oscillation criteria by examples, numerically solved in Matlab.
Large deviations for sojourn times in processor sharing queues.
Mandjes, M.R.H.; Zwart, B.
2006-01-01
Abstract: This paper presents a large deviation analysis of the steady-state sojourn time distribution in the GI/G/1 PS queue. Logarithmic estimates are obtained under the assumption of the service time distribution having a light tail, thus supplementing recent results for the heavy-tailed setting.
21 CFR 211.100 - Written procedures; deviations.
2010-04-01
...) Written production and process control procedures shall be followed in the execution of the various... 21 Food and Drugs 4 2010-04-01 2010-04-01 false Written procedures; deviations. 211.100 Section... (CONTINUED) DRUGS: GENERAL CURRENT GOOD MANUFACTURING PRACTICE FOR FINISHED PHARMACEUTICALS Production and...
Fluctuations and large deviations in non-equilibrium systems
Indian Academy of Sciences (India)
a possible way of extending the notion of free energy to non-equilibrium systems. This large deviation function of the density can be calculated explicitly for exclusion models in one dimension with open boundary conditions. For these models, one can also obtain the distribution of the current of particles flowing through the ...
International asset pricing under segmentation and PPP deviations
Chaieb, I.; Errunza, V.
2007-01-01
We analyze the impact of both purchasing power parity (PPP) deviations and market segmentation on asset pricing and investor's portfolio holdings. The freely traded securities command a world market risk premium and an inflation risk premium. The securities that can be held by only a subset of
On asymptotically efficient simulation of large deviation probabilities.
Dieker, A.B.; Mandjes, M.R.H.
2005-01-01
ABSTRACT: Consider a family of probabilities for which the decay is governed by a large deviation principle. To find an estimate for a fixed member of this family, one is often forced to use simulation techniques. Direct Monte Carlo simulation, however, is often impractical, particularly if the
Linguistics deviation, a tool for teaching English grammar: evidence ...
African Journals Online (AJOL)
We have always advocated that those teaching the Use of English must seek out novel ways of teaching the grammar of English to take out the drudgery of the present approach. Here, we proposed using Linguistic deviation as a tool for teaching English grammar. This approach will produce students who are both strong in ...
Linear Estimation of Standard Deviation of Logistic Distribution ...
African Journals Online (AJOL)
The paper presents a theoretical method based on order statistics and a FORTRAN program for computing the variance and relative efficiencies of the standard deviation of the logistic population with respect to the Cramer-Rao lower variance bound and the best linear unbiased estimators (BLUE\\'s) when the mean is ...
Semiparametric Bernstein-von Mises for the error standard deviation
de Jonge, R.; van Zanten, H.
2013-01-01
We study Bayes procedures for nonparametric regression problems with Gaussian errors, giving conditions under which a Bernstein-von Mises result holds for the marginal posterior distribution of the error standard deviation. We apply our general results to show that a single Bayes procedure using a
The one-shot deviation principle for sequential rationality
DEFF Research Database (Denmark)
Hendon, Ebbe; Whitta-Jacobsen, Hans Jørgen; Sloth, Birgitte
1996-01-01
We present a decentralization result which is useful for practical and theoretical work with sequential equilibrium, perfect Bayesian equilibrium, and related equilibrium concepts for extensive form games. A weak consistency condition is sufficient to obtain an analogy to the well known One-Stage......-Stage-Deviation Principle for subgame perfect equilibrium...
48 CFR 552.252-6 - Authorized Deviations in Clauses.
2010-10-01
... published in the General Services Administration Acquisition Regulation (48 CFR chapter 5). (2) This... published in the General Services Administration Acquisition Regulation by the addition of “(DEVIATION (FAR... ADMINISTRATION CLAUSES AND FORMS SOLICITATION PROVISIONS AND CONTRACT CLAUSES Text of Provisions and Clauses 552...
Path deviations outperform approximate stability in heterogeneous congestion games
P.S. Kleer (Pieter); G. Schäfer (Guido)
2017-01-01
textabstractWe consider non-atomic network congestion games with heterogeneous players where the latencies of the paths are subject to some bounded deviations. This model encompasses several well-studied extensions of the classical Wardrop model which incorporate, for example, risk-aversion,
Deviation from tri-bimaximal mixings through flavour twisters in ...
Indian Academy of Sciences (India)
without sacrificing maximal atmospheric mixing and exact zero value of reactor angle. This amounts to minimal deviation from S3 symmetry while preserving. 2-3 symmetry (1). We confine the present analysis in inverted as well as normal hierarchical neutrino mass models. At the end we attempt to give some simple.
The Scalar-Tensor Theory of Gravitation
International Nuclear Information System (INIS)
Ibanez, J
2003-01-01
Since the scalar-tensor theory of gravitation was proposed almost 50 years ago, it has recently become a robust alternative theory to Einstein's general relativity due to the fact that it appears to represent the lower level of a more fundamental theory and can serve both as a phenomenological theory to explain the recently observed acceleration of the universe, and to solve the cosmological constant problem. To my knowledge The Scalar-Tensor Theory of Gravitation by Y Fujii and K Maeda is the first book to develop a modern view on this topic and is one of the latest titles in the well-presented Cambridge Monographs on Mathematical Physics series. This book is an excellent readable introduction and up-to-date review of the subject. The discussion is well organized; after a comprehensible introduction to the Brans-Dicke theory and the important role played by conformal transformations, the authors review cosmologies with the cosmological constant and how the scalar-tensor theory can serve to explain the accelerating universe, including discussions on dark energy, quintessence and braneworld cosmologies. The book ends with a chapter devoted to quantum effects. To make easy the lectures of the book, each chapter starts with a summary of the subject to be dealt with. As the book proceeds, important issues like conformal frames and the weak equivalence principle are fully discussed. As the authors warn in the preface, the book is not encyclopedic (from my point of view the list of references is fairly short, for example, but this is a minor drawback) and the choice of included topics corresponds to the authors' interests. Nevertheless, the book seems to cover a broad range of the most essential aspects of the subject. Long and 'boring' mathematical derivations are left to appendices so as not to interrupt the flow of the reasoning, allowing the reader to focus on the physical aspects of each subject. These appendices are a valuable help in entering into the mathematical
Permeability tensor and representative elementary volume of fractured rock masses
Rong, Guan; Peng, Jun; Wang, Xiaojiang; Liu, Guang; Hou, Di
2013-11-01
Based on a simulation of three-dimensional fracture networks and a superposition principle of liquid dissipation energy for fractured rock masses, a model of the fracture permeability tensor is proposed. An elastic constitutive model of rock fractures, considering fracture closure and dilation during shearing, is also proposed, based on the dilation angle of the fracture. Algorithms of flow-path searching and calculation of the effective flow coefficients for fracture networks are presented, together with a discussion on the influence of geometric parameters of the fractures (trace length, spacing, aperture, orientation and the number of fracture sets) on magnitude, anisotropy of hydraulic permeability and the size of a representative elementary volume (REV). The anisotropy of hydraulic permeability of fractured rock masses is mainly affected by orientation and the number of fracture sets, and the REV size is mainly influenced by trace length, spacing and the number of fracture sets. The results of studies on REV size and the influence of in-situ stress on hydraulic conductivity of the rock mass on the slope of Jinping-I hydropower station, China, are presented using the developed models and methods. The simulation results agreed well with the results obtained from field water-pressure measurements, with an error of less than 10 %.
Tensor Algebra and Tensor Analysis for Engineers With Applications to Continuum Mechanics
Itskov, Mikhail
2013-01-01
There is a large gap between the engineering course in tensor algebra on the one hand and the treatment of linear transformations within classical linear algebra on the other hand. The aim of this modern textbook is to bridge this gap by means of the consequent and fundamental exposition. The book primarily addresses engineering students with some initial knowledge of matrix algebra. Thereby the mathematical formalism is applied as far as it is absolutely necessary. Numerous exercises are provided in the book and are accompanied by solutions, enabling self-study. The last chapters of the book deal with modern developments in the theory of isotropic and anisotropic tensor functions and their applications to continuum mechanics and are therefore of high interest for PhD-students and scientists working in this area. This third edition is completed by a number of additional figures, examples and exercises. The text and formulae have been revised and improved where necessary.
Causal structure in the scalar–tensor theory with field derivative coupling to the Einstein tensor
Directory of Open Access Journals (Sweden)
Masato Minamitsuji
2015-04-01
Full Text Available We investigate the causal structure in the scalar–tensor theory with the field derivative coupling to the Einstein tensor, which is a class of the Horndeski theory in the four-dimensional spacetime. We show that in general the characteristic hypersurface is non-null, which admits the superluminal propagations. We also derive the conditions that the characteristic hypersurface becomes null and show that a Killing horizon can be the causal edge for all the propagating degrees of freedom, if the additional conditions for the scalar field are satisfied. Finally, we find the position of the characteristic hypersurface in the dynamical spacetime with the maximally symmetric space, and that the fastest propagation can be superluminal, especially if the coupling constant becomes positive. We also argue that the superluminality itself may not lead to the acausality of the theory.
Image denoising using non linear diffusion tensors
International Nuclear Information System (INIS)
Benzarti, F.; Amiri, H.
2011-01-01
Image denoising is an important pre-processing step for many image analysis and computer vision system. It refers to the task of recovering a good estimate of the true image from a degraded observation without altering and changing useful structure in the image such as discontinuities and edges. In this paper, we propose a new approach for image denoising based on the combination of two non linear diffusion tensors. One allows diffusion along the orientation of greatest coherences, while the other allows diffusion along orthogonal directions. The idea is to track perfectly the local geometry of the degraded image and applying anisotropic diffusion mainly along the preferred structure direction. To illustrate the effective performance of our model, we present some experimental results on a test and real photographic color images.
Diffusion tensor in electron swarm transport
International Nuclear Information System (INIS)
Makabe, T.; Mori, T.
1983-01-01
Expression for the diffusion tensor of the electron (or light ion) swarm is presented from the higher-order expansion of the velocity distribution in the Boltzmann equation in hydrodynamic stage. Derived diffusion coefficients for the transverse and longitudinal directions include the additional terms representative of the curvature effect under the action of an electric field with the usual-two-term expressions. Numerical analysis is given for the electron swarm in model gases having the momentum transfer cross section Qsub(m)(epsilon)=Q 0 epsilon sup(beta) (β=0, 1/2, 1) using the present theory. As the result, appreciable degree of discrepancy appears between the transverse diffusion coefficient defined here and the conventional expression with increasing of β in Qsub(m). (Author)
Poisson-Jacobi reduction of homogeneous tensors
International Nuclear Information System (INIS)
Grabowski, J; Iglesias, D; Marrero, J C; Padron, E; Urbanski, P
2004-01-01
The notion of homogeneous tensors is discussed. We show that there is a one-to-one correspondence between multivector fields on a manifold M, homogeneous with respect to a vector field Δ on M, and first-order polydifferential operators on a closed submanifold N of codimension 1 such that Δ is transversal to N. This correspondence relates the Schouten-Nijenhuis bracket of multivector fields on M to the Schouten-Jacobi bracket of first-order polydifferential operators on N and generalizes the Poissonization of Jacobi manifolds. Actually, it can be viewed as a super-Poissonization. This procedure of passing from a homogeneous multivector field to a first-order polydifferential operator can also be understood as a sort of reduction; in the standard case-a half of a Poisson reduction. A dual version of the above correspondence yields in particular the correspondence between Δ-homogeneous symplectic structures on M and contact structures on N
CANDECOMP/PARAFAC Decomposition of High-Order Tensors Through Tensor Reshaping
Czech Academy of Sciences Publication Activity Database
Phan, A. H.; Tichavský, Petr; Cichocki, A.
2013-01-01
Roč. 61, č. 19 (2013), s. 4847-4860 ISSN 1053-587X R&D Projects: GA ČR GA102/09/1278 Institutional support: RVO:67985556 Keywords : tensor factorization * canonical polyadic decomposition * Cramer-Rao bound Subject RIV: BB - Applied Statistics, Operational Research Impact factor: 3.198, year: 2013 http://library.utia.cas.cz/separaty/2013/SI/tichavsky-0396775.pdf
Measuring type II stresses using 3DXRD
DEFF Research Database (Denmark)
Oddershede, Jette; Schmidt, Søren; Poulsen, Henning Friis
2010-01-01
An algorithm is presented for characterization of the grain resolved (type II) stress states in a polycrystalline sample based on monochromatic X-ray diffraction data. The algorithm is a robust 12-parameter-per-grain fit of the centre-of-mass grain positions, orientations and stress tensors...
Holographic spin networks from tensor network states
Singh, Sukhwinder; McMahon, Nathan A.; Brennen, Gavin K.
2018-01-01
In the holographic correspondence of quantum gravity, a global on-site symmetry at the boundary generally translates to a local gauge symmetry in the bulk. We describe one way how the global boundary on-site symmetries can be gauged within the formalism of the multiscale renormalization ansatz (MERA), in light of the ongoing discussion between tensor networks and holography. We describe how to "lift" the MERA representation of the ground state of a generic one dimensional (1D) local Hamiltonian, which has a global on-site symmetry, to a dual quantum state of a 2D "bulk" lattice on which the symmetry appears gauged. The 2D bulk state decomposes in terms of spin network states, which label a basis in the gauge-invariant sector of the bulk lattice. This decomposition is instrumental to obtain expectation values of gauge-invariant observables in the bulk, and also reveals that the bulk state is generally entangled between the gauge and the remaining ("gravitational") bulk degrees of freedom that are not fixed by the symmetry. We present numerical results for ground states of several 1D critical spin chains to illustrate that the bulk entanglement potentially depends on the central charge of the underlying conformal field theory. We also discuss the possibility of emergent topological order in the bulk using a simple example, and also of emergent symmetries in the nongauge (gravitational) sector in the bulk. More broadly, our holographic model translates the MERA, a tensor network state, to a superposition of spin network states, as they appear in lattice gauge theories in one higher dimension.
Affinity learning with diffusion on tensor product graph.
Yang, Xingwei; Prasad, Lakshman; Latecki, Longin Jan
2013-01-01
In many applications, we are given a finite set of data points sampled from a data manifold and represented as a graph with edge weights determined by pairwise similarities of the samples. Often the pairwise similarities (which are also called affinities) are unreliable due to noise or due to intrinsic difficulties in estimating similarity values of the samples. As observed in several recent approaches, more reliable similarities can be obtained if the original similarities are diffused in the context of other data points, where the context of each point is a set of points most similar to it. Compared to the existing methods, our approach differs in two main aspects. First, instead of diffusing the similarity information on the original graph, we propose to utilize the tensor product graph (TPG) obtained by the tensor product of the original graph with itself. Since TPG takes into account higher order information, it is not a surprise that we obtain more reliable similarities. However, it comes at the price of higher order computational complexity and storage requirement. The key contribution of the proposed approach is that the information propagation on TPG can be computed with the same computational complexity and the same amount of storage as the propagation on the original graph. We prove that a graph diffusion process on TPG is equivalent to a novel iterative algorithm on the original graph, which is guaranteed to converge. After its convergence we obtain new edge weights that can be interpreted as new, learned affinities. We stress that the affinities are learned in an unsupervised setting. We illustrate the benefits of the proposed approach for data manifolds composed of shapes, images, and image patches on two very different tasks of image retrieval and image segmentation. With learned affinities, we achieve the bull's eye retrieval score of 99.99 percent on the MPEG-7 shape dataset, which is much higher than the state-of-the-art algorithms. When the data
Exact tensor network ansatz for strongly interacting systems
Zaletel, Michael P.
It appears that the tensor network ansatz, while not quite complete, is an efficient coordinate system for the tiny subset of a many-body Hilbert space which can be realized as a low energy state of a local Hamiltonian. However, we don't fully understand precisely which phases are captured by the tensor network ansatz, how to compute their physical observables (even numerically), or how to compute a tensor network representation for a ground state given a microscopic Hamiltonian. These questions are algorithmic in nature, but their resolution is intimately related to understanding the nature of quantum entanglement in many-body systems. For this reason it is useful to compute the tensor network representation of various `model' wavefunctions representative of different phases of matter; this allows us to understand how the entanglement properties of each phase are expressed in the tensor network ansatz, and can serve as test cases for algorithm development. Condensed matter physics has many illuminating model wavefunctions, such as Laughlin's celebrated wave function for the fractional quantum Hall effect, the Bardeen-Cooper-Schrieffer wave function for superconductivity, and Anderson's resonating valence bond ansatz for spin liquids. This thesis presents some results on exact tensor network representations of these model wavefunctions. In addition, a tensor network representation is given for the time evolution operator of a long-range one-dimensional Hamiltonian, which allows one to numerically simulate the time evolution of power-law interacting spin chains as well as two-dimensional strips and cylinders.
Tensor-based Dictionary Learning for Spectral CT Reconstruction
Zhang, Yanbo; Wang, Ge
2016-01-01
Spectral computed tomography (CT) produces an energy-discriminative attenuation map of an object, extending a conventional image volume with a spectral dimension. In spectral CT, an image can be sparsely represented in each of multiple energy channels, and are highly correlated among energy channels. According to this characteristics, we propose a tensor-based dictionary learning method for spectral CT reconstruction. In our method, tensor patches are extracted from an image tensor, which is reconstructed using the filtered backprojection (FBP), to form a training dataset. With the Candecomp/Parafac decomposition, a tensor-based dictionary is trained, in which each atom is a rank-one tensor. Then, the trained dictionary is used to sparsely represent image tensor patches during an iterative reconstruction process, and the alternating minimization scheme is adapted for optimization. The effectiveness of our proposed method is validated with both numerically simulated and real preclinical mouse datasets. The results demonstrate that the proposed tensor-based method generally produces superior image quality, and leads to more accurate material decomposition than the currently popular popular methods. PMID:27541628
Reduction schemes for one-loop tensor integrals
International Nuclear Information System (INIS)
Denner, A.; Dittmaier, S.
2006-01-01
We present new methods for the evaluation of one-loop tensor integrals which have been used in the calculation of the complete electroweak one-loop corrections to e + e - ->4 fermions. The described methods for 3-point and 4-point integrals are, in particular, applicable in the case where the conventional Passarino-Veltman reduction breaks down owing to the appearance of Gram determinants in the denominator. One method consists of different variants for expanding tensor coefficients about limits of vanishing Gram determinants or other kinematical determinants, thereby reducing all tensor coefficients to the usual scalar integrals. In a second method a specific tensor coefficient with a logarithmic integrand is evaluated numerically, and the remaining coefficients as well as the standard scalar integral are algebraically derived from this coefficient. For 5-point tensor integrals, we give explicit formulas that reduce the corresponding tensor coefficients to coefficients of 4-point integrals with tensor rank reduced by one. Similar formulas are provided for 6-point functions, and the generalization to functions with more internal propagators is straightforward. All the presented methods are also applicable if infrared (soft or collinear) divergences are treated in dimensional regularization or if mass parameters (for unstable particles) become complex
Tensor-Based Dictionary Learning for Spectral CT Reconstruction.
Zhang, Yanbo; Mou, Xuanqin; Wang, Ge; Yu, Hengyong
2017-01-01
Spectral computed tomography (CT) produces an energy-discriminative attenuation map of an object, extending a conventional image volume with a spectral dimension. In spectral CT, an image can be sparsely represented in each of multiple energy channels, and are highly correlated among energy channels. According to this characteristics, we propose a tensor-based dictionary learning method for spectral CT reconstruction. In our method, tensor patches are extracted from an image tensor, which is reconstructed using the filtered backprojection (FBP), to form a training dataset. With the Candecomp/Parafac decomposition, a tensor-based dictionary is trained, in which each atom is a rank-one tensor. Then, the trained dictionary is used to sparsely represent image tensor patches during an iterative reconstruction process, and the alternating minimization scheme is adapted for optimization. The effectiveness of our proposed method is validated with both numerically simulated and real preclinical mouse datasets. The results demonstrate that the proposed tensor-based method generally produces superior image quality, and leads to more accurate material decomposition than the currently popular popular methods.
Tensor Rank Preserving Discriminant Analysis for Facial Recognition.
Tao, Dapeng; Guo, Yanan; Li, Yaotang; Gao, Xinbo
2017-10-12
Facial recognition, one of the basic topics in computer vision and pattern recognition, has received substantial attention in recent years. However, for those traditional facial recognition algorithms, the facial images are reshaped to a long vector, thereby losing part of the original spatial constraints of each pixel. In this paper, a new tensor-based feature extraction algorithm termed tensor rank preserving discriminant analysis (TRPDA) for facial image recognition is proposed; the proposed method involves two stages: in the first stage, the low-dimensional tensor subspace of the original input tensor samples was obtained; in the second stage, discriminative locality alignment was utilized to obtain the ultimate vector feature representation for subsequent facial recognition. On the one hand, the proposed TRPDA algorithm fully utilizes the natural structure of the input samples, and it applies an optimization criterion that can directly handle the tensor spectral analysis problem, thereby decreasing the computation cost compared those traditional tensor-based feature selection algorithms. On the other hand, the proposed TRPDA algorithm extracts feature by finding a tensor subspace that preserves most of the rank order information of the intra-class input samples. Experiments on the three facial databases are performed here to determine the effectiveness of the proposed TRPDA algorithm.
Algebraic Rainich conditions for the fourth rank tensor V
International Nuclear Information System (INIS)
So, Lau Loi
2011-01-01
Algebraic conditions on the Ricci tensor in the Rainich-Misner-Wheeler unified field theory are known as the Rainich conditions. Penrose and more recently Bergqvist and Lankinen made an analogy from the Ricci tensor to the Bel-Robinson tensor B αβμν , a certain fourth rank tensor quadratic in the Weyl curvature, which also satisfies algebraic Rainich-like conditions. However, we found that not only does the tensor B αβμν fulfill these conditions, but so also does our recently proposed tensor V αβμν , which has many of the desirable properties of B αβμν . For the quasilocal small sphere limit restriction, we found that there are only two fourth rank tensors, B αβμν and V αβμν , which form a basis for good energy expressions. Both of them have the completely trace free and causal properties, these two form necessary and sufficient conditions. Surprisingly either completely traceless or causal is enough to fulfill the algebraic Rainich conditions.
Deviations in delineated GTV caused by artefacts in 4DCT
DEFF Research Database (Denmark)
Persson, Gitte Fredberg; Nygaard, Ditte Eklund; Brink, Carsten
2010-01-01
BACKGROUND AND PURPOSE: Four-dimensional computed tomography (4DCT) is used for breathing-adapted radiotherapy planning. Irregular breathing, large tumour motion or interpolation of images can cause artefacts in the 4DCT. This study evaluates the impact of artefacts on gross tumour volume (GTV......-expiration GTV size (GTVexp) was considered as reference for GTV size. Intra-session delineation error was estimated by re-delineation of GTV in eight of the 4DCT scans. RESULTS: In 16 of the 4DCT scans the maximum deviations from GTVexp were larger than could be explained by delineation error. The deviations...... in GTV size throughout the 4DCT scans. Awareness of the error introduced by artefacts is important especially if radiotherapy planning is based on a single 4DCT bin....
Moderate Deviation Analysis for Classical Communication over Quantum Channels
Chubb, Christopher T.; Tan, Vincent Y. F.; Tomamichel, Marco
2017-11-01
We analyse families of codes for classical data transmission over quantum channels that have both a vanishing probability of error and a code rate approaching capacity as the code length increases. To characterise the fundamental tradeoff between decoding error, code rate and code length for such codes we introduce a quantum generalisation of the moderate deviation analysis proposed by Altŭg and Wagner as well as Polyanskiy and Verdú. We derive such a tradeoff for classical-quantum (as well as image-additive) channels in terms of the channel capacity and the channel dispersion, giving further evidence that the latter quantity characterises the necessary backoff from capacity when transmitting finite blocks of classical data. To derive these results we also study asymmetric binary quantum hypothesis testing in the moderate deviations regime. Due to the central importance of the latter task, we expect that our techniques will find further applications in the analysis of other quantum information processing tasks.
Deviation from the superparamagnetic behaviour of fine-particle systems
Malaescu, I
2000-01-01
Studies concerning superparamagnetic behaviour of fine magnetic particle systems were performed using static and radiofrequency measurements, in the range 1-60 MHz. The samples were: a ferrofluid with magnetite particles dispersed in kerosene (sample A), magnetite powder (sample B) and the same magnetite powder dispersed in a polymer (sample C). Radiofrequency measurements indicated a maximum in the imaginary part of the complex magnetic susceptibility, for each of the samples, at frequencies with the magnitude order of tens of MHz, the origin of which was assigned to Neel-type relaxation processes. The static measurements showed a Langevin-type dependence of magnetisation M and of susceptibility chi, on the magnetic field for sample A. For samples B and C deviations from this type of dependence were found. These deviations were analysed qualitatively and explained in terms of the interparticle interactions, dispersion medium influence and surface effects.
Moderate deviations for stabilizing functionals in geometric probability
Eichelsbacher, P.; Raič, M.; Schreiber, T.
2015-02-01
The purpose of the present paper is to establish explicit bounds on moderate deviation probabilities for a rather general class of geometric functionals enjoying the stabilization property, under Poisson input and the assumption of a certain control over the growth of the moments of the functional and its radius of stabilization. Our proof techniques rely on cumulant expansions and cluster measures and yield completely explicit bounds on deviation probabilities. In addition, we establish a new criterion for the limiting variance to be non-degenerate. Moreover, our main result provides a new central limit theorem, which, though stated under strong moment assumptions, does not require bounded support of the intensity of the Poisson input. We apply our results to three groups of examples: random packing models, geometric functionals based on Euclidean nearest neighbors and the sphere of influence graphs.
OBSERVABLE DEVIATIONS FROM HOMOGENEITY IN AN INHOMOGENEOUS UNIVERSE
International Nuclear Information System (INIS)
Giblin, John T. Jr.; Mertens, James B.; Starkman, Glenn D.
2016-01-01
How does inhomogeneity affect our interpretation of cosmological observations? It has long been wondered to what extent the observable properties of an inhomogeneous universe differ from those of a corresponding Friedmann–Lemaître–Robertson–Walker (FLRW) model, and how the inhomogeneities affect that correspondence. Here, we use numerical relativity to study the behavior of light beams traversing an inhomogeneous universe, and construct the resulting Hubble diagrams. The universe that emerges exhibits an average FLRW behavior, but inhomogeneous structures contribute to deviations in observables across the observer’s sky. We also investigate the relationship between angular diameter distance and the angular extent of a source, finding deviations that grow with source redshift. These departures from FLRW are important path-dependent effects, with implications for using real observables in an inhomogeneous universe such as our own.